Finite Group Databasebeta

← C3×#84019 #11886649

Subgroups — C3×#84019 #11886649

Order 1152.

1020 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#578C211yesmaximal, characteristic, complemented
2C3×#5838C211yesmaximal, characteristic, complemented
3C3×#5837C211yesmaximal, characteristic, complemented
4C3×#5770C211yesmaximal, characteristic, complemented
5C3×#5246C211yesmaximal, characteristic, complemented
6C3×#5245C211yesmaximal, characteristic, complemented
7C3×#5205C211yesmaximal, characteristic, complemented
8C3×#5204C211yesmaximal, characteristic, complemented
9C3×#5203C211yesmaximal, characteristic, complemented
10C3×#5202C211yesmaximal, characteristic, complemented
11C3×#5197C211yesmaximal, characteristic, complemented
12C3×#5192C211yesmaximal, characteristic, complemented
13C3×#5190C211yesmaximal, characteristic, complemented
14C3×#5145C211yesmaximal, characteristic, complemented
15C3×#5141C211yesmaximal, characteristic, complemented
16C3×#3289—31nomaximal
17#84019C311yesmaximal, characteristic, direct product factor
18C32×2−1+4C2211yescharacteristic
19C32×2−1+4C2211yescharacteristic, complemented
20C3×#1010C2211yescharacteristic
21C3×#1009C2211yescharacteristic
22C32×#137—21no—
23C32×#137—21no—
24C32×#137C2211yescharacteristic
25C32×#137C2211yescharacteristic, complemented
26C32×#135—21no—
27C32×#135C2211yescharacteristic
28C2×C32×Q16—21no—
29C2×C32×Q16C2211yescharacteristic, complemented
30C32×#131C2211yescharacteristic, complemented
31C3×#951—21no—
32C3×#951C2211yescharacteristic
33C3×#951C2211yescharacteristic, complemented
34C3×#950—21no—
35C3×#950—21no—
36C3×#950C2211yescharacteristic
37C3×#949—21no—
38C3×#949C2211yescharacteristic
39C3×#949C2211yescharacteristic
40C3×#948C2211yescharacteristic
41C3×#948C2211yescharacteristic, complemented
42C3×#947C2211yescharacteristic
43C3×#944C2211yescharacteristic, complemented
44C2×C3×#216—21no—
45C2×C3×#216C2211yescharacteristic, complemented
46C3×#942—21no—
47C3×#942—21no—
48C3×#942C2211yescharacteristic
49C3×#942C2211yescharacteristic
50C2×C3×#215—21no—
51C2×C3×#215C2211yescharacteristic
52C3×#918—21no—
53C3×#916—21no—
54C3×D3×SD16—21no—
55C3×#911—21no—
56C2×C3×#204C2211yescharacteristic
57C3×#901C2211yescharacteristic
58C3×#837C2211yescharacteristic
59C3×#837C2211yescharacteristic, complemented
60C3×#837C2211yescharacteristic, complemented
61C3×#836C2211yescharacteristic, complemented
62C3×#836C2211yescharacteristic, complemented
63C3×#825C2211yescharacteristic
64C3×#824C2211yescharacteristic, complemented
65C3×#823C2211yescharacteristic
66C3×#822C2211yescharacteristic, complemented
67C3×#819C2211yescharacteristic, complemented
68C3×#815C2211yescharacteristic, complemented
69C3×#578—21no—
70C3×#578—31no—
71C3×#578D311yescharacteristic, complemented
72C3×#578C2×C311yescharacteristic, complemented
73C3×#577—31no—
74C3×#577—31no—
75#5838C2×C311yescharacteristic, complemented
