Finite Group Databasebeta

← C3×#84009 #11886567

Subgroups — C3×#84009 #11886567

Order 1152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#576C211yesmaximal, characteristic, complemented
2C3×#5836C211yesmaximal, characteristic, complemented
3C3×#5835C211yesmaximal, characteristic, complemented
4C3×#5770C211yesmaximal, characteristic, complemented
5C3×#5242C211yesmaximal, characteristic, complemented
6C3×#5241C211yesmaximal, characteristic, complemented
7C3×#5201C211yesmaximal, characteristic, complemented
8C3×#5200C211yesmaximal, characteristic, complemented
9C3×#5199C211yesmaximal, characteristic, complemented
10C3×#5198C211yesmaximal, characteristic, complemented
11C3×#5197C211yesmaximal, characteristic, complemented
12C3×#5160C211yesmaximal, characteristic, complemented
13C3×#5154C211yesmaximal, characteristic, complemented
14C3×#5145C211yesmaximal, characteristic, complemented
15C3×#5141C211yesmaximal, characteristic, complemented
16C3×#3288—31nomaximal
17#84009C311yesmaximal, characteristic, direct product factor
18C32×H(5,𝔽2)C2211yescharacteristic
19C32×H(5,𝔽2)C2211yescharacteristic, complemented
20C3×#1010C2211yescharacteristic, complemented
21C3×#1009C2211yescharacteristic, complemented
22C32×AGL(1,ℤ/8)—21no—
23C32×AGL(1,ℤ/8)—21no—
24C32×AGL(1,ℤ/8)C2211yescharacteristic
25C32×AGL(1,ℤ/8)C2211yescharacteristic, complemented
26C32×#135—21no—
27C32×#135C2211yescharacteristic
28C2×C32×D8—21no—
29C2×C32×D8C2211yescharacteristic, complemented
30C32×#131C2211yescharacteristic, complemented
31C3×#951—21no—
32C3×#951C2211yescharacteristic, complemented
33C3×#951C2211yescharacteristic, complemented
34C3×#950—21no—
35C3×#950—21no—
36C3×#950C2211yescharacteristic
37C3×#949—21no—
38C3×#949C2211yescharacteristic
39C3×#949C2211yescharacteristic, complemented
40C3×#948C2211yescharacteristic, complemented
41C3×#948C2211yescharacteristic, complemented
42C3×#940C2211yescharacteristic, complemented
43C3×#936C2211yescharacteristic, complemented
44C2×C3×#214—21no—
45C2×C3×#214C2211yescharacteristic, complemented
46C3×#932—21no—
47C3×#932—21no—
48C3×#932C2211yescharacteristic, complemented
49C3×#932C2211yescharacteristic, complemented
50C2×C3×#213—21no—
51C2×C3×#213C2211yescharacteristic, complemented
52C3×#918—21no—
53C3×#916—21no—
54C3×D3×SD16—21no—
55C3×#911—21no—
56C2×C3×#204C2211yescharacteristic, complemented
57C3×#901C2211yescharacteristic, complemented
58C3×#837C2211yescharacteristic, complemented
59C3×#837C2211yescharacteristic, complemented
60C3×#837C2211yescharacteristic, complemented
61C3×#833C2211yescharacteristic, complemented
62C3×#833C2211yescharacteristic, complemented
63C3×#825C2211yescharacteristic, complemented
64C3×#824C2211yescharacteristic, complemented
65C3×#823C2211yescharacteristic, complemented
66C3×#822C2211yescharacteristic, complemented
67C3×#819C2211yescharacteristic, complemented
68C3×#815C2211yescharacteristic, complemented
69C3×#577—31no—
70C3×#577—31no—
71C3×#576—21no—
72C3×#576—31no—
73C3×#576D311yescharacteristic, complemented
74C3×#576C2×C311yescharacteristic, complemented
75#5836C2×C311yescharacteristic, complemented
76#5835C2×C311yescharacteristic, complemented
77#5770C2×C311yescharacteristic, complemented
78C3×#496—31no—
79C3×#472—31no—
80C3×#472—31no—
81C3×#471—31no—
82C3×#471—31no—
83C3×#455—31no—
84C3×#454—31no—
85C3×#453—31no—
