Finite Group Databasebeta

← C3×#80267 #11884512

Subgroups — C3×#80267 #11884512

Order 1152.

1032 conjugacy classes of subgroups.

The subgroup lattice has 869 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5831C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic, complemented
3C2×C3×#918C211yesmaximal, characteristic, complemented
4C3×#5631C211yesmaximal, characteristic, complemented
5C32×#452C211yesmaximal, characteristic, complemented
6C3×#5182C211yesmaximal, characteristic, complemented
7C3×#5172C211yesmaximal, characteristic, complemented
8C3×#5167C211yesmaximal, characteristic, complemented
9C3×#5051C211yesmaximal, characteristic, complemented
10C3×#4817C211yesmaximal, characteristic, complemented
11C3×#4809C211yesmaximal, characteristic, complemented
12C3×#4787C211yesmaximal, characteristic, complemented
13C3×#4780C211yesmaximal, characteristic, complemented
14C3×#4733C211yesmaximal, characteristic, complemented
15C3×#4730C211yesmaximal, characteristic, complemented
16C3×#3269—31nomaximal
17#80267C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C2×C32×Q16C2211yescharacteristic
23C2×C32×SD16C2211yescharacteristic
24C32×C22⋊Q8C2211yescharacteristic
25C3×#950—24no—
26C3×Q8×Dic3C2211yescharacteristic
27C3×#944C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C3×#938—21no—
32C3×#938C2211yescharacteristic
33C3×#936—21no—
34C3×#936C2211yescharacteristic
35C2×C3×#214C2211yescharacteristic
36C2×C3×#213C2211yescharacteristic
37C3×C4×#67—21no—
38C3×C4×#67C2211yescharacteristic
39C3×#924—21no—
40C3×#924C2211yescharacteristic
41C22×C3×C3⋊C8C2211yescharacteristic
42C3×#918—24no—
43C2×C3×Dic12C2211yescharacteristic
44C2×C3×#204C2211yescharacteristic
45C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
46C3×#897C2211yescharacteristic
47C3×#894—21no—
48C3×#893C2211yescharacteristic
49C3×D3×C4⋊C4—21no—
50C3×#884—21no—
51C3×#883—21no—
52C32×#103C2211yescharacteristic
53C32×#102C2211yescharacteristic
54C32×C22⋊C8C2211yescharacteristic
55C3×#835C2211yescharacteristic
56C3×#821C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic
58C3×#816C2211yescharacteristic
59C3×#815C2211yescharacteristic
60C3×Dic3⋊C8C2211yescharacteristic
61C3×#810C2211yescharacteristic
62C3×#807C2211yescharacteristic
63C2×C3×#137—31no—
64C2×C3×#135—31no—
65C3×#548—31no—
66C3×#547—31no—
67#5831C2×C311yescharacteristic, complemented
68C2×#950C2×C311yescharacteristic, complemented
69C2×#918C2×C311yescharacteristic, complemented
70#5631C2×C311yescharacteristic, complemented
71C3×#497—31no—
72C3×#468—31no—
73C3×#467—31no—
74C3×#463—31no—
75C3×#462—31no—
76C3×#452—21no—
77C3×#452—31no—
78C3×#452D311yescharacteristic, complemented
79C3×#452C2×C311yescharacteristic, complemented
80C3×#451—31no—
81C3×#449—31no—
82C3×#440—31no—
83C3×#435—31no—
84#5182C2×C311yescharacteristic, complemented
85#5172C2×C311yescharacteristic, complemented