76#5837C2×C311yescharacteristic, complemented
77#5770C2×C311yescharacteristic, complemented
78C3×#497—31no—
79C3×#473—31no—
80C3×#473—31no—
81C3×#471—31no—
82C3×#471—31no—
83C3×#456—31no—
84C3×#456—31no—
85C3×#455—31no—
86C3×#454—31no—
87C3×#444—31no—
88C3×#444—31no—
89#5246C2×C311yescharacteristic, complemented
90#5245C2×C311yescharacteristic, complemented
91#5205C2×C311yescharacteristic, complemented
92#5204C2×C311yescharacteristic, complemented
93#5203C2×C311yescharacteristic, complemented
94#5202C2×C311yescharacteristic, complemented
95#5197C2×C311yescharacteristic, complemented
96#5192C2×C311yescharacteristic, complemented
97#5190C2×C311yescharacteristic, complemented
98#5145C2×C311yescharacteristic, complemented
99#5141C2×C311yescharacteristic, complemented
100C32×#41—21no—
101C32×#41—21no—
102C32×#41—21no—
103C32×#41—21no—
104C32×#41—41no—
105C32×#41—41no—
106C32×#41C2311yescharacteristic
107C32×#41C2311yescharacteristic
108C32×#41C2311yescharacteristic
109C2×C32×Q8—21no—
110C2×C32×Q8—21no—
111C2×C32×Q8—21no—
112C2×C32×Q8—21no—
113C2×C32×Q8C2311yescharacteristic
114C2×C32×Q8C2311yescharacteristic
115C3×#239—21no—
116C3×D3×Q8—21no—
117C3×#237—21no—
118C3×#237—41no—
119C3×D3×D4—21no—
120C3×D3×D4—41no—
121C3×#235—21no—
122C3×#235—21no—
123C3×#235C2311yescharacteristic
124C2×C3×D12—21no—
125C2×C3×D12C2311yescharacteristic
126C2×C3×Dic6—21no—
127C2×C3×Dic6C2311yescharacteristic
128C32×Q16—21no—
129C32×Q16—21no—
130C32×Q16—21no—
131C32×Q16—21no—
132C32×Q16D411yescharacteristic
133C32×SD16—21no—
134C32×SD16—21no—
135C32×SD16D411yescharacteristic
136C32×SD16D411yescharacteristic
137C32×D8D411yescharacteristic
138C32×M16—21no—
139C32×M16C2311yescharacteristic
140C2×C32×C8—21no—
141C2×C32×C8C2311yescharacteristic
142C3×#216—21no—
143C3×#216—21no—
144C3×#216—21no—
145C3×#216—21no—
146C3×#216—21no—
147C3×#216—21no—
148C3×#216D411yescharacteristic
149C3×#215—21no—
150C3×#215—21no—
151C3×#215—21no—
152C3×#215—21no—
153C3×#215—21no—
154C3×#215—21no—
155C3×#215D411yescharacteristic
156C3×#214—21no—
157C3×#214—21no—
158C3×#214D411yescharacteristic
159C3×#213—21no—
160C3×#213—21no—
161C3×#213D411yescharacteristic
162C3×(C2×D3)⋊C4—41no—
163C3×Dic3⋊C4—41no—
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#3289—31noSylow
178C3×2−1+4—21no—
179C3×2−1+4—21no—
180C3×2−1+4—31no—
181C3×2−1+4C2×D311yescharacteristic
182C3×2−1+4C2×D311yescharacteristic, complemented
183C3×2−1+4C22×C311yescharacteristic
184C3×2−1+4C22×C311yescharacteristic, complemented
185C3×H(5,𝔽2)—31no—
186#1010C22×C311yescharacteristic
187#1009C22×C311yescharacteristic
188C3×#137—22no—
189C3×#137—22no—
190C3×#137—21no—
191C3×#137—21no—
192C3×#137—21no—
193C3×#137—21no—
194C3×#137—21no—
195C3×#137—21no—
196C3×#137—31no—
197C3×#137—31no—
198C3×#137—31no—
199C3×#137—31no—
200C3×#137—61no—
201C3×#137—61no—
202C3×#137—61no—
203C3×#137—61no—
204C3×#137C2×D311yescharacteristic
205C3×#137C2×D311yescharacteristic, complemented