86C3×#453—31no—
87C3×#444—31no—
88C3×#444—31no—
89#5242C2×C311yescharacteristic, complemented
90#5241C2×C311yescharacteristic, complemented
91#5201C2×C311yescharacteristic, complemented
92#5200C2×C311yescharacteristic, complemented
93#5199C2×C311yescharacteristic, complemented
94#5198C2×C311yescharacteristic, complemented
95#5197C2×C311yescharacteristic, complemented
96#5160C2×C311yescharacteristic, complemented
97#5154C2×C311yescharacteristic, complemented
98#5145C2×C311yescharacteristic, complemented
99#5141C2×C311yescharacteristic, complemented
100C32×#41—21no—
101C32×#41—21no—
102C32×#41—21no—
103C32×#41—21no—
104C32×#41C2311yescharacteristic
105C32×#41C2311yescharacteristic
106C32×#41C2311yescharacteristic
107C2×C32×D4—21no—
108C2×C32×D4—21no—
109C2×C32×D4—21no—
110C2×C32×D4—21no—
111C2×C32×D4—41no—
112C2×C32×D4—41no—
113C2×C32×D4C2311yescharacteristic
114C2×C32×D4C2311yescharacteristic
115C2×C3×#67—41no—
116C3×#239—21no—
117C3×D3×Q8—21no—
118C3×#237—21no—
119C3×#237—41no—
120C3×D3×D4—21no—
121C3×D3×D4—41no—
122C3×#235—21no—
123C3×#235—21no—
124C3×#235C2311yescharacteristic
125C2×C3×D12—21no—
126C2×C3×D12C2311yescharacteristic
127C2×C3×Dic6—21no—
128C2×C3×Dic6C2311yescharacteristic
129C32×Q16D411yescharacteristic, complemented
130C32×SD16—21no—
131C32×SD16—21no—
132C32×SD16D411yescharacteristic, complemented
133C32×SD16D411yescharacteristic, complemented
134C32×D8—21no—
135C32×D8—21no—
136C32×D8—21no—
137C32×D8—21no—
138C32×D8D411yescharacteristic, complemented
139C32×M16—21no—
140C32×M16C2311yescharacteristic
141C2×C32×C8—21no—
142C2×C32×C8C2311yescharacteristic
143C3×#217—41no—
144C3×#216—21no—
145C3×#216—21no—
146C3×#216D411yescharacteristic, complemented
147C3×#215—21no—
148C3×#215—21no—
149C3×#215D411yescharacteristic, complemented
150C3×#214—21no—
151C3×#214—21no—
152C3×#214—21no—
153C3×#214—21no—
154C3×#214—21no—
155C3×#214—21no—
156C3×#214D411yescharacteristic, complemented
157C3×#213—21no—
158C3×#213—21no—
159C3×#213—21no—
160C3×#213—21no—
161C3×#213—21no—
162C3×#213—21no—
163C3×#213D411yescharacteristic, complemented
164C3×C4×Dic3C2311yescharacteristic
165C3×#208—21no—
166C3×#208—21no—
167C3×#208C2311yescharacteristic
168C3×#208C2311yescharacteristic
169C3×#208C2311yescharacteristic
170C2×C3×C3⋊C8—21no—
171C2×C3×C3⋊C8—21no—
172C2×C3×C3⋊C8C2311yescharacteristic
173C3×#204—21no—
174C3×#204—21no—
175C3×ΓL(1,𝔽25)—21no—
176C3×D3×C8—21no—
177#3288—31noSylow
178C3×2−1+4—31no—
179C3×H(5,𝔽2)—21no—
180C3×H(5,𝔽2)—21no—
181C3×H(5,𝔽2)—31no—
182C3×H(5,𝔽2)C2×D311yescharacteristic
183C3×H(5,𝔽2)C2×D311yescharacteristic, complemented
184C3×H(5,𝔽2)C22×C311yescharacteristic
185C3×H(5,𝔽2)C22×C311yescharacteristic, complemented
186#1010C22×C311yescharacteristic, complemented
187#1009C22×C311yescharacteristic, complemented
188C3×#137—31no—
189C3×#137—31no—
190C3×#137—61no—
191C3×#137—61no—
192C3×AGL(1,ℤ/8)—22no—
193C3×AGL(1,ℤ/8)—22no—
194C3×AGL(1,ℤ/8)—21no—
195C3×AGL(1,ℤ/8)—21no—
196C3×AGL(1,ℤ/8)—21no—
197C3×AGL(1,ℤ/8)—21no—
198C3×AGL(1,ℤ/8)—21no—
199C3×AGL(1,ℤ/8)—21no—
200C3×AGL(1,ℤ/8)—31no—
201C3×AGL(1,ℤ/8)—31no—
202C3×AGL(1,ℤ/8)—31no—
203C3×AGL(1,ℤ/8)—31no—
204C3×AGL(1,ℤ/8)—61no—
205C3×AGL(1,ℤ/8)—61no—
206C3×AGL(1,ℤ/8)—61no—
207C3×AGL(1,ℤ/8)—61no—
208C3×AGL(1,ℤ/8)C2×D311yescharacteristic
209C3×AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
210C3×AGL(1,ℤ/8)C22×C311yescharacteristic
