Finite Group Databasebeta

← C3×#80688 #11884834

Subgroups — C3×#80688 #11884834

Order 1152.

1038 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#915C211yesmaximal, characteristic, complemented
2C2×C3×#904C211yesmaximal, characteristic, complemented
3C3×#5633C211yesmaximal, characteristic, complemented
4C3×#5599C211yesmaximal, characteristic, complemented
5C32×#465C211yesmaximal, characteristic, complemented
6C3×#5176C211yesmaximal, characteristic, complemented
7C3×#5111C211yesmaximal, characteristic, complemented
8C3×#5047C211yesmaximal, characteristic, complemented
9C3×#5037C211yesmaximal, characteristic, complemented
10C3×#4865C211yesmaximal, characteristic, complemented
11C3×#4853C211yesmaximal, characteristic, complemented
12C3×#4806C211yesmaximal, characteristic, complemented
13C3×#4798C211yesmaximal, characteristic, complemented
14C3×#4781C211yesmaximal, characteristic, complemented
15C3×#4762C211yesmaximal, characteristic, complemented
16C3×#3271—31nomaximal
17#80688C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23C22×C32×C8C2211yescharacteristic
24C32×C22⋊Q8C2211yescharacteristic
25C32×#121C2211yescharacteristic
26C3×#947C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic
29C3×#940—21no—
30C3×#940C2211yescharacteristic
31C3×#939—21no—
32C2×C3×#214C2211yescharacteristic
33C2×C3×#213C2211yescharacteristic
34C3×C4×#67C2211yescharacteristic
35C3×#915—24no—
36C2×C3×Dic12C2211yescharacteristic
37C3×#904—24no—
38C2×C3×D24C2211yescharacteristic
39C2×C3×#204C2211yescharacteristic
40C2×C3×#204C2211yescharacteristic
41C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
42C3×#896—21no—
43C3×#895C2211yescharacteristic
44C3×#895C2211yescharacteristic
45C3×#893—21no—
46C3×#887C2211yescharacteristic
47C3×#887C2211yescharacteristic
48C3×#885—21no—
49C3×#884—21no—
50C3×#884—21no—
51C3×#67⋊C4—21no—
52C32×#106C2211yescharacteristic
53C32×#103C2211yescharacteristic
54C32×#102C2211yescharacteristic
55C3×#830C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×#815C2211yescharacteristic
58C3×Dic3⋊C8C2211yescharacteristic
59C3×#810C2211yescharacteristic
60C3×#810C2211yescharacteristic
61C3×#809C2211yescharacteristic
62C3×#809C2211yescharacteristic
63C2×C3×#137—31no—
64C2×C3×#135—31no—
65C3×#550—31no—
66C3×#548—31no—
67C2×#915C2×C311yescharacteristic, complemented
68C2×#904C2×C311yescharacteristic, complemented
69#5633C2×C311yescharacteristic, complemented
70#5599C2×C311yescharacteristic, complemented
71C3×#496—31no—
72C3×#469—31no—
73C3×#465—21no—
74C3×#465D311yescharacteristic, complemented
75C3×#465C2×C311yescharacteristic, complemented
76C3×#464—31no—
77C3×#460—31no—
78C3×#452—31no—
79C3×#449—31no—
80C3×#449—31no—
81C3×#448—31no—
82C3×#441—31no—
83C3×#435—31no—
84#5176C2×C311yescharacteristic, complemented
85#5111C2×C311yescharacteristic, complemented
86#5047C2×C311yescharacteristic, complemented
87#5037C2×C311yescharacteristic, complemented
88#4865C2×C311yescharacteristic, complemented
89#4853C2×C311yescharacteristic, complemented
90#4806C2×C311yescharacteristic, complemented
91#4798C2×C311yescharacteristic, complemented