206C3×#137C22×C311yescharacteristic
207C3×#137C22×C311yescharacteristic, complemented
208C3×AGL(1,ℤ/8)—31no—
209C3×AGL(1,ℤ/8)—31no—
210C3×AGL(1,ℤ/8)—61no—
211C3×AGL(1,ℤ/8)—61no—
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×Q16—22no—
223C2×C3×Q16—21no—
224C2×C3×Q16—21no—
225C2×C3×Q16—21no—
226C2×C3×Q16—31no—
227C2×C3×Q16—61no—
228C2×C3×Q16C2×D311yescharacteristic, complemented
229C2×C3×Q16C22×C311yescharacteristic, complemented
230C2×C3×SD16—31no—
231C2×C3×SD16—31no—
232C2×C3×SD16—61no—
233C2×C3×SD16—61no—
234C3×#131—21no—
235C3×#131—31no—
236C3×#131—31no—
237C3×#131—31no—
238C3×#131C2×D311yescharacteristic, complemented
239C3×#131C22×C311yescharacteristic, complemented
240C3×C4⋊Q8—31no—
241C3×#124—31no—
242#951—21no—
243#951C22×C311yescharacteristic
244#951C22×C311yescharacteristic, complemented
245#950—21no—
246#950—21no—
247#950C22×C311yescharacteristic
248#949—21no—
249#949C22×C311yescharacteristic
250#949C22×C311yescharacteristic
251#948C22×C311yescharacteristic
252#948C22×C311yescharacteristic, complemented
253#947C22×C311yescharacteristic
254#944C22×C311yescharacteristic, complemented
255C2×#216—21no—
256C2×#216C22×C311yescharacteristic, complemented
257#942—21no—
258#942—21no—
259#942C22×C311yescharacteristic
260#942C22×C311yescharacteristic
261C2×#215—21no—
262C2×#215C22×C311yescharacteristic
263#918—21no—
264#916—21no—
265D3×SD16—21no—
266#911—21no—
267C2×#204C22×C311yescharacteristic
268#901C22×C311yescharacteristic
269C3×#108—31no—
270C3×#108—31no—
271C3×#104—31no—
272C3×#104—31no—
273C3×#104—31no—
274C3×#104—31no—
275C3×#101—31no—
276C3×#101—31no—
277C3×#101—31no—
278C3×#100—31no—
279C3×#97—31no—
280#837C22×C311yescharacteristic
281#837C22×C311yescharacteristic, complemented
282#837C22×C311yescharacteristic, complemented
283#836C22×C311yescharacteristic, complemented
284#836C22×C311yescharacteristic, complemented
285#825C22×C311yescharacteristic
286#824C22×C311yescharacteristic, complemented
287#823C22×C311yescharacteristic
288#822C22×C311yescharacteristic, complemented
289#819C22×C311yescharacteristic, complemented
290#815C22×C311yescharacteristic, complemented
291C22×C3×D3—21no—
292C22×C3×D3—41no—
293C32×Q8—21no—
294C32×Q8—21no—
295C32×Q8—21no—
296C32×Q8—21no—
297C32×Q8—41no—
298C32×Q8—41no—
299C32×Q8C2×D411yescharacteristic
300C32×Q8C2×D411yescharacteristic
301C32×Q8C2×D411yescharacteristic
302C32×D4—21no—
303C32×D4—21no—
304C32×D4—21no—
305C32×D4—41no—
306C32×D4—41no—
307C32×D4C2×D411yescharacteristic
308C32×D4C2×D411yescharacteristic
309C32×D4C2×D411yescharacteristic
310C2×C32×C4—21no—
311C2×C32×C4—21no—
312C2×C32×C4—21no—
313C2×C32×C4—21no—
314C2×C32×C4—21no—
315C2×C32×C4—41no—
316C2×C32×C4—41no—
317C2×C32×C4—41no—
318C2×C32×C4—41no—
319C2×C32×C4C2411yescharacteristic
320C3×#67—21no—
321C3×#67—41no—
322C3×#67—41no—
323C2×C3×Dic3—21no—
324C2×C3×Dic3—21no—
325C2×C3×Dic3—41no—
326C3×D12—21no—
327C3×D12—21no—