86#5167C2×C311yescharacteristic, complemented
87#5051C2×C311yescharacteristic, complemented
88#4817C2×C311yescharacteristic, complemented
89#4809C2×C311yescharacteristic, complemented
90#4787C2×C311yescharacteristic, complemented
91#4780C2×C311yescharacteristic, complemented
92#4733C2×C311yescharacteristic, complemented
93#4730C2×C311yescharacteristic, complemented
94C32×#41—22no—
95C32×#41—41no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×Q8C2311yescharacteristic
98C2×C32×D4—21no—
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4—21no—
101C22×C32×C4C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67D411yescharacteristic
105C3×#239—22no—
106C3×#239—41no—
107C3×D3×Q8—22no—
108C3×D3×Q8—41no—
109C3×#235—22no—
110C3×#235—41no—
111C2×C3×D12—21no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6—21no—
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C32×Q16—22no—
122C32×SD16—41no—
123C2×C32×C8C2311yescharacteristic
124C2×C32×C8C2311yescharacteristic
125C32×C4⋊C4—21no—
126C32×C4⋊C4C2311yescharacteristic
127C32×C22⋊C4—21no—
128C3×#217—21no—
129C3×#217—21no—
130C3×#217—21no—
131C3×#217—21no—
132C3×#217D411yescharacteristic
133C3×#216—22no—
134C3×#216—22no—
135C3×#215D414yescomplemented
136C3×#214—22no—
137C3×#213—22no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×C4⋊Dic3—21no—
142C3×C4⋊Dic3—21no—
143C3×C4⋊Dic3C2311yescharacteristic
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4—21no—
146C3×Dic3⋊C4—21no—
147C3×Dic3⋊C4D411yescharacteristic
148C3×C4×Dic3—21no—
149C3×C4×Dic3C2311yescharacteristic
150C2×C3×C3⋊C8—22no—
151C2×C3×C3⋊C8C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×Dic12—41no—
154C3×#204—22no—
155C3×ΓL(1,𝔽25)—22no—
156#3269—31noSylow
157C2×C3×#41—21no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C2×C3×#41C2×D311yescharacteristic
161C2×C3×#41C22×C311yescharacteristic
162C22×C3×Q8—31no—
163C2×#239C22×C311yescharacteristic
164C2×D3×Q8C22×C311yescharacteristic
165C2×#235C22×C311yescharacteristic
166C3×#137—64no—
167C3×#135—64no—
168C2×C3×Q16—21no—
169C2×C3×Q16—31no—
170C2×C3×Q16—31no—
171C2×C3×Q16—31no—
172C2×C3×Q16C2×D311yescharacteristic
173C2×C3×Q16C22×C311yescharacteristic
174C2×C3×SD16—21no—
175C2×C3×SD16—31no—
176C2×C3×SD16—31no—
177C2×C3×SD16—31no—
178C2×C3×SD16C2×D311yescharacteristic
179C2×C3×SD16C22×C311yescharacteristic
180C2×C3×D8—31no—
181C2×C3×M16—31no—
182C22×C3×C8—31no—
183C3×C4⋊Q8—31no—
184C3×#124—31no—
185C3×#124—61no—
186C3×#123—61no—
187C3×#123—61no—
188C3×C22⋊Q8—21no—
189C3×C22⋊Q8—31no—
190C3×C22⋊Q8—31no—
191C3×C22⋊Q8—61no—
192C3×C22⋊Q8C2×D311yescharacteristic
193C3×C22⋊Q8C22×C311yescharacteristic
194C3×#121—31no—
195C3×#121—61no—
196C3×#121—61no—
197C3×C4×Q8—31no—
198C3×C4×D4—31no—
199C3×C4×D4—31no—
200C3×C4×D4—61no—
201C2×C3×C4⋊C4—61no—
202#950—24no—
203Q8×Dic3C22×C311yescharacteristic
204#944C22×C311yescharacteristic
205C2×#216C22×C311yescharacteristic