92#4781C2×C311yescharacteristic, complemented
93#4762C2×C311yescharacteristic, complemented
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67D411yescharacteristic
104C22×C3×Dic3—21no—
105C3×D3×Q8—22no—
106C3×D3×Q8—41no—
107C3×#237—22no—
108C3×#237—41no—
109C3×#235—22no—
110C3×#235—22no—
111C3×#235—41no—
112C3×#235—41no—
113C2×C3×D12—21no—
114C2×C3×D12—21no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×Dic6—21no—
122C2×C3×Dic6C2311yescharacteristic
123C2×C3×Dic6C2311yescharacteristic
124C32×SD16—22no—
125C2×C32×C8—22no—
126C2×C32×C8C2311yescharacteristic
127C2×C32×C8C2311yescharacteristic
128C32×C4⋊C4—21no—
129C32×C4⋊C4C2311yescharacteristic
130C32×C4⋊C4C2311yescharacteristic
131C32×C22⋊C4—21no—
132C32×C22⋊C4—21no—
133C3×#217D411yescharacteristic
134C3×#216—22no—
135C3×#215—41no—
136C3×#214—22no—
137C3×#213—41no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4—21no—
142C3×(C2×D3)⋊C4D411yescharacteristic
143C3×Dic3⋊C4—21no—
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4D411yescharacteristic
146C3×C4×Dic3—21no—
147C3×C4×Dic3—21no—
148C3×C4×Dic3C2311yescharacteristic
149C2×C3×C3⋊C8C2311yescharacteristic
150C2×C3×C3⋊C8C2311yescharacteristic
151C3×Dic12D414yescomplemented
152C3×D24—22no—
153C3×#204—22no—
154C3×#204—22no—
155C3×ΓL(1,𝔽25)—22no—
156#3271—31noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C22×C3×Q8—31no—
161C2×D3×Q8C22×C311yescharacteristic
162C2×#237C22×C311yescharacteristic
163C2×#235C22×C311yescharacteristic
164C2×#235C22×C311yescharacteristic
165C3×#137—64no—
166C3×#135—64no—
167C2×C3×Q16—31no—
168C2×C3×Q16—31no—
169C2×C3×SD16—21no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—31no—
174C2×C3×SD16C2×D311yescharacteristic
175C2×C3×SD16C22×C311yescharacteristic
176C2×C3×D8—31no—
177C2×C3×D8—31no—
178C2×C3×M16—31no—
179C22×C3×C8—21no—
180C22×C3×C8C2×D311yescharacteristic
181C22×C3×C8C22×C311yescharacteristic
182C3×#127—31no—
183C3×#127—61no—
184C3×#124—31no—
185C3×#124—61no—
186C3×C22⋊Q8—21no—
187C3×C22⋊Q8—61no—
188C3×C22⋊Q8C2×D311yescharacteristic
189C3×C22⋊Q8C22×C311yescharacteristic
190C3×#121—21no—
191C3×#121—31no—
192C3×#121—31no—
193C3×#121—61no—
194C3×#121—61no—
195C3×#121—61no—
196C3×#121C2×D311yescharacteristic
197C3×#121C22×C311yescharacteristic
198C3×C4×Q8—31no—
199C3×C4×Q8—31no—
200C3×C4×D4—31no—
201C3×C4×D4—61no—
202C3×C4×D4—61no—
203#947C22×C311yescharacteristic
204C2×#216C22×C311yescharacteristic
205C2×#215C22×C311yescharacteristic
206#940—21no—
207#940C22×C311yescharacteristic
208#939—21no—
209C2×#214C22×C311yescharacteristic
210C2×#213C22×C311yescharacteristic
211C4×#67C22×C311yescharacteristic
212#915—24no—
213C2×Dic12C22×C311yescharacteristic
214#904—24no—
215C2×D24C22×C311yescharacteristic
216C2×#204C22×C311yescharacteristic
217C2×#204C22×C311yescharacteristic
218C2×ΓL(1,𝔽25)C22×C311yescharacteristic
219#896—21no—
220#895C22×C311yescharacteristic
221#895C22×C311yescharacteristic
222#893—21no—
223#887C22×C311yescharacteristic
224#887C22×C311yescharacteristic
225#885—21no—
226#884—21no—
227#884—21no—
228#67⋊C4—21no—
229C3×#106—21no—
230C3×#106C2×D311yescharacteristic