328C3×D12—41no—
329C3×D12C2×D411yescharacteristic
330C3×C4×D3—21no—
331C3×C4×D3—41no—
332C3×C4×D3—41no—
333C3×Dic6—21no—
334C3×Dic6—21no—
335C3×Dic6—41no—
336C3×Dic6C2×D411yescharacteristic
337C32×C8—21no—
338C32×C8C2×D411yescharacteristic
339C32×C8C2×D411yescharacteristic
340C3×C3⋊C8—21no—
341C3×C3⋊C8—21no—
342C3×C3⋊C8—21no—
343C3×C3⋊C8C2×D411yescharacteristic
344C3×C3⋊C8C2×D411yescharacteristic
345#578—31no—
346#578C3×D311yescharacteristic, complemented
347#577—31no—
348#577—31no—
349#497—31no—
350#473—31no—
351#473—31no—
352#471—31no—
353#471—31no—
354#456—31no—
355#456—31no—
356#455—31no—
357#454—31no—
358#444—31no—
359#444—31no—
360C3×#41—22no—
361C3×#41—22no—
362C3×#41—21no—
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—31no—
374C3×#41—41no—
375C3×#41—41no—
376C3×#41—41no—
377C3×#41—41no—
378C3×#41—41no—
379C3×#41—41no—
380C3×#41—42no—
381C3×#41—42no—
382C3×#41—61no—
383C3×#41—61no—
384C3×#41—61no—
385C3×#41—61no—
386C3×#41—121no—
387C3×#41C22×D311yescharacteristic
388C3×#41C22×D311yescharacteristic
389C3×#41C22×D311yescharacteristic
390C3×#41C23×C311yescharacteristic
391C3×#41C23×C311yescharacteristic
392C3×#41C23×C311yescharacteristic
393C2×C3×Q8—22no—
394C2×C3×Q8—22no—
395C2×C3×Q8—21no—
396C2×C3×Q8—21no—
397C2×C3×Q8—21no—
398C2×C3×Q8—21no—
399C2×C3×Q8—21no—
400C2×C3×Q8—21no—
401C2×C3×Q8—21no—
402C2×C3×Q8—21no—
403C2×C3×Q8—21no—
404C2×C3×Q8—21no—
405C2×C3×Q8—31no—
406C2×C3×Q8—41no—
407C2×C3×Q8—41no—
408C2×C3×Q8—61no—
409C2×C3×Q8—61no—
410C2×C3×Q8C22×D311yescharacteristic
411C2×C3×Q8C22×D311yescharacteristic
412C2×C3×Q8C23×C311yescharacteristic
413C2×C3×Q8C23×C311yescharacteristic
414C2×C3×D4—31no—
415C2×C3×D4—61no—
416C2×C3×D4—61no—
417C2×C3×D4—121no—
418#239—21no—
419D3×Q8—21no—
420#237—21no—
421#237—41no—
422D3×D4—21no—
423D3×D4—41no—
424#235—21no—
425#235—21no—
426#235C23×C311yescharacteristic
427C2×D12—21no—
428C2×D12C23×C311yescharacteristic
429C2×Dic6—21no—
430C2×Dic6C23×C311yescharacteristic
431C3×Q16—22no—
432C3×Q16—22no—
433C3×Q16—22no—
434C3×Q16—22no—
435C3×Q16—21no—
436C3×Q16—21no—
437C3×Q16—21no—
438C3×Q16—21no—
439C3×Q16—21no—
440C3×Q16—21no—
441C3×Q16—21no—
442C3×Q16—21no—
443C3×Q16—21no—
444C3×Q16—31no—
445C3×Q16—61no—
446C3×Q16—61no—
447C3×Q16—61no—
448C3×Q16—61no—
449C3×Q16—61no—
450C3×Q16—61no—
451C3×Q16#6711yescharacteristic
452C3×Q16C3×D411yescharacteristic
453C3×SD16—22no—
454C3×SD16—22no—
455C3×SD16—21no—
456C3×SD16—21no—
457C3×SD16—21no—
458C3×SD16—21no—
459C3×SD16—21no—
460C3×SD16—21no—
461C3×SD16—31no—
462C3×SD16—31no—
463C3×SD16—61no—
464C3×SD16—61no—
465C3×SD16—61no—
466C3×SD16—61no—
467C3×SD16—61no—
468C3×SD16—61no—
469C3×SD16—61no—
470C3×SD16—61no—
471C3×SD16—61no—
472C3×SD16—61no—
473C3×SD16#6711yescharacteristic
474C3×SD16#6711yescharacteristic
475C3×SD16C3×D411yescharacteristic
476C3×SD16C3×D411yescharacteristic
477C3×D8—21no—
478C3×D8—31no—
479C3×D8—61no—
480C3×D8—61no—
481C3×D8#6711yescharacteristic