211C3×AGL(1,ℤ/8)C22×C311yescharacteristic, complemented
212C3×#135—22no—
213C3×#135—21no—
214C3×#135—21no—
215C3×#135—21no—
216C3×#135—31no—
217C3×#135—61no—
218C3×#135—61no—
219C3×#135—61no—
220C3×#135C2×D311yescharacteristic
221C3×#135C22×C311yescharacteristic
222C2×C3×SD16—31no—
223C2×C3×SD16—31no—
224C2×C3×SD16—61no—
225C2×C3×SD16—61no—
226C2×C3×D8—22no—
227C2×C3×D8—21no—
228C2×C3×D8—21no—
229C2×C3×D8—21no—
230C2×C3×D8—31no—
231C2×C3×D8—61no—
232C2×C3×D8C2×D311yescharacteristic, complemented
233C2×C3×D8C22×C311yescharacteristic, complemented
234C3×#131—21no—
235C3×#131—31no—
236C3×#131—31no—
237C3×#131—31no—
238C3×#131C2×D311yescharacteristic, complemented
239C3×#131C22×C311yescharacteristic, complemented
240C3×#127—31no—
241C3×#124—31no—
242#951—21no—
243#951C22×C311yescharacteristic, complemented
244#951C22×C311yescharacteristic, complemented
245#950—21no—
246#950—21no—
247#950C22×C311yescharacteristic
248#949—21no—
249#949C22×C311yescharacteristic
250#949C22×C311yescharacteristic, complemented
251#948C22×C311yescharacteristic, complemented
252#948C22×C311yescharacteristic, complemented
253#940C22×C311yescharacteristic, complemented
254#936C22×C311yescharacteristic, complemented
255C2×#214—21no—
256C2×#214C22×C311yescharacteristic, complemented
257#932—21no—
258#932—21no—
259#932C22×C311yescharacteristic, complemented
260#932C22×C311yescharacteristic, complemented
261C2×#213—21no—
262C2×#213C22×C311yescharacteristic, complemented
263#918—21no—
264#916—21no—
265D3×SD16—21no—
266#911—21no—
267C2×#204C22×C311yescharacteristic, complemented
268#901C22×C311yescharacteristic, complemented
269C3×#108—31no—
270C3×#108—31no—
271C3×#104—31no—
272C3×#104—31no—
273C3×#104—31no—
274C3×#104—31no—
275C3×#101—31no—
276C3×#100—31no—
277C3×#100—31no—
278C3×#100—31no—
279C3×#97—31no—
280#837C22×C311yescharacteristic, complemented
281#837C22×C311yescharacteristic, complemented
282#837C22×C311yescharacteristic, complemented
283#833C22×C311yescharacteristic, complemented
284#833C22×C311yescharacteristic, complemented
285#825C22×C311yescharacteristic, complemented
286#824C22×C311yescharacteristic, complemented
287#823C22×C311yescharacteristic, complemented
288#822C22×C311yescharacteristic, complemented
289#819C22×C311yescharacteristic, complemented
290#815C22×C311yescharacteristic, complemented
291C23×C32—21no—
292C23×C32—21no—
293C23×C32—41no—
294C23×C32—41no—
295C22×C3×D3—21no—
296C22×C3×D3—41no—
297C32×Q8C2×D411yescharacteristic
298C32×Q8C2×D411yescharacteristic
299C32×Q8C2×D411yescharacteristic
300C32×D4—21no—
301C32×D4—21no—
302C32×D4—21no—
303C32×D4—21no—
304C32×D4—21no—
305C32×D4—21no—
306C32×D4—21no—
307C32×D4—41no—
308C32×D4—41no—
309C32×D4—41no—
310C32×D4—41no—
311C32×D4C2×D411yescharacteristic
312C32×D4C2×D411yescharacteristic
313C32×D4C2×D411yescharacteristic
314C2×C32×C4—21no—
315C2×C32×C4—21no—
316C2×C32×C4—21no—
317C2×C32×C4—41no—
318C2×C32×C4—41no—
319C2×C32×C4C2411yescharacteristic
320C3×#67—21no—
321C3×#67—41no—
322C3×#67—41no—
323C3×#67—82no—
324C2×C3×Dic3—21no—
325C2×C3×Dic3—21no—
326C2×C3×Dic3—41no—
327C3×D12—21no—
328C3×D12—21no—
329C3×D12—41no—
330C3×D12C2×D411yescharacteristic
331C3×C4×D3—21no—
332C3×C4×D3—41no—
333C3×C4×D3—41no—
334C3×Dic6—21no—
335C3×Dic6—21no—
336C3×Dic6—41no—
337C3×Dic6C2×D411yescharacteristic
338C32×C8—21no—
339C32×C8C2×D411yescharacteristic