231C3×#106C22×C311yescharacteristic
232C3×C4⋊C8—31no—
233C3×#103—21no—
234C3×#103—31no—
235C3×#103—31no—
236C3×#103C2×D311yescharacteristic
237C3×#103C22×C311yescharacteristic
238C3×#102—21no—
239C3×#102—31no—
240C3×#102—31no—
241C3×#102C2×D311yescharacteristic
242C3×#102C22×C311yescharacteristic
243C3×C22⋊C8—31no—
244C3×C22⋊C8—31no—
245C3×#97—31no—
246#830C22×C311yescharacteristic
247(C2×D3)⋊C8C22×C311yescharacteristic
248#815C22×C311yescharacteristic
249Dic3⋊C8C22×C311yescharacteristic
250#810C22×C311yescharacteristic
251#810C22×C311yescharacteristic
252#809C22×C311yescharacteristic
253#809C22×C311yescharacteristic
254C23×C32—21no—
255C23×C32C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C32×Q8—21no—
260C32×Q8—21no—
261C32×D4—21no—
262C32×D4—21no—
263C32×D4—81no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271C3×#67—41no—
272C3×#67—42no—
273C3×#67—42no—
274C3×#67—42no—
275C3×#67—42no—
276C3×#67—81no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—42no—
288C3×D12—81no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—42no—
292C3×C4×D3—42no—
293C3×C4×D3—42no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—42no—
297C3×Dic6C2×D412yes—
298C3×Dic6C2×D412yes—
299C32×C8—21no—
300C32×C8C2×D412yes—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×#137—31no—
304C2×#135—31no—
305#550—31no—
306#548—31no—
307#496—31no—
308#469—31no—
309#465C3×D311yescharacteristic, complemented
310#464—31no—
311#460—31no—
312#452—31no—
313#449—31no—
314#449—31no—
315#448—31no—
316#441—31no—
317#435—31no—
318C3×#41—62no—
319C3×#41—62no—
320C3×#41—62no—
321C3×#41—121no—
322C3×#41—121no—
323C3×#41—121no—
324C2×C3×Q8—21no—
325C2×C3×Q8—31no—
326C2×C3×Q8—31no—
327C2×C3×Q8—61no—
328C2×C3×Q8—62no—
329C2×C3×Q8—121no—
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×Q8C23×C311yescharacteristic
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—41no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C2×C3×D4—61no—
346C2×C3×D4C22×D311yescharacteristic
347C2×C3×D4C23×C311yescharacteristic
348C22×C3×C4—21no—
349C22×C3×C4—31no—
350C22×C3×C4—61no—
351C22×C3×C4—61no—
352C22×C3×C4—61no—
353C22×C3×C4—61no—
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C23×C311yescharacteristic
356C2×#67—21no—
357C2×#67—21no—
358C2×#67—21no—
359C2×#67—21no—
360C2×#67—21no—
361C2×#67C3×D411yescharacteristic
362C22×Dic3—21no—
363D3×Q8—22no—
364D3×Q8—41no—
365#237—22no—
366#237—41no—
367#235—22no—
368#235—22no—
369#235—41no—
370#235—41no—
371C2×D12—21no—
372C2×D12—21no—
373C2×D12C23×C311yescharacteristic
374C2×D12C23×C311yescharacteristic
375C2×C4×D3—21no—
376C2×C4×D3—21no—
377C2×C4×D3—21no—
378C2×C4×D3C23×C311yescharacteristic
379C2×Dic6—21no—
380C2×Dic6C23×C311yescharacteristic
381C2×Dic6C23×C311yescharacteristic
382C3×Q16—34no—
383C3×Q16—62no—
384C3×SD16—22no—
385C3×SD16—22no—
386C3×SD16—42no—
387C3×SD16—62no—
388C3×SD16—62no—
389C3×SD16—62no—
390C3×SD16—121no—
391C3×D8—62no—
392C3×D8—121no—
393C3×M16—62no—
394C2×C3×C8—22no—
395C2×C3×C8—22no—
396C2×C3×C8—21no—
397C2×C3×C8—21no—
398C2×C3×C8—31no—
399C2×C3×C8—31no—
400C2×C3×C8—42no—
