Finite Group Databasebeta

← C3×#10594770 #13174367

Subgroups — C3×#10594770 #13174367

Order 1728.

1232 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64320C211yesmaximal, characteristic, complemented
2C3×#64315C211yesmaximal, characteristic, complemented
3C3×#64127C211yesmaximal, characteristic, complemented
4C32×#919C211yesmaximal, characteristic, complemented
5C32×#918C211yesmaximal, characteristic, complemented
6C3×#63950C211yesmaximal, characteristic, complemented
7C3×#63947C211yesmaximal, characteristic, complemented
8C3×#63943C211yesmaximal, characteristic, complemented
9C3×#63940C211yesmaximal, characteristic, complemented
10C3×#63939C211yesmaximal, characteristic, complemented
11C3×D3×#215C211yesmaximal, characteristic, complemented
12C3×#63804C211yesmaximal, characteristic, complemented
13C3×#63798C211yesmaximal, characteristic, complemented
14C3×#63795C211yesmaximal, characteristic, complemented
15C3×D3×#204C211yesmaximal, characteristic, complemented
16C3×#5778—31nomaximal
17C3×#5770—31nomaximal
18#10594770C311yesmaximal, characteristic, direct product factor
19C3×#3832C2211yescharacteristic
20C3×Q8×C3⋊D3C2211yescharacteristic, complemented
21C32×#239C2211yescharacteristic
22C32×#239C2211yescharacteristic
23C32×#239C2211yescharacteristic, complemented
24C32×D3×Q8C2211yescharacteristic, complemented
25C3×#3802—21no—
26C3×#3802C2211yescharacteristic
27C3×D3×D12—21no—
28C3×D3×D12—21no—
29C3×D3×D12C2211yescharacteristic
30C3×D3×D12C2211yescharacteristic
31C3×#3798—21no—
32C3×#3798—21no—
33C3×#3798C2211yescharacteristic
34C3×#3796—21no—
35C3×#3796C2211yescharacteristic, complemented
36C3×#3795—21no—
37C3×#3795C2211yescharacteristic, complemented
38C3×D3×Dic6—21no—
39C3×D3×Dic6C2211yescharacteristic, complemented
40C33×Q16C2211yescharacteristic, complemented
41C3×#3756C2211yescharacteristic, complemented
42C3×#3755C2211yescharacteristic, complemented
43C3×#3744C2211yescharacteristic, complemented
44C3×#3743C2211yescharacteristic, complemented
45C32×#216C2211yescharacteristic, complemented
46C32×#215C2211yescharacteristic, complemented
47C32×#215C2211yescharacteristic, complemented
48C32×#215C2211yescharacteristic, complemented
49C32×D24C2211yescharacteristic, complemented
50C32×#204C2211yescharacteristic, complemented
51C32×ΓL(1,𝔽25)C2211yescharacteristic, complemented
52C32×D3×C8C2211yescharacteristic, complemented
53C3×#3717C2211yescharacteristic, complemented
54C3×#3716C2211yescharacteristic, complemented
55C3×#3716C2211yescharacteristic, complemented
56C3×#3715C2211yescharacteristic, complemented
57C3×#3714C2211yescharacteristic, complemented
58C3×#3713C2211yescharacteristic, complemented
59C3×#3711C2211yescharacteristic, complemented
60C3×#3710C2211yescharacteristic, complemented
61C3×D3×C3⋊C8C2211yescharacteristic, complemented
62C3×#1010—31no—
63C3×#1009—31no—
64C3×#1009—31no—
65C3×#1007—31no—
66#64320C2×C311yescharacteristic, complemented
67#64315C2×C311yescharacteristic, complemented
68C32×#137—31no—
69C32×#135—31no—
70#64127C2×C311yescharacteristic, complemented
71C3×#951—31no—
72C3×#950—31no—
73C3×#949—31no—
74C2×C3×#215—31no—
75C3×#919—21no—
76C3×#919—31no—
77C3×#919D311yescharacteristic, complemented
78C3×#919C2×C311yescharacteristic, complemented
79C3×#918—21no—
80C3×#918—31no—
81C3×#918—31no—
82C3×#918—31no—
83C3×#918—61no—
84C3×#918D311yescharacteristic, complemented
85C3×#918C2×C311yescharacteristic, complemented
86C3×#916—31no—
87C3×#916—31no—
88C3×#914—31no—
89C3×#914—31no—
90C3×D3×SD16—31no—
91C3×D3×SD16—31no—
92C3×D3×SD16—31no—
93C3×D3×SD16—31no—
94C3×#911—31no—
95C3×#911—31no—
96C3×#908—31no—
97C3×#907—31no—
98C2×C3×#204—31no—
99C3×#901—31no—
100#63950C2×C311yescharacteristic, complemented
101#63947C2×C311yescharacteristic, complemented
102#63943C2×C311yescharacteristic, complemented