340C32×C8C2×D411yescharacteristic
341C3×C3⋊C8—21no—
342C3×C3⋊C8—21no—
343C3×C3⋊C8—21no—
344C3×C3⋊C8C2×D411yescharacteristic
345C3×C3⋊C8C2×D411yescharacteristic
346#577—31no—
347#577—31no—
348#576—31no—
349#576C3×D311yescharacteristic, complemented
350#496—31no—
351#472—31no—
352#472—31no—
353#471—31no—
354#471—31no—
355#455—31no—
356#454—31no—
357#453—31no—
358#453—31no—
359#444—31no—
360#444—31no—
361C3×#41—22no—
362C3×#41—22no—
363C3×#41—21no—
364C3×#41—21no—
365C3×#41—21no—
366C3×#41—21no—
367C3×#41—21no—
368C3×#41—21no—
369C3×#41—21no—
370C3×#41—21no—
371C3×#41—21no—
372C3×#41—21no—
373C3×#41—21no—
374C3×#41—31no—
375C3×#41—41no—
376C3×#41—41no—
377C3×#41—61no—
378C3×#41—61no—
379C3×#41—61no—
380C3×#41—61no—
381C3×#41—121no—
382C3×#41C22×D311yescharacteristic
383C3×#41C22×D311yescharacteristic
384C3×#41C22×D311yescharacteristic
385C3×#41C23×C311yescharacteristic
386C3×#41C23×C311yescharacteristic
387C3×#41C23×C311yescharacteristic
388C2×C3×Q8—31no—
389C2×C3×Q8—61no—
390C2×C3×Q8—61no—
391C2×C3×D4—22no—
392C2×C3×D4—22no—
393C2×C3×D4—21no—
394C2×C3×D4—21no—
395C2×C3×D4—21no—
396C2×C3×D4—21no—
397C2×C3×D4—21no—
398C2×C3×D4—21no—
399C2×C3×D4—21no—
400C2×C3×D4—21no—
401C2×C3×D4—21no—
402C2×C3×D4—21no—
403C2×C3×D4—31no—
404C2×C3×D4—41no—
405C2×C3×D4—41no—
406C2×C3×D4—41no—
407C2×C3×D4—41no—
408C2×C3×D4—41no—
409C2×C3×D4—41no—
410C2×C3×D4—42no—
411C2×C3×D4—42no—
412C2×C3×D4—61no—
413C2×C3×D4—61no—
414C2×C3×D4—121no—
415C2×C3×D4—121no—
416C2×C3×D4C22×D311yescharacteristic
417C2×C3×D4C22×D311yescharacteristic
418C2×C3×D4C23×C311yescharacteristic
419C2×C3×D4C23×C311yescharacteristic
420C2×#67—41no—
421#239—21no—
422D3×Q8—21no—
423#237—21no—
424#237—41no—
425D3×D4—21no—
426D3×D4—41no—
427#235—21no—
428#235—21no—
429#235C23×C311yescharacteristic
430C2×D12—21no—
431C2×D12C23×C311yescharacteristic
432C2×Dic6—21no—
433C2×Dic6C23×C311yescharacteristic
434C3×Q16—21no—
435C3×Q16—31no—
436C3×Q16—61no—
437C3×Q16—61no—
438C3×Q16#6711yescharacteristic, complemented
439C3×Q16C3×D411yescharacteristic, complemented
440C3×SD16—22no—
441C3×SD16—22no—
442C3×SD16—21no—
443C3×SD16—21no—
444C3×SD16—21no—
445C3×SD16—21no—
446C3×SD16—21no—
447C3×SD16—21no—
448C3×SD16—31no—
449C3×SD16—31no—
450C3×SD16—61no—
451C3×SD16—61no—
452C3×SD16—61no—
453C3×SD16—61no—
454C3×SD16—61no—
455C3×SD16—61no—
456C3×SD16—61no—
457C3×SD16—61no—
458C3×SD16—61no—
459C3×SD16—61no—
460C3×SD16#6711yescharacteristic, complemented
461C3×SD16#6711yescharacteristic, complemented
462C3×SD16C3×D411yescharacteristic, complemented
463C3×SD16C3×D411yescharacteristic, complemented
464C3×D8—22no—
465C3×D8—22no—
466C3×D8—22no—
467C3×D8—22no—
468C3×D8—21no—
469C3×D8—21no—
470C3×D8—21no—
471C3×D8—21no—
472C3×D8—21no—
473C3×D8—21no—
474C3×D8—21no—
475C3×D8—21no—
476C3×D8—21no—
477C3×D8—31no—
478C3×D8—61no—
479C3×D8—61no—
480C3×D8—61no—
481C3×D8—61no—
482C3×D8—61no—
483C3×D8—61no—
484C3×D8#6711yescharacteristic, complemented
485C3×D8C3×D411yescharacteristic, complemented
486C3×M16—22no—
487C3×M16—21no—
488C3×M16—21no—
489C3×M16—21no—
490C3×M16—31no—
491C3×M16—31no—
492C3×M16—31no—
493C3×M16—61no—
494C3×M16—61no—
495C3×M16—61no—
496C3×M16C22×D311yescharacteristic
497C3×M16C23×C311yescharacteristic
498C2×C3×C8—22no—
499C2×C3×C8—21no—
500C2×C3×C8—21no—
501C2×C3×C8—21no—
502C2×C3×C8—31no—
503C2×C3×C8—61no—
504C2×C3×C8—61no—