401C2×C3×C8C22×D311yescharacteristic
402C2×C3×C8C22×D311yescharacteristic
403C2×C3×C8C23×C311yescharacteristic
404C2×C3×C8C23×C311yescharacteristic
405C3×C4⋊C4—21no—
406C3×C4⋊C4—21no—
407C3×C4⋊C4—21no—
408C3×C4⋊C4—21no—
409C3×C4⋊C4—31no—
410C3×C4⋊C4—41no—
411C3×C4⋊C4—61no—
412C3×C4⋊C4—61no—
413C3×C4⋊C4C22×D311yescharacteristic
414C3×C4⋊C4C22×D311yescharacteristic
415C3×C4⋊C4C23×C311yescharacteristic
416C3×C4⋊C4C23×C311yescharacteristic
417C3×C22⋊C4—21no—
418C3×C22⋊C4—21no—
419C3×C22⋊C4—21no—
420C3×C22⋊C4—21no—
421C3×C22⋊C4—31no—
422C3×C22⋊C4—31no—
423C3×C22⋊C4—41no—
424C3×C22⋊C4—41no—
425C3×C22⋊C4—61no—
426C3×C22⋊C4—61no—
427C3×C22⋊C4—61no—
428C3×C22⋊C4—61no—
429C3×C42—31no—
430C3×C42—61no—
431C3×C42—61no—
432#217C3×D411yescharacteristic
433#216—22no—
434#215—41no—
435#214—22no—
436#213—41no—
437(C2×D3)⋊C4—21no—
438(C2×D3)⋊C4—21no—
439(C2×D3)⋊C4—21no—
440(C2×D3)⋊C4—21no—
441(C2×D3)⋊C4C3×D411yescharacteristic
442Dic3⋊C4—21no—
443Dic3⋊C4—21no—
444Dic3⋊C4C3×D411yescharacteristic
445C4×Dic3—21no—
446C4×Dic3—21no—
447C4×Dic3C23×C311yescharacteristic
448C2×C3⋊C8C23×C311yescharacteristic
449C2×C3⋊C8C23×C311yescharacteristic
450Dic12C3×D414yescomplemented
451D24—22no—
452#204—22no—
453#204—22no—
454ΓL(1,𝔽25)—22no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32C22×D411yescharacteristic
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C32×C4—21no—
472C32×C4—41no—
473C32×C4—41no—
474C32×C4—41no—
475C32×C4C22×D411yescharacteristic
476C32×C4H(5,𝔽2)11yescharacteristic
477C3×Dic3—22no—
478C3×Dic3—22no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C2×#41—31no—
483C2×#41—31no—
484C2×#41—31no—
485C22×Q8—31no—
486#137—64no—
487#135—64no—
488C2×Q16—31no—
489C2×Q16—31no—
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—31no—
494C2×SD16C2×C3×D311yescharacteristic
495C2×D8—31no—
496C2×D8—31no—
497C2×M16—31no—
498C22×C8C2×C3×D311yescharacteristic
499#127—31no—
500#127—61no—
501#124—31no—
502#124—61no—
503C22⋊Q8—61no—
504C22⋊Q8C2×C3×D311yescharacteristic
505#121—31no—
506#121—31no—
507#121—61no—
508#121—61no—
509#121—61no—
510#121C2×C3×D311yescharacteristic
511C4×Q8—31no—
512C4×Q8—31no—
513C4×D4—31no—
514C4×D4—61no—
515C4×D4—61no—
516#106C2×C3×D311yescharacteristic
517C4⋊C8—31no—
518#103—31no—
519#103—31no—
520#103C2×C3×D311yescharacteristic
521#102—31no—
522#102—31no—
523#102C2×C3×D311yescharacteristic
524C22⋊C8—31no—
525C22⋊C8—31no—
526#97—31no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—31no—
531C23×C3—41no—
532C23×C3—61no—
533C23×C3—61no—
534C23×C3D3×D411yescharacteristic
535C23×C3C2×C3×D411yescharacteristic
536C22×D3—21no—
537C22×D3—21no—
538C22×D3C2×C3×D411yescharacteristic
539C3×Q8—21no—
540C3×Q8—21no—
541C3×Q8—21no—
542C3×Q8—21no—
543C3×Q8—32no—
544C3×Q8—32no—
545C3×Q8—41no—
546C3×Q8—41no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—122no—
550C3×D4—21no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—41no—
555C3×D4—41no—
556C3×D4—61no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—81no—
561C3×D4—81no—
562C3×D4—82no—
563C3×D4—122no—
564C3×D4—121no—
565C3×D4—122no—
566C3×D4—122no—
567C3×D4—122no—