103#63940C2×C311yescharacteristic, complemented
104#63939C2×C311yescharacteristic, complemented
105D3×#215C2×C311yescharacteristic, complemented
106#63804C2×C311yescharacteristic, complemented
107#63798C2×C311yescharacteristic, complemented
108#63795C2×C311yescharacteristic, complemented
109D3×#204C2×C311yescharacteristic, complemented
110C2×C3×D32—21no—
111C2×C3×D32—21no—
112C2×C3×D32—21no—
113C33×Q8C2311yescharacteristic
114C33×Q8C2311yescharacteristic
115C3×C4⋊(C3⋊D3)—21no—
116C3×C4⋊(C3⋊D3)C2311yescharacteristic
117C3×C4×C3⋊D3—21no—
118C3×C4×C3⋊D3—21no—
119C3×C4×C3⋊D3C2311yescharacteristic
120C3×#634—21no—
121C3×#634C2311yescharacteristic
122C32×D12—21no—
123C32×D12—21no—
124C32×D12—21no—
125C32×D12C2311yescharacteristic
126C32×D12C2311yescharacteristic
127C32×D12C2311yescharacteristic
128C32×C4×D3—21no—
129C32×C4×D3—21no—
130C32×C4×D3—21no—
131C32×C4×D3—21no—
132C32×C4×D3C2311yescharacteristic
133C32×C4×D3C2311yescharacteristic
134C32×Dic6—21no—
135C32×Dic6C2311yescharacteristic
136C3×#627—21no—
137C3×#627D411yescharacteristic
138C3×#626—21no—
139C3×#626—21no—
140C3×#626—21no—
141C3×#626D411yescharacteristic
142C3×#626D411yescharacteristic
143C3×#625—21no—
144C3×#625—21no—
145C3×#625D411yescharacteristic
146C3×D3×Dic3—21no—
147C3×D3×Dic3—21no—
148C3×D3×Dic3—21no—
149C33×C8C2311yescharacteristic
150C3×C3⋊(C3⋊C8)C2311yescharacteristic
151C32×C3⋊C8C2311yescharacteristic
152C32×C3⋊C8C2311yescharacteristic
153C3×#577—91no—
154#5778—31no—
155#5770—31no—
156C32×#41—31no—
157C32×#41—31no—
158C32×#41—31no—
159C2×C32×Q8—31no—
160#3832C22×C311yescharacteristic
161Q8×C3⋊D3C22×C311yescharacteristic, complemented
162C3×#239—21no—
163C3×#239—21no—
164C3×#239—21no—
165C3×#239—31no—
166C3×#239—31no—
167C3×#239—31no—
168C3×#239—61no—
169C3×#239—61no—
170C3×#239C2×D311yescharacteristic
171C3×#239C2×D311yescharacteristic
172C3×#239C2×D311yescharacteristic, complemented
173C3×#239C22×C311yescharacteristic
174C3×#239C22×C311yescharacteristic
175C3×#239C22×C311yescharacteristic, complemented
176C3×D3×Q8—21no—
177C3×D3×Q8—31no—
178C3×D3×Q8—31no—
179C3×D3×Q8—31no—
180C3×D3×Q8—61no—
181C3×D3×Q8—61no—
182C3×D3×Q8C2×D311yescharacteristic, complemented
183C3×D3×Q8C22×C311yescharacteristic, complemented
184C3×#237—31no—
185C3×#237—31no—
186C3×#237—61no—
187C3×#237—61no—
188C3×D3×D4—31no—
189C3×D3×D4—31no—
190C3×D3×D4—31no—
191C3×D3×D4—31no—
192C3×D3×D4—61no—
193C3×D3×D4—61no—
194C3×D3×D4—61no—
195C3×D3×D4—61no—
196C3×#235—31no—
197C3×#235—31no—
198C3×#235—31no—
199C3×#235—61no—
200C3×#235—61no—
201C3×#235—61no—
202C3×#235—61no—
203C3×#235—61no—
204C2×C3×D12—31no—
205C2×C3×D12—31no—
206C2×C3×D12—61no—
207C2×C3×D12—61no—
208C2×C3×Dic6—31no—
209C2×C3×Dic6—61no—
210#3802—21no—
211#3802C22×C311yescharacteristic
212D3×D12—21no—
213D3×D12—21no—
214D3×D12C22×C311yescharacteristic
215D3×D12C22×C311yescharacteristic
216#3798—21no—
217#3798—21no—
218#3798C22×C311yescharacteristic
219#3796—21no—
220#3796C22×C311yescharacteristic, complemented
221#3795—21no—
222#3795C22×C311yescharacteristic, complemented
223D3×Dic6—21no—
224D3×Dic6C22×C311yescharacteristic, complemented
225C32×Q16—21no—
226C32×Q16—21no—
227C32×Q16—21no—
228C32×Q16—31no—
229C32×Q16—41no—
230C32×Q16C2×D311yescharacteristic, complemented
231C32×Q16C2×D311yescharacteristic, complemented
232C32×Q16C22×C311yescharacteristic, complemented
233C32×SD16—31no—
234C32×SD16—31no—
235C32×SD16—31no—
236C32×SD16—31no—
237C32×D8—31no—
238C32×M16—31no—
239C2×C32×C8—31no—
240#3756C22×C311yescharacteristic, complemented
241#3755C22×C311yescharacteristic, complemented
242#3744C22×C311yescharacteristic, complemented
243#3743C22×C311yescharacteristic, complemented
244C3×#216—21no—
245C3×#216—31no—
246C3×#216—31no—
247C3×#216—61no—
248C3×#216C2×D311yescharacteristic, complemented
249C3×#216C22×C311yescharacteristic, complemented
250C3×#215—21no—
251C3×#215—21no—