505C2×C3×C8—61no—
506C2×C3×C8C22×D311yescharacteristic
507C2×C3×C8C23×C311yescharacteristic
508C3×C22⋊C4—121no—
509C3×C42—31no—
510#217—41no—
511#216—21no—
512#216—21no—
513#216C3×D411yescharacteristic, complemented
514#215—21no—
515#215—21no—
516#215C3×D411yescharacteristic, complemented
517#214—21no—
518#214—21no—
519#214—21no—
520#214—21no—
521#214—21no—
522#214—21no—
523#214C3×D411yescharacteristic, complemented
524#213—21no—
525#213—21no—
526#213—21no—
527#213—21no—
528#213—21no—
529#213—21no—
530#213C3×D411yescharacteristic, complemented
531C4×Dic3C23×C311yescharacteristic
532#208—21no—
533#208—21no—
534#208C23×C311yescharacteristic
535#208C23×C311yescharacteristic
536#208C23×C311yescharacteristic
537C2×C3⋊C8—21no—
538C2×C3⋊C8—21no—
539C2×C3⋊C8C23×C311yescharacteristic
540#204—21no—
541#204—21no—
542ΓL(1,𝔽25)—21no—
543D3×C8—21no—
544C22×C32—21no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—41no—
548C22×C32—41no—
549C22×C32—81no—
550C22×C32—81no—
551C22×C32—161no—
552C22×C32—161no—
553C22×C32H(5,𝔽2)11yescharacteristic
554C2×C3×D3—21no—
555C2×C3×D3—41no—
556C2×C3×D3—81no—
557C2×C3×D3—161no—
558C32×C4—21no—
559C32×C4—21no—
560C32×C4—21no—
561C32×C4C22×D411yescharacteristic
562C32×C4C22×D411yescharacteristic
563C3×Dic3—21no—
564C3×Dic3—41no—
565C3×Dic3—41no—
5662−1+4—31no—
567H(5,𝔽2)—31no—
568H(5,𝔽2)C2×C3×D311yescharacteristic
569H(5,𝔽2)C2×C3×D311yescharacteristic, complemented
570#137—31no—
571#137—31no—
572#137—61no—
573#137—61no—
574AGL(1,ℤ/8)—21no—
575AGL(1,ℤ/8)—21no—
576AGL(1,ℤ/8)—31no—
577AGL(1,ℤ/8)—31no—
578AGL(1,ℤ/8)—31no—
579AGL(1,ℤ/8)—31no—
580AGL(1,ℤ/8)—61no—
581AGL(1,ℤ/8)—61no—
582AGL(1,ℤ/8)—61no—
583AGL(1,ℤ/8)—61no—
584AGL(1,ℤ/8)C2×C3×D311yescharacteristic
585AGL(1,ℤ/8)C2×C3×D311yescharacteristic, complemented
586#135—21no—
587#135—31no—
588#135—61no—
589#135—61no—
590#135—61no—
591#135C2×C3×D311yescharacteristic
592C2×SD16—31no—
593C2×SD16—31no—
594C2×SD16—61no—
595C2×SD16—61no—
596C2×D8—21no—
597C2×D8—31no—
598C2×D8—61no—
599C2×D8C2×C3×D311yescharacteristic, complemented
600#131—31no—
601#131—31no—
602#131—31no—
603#131C2×C3×D311yescharacteristic, complemented
604#127—31no—
605#124—31no—
606#108—31no—
607#108—31no—
608#104—31no—
609#104—31no—
610#104—31no—
611#104—31no—
612#101—31no—
613#100—31no—
614#100—31no—
615#100—31no—
616#97—31no—
617C23×C3—21no—
618C23×C3—21no—
619C23×C3—21no—
620C23×C3—21no—
621C23×C3—41no—
622C23×C3—41no—
623C23×C3—41no—
624C23×C3—41no—
625C23×C3—41no—
626C23×C3—41no—
627C23×C3—42no—
628C23×C3—42no—
629C23×C3—61no—
630C23×C3—121no—
631C22×D3—21no—
632C22×D3—41no—
633C3×Q8—21no—
634C3×Q8—21no—
635C3×Q8—21no—
636C3×Q8—31no—
637C3×Q8—61no—
638C3×Q8—61no—
639C3×Q8—121no—
640C3×Q8D3×D411yescharacteristic
641C3×Q8C2×#6711yescharacteristic
642C3×Q8C2×#6711yescharacteristic
643C3×Q8C2×C3×D411yescharacteristic
644C3×Q8C2×C3×D411yescharacteristic
645C3×Q8C2×C3×D411yescharacteristic
646C3×D4—22no—
647C3×D4—21no—
648C3×D4—21no—
649C3×D4—21no—
650C3×D4—21no—
651C3×D4—21no—
652C3×D4—21no—
653C3×D4—22no—
654C3×D4—22no—
655C3×D4—21no—
656C3×D4—21no—
657C3×D4—21no—
658C3×D4—21no—
659C3×D4—21no—
660C3×D4—21no—
661C3×D4—21no—
662C3×D4—21no—
663C3×D4—21no—
664C3×D4—21no—
665C3×D4—21no—
666C3×D4—31no—
667C3×D4—41no—
668C3×D4—41no—
669C3×D4—41no—
670C3×D4—41no—
671C3×D4—41no—
672C3×D4—41no—
673C3×D4—41no—
674C3×D4—41no—
675C3×D4—41no—
676C3×D4—41no—