206C2×#216C22×C311yescharacteristic
207C2×#215C22×C311yescharacteristic
208#938—21no—
209#938C22×C311yescharacteristic
210#936—21no—
211#936C22×C311yescharacteristic
212C2×#214C22×C311yescharacteristic
213C2×#213C22×C311yescharacteristic
214C4×#67—21no—
215C4×#67C22×C311yescharacteristic
216#924—21no—
217#924C22×C311yescharacteristic
218C22×C3⋊C8C22×C311yescharacteristic
219#918—24no—
220C2×Dic12C22×C311yescharacteristic
221C2×#204C22×C311yescharacteristic
222C2×ΓL(1,𝔽25)C22×C311yescharacteristic
223#897C22×C311yescharacteristic
224#894—21no—
225#893C22×C311yescharacteristic
226D3×C4⋊C4—21no—
227#884—21no—
228#883—21no—
229C3×#107—31no—
230C3×C4⋊C8—31no—
231C3×#103—21no—
232C3×#103—31no—
233C3×#103—31no—
234C3×#103—31no—
235C3×#103C2×D311yescharacteristic
236C3×#103C22×C311yescharacteristic
237C3×#102—21no—
238C3×#102—31no—
239C3×#102C2×D311yescharacteristic
240C3×#102C22×C311yescharacteristic
241C3×C22⋊C8—21no—
242C3×C22⋊C8—31no—
243C3×C22⋊C8C2×D311yescharacteristic
244C3×C22⋊C8C22×C311yescharacteristic
245C3×#97—31no—
246#835C22×C311yescharacteristic
247#821C22×C311yescharacteristic
248(C2×D3)⋊C8C22×C311yescharacteristic
249#816C22×C311yescharacteristic
250#815C22×C311yescharacteristic
251Dic3⋊C8C22×C311yescharacteristic
252#810C22×C311yescharacteristic
253#807C22×C311yescharacteristic
254C23×C32—21no—
255C23×C32C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3C2×D411yescharacteristic
258C32×Q8—21no—
259C32×Q8—21no—
260C32×Q8—21no—
261C32×Q8C2×D412yes—
262C32×D4—21no—
263C32×D4—21no—
264C32×D4—42no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—42no—
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2411yescharacteristic
273C3×#67—41no—
274C3×#67—42no—
275C3×#67—42no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—42no—
284C3×D12C2×D412yes—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—42no—
288C3×C4×D3—42no—
289C3×C4×D3—42no—
290C3×C4×D3—42no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—42no—
296C32×C8—21no—
297C32×C8—21no—
298C3×C3⋊C8—21no—
299C3×C3⋊C8C2×D412yes—
300C2×#137—31no—
301C2×#135—31no—
302#548—31no—
303#547—31no—
304#497—31no—
305#468—31no—
306#467—31no—
307#463—31no—
308#462—31no—
309#452—31no—
310#452C3×D311yescharacteristic, complemented
311#451—31no—
312#449—31no—
313#440—31no—
314#435—31no—
315C3×#41—22no—
316C3×#41—22no—
317C3×#41—42no—
318C3×#41—41no—
319C3×#41—41no—
320C3×#41—42no—
321C3×#41—62no—
322C3×#41—62no—
323C3×#41—121no—
324C3×#41—121no—
325C2×C3×Q8—21no—
326C2×C3×Q8—21no—
327C2×C3×Q8—31no—
328C2×C3×Q8—31no—
329C2×C3×Q8—61no—
330C2×C3×Q8—62no—
331C2×C3×Q8—121no—
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×Q8C22×D311yescharacteristic
334C2×C3×Q8C23×C311yescharacteristic
335C2×C3×Q8C23×C311yescharacteristic
336C2×C3×D4—21no—
337C2×C3×D4—21no—
338C2×C3×D4—21no—
339C2×C3×D4—31no—
340C2×C3×D4—31no—
341C2×C3×D4—41no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C2×C3×D4C22×D311yescharacteristic