252C3×#215—21no—
253C3×#215—31no—
254C3×#215—31no—
255C3×#215—31no—
256C3×#215—31no—
257C3×#215—61no—
258C3×#215C2×D311yescharacteristic, complemented
259C3×#215C2×D311yescharacteristic, complemented
260C3×#215C2×D311yescharacteristic, complemented
261C3×#215C22×C311yescharacteristic, complemented
262C3×#215C22×C311yescharacteristic, complemented
263C3×#215C22×C311yescharacteristic, complemented
264C3×#214—31no—
265C3×#214—31no—
266C3×#214—31no—
267C3×#213—31no—
268C3×#213—31no—
269C3×#213—31no—
270C3×#208—31no—
271C2×C3×C3⋊C8—31no—
272C3×D24—21no—
273C3×D24—31no—
274C3×D24C2×D311yescharacteristic, complemented
275C3×D24C22×C311yescharacteristic, complemented
276C3×#204—21no—
277C3×#204—31no—
278C3×#204—31no—
279C3×#204—31no—
280C3×#204—31no—
281C3×#204—31no—
282C3×#204—61no—
283C3×#204C2×D311yescharacteristic, complemented
284C3×#204C22×C311yescharacteristic, complemented
285C3×ΓL(1,𝔽25)—21no—
286C3×ΓL(1,𝔽25)—31no—
287C3×ΓL(1,𝔽25)—31no—
288C3×ΓL(1,𝔽25)—31no—
289C3×ΓL(1,𝔽25)—61no—
290C3×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
291C3×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
292C3×D3×C8—21no—
293C3×D3×C8—31no—
294C3×D3×C8—31no—
295C3×D3×C8—31no—
296C3×D3×C8C2×D311yescharacteristic, complemented
297C3×D3×C8C22×C311yescharacteristic, complemented
298#3717C22×C311yescharacteristic, complemented
299#3716C22×C311yescharacteristic, complemented
300#3716C22×C311yescharacteristic, complemented
301#3715C22×C311yescharacteristic, complemented
302#3714C22×C311yescharacteristic, complemented
303#3713C22×C311yescharacteristic, complemented
304#3711C22×C311yescharacteristic, complemented
305#3710C22×C311yescharacteristic, complemented
306D3×C3⋊C8C22×C311yescharacteristic, complemented
307C2×C3×C3⋊D3—21no—
308C2×C3×C3⋊D3C2×D411yescharacteristic
309C2×C32×D3—21no—
310C2×C32×D3—21no—
311C2×C32×D3—21no—
312C2×C32×D3C2×D411yescharacteristic
313C2×C32×D3C2×D411yescharacteristic
314C3×D32—81no—
315C3×D32—81no—
316C3×D32—81no—
317C33×C4—21no—
318C33×C4—21no—
319C33×C4C2411yescharacteristic
320C3×C3⋊Dic3—21no—
321C3×C3⋊Dic3C2×D411yescharacteristic
322C32×Dic3—21no—
323C32×Dic3C2×D411yescharacteristic
324C32×Dic3C2×D411yescharacteristic
325C3×2−1+4—91no—
326C3×H(5,𝔽2)—91no—
327#1010—31no—
328#1009—31no—
329#1009—31no—
330#1007—31no—
331C3×#137—31no—
332C3×#137—31no—
333C3×#137—61no—
334C3×#137—91no—
335C3×#137—91no—
336C3×AGL(1,ℤ/8)—91no—
337C3×AGL(1,ℤ/8)—91no—
338C3×AGL(1,ℤ/8)—91no—
339C3×#135—31no—
340C3×#135—31no—
341C3×#135—61no—
342C3×#135—91no—
343C3×#135—91no—
344C2×C3×SD16—91no—
345C2×C3×SD16—91no—
346C2×C3×SD16—91no—
347C3×#131—91no—
348#951—31no—
349#950—31no—
350#949—31no—
351C2×#215—31no—
352#919—31no—
353#919C3×D311yescharacteristic, complemented
354#918—31no—
355#918—31no—
356#918—31no—
357#918—61no—
358#918C3×D311yescharacteristic, complemented
359#916—31no—
360#916—31no—
361#914—31no—
362#914—31no—
363D3×SD16—31no—
364D3×SD16—31no—
365D3×SD16—31no—
366D3×SD16—31no—
367#911—31no—
368#911—31no—
369#908—31no—
370#907—31no—
371C2×#204—31no—
372#901—31no—
373C22×C3×D3—61no—
374C22×C3×D3—61no—
375C22×C3×D3—61no—
376C22×C3×D3—61no—
377C22×C3×D3—61no—
378C22×C3×D3—61no—
379C2×D32—21no—
380C2×D32—21no—
381C2×D32—21no—
382C32×Q8—21no—
383C32×Q8—21no—
384C32×Q8—21no—
385C32×Q8—21no—
386C32×Q8—21no—
387C32×Q8—21no—
388C32×Q8—31no—
389C32×Q8—41no—
390C32×Q8—41no—
391C32×Q8—61no—
392C32×Q8C22×D311yescharacteristic
393C32×Q8C22×D311yescharacteristic
394C32×Q8C22×D311yescharacteristic
395C32×Q8C22×D311yescharacteristic
396C32×Q8C23×C311yescharacteristic
397C32×Q8C23×C311yescharacteristic
398C32×D4—31no—
399C32×D4—31no—
400C32×D4—31no—
401C32×D4—61no—
402C32×D4—61no—
403C32×D4—61no—
404C2×C32×C4—31no—
405C2×C32×C4—31no—
406C2×C32×C4—61no—
407C2×C32×C4—61no—
408C2×C32×C4—61no—
409C2×C32×C4—61no—
410C4⋊(C3⋊D3)—21no—
411C4⋊(C3⋊D3)C23×C311yescharacteristic