677C3×D4—41no—
678C3×D4—41no—
679C3×D4—42no—
680C3×D4—42no—
681C3×D4—42no—
682C3×D4—42no—
683C3×D4—61no—
684C3×D4—61no—
685C3×D4—61no—
686C3×D4—121no—
687C3×D4—121no—
688C3×D4—121no—
689C3×D4—242no—
690C3×D4D3×D411yescharacteristic
691C3×D4C2×#6711yescharacteristic
692C3×D4C2×#6711yescharacteristic
693C3×D4C2×C3×D411yescharacteristic
694C3×D4C2×C3×D411yescharacteristic
695C3×D4C2×C3×D411yescharacteristic
696C2×C3×C4—22no—
697C2×C3×C4—21no—
698C2×C3×C4—21no—
699C2×C3×C4—21no—
700C2×C3×C4—21no—
701C2×C3×C4—21no—
702C2×C3×C4—21no—
703C2×C3×C4—21no—
704C2×C3×C4—41no—
705C2×C3×C4—41no—
706C2×C3×C4—41no—
707C2×C3×C4—41no—
708C2×C3×C4—41no—
709C2×C3×C4—41no—
710C2×C3×C4—42no—
711C2×C3×C4—42no—
712C2×C3×C4—61no—
713C2×C3×C4—61no—
714C2×C3×C4—61no—
715C2×C3×C4—121no—
716C2×C3×C4—121no—
717C2×C3×C4—121no—
718C2×C3×C4C23×D311yescharacteristic
719C2×C3×C4C24×C311yescharacteristic
720#67—21no—
721#67—41no—
722#67—41no—
723#67—82no—
724C2×Dic3—21no—
725C2×Dic3—21no—
726C2×Dic3—41no—
727D12—21no—
728D12—21no—
729D12—41no—
730D12C2×C3×D411yescharacteristic
731C4×D3—21no—
732C4×D3—41no—
733C4×D3—41no—
734Dic6—21no—
735Dic6—21no—
736Dic6—41no—
737Dic6C2×C3×D411yescharacteristic
738C3×C8—22no—
739C3×C8—21no—
740C3×C8—21no—
741C3×C8—21no—
742C3×C8—21no—
743C3×C8—31no—
744C3×C8—31no—
745C3×C8—61no—
746C3×C8—61no—
747C3×C8—61no—
748C3×C8C2×#6711yescharacteristic
749C3×C8C2×#6711yescharacteristic
750C3×C8C2×C3×D411yescharacteristic
751C3×C8C2×C3×D411yescharacteristic
752C3⋊C8—21no—
753C3⋊C8—21no—
754C3⋊C8—21no—
755C3⋊C8C2×C3×D411yescharacteristic
756C3⋊C8C2×C3×D411yescharacteristic
757C2×C32—21no—
758C2×C32—41no—
759C2×C32—41no—
760C2×C32—41no—
761C2×C32—81no—
762C2×C32—81no—
763C2×C32D4211yescharacteristic
764C3×D3—41no—
765C3×D3—81no—
766#41—21no—
767#41—21no—
768#41—21no—
769#41—21no—
770#41—31no—
771#41—61no—
772#41—61no—
773#41—61no—
774#41—61no—
775#41—121no—
776#41C22×C3×D311yescharacteristic
777#41C22×C3×D311yescharacteristic
778#41C22×C3×D311yescharacteristic
779C2×Q8—31no—
780C2×Q8—61no—
781C2×Q8—61no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—31no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—61no—
790C2×D4—61no—
791C2×D4—121no—
792C2×D4—121no—
793C2×D4C22×C3×D311yescharacteristic
794C2×D4C22×C3×D311yescharacteristic
795Q16—31no—
796Q16—61no—
797Q16—61no—
798Q16C3×#6711yescharacteristic, complemented
799SD16—21no—
800SD16—21no—
801SD16—31no—
802SD16—31no—
803SD16—61no—
804SD16—61no—
805SD16—61no—
806SD16—61no—
807SD16—61no—
808SD16—61no—
809SD16—61no—
810SD16—61no—
811SD16—61no—
812SD16—61no—
813SD16C3×#6711yescharacteristic, complemented
814SD16C3×#6711yescharacteristic, complemented
815D8—21no—
816D8—21no—
817D8—21no—
818D8—21no—
819D8—31no—
820D8—61no—
821D8—61no—
822D8—61no—
823D8—61no—
824D8—61no—
825D8—61no—
826D8C3×#6711yescharacteristic, complemented
827M16—21no—
828M16—31no—
829M16—31no—
830M16—31no—
831M16—61no—
832M16—61no—
833M16—61no—
834M16C22×C3×D311yescharacteristic
835C2×C8—21no—
836C2×C8—31no—
837C2×C8—61no—
838C2×C8—61no—
839C2×C8—61no—
840C2×C8C22×C3×D311yescharacteristic
841C22⋊C4—121no—
842C42—31no—
843C22×C3—22no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—21no—
847C22×C3—21no—
848C22×C3—21no—
849C22×C3—21no—
850C22×C3—21no—
851C22×C3—41no—
852C22×C3—41no—
853C22×C3—42no—
854C22×C3—42no—
855C22×C3—41no—
856C22×C3—41no—
857C22×C3—41no—