346C2×C3×D4C23×C311yescharacteristic
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—21no—
350C22×C3×C4—31no—
351C22×C3×C4—41no—
352C22×C3×C4—61no—
353C22×C3×C4—61no—
354C22×C3×C4—61no—
355C22×C3×C4—61no—
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C23×C311yescharacteristic
358C2×#67—21no—
359C2×#67—21no—
360C2×#67C3×D411yescharacteristic
361#239—22no—
362#239—41no—
363D3×Q8—22no—
364D3×Q8—41no—
365#235—22no—
366#235—41no—
367C2×D12—21no—
368C2×D12C23×C311yescharacteristic
369C2×C4×D3—21no—
370C2×C4×D3—21no—
371C2×C4×D3—21no—
372C2×C4×D3—21no—
373C2×C4×D3C23×C311yescharacteristic
374C2×Dic6—21no—
375C2×Dic6C23×C311yescharacteristic
376C2×Dic6C23×C311yescharacteristic
377C3×Q16—22no—
378C3×Q16—22no—
379C3×Q16—42no—
380C3×Q16—62no—
381C3×Q16—62no—
382C3×Q16—121no—
383C3×SD16—34no—
384C3×SD16—41no—
385C3×SD16—41no—
386C3×SD16—42no—
387C3×SD16—62no—
388C3×SD16—62no—
389C3×D8—62no—
390C3×M16—62no—
391C2×C3×C8—21no—
392C2×C3×C8—21no—
393C2×C3×C8—31no—
394C2×C3×C8—31no—
395C2×C3×C8—62no—
396C2×C3×C8C22×D311yescharacteristic
397C2×C3×C8C22×D311yescharacteristic
398C2×C3×C8C23×C311yescharacteristic
399C2×C3×C8C23×C311yescharacteristic
400C3×C4⋊C4—21no—
401C3×C4⋊C4—21no—
402C3×C4⋊C4—21no—
403C3×C4⋊C4—31no—
404C3×C4⋊C4—31no—
405C3×C4⋊C4—41no—
406C3×C4⋊C4—61no—
407C3×C4⋊C4—61no—
408C3×C4⋊C4—61no—
409C3×C4⋊C4—61no—
410C3×C4⋊C4—61no—
411C3×C4⋊C4C22×D311yescharacteristic
412C3×C4⋊C4C23×C311yescharacteristic
413C3×C22⋊C4—21no—
414C3×C22⋊C4—21no—
415C3×C22⋊C4—31no—
416C3×C22⋊C4—31no—
417C3×C22⋊C4—41no—
418C3×C22⋊C4—61no—
419C3×C22⋊C4—61no—
420C3×C22⋊C4—61no—
421C3×C22⋊C4—61no—
422C3×C22⋊C4—61no—
423C3×C22⋊C4—61no—
424C3×C42—31no—
425C3×C42—61no—
426#217—21no—
427#217—21no—
428#217—21no—
429#217—21no—
430#217C3×D411yescharacteristic
431#216—22no—
432#216—22no—
433#215C3×D414yescomplemented
434#214—22no—
435#213—22no—
436(C2×D3)⋊C4—21no—
437(C2×D3)⋊C4—21no—
438(C2×D3)⋊C4C3×D411yescharacteristic
439C4⋊Dic3—21no—
440C4⋊Dic3—21no—
441C4⋊Dic3C23×C311yescharacteristic
442Dic3⋊C4—21no—
443Dic3⋊C4—21no—
444Dic3⋊C4—21no—
445Dic3⋊C4C3×D411yescharacteristic
446C4×Dic3—21no—
447C4×Dic3C23×C311yescharacteristic
448C2×C3⋊C8—22no—
449C2×C3⋊C8C23×C311yescharacteristic
450C2×C3⋊C8C23×C311yescharacteristic
451Dic12—41no—
452#204—22no—
453ΓL(1,𝔽25)—22no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—41no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32C22×D411yescharacteristic
461C2×C3×D3—21no—
462C2×C3×D3—22no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C32×C4—22no—
468C32×C4—21no—
469C32×C4—41no—
470C32×C4—41no—
471C32×C4C22×D411yescharacteristic
472C32×C4H(5,𝔽2)11yescharacteristic
473C3×Dic3—21no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C2×#41—31no—
480C2×#41—31no—
481C2×#41C2×C3×D311yescharacteristic
482C22×Q8—31no—
483#137—64no—
484#135—64no—
485C2×Q16—31no—
486C2×Q16—31no—