482C3×D8C3×D411yescharacteristic
483C3×M16—22no—
484C3×M16—21no—
485C3×M16—21no—
486C3×M16—21no—
487C3×M16—31no—
488C3×M16—31no—
489C3×M16—31no—
490C3×M16—61no—
491C3×M16—61no—
492C3×M16—61no—
493C3×M16C22×D311yescharacteristic
494C3×M16C23×C311yescharacteristic
495C2×C3×C8—22no—
496C2×C3×C8—21no—
497C2×C3×C8—21no—
498C2×C3×C8—21no—
499C2×C3×C8—31no—
500C2×C3×C8—61no—
501C2×C3×C8—61no—
502C2×C3×C8—61no—
503C2×C3×C8C22×D311yescharacteristic
504C2×C3×C8C23×C311yescharacteristic
505C3×C4⋊C4—121no—
506C3×C22⋊C4—121no—
507C3×C42—31no—
508#216—21no—
509#216—21no—
510#216—21no—
511#216—21no—
512#216—21no—
513#216—21no—
514#216C3×D411yescharacteristic
515#215—21no—
516#215—21no—
517#215—21no—
518#215—21no—
519#215—21no—
520#215—21no—
521#215C3×D411yescharacteristic
522#214—21no—
523#214—21no—
524#214C3×D411yescharacteristic
525#213—21no—
526#213—21no—
527#213C3×D411yescharacteristic
528(C2×D3)⋊C4—41no—
529Dic3⋊C4—41no—
530C4×Dic3C23×C311yescharacteristic
531#208—21no—
532#208—21no—
533#208C23×C311yescharacteristic
534#208C23×C311yescharacteristic
535#208C23×C311yescharacteristic
536C2×C3⋊C8—21no—
537C2×C3⋊C8—21no—
538C2×C3⋊C8C23×C311yescharacteristic
539#204—21no—
540#204—21no—
541ΓL(1,𝔽25)—21no—
542D3×C8—21no—
543C22×C32—21no—
544C22×C32—21no—
545C22×C32—21no—
546C22×C32H(5,𝔽2)11yescharacteristic
547C2×C3×D3—21no—
548C2×C3×D3—41no—
549C2×C3×D3—81no—
550C2×C3×D3—161no—
551C32×C4—21no—
552C32×C4—21no—
553C32×C4—21no—
554C32×C4—41no—
555C32×C4—41no—
556C32×C4C22×D411yescharacteristic
557C32×C4C22×D411yescharacteristic
558C3×Dic3—21no—
559C3×Dic3—41no—
560C3×Dic3—41no—
5612−1+4—31no—
5622−1+4C2×C3×D311yescharacteristic
5632−1+4C2×C3×D311yescharacteristic, complemented
564H(5,𝔽2)—31no—
565#137—21no—
566#137—21no—
567#137—31no—
568#137—31no—
569#137—31no—
570#137—31no—
571#137—61no—
572#137—61no—
573#137—61no—
574#137—61no—
575#137C2×C3×D311yescharacteristic
576#137C2×C3×D311yescharacteristic, complemented
577AGL(1,ℤ/8)—31no—
578AGL(1,ℤ/8)—31no—
579AGL(1,ℤ/8)—61no—
580AGL(1,ℤ/8)—61no—
581#135—21no—
582#135—31no—
583#135—61no—
584#135—61no—
585#135—61no—
586#135C2×C3×D311yescharacteristic
587C2×Q16—21no—
588C2×Q16—31no—
589C2×Q16—61no—
590C2×Q16C2×C3×D311yescharacteristic, complemented
591C2×SD16—31no—
592C2×SD16—31no—
593C2×SD16—61no—
594C2×SD16—61no—
595#131—31no—
596#131—31no—
597#131—31no—
598#131C2×C3×D311yescharacteristic, complemented
599C4⋊Q8—31no—
600#124—31no—
601#108—31no—
602#108—31no—
603#104—31no—
604#104—31no—
605#104—31no—
606#104—31no—
607#101—31no—
608#101—31no—
609#101—31no—
610#100—31no—
611#97—31no—
612C23×C3—61no—
613C23×C3—121no—
614C22×D3—21no—
615C22×D3—41no—
616C3×Q8—22no—
617C3×Q8—22no—
618C3×Q8—21no—
619C3×Q8—21no—
620C3×Q8—21no—
621C3×Q8—21no—
622C3×Q8—21no—
623C3×Q8—21no—
624C3×Q8—21no—
625C3×Q8—21no—
626C3×Q8—21no—
627C3×Q8—21no—
628C3×Q8—21no—
629C3×Q8—31no—
630C3×Q8—41no—
631C3×Q8—41no—
632C3×Q8—41no—
633C3×Q8—41no—
634C3×Q8—41no—