568C3×D4—122no—
569C3×D4—241no—
570C3×D4—241no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—31no—
584C2×C3×C4—31no—
585C2×C3×C4—31no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—122no—
596C2×C3×C4—122no—
597C2×C3×C4—122no—
598C2×C3×C4—122no—
599C2×C3×C4D3×D411yescharacteristic
600C2×C3×C4C2×C3×D411yescharacteristic
601C2×C3×C4C23×D311yescharacteristic
602C2×C3×C4C24×C311yescharacteristic
603#67—41no—
604#67—42no—
605#67—42no—
606#67—42no—
607#67—42no—
608#67—81no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—42no—
612C2×Dic3C2×C3×D411yescharacteristic
613C2×Dic3C2×C3×D411yescharacteristic
614C2×Dic3C2×C3×D411yescharacteristic
615D12—21no—
616D12—21no—
617D12—21no—
618D12—21no—
619D12—42no—
620D12—81no—
621C4×D3—21no—
622C4×D3—21no—
623C4×D3—42no—
624C4×D3—42no—
625C4×D3—42no—
626Dic6—21no—
627Dic6—21no—
628Dic6—42no—
629Dic6C2×C3×D412yes—
630Dic6C2×C3×D412yes—
631C3×C8—21no—
632C3×C8—21no—
633C3×C8—22no—
634C3×C8—41no—
635C3×C8—61no—
636C3×C8—61no—
637C3×C8D3×D412yes—
638C3×C8C2×C3×D412yes—
639C3⋊C8—21no—
640C3⋊C8—21no—
641C2×C32—41no—
642C2×C32—81no—
643C2×C32D4211yescharacteristic
644C2×C32#57511yescharacteristic
645C2×C32#57711yescharacteristic
646C3×D3—41no—
647C3×D3—81no—
648C3×D3—81no—
649#41—62no—
650#41—62no—
651#41—62no—
652#41—121no—
653#41—121no—
654#41—121no—
655C2×Q8—31no—
656C2×Q8—31no—
657C2×Q8—61no—
658C2×Q8—62no—
659C2×Q8—121no—
660C2×Q8C22×C3×D311yescharacteristic
661C2×D4—21no—
662C2×D4—31no—
663C2×D4—31no—
664C2×D4—31no—
665C2×D4—61no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—61no—
670C2×D4—61no—
671C2×D4—61no—
672C2×D4C22×C3×D311yescharacteristic
673C22×C4—31no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4C22×C3×D311yescharacteristic
679Q16—34no—
680Q16—62no—
681SD16—22no—
682SD16—62no—
683SD16—62no—
684SD16—62no—
685SD16—121no—
686D8—62no—
687D8—121no—
688M16—62no—
689C2×C8—22no—
690C2×C8—31no—
691C2×C8—31no—
692C2×C8C22×C3×D311yescharacteristic
693C2×C8C22×C3×D311yescharacteristic
694C4⋊C4—21no—
695C4⋊C4—31no—
696C4⋊C4—61no—
697C4⋊C4—61no—
698C4⋊C4C22×C3×D311yescharacteristic
699C4⋊C4C22×C3×D311yescharacteristic
700C22⋊C4—21no—
701C22⋊C4—21no—
702C22⋊C4—31no—
703C22⋊C4—31no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C42—31no—
709C42—61no—
710C42—61no—
711C22×C3—22no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—81no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3C2×D3×D411yescharacteristic
740C22×C3C22×C3×D411yescharacteristic
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C3×C4—21no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—41no—
760C3×C4—41no—
761C3×C4—61no—
762C3×C4—61no—
763C3×C4—61no—
764C3×C4—62no—
765C3×C4—62no—
766C3×C4—81no—
767C3×C4—81no—
768C3×C4—81no—
769C3×C4C2×D3×D411yescharacteristic
770C3×C4#100911yescharacteristic
771C3×C4C22×C3×D411yescharacteristic
772C3×C4C3×H(5,𝔽2)11yescharacteristic
773Dic3—21no—
774Dic3—21no—
775Dic3—22no—
776Dic3—22no—
777Dic3—21no—
778C32#327111yescharacteristic, complemented, Sylow
779C23—21no—
780C23—31no—
781C23—61no—
782C23—61no—
783C23C3×D3×D411yescharacteristic
784Q8—21no—