858C22×C3—41no—
859C22×C3—61no—
860C22×C3—81no—
861C22×C3—81no—
862C22×C3—81no—
863C22×C3—81no—
864C22×C3—121no—
865C22×C3—161no—
866C22×C3—161no—
867C22×C3—161no—
868C22×C3—161no—
869C22×C3—161no—
870C22×C3—161no—
871C22×C3—162no—
872C22×C3—162no—
873C22×C3—241no—
874C22×C3—481no—
875C22×C3#100411yescharacteristic
876C22×C3C3×H(5,𝔽2)11yescharacteristic
877C2×D3—21no—
878C2×D3—41no—
879C2×D3—81no—
880C2×D3—161no—
881C3×C4—22no—
882C3×C4—21no—
883C3×C4—21no—
884C3×C4—21no—
885C3×C4—21no—
886C3×C4—21no—
887C3×C4—21no—
888C3×C4—21no—
889C3×C4—21no—
890C3×C4—41no—
891C3×C4—41no—
892C3×C4—61no—
893C3×C4—121no—
894C3×C4—121no—
895C3×C4C2×D3×D411yescharacteristic
896C3×C4C22×#6711yescharacteristic
897C3×C4C22×C3×D411yescharacteristic
898C3×C4C22×C3×D411yescharacteristic
899Dic3—21no—
900Dic3—41no—
901Dic3—41no—
902C32#328811yescharacteristic, complemented, Sylow
903C23—21no—
904C23—21no—
905C23—41no—
906C23—41no—
907C23—61no—
908C23—121no—
909Q8—31no—
910Q8—61no—
911Q8—61no—
912Q8—121no—
913Q8C3×D3×D411yescharacteristic
914Q8C2×C3×#6711yescharacteristic
915Q8C2×C3×#6711yescharacteristic
916D4—21no—
917D4—21no—
918D4—21no—
919D4—21no—
920D4—21no—
921D4—21no—
922D4—21no—
923D4—31no—
924D4—41no—
925D4—41no—
926D4—41no—
927D4—41no—
928D4—61no—
929D4—61no—
930D4—61no—
931D4—121no—
932D4—121no—
933D4—121no—
934D4—242no—
935D4C3×D3×D411yescharacteristic
936D4C2×C3×#6711yescharacteristic
937D4C2×C3×#6711yescharacteristic
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—61no—
944C2×C4—61no—
945C2×C4—61no—
946C2×C4—121no—
947C2×C4—121no—
948C2×C4—121no—
949C2×C4C23×C3×D311yescharacteristic
950C8—21no—
951C8—31no—
952C8—31no—
953C8—61no—
954C8—61no—
955C8—61no—
956C8C2×C3×#6711yescharacteristic
957C8C2×C3×#6711yescharacteristic
958C2×C3—21no—
959C2×C3—21no—
960C2×C3—21no—
961C2×C3—41no—
962C2×C3—42no—
963C2×C3—41no—
964C2×C3—41no—
965C2×C3—41no—
966C2×C3—41no—
967C2×C3—41no—
968C2×C3—41no—
969C2×C3—81no—
970C2×C3—81no—
971C2×C3—82no—
972C2×C3—82no—
973C2×C3—81no—
974C2×C3—81no—
975C2×C3—81no—
976C2×C3—81no—
977C2×C3—121no—
978C2×C3—241no—
979C2×C3D4×#6711yescharacteristic
980C2×C3C3×D4211yescharacteristic
981D3—41no—
982D3—81no—
983C22—21no—
984C22—21no—
985C22—21no—
986C22—41no—
987C22—41no—
988C22—61no—
989C22—81no—
990C22—81no—
991C22—121no—
992C22—161no—
993C22—161no—
994C22—241no—
995C22—481no—
996C22C3×#100411yescharacteristic
997C4—21no—
998C4—21no—
999C4—21no—
1000C4—61no—
1001C4—121no—
1002C4—121no—
1003C4C2×C3×D3×D411yescharacteristic
1004C4C22×C3×#6711yescharacteristic
1005C3—21no—
1006C3#8400911yescharacteristic, direct product factor
1007C3C3×#328811yescharacteristic, complemented
1008C2—21no—
1009C2—41no—
1010C2—41no—
1011C2—41no—
1012C2—81no—
1013C2—81no—
1014C2—121no—
1015C2—241no—
1016C2C3×D4×#6711yescharacteristic
subgroupG/H
centerC2×C3D4×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#576C2
socleC2×C32D42
hypercenterC3×#576D3
hypocenterC3C3×#3288
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#576

Complements

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

NH ≅ G/Ntype
1. C32×#576C2semidirect
2. C3×#5836C2semidirect
3. C3×#5835C2semidirect
4. C3×#5770C2semidirect
5. C3×#5242C2semidirect
6. C3×#5241C2semidirect
7. C3×#5201C2semidirect
8. C3×#5200C2semidirect
9. C3×#5199C2semidirect
10. C3×#5198C2semidirect
11. C3×#5197C2semidirect