412C4×C3⋊D3—21no—
413C4×C3⋊D3—21no—
414C4×C3⋊D3C23×C311yescharacteristic
415#634—21no—
416#634C23×C311yescharacteristic
417C3×#67—31no—
418C3×#67—31no—
419C3×#67—31no—
420C3×#67—31no—
421C3×#67—61no—
422C3×#67—61no—
423C3×#67—61no—
424C3×#67—61no—
425C3×#67—61no—
426C3×#67—61no—
427C3×#67—61no—
428C2×C3×Dic3—61no—
429C2×C3×Dic3—61no—
430C2×C3×Dic3—61no—
431C3×D12—21no—
432C3×D12—21no—
433C3×D12—21no—
434C3×D12—21no—
435C3×D12—21no—
436C3×D12—21no—
437C3×D12—21no—
438C3×D12—21no—
439C3×D12—21no—
440C3×D12—31no—
441C3×D12—31no—
442C3×D12—31no—
443C3×D12—31no—
444C3×D12—41no—
445C3×D12—41no—
446C3×D12—41no—
447C3×D12—61no—
448C3×D12—61no—
449C3×D12—61no—
450C3×D12—61no—
451C3×D12—61no—
452C3×D12—61no—
453C3×D12—121no—
454C3×D12C22×D311yescharacteristic
455C3×D12C22×D311yescharacteristic
456C3×D12C22×D311yescharacteristic
457C3×D12C23×C311yescharacteristic
458C3×D12C23×C311yescharacteristic
459C3×D12C23×C311yescharacteristic
460C3×C4×D3—21no—
461C3×C4×D3—21no—
462C3×C4×D3—21no—
463C3×C4×D3—21no—
464C3×C4×D3—21no—
465C3×C4×D3—21no—
466C3×C4×D3—21no—
467C3×C4×D3—21no—
468C3×C4×D3—21no—
469C3×C4×D3—21no—
470C3×C4×D3—31no—
471C3×C4×D3—31no—
472C3×C4×D3—41no—
473C3×C4×D3—41no—
474C3×C4×D3—41no—
475C3×C4×D3—41no—
476C3×C4×D3—61no—
477C3×C4×D3—61no—
478C3×C4×D3—61no—
479C3×C4×D3—61no—
480C3×C4×D3—61no—
481C3×C4×D3—61no—
482C3×C4×D3—61no—
483C3×C4×D3—61no—
484C3×C4×D3—121no—
485C3×C4×D3—121no—
486C3×C4×D3C22×D311yescharacteristic
487C3×C4×D3C22×D311yescharacteristic
488C3×C4×D3C23×C311yescharacteristic
489C3×C4×D3C23×C311yescharacteristic
490C3×Dic6—21no—
491C3×Dic6—21no—
492C3×Dic6—21no—
493C3×Dic6—31no—
494C3×Dic6—31no—
495C3×Dic6—31no—
496C3×Dic6—31no—
497C3×Dic6—41no—
498C3×Dic6—61no—
499C3×Dic6—61no—
500C3×Dic6—61no—
501C3×Dic6—61no—
502C3×Dic6—61no—
503C3×Dic6—121no—
504C3×Dic6C22×D311yescharacteristic
505C3×Dic6C23×C311yescharacteristic
506#627—21no—
507#627C3×D411yescharacteristic
508#626—21no—
509#626—21no—
510#626—21no—
511#626C3×D411yescharacteristic
512#626C3×D411yescharacteristic
513#625—21no—
514#625—21no—
515#625C3×D411yescharacteristic
516D3×Dic3—21no—
517D3×Dic3—21no—
518D3×Dic3—21no—
519C32×C8—21no—
520C32×C8—21no—
521C32×C8—21no—
522C32×C8—31no—
523C32×C8—31no—
524C32×C8—41no—
525C32×C8C22×D311yescharacteristic
526C32×C8C22×D311yescharacteristic
527C32×C8C23×C311yescharacteristic
528C3⋊(C3⋊C8)C23×C311yescharacteristic
529C3×C3⋊C8—21no—
530C3×C3⋊C8—21no—
531C3×C3⋊C8—31no—
532C3×C3⋊C8—31no—
533C3×C3⋊C8—61no—
534C3×C3⋊C8C22×D311yescharacteristic
535C3×C3⋊C8C22×D311yescharacteristic
536C3×C3⋊C8C23×C311yescharacteristic
537C3×C3⋊C8C23×C311yescharacteristic
538#577—91noSylow
539C2×C33C22×D411yescharacteristic
540C3×C3⋊D3—21no—
541C3×C3⋊D3—41no—
542C32×D3—21no—
543C32×D3—21no—
544C32×D3—41no—
545C32×D3—41no—
546C32×D3—41no—
547C3×#41—31no—
548C3×#41—31no—
549C3×#41—31no—
550C3×#41—31no—
551C3×#41—31no—
552C3×#41—31no—
553C3×#41—61no—
554C3×#41—61no—
555C3×#41—61no—
556C3×#41—91no—
557C3×#41—91no—
558C3×#41—91no—
559C3×#41—91no—
560C3×#41—181no—
561C3×#41—181no—
562C3×#41—181no—
563C3×#41—181no—
564C2×C3×Q8—31no—
565C2×C3×Q8—31no—
566C2×C3×Q8—61no—
567C2×C3×Q8—91no—
568C2×C3×Q8—91no—
569C2×C3×Q8—181no—
570C2×C3×D4—91no—
571C2×C3×D4—91no—
572C2×C3×D4—91no—
573C2×C3×D4—181no—
574C2×C3×D4—181no—
575C2×C3×D4—181no—
576#239—31no—
577#239—31no—
578#239—31no—
579#239—61no—
580#239—61no—
581#239C2×C3×D311yescharacteristic
582#239C2×C3×D311yescharacteristic
583#239C2×C3×D311yescharacteristic, complemented
584D3×Q8—31no—
585D3×Q8—31no—
586D3×Q8—31no—
587D3×Q8—61no—
588D3×Q8—61no—
589D3×Q8C2×C3×D311yescharacteristic, complemented
590#237—31no—
591#237—31no—
592#237—61no—
593#237—61no—
594D3×D4—31no—
595D3×D4—31no—
596D3×D4—31no—
597D3×D4—31no—
598D3×D4—61no—
599D3×D4—61no—
600D3×D4—61no—
601D3×D4—61no—
602#235—31no—
603#235—31no—
604#235—31no—