635C3×Q8—41no—
636C3×Q8—42no—
637C3×Q8—42no—
638C3×Q8—61no—
639C3×Q8—61no—
640C3×Q8—121no—
641C3×Q8D3×D411yescharacteristic
642C3×Q8C2×#6711yescharacteristic
643C3×Q8C2×#6711yescharacteristic
644C3×Q8C2×C3×D411yescharacteristic
645C3×Q8C2×C3×D411yescharacteristic
646C3×Q8C2×C3×D411yescharacteristic
647C3×D4—22no—
648C3×D4—21no—
649C3×D4—21no—
650C3×D4—21no—
651C3×D4—21no—
652C3×D4—21no—
653C3×D4—21no—
654C3×D4—21no—
655C3×D4—21no—
656C3×D4—21no—
657C3×D4—31no—
658C3×D4—41no—
659C3×D4—41no—
660C3×D4—41no—
661C3×D4—41no—
662C3×D4—41no—
663C3×D4—41no—
664C3×D4—42no—
665C3×D4—42no—
666C3×D4—61no—
667C3×D4—61no—
668C3×D4—61no—
669C3×D4—121no—
670C3×D4—121no—
671C3×D4—121no—
672C3×D4D3×D411yescharacteristic
673C3×D4C2×#6711yescharacteristic
674C3×D4C2×#6711yescharacteristic
675C3×D4C2×C3×D411yescharacteristic
676C3×D4C2×C3×D411yescharacteristic
677C3×D4C2×C3×D411yescharacteristic
678C2×C3×C4—22no—
679C2×C3×C4—21no—
680C2×C3×C4—21no—
681C2×C3×C4—21no—
682C2×C3×C4—21no—
683C2×C3×C4—21no—
684C2×C3×C4—21no—
685C2×C3×C4—21no—
686C2×C3×C4—21no—
687C2×C3×C4—21no—
688C2×C3×C4—21no—
689C2×C3×C4—21no—
690C2×C3×C4—41no—
691C2×C3×C4—41no—
692C2×C3×C4—41no—
693C2×C3×C4—41no—
694C2×C3×C4—41no—
695C2×C3×C4—41no—
696C2×C3×C4—41no—
697C2×C3×C4—41no—
698C2×C3×C4—41no—
699C2×C3×C4—41no—
700C2×C3×C4—41no—
701C2×C3×C4—41no—
702C2×C3×C4—42no—
703C2×C3×C4—42no—
704C2×C3×C4—42no—
705C2×C3×C4—42no—
706C2×C3×C4—61no—
707C2×C3×C4—61no—
708C2×C3×C4—61no—
709C2×C3×C4—121no—
710C2×C3×C4—121no—
711C2×C3×C4—121no—
712C2×C3×C4C23×D311yescharacteristic
713C2×C3×C4C24×C311yescharacteristic
714#67—21no—
715#67—41no—
716#67—41no—
717C2×Dic3—21no—
718C2×Dic3—21no—
719C2×Dic3—41no—
720D12—21no—
721D12—21no—
722D12—41no—
723D12C2×C3×D411yescharacteristic
724C4×D3—21no—
725C4×D3—41no—
726C4×D3—41no—
727Dic6—21no—
728Dic6—21no—
729Dic6—41no—
730Dic6C2×C3×D411yescharacteristic
731C3×C8—22no—
732C3×C8—21no—
733C3×C8—21no—
734C3×C8—21no—
735C3×C8—21no—
736C3×C8—31no—
737C3×C8—31no—
738C3×C8—61no—
739C3×C8—61no—
740C3×C8—61no—
741C3×C8C2×#6711yescharacteristic
742C3×C8C2×#6711yescharacteristic
743C3×C8C2×C3×D411yescharacteristic
744C3×C8C2×C3×D411yescharacteristic
745C3⋊C8—21no—
746C3⋊C8—21no—
747C3⋊C8—21no—
748C3⋊C8C2×C3×D411yescharacteristic
749C3⋊C8C2×C3×D411yescharacteristic
750C2×C32—21no—
751C2×C32—41no—
752C2×C32—41no—
753C2×C32—41no—
754C2×C32D4211yescharacteristic
755C3×D3—41no—
756C3×D3—81no—
757#41—21no—
758#41—21no—
759#41—21no—
760#41—21no—
761#41—31no—
762#41—41no—
763#41—41no—
764#41—61no—
765#41—61no—
766#41—61no—
767#41—61no—
768#41—121no—
769#41C22×C3×D311yescharacteristic
770#41C22×C3×D311yescharacteristic
771#41C22×C3×D311yescharacteristic
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—31no—
777C2×Q8—61no—
778C2×Q8—61no—
779C2×Q8C22×C3×D311yescharacteristic
780C2×Q8C22×C3×D311yescharacteristic
781C2×D4—31no—
782C2×D4—61no—
783C2×D4—61no—
784C2×D4—121no—
785Q16—21no—