785Q8—21no—
786Q8—32no—
787Q8—32no—
788Q8—61no—
789Q8—61no—
790Q8—122no—
791D4—21no—
792D4—21no—
793D4—61no—
794D4—61no—
795D4—61no—
796D4—61no—
797D4—81no—
798D4—122no—
799D4—121no—
800D4—122no—
801D4—122no—
802D4—122no—
803D4—122no—
804D4—241no—
805D4—241no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—31no—
812C2×C4—31no—
813C2×C4—31no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—122no—
819C2×C4—122no—
820C2×C4—122no—
821C2×C4—122no—
822C2×C4C3×D3×D411yescharacteristic
823C2×C4C23×C3×D311yescharacteristic
824C8—21no—
825C8—61no—
826C8—61no—
827C8C3×D3×D412yes—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—42no—
832C2×C3—41no—
833C2×C3—41no—
834C2×C3—81no—
835C2×C3—81no—
836C2×C3—121no—
837C2×C3—161no—
838C2×C3—241no—
839C2×C3—241no—
840C2×C3#560911yescharacteristic
841C2×C3#576211yescharacteristic
842C2×C3#576811yescharacteristic
843C2×C3C3×D4211yescharacteristic
844C2×C3C3×#57511yescharacteristic
845C2×C3C3×#57711yescharacteristic
846D3—41no—
847D3—81no—
848D3—81no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—61no—
856C22—61no—
857C22—61no—
858C22—121no—
859C22—121no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—121no—
864C22C2×C3×D3×D411yescharacteristic
865C4—21no—
866C4—41no—
867C4—41no—
868C4—41no—
869C4—61no—
870C4—61no—
871C4—61no—
872C4—62no—
873C4—62no—
874C4C2×C3×D3×D411yescharacteristic
875C4C3×#100911yescharacteristic
876C3—21no—
877C3#8068811yescharacteristic, direct product factor
878C3C3×#327111yescharacteristic, complemented
879C2—41no—
880C2—81no—
881C2—121no—
882C2—241no—
883C2—241no—
884C2C3×#560911yescharacteristic
885C2C3×#576211yescharacteristic
886C2C3×#576811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#465C2
socleC22×C32C22×D4
hypercenterC3×#465D3
hypocenterC3C3×#3271
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#465

Complements

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

NH ≅ G/Ntype
1. C2×C3×#915C2semidirect
2. C2×C3×#904C2semidirect
3. C3×#5633C2semidirect
4. C3×#5599C2semidirect
5. C32×#465C2semidirect
6. C3×#5176C2semidirect
7. C3×#5111C2semidirect
8. C3×#5047C2semidirect
9. C3×#5037C2semidirect
10. C3×#4865C2semidirect
11. C3×#4853C2semidirect
12. C3×#4806C2semidirect
13. C3×#4798C2semidirect
14. C3×#4781C2semidirect
15. C3×#4762C2semidirect
17. #80688C3direct (N × H)
67. C2×#915C2×C3semidirect
68. C2×#904C2×C3semidirect
69. #5633C2×C3semidirect
70. #5599C2×C3semidirect
74. C3×#465D3semidirect
75. C3×#465C2×C3semidirect
84. #5176C2×C3semidirect
85. #5111C2×C3semidirect
86. #5047C2×C3semidirect
87. #5037C2×C3semidirect
88. #4865C2×C3semidirect
89. #4853C2×C3semidirect
90. #4806C2×C3semidirect
91. #4798C2×C3semidirect
92. #4781C2×C3semidirect
93. #4762C2×C3semidirect
151. C3×Dic12D4semidirect
309. #465C3×D3semidirect
450. Dic12C3×D4semidirect
778. C32#3271semidirect
877. C3#80688direct (N × H)
878. C3C3×#3271semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9152
C2×C3×#9042
C3×#56332
C3×#55992
C32×#4652
C3×#51762
C3×#51112
C3×#50472
C3×#50372
C3×#48652
C3×#48532
C3×#48062
C3×#47982
C3×#47812
C3×#47622
C3×#32713
#806883