605#235—61no—
606#235—61no—
607#235—61no—
608#235—61no—
609#235—61no—
610C2×D12—31no—
611C2×D12—31no—
612C2×D12—61no—
613C2×D12—61no—
614C2×Dic6—31no—
615C2×Dic6—61no—
616C3×Q16—21no—
617C3×Q16—21no—
618C3×Q16—21no—
619C3×Q16—31no—
620C3×Q16—31no—
621C3×Q16—41no—
622C3×Q16—61no—
623C3×Q16—91no—
624C3×Q16D3211yescharacteristic, complemented
625C3×Q16C2×C3×D311yescharacteristic, complemented
626C3×Q16C2×C3×D311yescharacteristic, complemented
627C3×SD16—31no—
628C3×SD16—31no—
629C3×SD16—31no—
630C3×SD16—31no—
631C3×SD16—31no—
632C3×SD16—31no—
633C3×SD16—31no—
634C3×SD16—31no—
635C3×SD16—61no—
636C3×SD16—61no—
637C3×SD16—61no—
638C3×SD16—61no—
639C3×SD16—91no—
640C3×SD16—91no—
641C3×SD16—91no—
642C3×SD16—91no—
643C3×SD16—91no—
644C3×SD16—91no—
645C3×D8—31no—
646C3×D8—31no—
647C3×D8—61no—
648C3×D8—91no—
649C3×D8—91no—
650C3×M16—31no—
651C3×M16—31no—
652C3×M16—61no—
653C3×M16—91no—
654C3×M16—91no—
655C2×C3×C8—31no—
656C2×C3×C8—31no—
657C2×C3×C8—61no—
658C2×C3×C8—91no—
659C2×C3×C8—91no—
660#216—31no—
661#216—31no—
662#216—61no—
663#216C2×C3×D311yescharacteristic, complemented
664#215—31no—
665#215—31no—
666#215—31no—
667#215—31no—
668#215—61no—
669#215C2×C3×D311yescharacteristic, complemented
670#215C2×C3×D311yescharacteristic, complemented
671#215C2×C3×D311yescharacteristic, complemented
672#214—31no—
673#214—31no—
674#214—31no—
675#213—31no—
676#213—31no—
677#213—31no—
678#208—31no—
679C2×C3⋊C8—31no—
680D24—31no—
681D24C2×C3×D311yescharacteristic, complemented
682#204—31no—
683#204—31no—
684#204—31no—
685#204—31no—
686#204—31no—
687#204—61no—
688#204C2×C3×D311yescharacteristic, complemented
689ΓL(1,𝔽25)—31no—
690ΓL(1,𝔽25)—31no—
691ΓL(1,𝔽25)—31no—
692ΓL(1,𝔽25)—61no—
693ΓL(1,𝔽25)C2×C3×D311yescharacteristic, complemented
694D3×C8—31no—
695D3×C8—31no—
696D3×C8—31no—
697D3×C8C2×C3×D311yescharacteristic, complemented
698C22×C32—31no—
699C22×C32—31no—
700C22×C32—61no—
701C22×C32—61no—
702C22×C32—61no—
703C2×C3⋊D3—21no—
704C2×C3⋊D3C2×C3×D411yescharacteristic
705C2×C3×D3—21no—
706C2×C3×D3—21no—
707C2×C3×D3—21no—
708C2×C3×D3—21no—
709C2×C3×D3—21no—
710C2×C3×D3—21no—
711C2×C3×D3—21no—
712C2×C3×D3—21no—
713C2×C3×D3—31no—
714C2×C3×D3—31no—
715C2×C3×D3—41no—
716C2×C3×D3—41no—
717C2×C3×D3—41no—
718C2×C3×D3—61no—
719C2×C3×D3—61no—
720C2×C3×D3—61no—
721C2×C3×D3—121no—
722C2×C3×D3—241no—
723C2×C3×D3—241no—
724C2×C3×D3—241no—
725C2×C3×D3—241no—
726C2×C3×D3—241no—
727C2×C3×D3—241no—
728C2×C3×D3D3×D411yescharacteristic
729C2×C3×D3D3×D411yescharacteristic
730C2×C3×D3C2×C3×D411yescharacteristic
731C2×C3×D3C2×C3×D411yescharacteristic
732D32—81no—
733D32—81no—
734D32—81no—
735C32×C4—21no—
736C32×C4—21no—
737C32×C4—21no—
738C32×C4—21no—
739C32×C4—21no—
740C32×C4—21no—
741C32×C4—21no—
742C32×C4—21no—
743C32×C4—21no—
744C32×C4—31no—
745C32×C4—31no—
746C32×C4—41no—
747C32×C4—41no—
748C32×C4—41no—
749C32×C4—41no—
750C32×C4—41no—
751C32×C4—41no—
752C32×C4—41no—
753C32×C4—61no—
754C32×C4—81no—
755C32×C4—81no—
756C32×C4C23×D311yescharacteristic
757C32×C4C23×D311yescharacteristic
758C32×C4C24×C311yescharacteristic
759C3⋊Dic3—21no—
760C3⋊Dic3C2×C3×D411yescharacteristic
761C3×Dic3—21no—
762C3×Dic3—21no—
763C3×Dic3—21no—
764C3×Dic3—21no—
765C3×Dic3—31no—
766C3×Dic3—31no—
767C3×Dic3—41no—
768C3×Dic3—61no—
769C3×Dic3—61no—
770C3×Dic3—61no—
771C3×Dic3—121no—
772C3×Dic3D3×D411yescharacteristic
773C3×Dic3D3×D411yescharacteristic
774C3×Dic3C2×C3×D411yescharacteristic
775C3×Dic3C2×C3×D411yescharacteristic
7762−1+4—91no—
777H(5,𝔽2)—91no—
778#137—31no—
779#137—91no—
780#137—91no—
781AGL(1,ℤ/8)—91no—
782AGL(1,ℤ/8)—91no—
783AGL(1,ℤ/8)—91no—
784#135—31no—
785#135—91no—
786#135—91no—
787C2×SD16—91no—
788C2×SD16—91no—
789C2×SD16—91no—
790#131—91no—
791C33#57711yescharacteristic, complemented, Sylow
792C23×C3—181no—
793C23×C3—181no—
794C23×C3—181no—
795C22×D3—61no—
796C22×D3—61no—
797C22×D3—61no—