12. C3×#5160C2semidirect
13. C3×#5154C2semidirect
14. C3×#5145C2semidirect
15. C3×#5141C2semidirect
17. #84009C3direct (N × H)
19. C32×H(5,𝔽2)C22semidirect
20. C3×#1010C22semidirect
21. C3×#1009C22semidirect
25. C32×AGL(1,ℤ/8)C22semidirect
29. C2×C32×D8C22semidirect
30. C32×#131C22semidirect
32. C3×#951C22semidirect
33. C3×#951C22semidirect
39. C3×#949C22semidirect
40. C3×#948C22semidirect
41. C3×#948C22semidirect
42. C3×#940C22semidirect
43. C3×#936C22semidirect
45. C2×C3×#214C22semidirect
48. C3×#932C22semidirect
49. C3×#932C22semidirect
51. C2×C3×#213C22semidirect
56. C2×C3×#204C22semidirect
57. C3×#901C22semidirect
58. C3×#837C22semidirect
59. C3×#837C22semidirect
60. C3×#837C22semidirect
61. C3×#833C22semidirect
62. C3×#833C22semidirect
63. C3×#825C22semidirect
64. C3×#824C22semidirect
65. C3×#823C22semidirect
66. C3×#822C22semidirect
67. C3×#819C22semidirect
68. C3×#815C22semidirect
73. C3×#576D3semidirect
74. C3×#576C2×C3semidirect
75. #5836C2×C3semidirect
76. #5835C2×C3semidirect
77. #5770C2×C3semidirect
89. #5242C2×C3semidirect
90. #5241C2×C3semidirect
91. #5201C2×C3semidirect
92. #5200C2×C3semidirect
93. #5199C2×C3semidirect
94. #5198C2×C3semidirect
95. #5197C2×C3semidirect
96. #5160C2×C3semidirect
97. #5154C2×C3semidirect
98. #5145C2×C3semidirect
99. #5141C2×C3semidirect
129. C32×Q16D4semidirect
132. C32×SD16D4semidirect
133. C32×SD16D4semidirect
138. C32×D8D4semidirect
146. C3×#216D4semidirect
149. C3×#215D4semidirect
156. C3×#214D4semidirect
163. C3×#213D4semidirect
183. C3×H(5,𝔽2)C2×D3semidirect
185. C3×H(5,𝔽2)C22×C3semidirect
186. #1010C22×C3semidirect
187. #1009C22×C3semidirect
209. C3×AGL(1,ℤ/8)C2×D3semidirect
211. C3×AGL(1,ℤ/8)C22×C3semidirect
232. C2×C3×D8C2×D3semidirect
233. C2×C3×D8C22×C3semidirect
238. C3×#131C2×D3semidirect
239. C3×#131C22×C3semidirect
243. #951C22×C3semidirect
244. #951C22×C3semidirect
250. #949C22×C3semidirect
251. #948C22×C3semidirect
252. #948C22×C3semidirect
253. #940C22×C3semidirect
254. #936C22×C3semidirect
256. C2×#214C22×C3semidirect
259. #932C22×C3semidirect
260. #932C22×C3semidirect
262. C2×#213C22×C3semidirect
267. C2×#204C22×C3semidirect
268. #901C22×C3semidirect
280. #837C22×C3semidirect
281. #837C22×C3semidirect
282. #837C22×C3semidirect
283. #833C22×C3semidirect
284. #833C22×C3semidirect
285. #825C22×C3semidirect
286. #824C22×C3semidirect
287. #823C22×C3semidirect
288. #822C22×C3semidirect
289. #819C22×C3semidirect
290. #815C22×C3semidirect
349. #576C3×D3semidirect
438. C3×Q16#67semidirect
439. C3×Q16C3×D4semidirect
460. C3×SD16#67semidirect
461. C3×SD16#67semidirect
462. C3×SD16C3×D4semidirect
463. C3×SD16C3×D4semidirect
484. C3×D8#67semidirect
485. C3×D8C3×D4semidirect
513. #216C3×D4semidirect
516. #215C3×D4semidirect
523. #214C3×D4semidirect
530. #213C3×D4semidirect
569. H(5,𝔽2)C2×C3×D3semidirect
585. AGL(1,ℤ/8)C2×C3×D3semidirect
599. C2×D8C2×C3×D3semidirect
603. #131C2×C3×D3semidirect
798. Q16C3×#67semidirect
813. SD16C3×#67semidirect
814. SD16C3×#67semidirect
826. D8C3×#67semidirect
902. C32#3288semidirect
1006. C3#84009direct (N × H)
1007. C3C3×#3288semidirect

Maximal subgroups

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

subgroupindex
C32×#5762
C3×#58362
C3×#58352
C3×#57702
C3×#52422
C3×#52412
C3×#52012
C3×#52002
C3×#51992
C3×#51982
C3×#51972
C3×#51602
C3×#51542
C3×#51452
C3×#51412
C3×#32883
#840093