786Q16—21no—
787Q16—21no—
788Q16—21no—
789Q16—31no—
790Q16—61no—
791Q16—61no—
792Q16—61no—
793Q16—61no—
794Q16—61no—
795Q16—61no—
796Q16C3×#6711yescharacteristic
797SD16—21no—
798SD16—21no—
799SD16—31no—
800SD16—31no—
801SD16—61no—
802SD16—61no—
803SD16—61no—
804SD16—61no—
805SD16—61no—
806SD16—61no—
807SD16—61no—
808SD16—61no—
809SD16—61no—
810SD16—61no—
811SD16C3×#6711yescharacteristic
812SD16C3×#6711yescharacteristic
813D8—31no—
814D8—61no—
815D8—61no—
816D8C3×#6711yescharacteristic
817M16—21no—
818M16—31no—
819M16—31no—
820M16—31no—
821M16—61no—
822M16—61no—
823M16—61no—
824M16C22×C3×D311yescharacteristic
825C2×C8—21no—
826C2×C8—31no—
827C2×C8—61no—
828C2×C8—61no—
829C2×C8—61no—
830C2×C8C22×C3×D311yescharacteristic
831C4⋊C4—121no—
832C22⋊C4—121no—
833C42—31no—
834C22×C3—22no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—21no—
839C22×C3—21no—
840C22×C3—21no—
841C22×C3—21no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—61no—
845C22×C3—121no—
846C22×C3—241no—
847C22×C3—481no—
848C22×C3#100411yescharacteristic
849C22×C3C3×H(5,𝔽2)11yescharacteristic
850C2×D3—21no—
851C2×D3—41no—
852C2×D3—81no—
853C2×D3—161no—
854C3×C4—22no—
855C3×C4—21no—
856C3×C4—21no—
857C3×C4—21no—
858C3×C4—21no—
859C3×C4—21no—
860C3×C4—21no—
861C3×C4—21no—
862C3×C4—21no—
863C3×C4—41no—
864C3×C4—41no—
865C3×C4—42no—
866C3×C4—42no—
867C3×C4—41no—
868C3×C4—41no—
869C3×C4—41no—
870C3×C4—41no—
871C3×C4—61no—
872C3×C4—121no—
873C3×C4—121no—
874C3×C4C2×D3×D411yescharacteristic
875C3×C4C22×#6711yescharacteristic
876C3×C4C22×C3×D411yescharacteristic
877C3×C4C22×C3×D411yescharacteristic
878Dic3—21no—
879Dic3—41no—
880Dic3—41no—
881C32#328911yescharacteristic, complemented, Sylow
882C23—61no—
883C23—121no—
884Q8—21no—
885Q8—21no—
886Q8—21no—
887Q8—21no—
888Q8—31no—
889Q8—41no—
890Q8—41no—
891Q8—61no—
892Q8—61no—
893Q8—121no—
894Q8C3×D3×D411yescharacteristic
895Q8C2×C3×#6711yescharacteristic
896Q8C2×C3×#6711yescharacteristic
897D4—21no—
898D4—21no—
899D4—21no—
900D4—31no—
901D4—41no—
902D4—41no—
903D4—61no—
904D4—61no—
905D4—61no—
906D4—121no—
907D4—121no—
908D4—121no—
909D4C3×D3×D411yescharacteristic
910D4C2×C3×#6711yescharacteristic
911D4C2×C3×#6711yescharacteristic
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—121no—
925C2×C4—121no—
926C2×C4—121no—
927C2×C4C23×C3×D311yescharacteristic
928C8—21no—
929C8—31no—
930C8—31no—
931C8—61no—
932C8—61no—
933C8—61no—
934C8C2×C3×#6711yescharacteristic
935C8C2×C3×#6711yescharacteristic
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—41no—
940C2×C3—42no—
941C2×C3—41no—
942C2×C3—41no—
943C2×C3—41no—
944C2×C3—41no—
945C2×C3—41no—
946C2×C3—41no—
947C2×C3—81no—
948C2×C3—81no—
949C2×C3—121no—
950C2×C3—241no—
951C2×C3D4×#6711yescharacteristic
952C2×C3C3×D4211yescharacteristic
953D3—41no—
954D3—81no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—61no—
959C22—121no—
960C22—241no—
961C22—481no—
962C22C3×#100411yescharacteristic