798C22×D3—61no—
799C22×D3—61no—
800C22×D3—61no—
801C3×Q8—21no—
802C3×Q8—21no—
803C3×Q8—21no—
804C3×Q8—21no—
805C3×Q8—21no—
806C3×Q8—21no—
807C3×Q8—31no—
808C3×Q8—31no—
809C3×Q8—41no—
810C3×Q8—41no—
811C3×Q8—61no—
812C3×Q8—61no—
813C3×Q8—61no—
814C3×Q8—91no—
815C3×Q8—91no—
816C3×Q8—121no—
817C3×Q8—181no—
818C3×Q8—181no—
819C3×Q8C2×D3211yescharacteristic
820C3×Q8C2×D3211yescharacteristic
821C3×Q8C22×C3×D311yescharacteristic
822C3×Q8C22×C3×D311yescharacteristic
823C3×Q8C22×C3×D311yescharacteristic
824C3×Q8C22×C3×D311yescharacteristic
825C3×D4—31no—
826C3×D4—31no—
827C3×D4—31no—
828C3×D4—31no—
829C3×D4—31no—
830C3×D4—31no—
831C3×D4—61no—
832C3×D4—61no—
833C3×D4—61no—
834C3×D4—61no—
835C3×D4—61no—
836C3×D4—61no—
837C3×D4—61no—
838C3×D4—61no—
839C3×D4—61no—
840C3×D4—91no—
841C3×D4—91no—
842C3×D4—91no—
843C3×D4—91no—
844C3×D4—121no—
845C3×D4—121no—
846C3×D4—121no—
847C3×D4—181no—
848C3×D4—181no—
849C3×D4—181no—
850C3×D4—181no—
851C3×D4—181no—
852C3×D4—181no—
853C2×C3×C4—31no—
854C2×C3×C4—31no—
855C2×C3×C4—31no—
856C2×C3×C4—31no—
857C2×C3×C4—61no—
858C2×C3×C4—61no—
859C2×C3×C4—61no—
860C2×C3×C4—61no—
861C2×C3×C4—61no—
862C2×C3×C4—61no—
863C2×C3×C4—61no—
864C2×C3×C4—61no—
865C2×C3×C4—61no—
866C2×C3×C4—61no—
867C2×C3×C4—91no—
868C2×C3×C4—121no—
869C2×C3×C4—121no—
870C2×C3×C4—121no—
871C2×C3×C4—121no—
872C2×C3×C4—181no—
873C2×C3×C4—181no—
874C2×C3×C4—181no—
875C2×C3×C4—181no—
876C2×C3×C4—181no—
877#67—31no—
878#67—31no—
879#67—31no—
880#67—31no—
881#67—61no—
882#67—61no—
883#67—61no—
884#67—61no—
885#67—61no—
886#67—61no—
887#67—61no—
888C2×Dic3—61no—
889C2×Dic3—61no—
890C2×Dic3—61no—
891D12—21no—
892D12—21no—
893D12—21no—
894D12—31no—
895D12—31no—
896D12—31no—
897D12—31no—
898D12—61no—
899D12—61no—
900D12—61no—
901D12—61no—
902D12—61no—
903D12—61no—
904D12—121no—
905D12C22×C3×D311yescharacteristic
906D12C22×C3×D311yescharacteristic
907D12C22×C3×D311yescharacteristic
908C4×D3—21no—
909C4×D3—21no—
910C4×D3—21no—
911C4×D3—21no—
912C4×D3—31no—
913C4×D3—31no—
914C4×D3—61no—
915C4×D3—61no—
916C4×D3—61no—
917C4×D3—61no—
918C4×D3—61no—
919C4×D3—61no—
920C4×D3—61no—
921C4×D3—61no—
922C4×D3—121no—
923C4×D3—121no—
924C4×D3C22×C3×D311yescharacteristic
925C4×D3C22×C3×D311yescharacteristic
926Dic6—21no—
927Dic6—31no—
928Dic6—31no—
929Dic6—31no—
930Dic6—31no—
931Dic6—61no—
932Dic6—61no—
933Dic6—61no—
934Dic6—61no—
935Dic6—61no—
936Dic6—121no—
937Dic6C22×C3×D311yescharacteristic
938C3×C8—21no—
939C3×C8—21no—
940C3×C8—21no—
941C3×C8—31no—
942C3×C8—31no—
943C3×C8—31no—
944C3×C8—31no—
945C3×C8—41no—
946C3×C8—61no—
947C3×C8—61no—
948C3×C8—91no—
949C3×C8C2×D3211yescharacteristic
950C3×C8C22×C3×D311yescharacteristic
951C3×C8C22×C3×D311yescharacteristic
952C3⋊C8—31no—
953C3⋊C8—31no—
954C3⋊C8—61no—
955C3⋊C8C22×C3×D311yescharacteristic
956C3⋊C8C22×C3×D311yescharacteristic
957C2×C32—21no—
958C2×C32—21no—
959C2×C32—21no—
960C2×C32—41no—
961C2×C32—61no—
962C2×C32—61no—
963C2×C32—121no—
964C2×C32—121no—
965C2×C32—121no—
966C2×C32C2×D3×D411yescharacteristic
967C2×C32C2×D3×D411yescharacteristic
968C2×C32C22×C3×D411yescharacteristic
969C3⋊D3—21no—
970C3⋊D3—41no—
971C3×D3—21no—
972C3×D3—21no—
973C3×D3—21no—
974C3×D3—21no—
975C3×D3—41no—
976C3×D3—41no—
977C3×D3—41no—
978C3×D3—41no—
979C3×D3—41no—
980C3×D3—41no—
981C3×D3—41no—
982C3×D3—41no—
983C3×D3—61no—
984C3×D3—61no—
985C3×D3—81no—
986C3×D3—81no—
987C3×D3—81no—
988C3×D3—121no—
989C3×D3—121no—
990C3×D3—121no—
991C3×D3—241no—
992#41—31no—
993#41—31no—
994#41—31no—
995#41—91no—
996#41—91no—
997#41—91no—
998#41—91no—
999#41—181no—
1000#41—181no—
1001#41—181no—
1002#41—181no—
1003C2×Q8—31no—
1004C2×Q8—91no—
1005C2×Q8—91no—
1006C2×Q8—181no—
1007C2×D4—91no—
1008C2×D4—91no—
1009C2×D4—91no—
1010C2×D4—181no—
1011C2×D4—181no—
1012C2×D4—181no—
1013Q16—31no—
1014Q16—91no—
1015Q16C3×D3211yescharacteristic, complemented
1016SD16—31no—
1017SD16—31no—
1018SD16—31no—
1019SD16—31no—
1020SD16—91no—
1021SD16—91no—
1022SD16—91no—
1023SD16—91no—
1024SD16—91no—
1025SD16—91no—
1026D8—31no—
1027D8—91no—
1028D8—91no—
1029M16—31no—
1030M16—91no—
1031M16—91no—
1032C2×C8—31no—
1033C2×C8—91no—
1034C2×C8—91no—
1035C22×C3—31no—
1036C22×C3—31no—
1037C22×C3—31no—
1038C22×C3—31no—
1039C22×C3—61no—
1040C22×C3—61no—
1041C22×C3—61no—
1042C22×C3—61no—
1043C22×C3—61no—
1044C22×C3—61no—
1045C22×C3—61no—
1046C22×C3—61no—
1047C22×C3—91no—
1048C22×C3—121no—
1049C22×C3—121no—
1050C22×C3—121no—
1051C22×C3—181no—
1052C22×C3—721no—
1053C22×C3—721no—
1054C22×C3—721no—
1055C2×D3—21no—
1056C2×D3—21no—
1057C2×D3—21no—
1058C2×D3—31no—
1059C2×D3—31no—
1060C2×D3—61no—
1061C2×D3—61no—
1062C2×D3—61no—
1063C2×D3—121no—
1064C2×D3—241no—
1065C2×D3—241no—
1066C2×D3—241no—
1067C2×D3—241no—
1068C2×D3—241no—
1069C2×D3—241no—
1070C2×D3C3×D3×D411yescharacteristic
1071C2×D3C3×D3×D411yescharacteristic
1072C3×C4—21no—
1073C3×C4—21no—
1074C3×C4—21no—
1075C3×C4—21no—
1076C3×C4—21no—
1077C3×C4—21no—
1078C3×C4—21no—
1079C3×C4—21no—
1080C3×C4—21no—
1081C3×C4—31no—
1082C3×C4—31no—
1083C3×C4—31no—
1084C3×C4—31no—
1085C3×C4—41no—
1086C3×C4—41no—
1087C3×C4—41no—
1088C3×C4—41no—
1089C3×C4—41no—
1090C3×C4—41no—
1091C3×C4—41no—
1092C3×C4—61no—
1093C3×C4—61no—
1094C3×C4—61no—
1095C3×C4—61no—
1096C3×C4—81no—
1097C3×C4—81no—
1098C3×C4—91no—
1099C3×C4—121no—
1100C3×C4—181no—
1101C3×C4C22×D3211yescharacteristic
1102C3×C4C23×C3×D311yescharacteristic
1103C3×C4C23×C3×D311yescharacteristic
1104Dic3—21no—
1105Dic3—31no—
1106Dic3—31no—
1107Dic3—61no—
1108Dic3—61no—
1109Dic3—61no—
1110Dic3—121no—
1111Dic3C3×D3×D411yescharacteristic
1112Dic3C3×D3×D411yescharacteristic
1113C32—21no—
1114C32—21no—
1115C32—21no—
1116C32—41no—
1117C32#577011yescharacteristic, complemented
1118C32#577811yescharacteristic, complemented
1119C32C3×#57711yescharacteristic, complemented
1120C23—181no—
1121C23—181no—
1122C23—181no—
1123Q8—31no—
1124Q8—61no—
1125Q8—91no—
1126Q8—91no—
1127Q8—181no—
1128Q8—181no—
1129Q8C2×C3×D3211yescharacteristic
1130Q8C2×C3×D3211yescharacteristic
1131D4—31no—
1132D4—31no—
1133D4—31no—
1134D4—61no—
1135D4—61no—
1136D4—61no—
1137D4—91no—
1138D4—91no—
1139D4—91no—
1140D4—91no—
1141D4—181no—
1142D4—181no—
1143D4—181no—
1144D4—181no—
1145D4—181no—
1146D4—181no—
1147C2×C4—31no—
1148C2×C4—31no—
1149C2×C4—61no—
1150C2×C4—61no—
1151C2×C4—61no—
1152C2×C4—61no—
1153C2×C4—91no—
1154C2×C4—181no—
1155C2×C4—181no—
1156C2×C4—181no—
1157C2×C4—181no—
1158C2×C4—181no—
1159C8—31no—
1160C8—31no—
1161C8—91no—
1162C8C2×C3×D3211yescharacteristic
1163C2×C3—21no—
1164C2×C3—21no—
1165C2×C3—21no—
1166C2×C3—41no—
1167C2×C3—61no—
1168C2×C3—61no—
1169C2×C3—61no—
1170C2×C3—61no—
1171C2×C3—121no—
1172C2×C3—121no—
1173C2×C3—121no—
1174C2×C3—121no—
1175C2×C3—121no—
1176C2×C3—121no—
1177C2×C3—121no—
1178C2×C3—121no—
1179C2×C3—181no—
1180C2×C3—241no—
1181C2×C3—241no—
1182C2×C3—241no—
1183C2×C3—361no—
1184C2×C3D32×D411yescharacteristic
1185C2×C3C2×C3×D3×D411yescharacteristic
1186C2×C3C2×C3×D3×D411yescharacteristic
1187D3—21no—
1188D3—21no—
1189D3—41no—
1190D3—41no—
1191D3—41no—
1192D3—61no—
1193D3—61no—
1194D3—121no—
1195D3—121no—
1196D3—121no—
1197D3—241no—
1198C22—31no—
1199C22—31no—
1200C22—61no—
1201C22—61no—
1202C22—61no—
1203C22—91no—
1204C22—181no—
1205C22—721no—
1206C22—721no—
1207C22—721no—
1208C4—21no—
1209C4—21no—
1210C4—31no—
1211C4—31no—
1212C4—61no—
1213C4—91no—
1214C4—181no—
1215C4C22×C3×D3211yescharacteristic
1216C3—21no—
1217C3—21no—
1218C3—21no—
1219C3—41no—
1220C3#1059477011yescharacteristic, direct product factor
1221C3C3×#577011yescharacteristic, complemented
1222C3C3×#577811yescharacteristic, complemented
1223C2—61no—
1224C2—61no—
1225C2—121no—
1226C2—121no—
1227C2—121no—
1228C2—181no—
1229C2—361no—
1230C2C3×D32×D411yescharacteristic
subgroupG/H
centerC2×C3D32×D4