963C4—21no—
964C4—21no—
965C4—21no—
966C4—41no—
967C4—41no—
968C4—61no—
969C4—121no—
970C4—121no—
971C4C2×C3×D3×D411yescharacteristic
972C4C22×C3×#6711yescharacteristic
973C3—21no—
974C3#8401911yescharacteristic, direct product factor
975C3C3×#328911yescharacteristic, complemented
976C2—21no—
977C2—41no—
978C2—41no—
979C2—41no—
980C2—121no—
981C2—241no—
982C2C3×D4×#6711yescharacteristic
subgroupG/H
centerC2×C3D4×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#578C2
socleC2×C32D42
hypercenterC3×#578D3
hypocenterC3C3×#3289
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#578

Complements

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

NH ≅ G/Ntype
1. C32×#578C2semidirect
2. C3×#5838C2semidirect
3. C3×#5837C2semidirect
4. C3×#5770C2semidirect
5. C3×#5246C2semidirect
6. C3×#5245C2semidirect
7. C3×#5205C2semidirect
8. C3×#5204C2semidirect
9. C3×#5203C2semidirect
10. C3×#5202C2semidirect
11. C3×#5197C2semidirect
12. C3×#5192C2semidirect
13. C3×#5190C2semidirect
14. C3×#5145C2semidirect
15. C3×#5141C2semidirect
17. #84019C3direct (N × H)
19. C32×2−1+4C22semidirect
25. C32×#137C22semidirect
29. C2×C32×Q16C22semidirect
30. C32×#131C22semidirect
33. C3×#951C22semidirect
41. C3×#948C22semidirect
43. C3×#944C22semidirect
45. C2×C3×#216C22semidirect
59. C3×#837C22semidirect
60. C3×#837C22semidirect
61. C3×#836C22semidirect
62. C3×#836C22semidirect
64. C3×#824C22semidirect
66. C3×#822C22semidirect
67. C3×#819C22semidirect
68. C3×#815C22semidirect
71. C3×#578D3semidirect
72. C3×#578C2×C3semidirect
75. #5838C2×C3semidirect
76. #5837C2×C3semidirect
77. #5770C2×C3semidirect
89. #5246C2×C3semidirect
90. #5245C2×C3semidirect
91. #5205C2×C3semidirect
92. #5204C2×C3semidirect
93. #5203C2×C3semidirect
94. #5202C2×C3semidirect
95. #5197C2×C3semidirect
96. #5192C2×C3semidirect
97. #5190C2×C3semidirect
98. #5145C2×C3semidirect
99. #5141C2×C3semidirect
182. C3×2−1+4C2×D3semidirect
184. C3×2−1+4C22×C3semidirect
205. C3×#137C2×D3semidirect
207. C3×#137C22×C3semidirect
228. C2×C3×Q16C2×D3semidirect
229. C2×C3×Q16C22×C3semidirect
238. C3×#131C2×D3semidirect
239. C3×#131C22×C3semidirect
244. #951C22×C3semidirect
252. #948C22×C3semidirect
254. #944C22×C3semidirect
256. C2×#216C22×C3semidirect
281. #837C22×C3semidirect
282. #837C22×C3semidirect
283. #836C22×C3semidirect
284. #836C22×C3semidirect
286. #824C22×C3semidirect
288. #822C22×C3semidirect
289. #819C22×C3semidirect
290. #815C22×C3semidirect
346. #578C3×D3semidirect
563. 2−1+4C2×C3×D3semidirect
576. #137C2×C3×D3semidirect
590. C2×Q16C2×C3×D3semidirect
598. #131C2×C3×D3semidirect
881. C32#3289semidirect
974. C3#84019direct (N × H)
975. C3C3×#3289semidirect

Maximal subgroups

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

subgroupindex
C32×#5782
C3×#58382
C3×#58372
C3×#57702
C3×#52462
C3×#52452
C3×#52052
C3×#52042
C3×#52032
C3×#52022
C3×#51972
C3×#51922
C3×#51902
C3×#51452
C3×#51412
C3×#32893
#840193