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×Q16C22
socleC2×C33C22×D4
hypercenterC3×Q16D32
hypocenterC32C3×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×Q16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#64320C2semidirect
2. C3×#64315C2semidirect
3. C3×#64127C2semidirect
4. C32×#919C2semidirect
5. C32×#918C2semidirect
6. C3×#63950C2semidirect
7. C3×#63947C2semidirect
8. C3×#63943C2semidirect
9. C3×#63940C2semidirect
10. C3×#63939C2semidirect
11. C3×D3×#215C2semidirect
12. C3×#63804C2semidirect
13. C3×#63798C2semidirect
14. C3×#63795C2semidirect
15. C3×D3×#204C2semidirect
18. #10594770C3direct (N × H)
20. C3×Q8×C3⋊D3C22semidirect
23. C32×#239C22semidirect
24. C32×D3×Q8C22semidirect
35. C3×#3796C22semidirect
37. C3×#3795C22semidirect
39. C3×D3×Dic6C22semidirect
40. C33×Q16C22semidirect
41. C3×#3756C22semidirect
42. C3×#3755C22semidirect
43. C3×#3744C22semidirect
44. C3×#3743C22semidirect
45. C32×#216C22semidirect
46. C32×#215C22semidirect
47. C32×#215C22semidirect
48. C32×#215C22semidirect
49. C32×D24C22semidirect
50. C32×#204C22semidirect
51. C32×ΓL(1,𝔽25)C22semidirect
52. C32×D3×C8C22semidirect
53. C3×#3717C22semidirect
54. C3×#3716C22semidirect
55. C3×#3716C22semidirect
56. C3×#3715C22semidirect
57. C3×#3714C22semidirect
58. C3×#3713C22semidirect
59. C3×#3711C22semidirect
60. C3×#3710C22semidirect
61. C3×D3×C3⋊C8C22semidirect
66. #64320C2×C3semidirect
67. #64315C2×C3semidirect
70. #64127C2×C3semidirect
77. C3×#919D3semidirect
78. C3×#919C2×C3semidirect
84. C3×#918D3semidirect
85. C3×#918C2×C3semidirect
100. #63950C2×C3semidirect
101. #63947C2×C3semidirect
102. #63943C2×C3semidirect
103. #63940C2×C3semidirect
104. #63939C2×C3semidirect
105. D3×#215C2×C3semidirect
106. #63804C2×C3semidirect
107. #63798C2×C3semidirect
108. #63795C2×C3semidirect
109. D3×#204C2×C3semidirect
161. Q8×C3⋊D3C22×C3semidirect
172. C3×#239C2×D3semidirect
175. C3×#239C22×C3semidirect
182. C3×D3×Q8C2×D3semidirect
183. C3×D3×Q8C22×C3semidirect
220. #3796C22×C3semidirect
222. #3795C22×C3semidirect
224. D3×Dic6C22×C3semidirect
230. C32×Q16C2×D3semidirect
231. C32×Q16C2×D3semidirect
232. C32×Q16C22×C3semidirect
240. #3756C22×C3semidirect
241. #3755C22×C3semidirect
242. #3744C22×C3semidirect
243. #3743C22×C3semidirect
248. C3×#216C2×D3semidirect
249. C3×#216C22×C3semidirect
258. C3×#215C2×D3semidirect
259. C3×#215C2×D3semidirect
260. C3×#215C2×D3semidirect
261. C3×#215C22×C3semidirect
262. C3×#215C22×C3semidirect
263. C3×#215C22×C3semidirect
274. C3×D24C2×D3semidirect
275. C3×D24C22×C3semidirect
283. C3×#204C2×D3semidirect
284. C3×#204C22×C3semidirect
290. C3×ΓL(1,𝔽25)C2×D3semidirect
291. C3×ΓL(1,𝔽25)C22×C3semidirect
296. C3×D3×C8C2×D3semidirect
297. C3×D3×C8C22×C3semidirect
298. #3717C22×C3semidirect
299. #3716C22×C3semidirect
300. #3716C22×C3semidirect
301. #3715C22×C3semidirect
302. #3714C22×C3semidirect
303. #3713C22×C3semidirect
304. #3711C22×C3semidirect
305. #3710C22×C3semidirect
306. D3×C3⋊C8C22×C3semidirect
353. #919C3×D3semidirect
358. #918C3×D3semidirect
583. #239C2×C3×D3semidirect
589. D3×Q8C2×C3×D3semidirect
624. C3×Q16D32semidirect
625. C3×Q16C2×C3×D3semidirect
626. C3×Q16C2×C3×D3semidirect
663. #216C2×C3×D3semidirect
669. #215C2×C3×D3semidirect
670. #215C2×C3×D3semidirect
671. #215C2×C3×D3semidirect
681. D24C2×C3×D3semidirect
688. #204C2×C3×D3semidirect
693. ΓL(1,𝔽25)C2×C3×D3semidirect
697. D3×C8C2×C3×D3semidirect
791. C33#577semidirect
1015. Q16C3×D32semidirect
1117. C32#5770semidirect
1118. C32#5778semidirect
1119. C32C3×#577semidirect
1220. C3#10594770direct (N × H)
1221. C3C3×#5770semidirect
1222. C3C3×#5778semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#643202
C3×#643152
C3×#641272
C32×#9192
C32×#9182
C3×#639502
C3×#639472
C3×#639432
C3×#639402
C3×#639392
C3×D3×#2152
C3×#638042
C3×#637982
C3×#637952
C3×D3×#2042
C3×#57783
C3×#57703
#105947703