487C2×Q16—31no—
488C2×Q16C2×C3×D311yescharacteristic
489C2×SD16—31no—
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16C2×C3×D311yescharacteristic
493C2×D8—31no—
494C2×M16—31no—
495C22×C8—31no—
496C4⋊Q8—31no—
497#124—31no—
498#124—61no—
499#123—61no—
500#123—61no—
501C22⋊Q8—31no—
502C22⋊Q8—31no—
503C22⋊Q8—61no—
504C22⋊Q8C2×C3×D311yescharacteristic
505#121—31no—
506#121—61no—
507#121—61no—
508C4×Q8—31no—
509C4×D4—31no—
510C4×D4—31no—
511C4×D4—61no—
512C2×C4⋊C4—61no—
513#107—31no—
514C4⋊C8—31no—
515#103—31no—
516#103—31no—
517#103—31no—
518#103C2×C3×D311yescharacteristic
519#102—31no—
520#102C2×C3×D311yescharacteristic
521C22⋊C8—31no—
522C22⋊C8C2×C3×D311yescharacteristic
523#97—31no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—31no—
528C23×C3—41no—
529C23×C3—61no—
530C23×C3D3×D411yescharacteristic
531C23×C3C2×C3×D411yescharacteristic
532C22×D3—21no—
533C22×D3C2×C3×D411yescharacteristic
534C3×Q8—21no—
535C3×Q8—21no—
536C3×Q8—21no—
537C3×Q8—21no—
538C3×Q8—21no—
539C3×Q8—21no—
540C3×Q8—22no—
541C3×Q8—41no—
542C3×Q8—41no—
543C3×Q8—41no—
544C3×Q8—61no—
545C3×Q8—61no—
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—122no—
549C3×Q8D3×D412yes—
550C3×Q8C2×C3×D412yes—
551C3×D4—22no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—32no—
557C3×D4—41no—
558C3×D4—42no—
559C3×D4—42no—
560C3×D4—44no—
561C3×D4—61no—
562C3×D4—122no—
563C3×D4—121no—
564C3×D4—122no—
565C3×D4—122no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
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—31no—
579C2×C3×C4—31no—
580C2×C3×C4—31no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—42no—
587C2×C3×C4—42no—
588C2×C3×C4—44no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—122no—
595C2×C3×C4—122no—
596C2×C3×C4—122no—
597C2×C3×C4—122no—
598C2×C3×C4D3×D411yescharacteristic
599C2×C3×C4C2×C3×D411yescharacteristic
600C2×C3×C4C23×D311yescharacteristic
601C2×C3×C4C24×C311yescharacteristic
602#67—41no—
603#67—42no—
604#67—42no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3C2×C3×D411yescharacteristic
609C2×Dic3C2×C3×D411yescharacteristic
610C2×Dic3C2×C3×D411yescharacteristic
611D12—21no—
612D12—42no—
613D12C2×C3×D412yes—
614C4×D3—21no—
615C4×D3—21no—
616C4×D3—42no—
617C4×D3—42no—
618C4×D3—42no—
619C4×D3—42no—
620Dic6—21no—
621Dic6—21no—
622Dic6—21no—
623Dic6—21no—
624Dic6—42no—
625C3×C8—21no—
626C3×C8—21no—
627C3×C8—21no—
628C3×C8—21no—
629C3×C8—32no—
630C3×C8—41no—
631C3×C8—41no—
632C3×C8—61no—
633C3⋊C8—21no—
634C3⋊C8C2×C3×D412yes—
635C2×C32—41no—
636C2×C32—81no—
637C2×C32D4211yescharacteristic
638C2×C32#57511yescharacteristic
639C2×C32#57811yescharacteristic
640C3×D3—41no—
641C3×D3—42no—
642#41—22no—
643#41—41no—
644#41—62no—
645#41—62no—
646#41—121no—
647#41—121no—
648C2×Q8—31no—
649C2×Q8—31no—
650C2×Q8—61no—
651C2×Q8—62no—
652C2×Q8—121no—
653C2×Q8C22×C3×D311yescharacteristic
654C2×Q8C22×C3×D311yescharacteristic
655C2×D4—21no—
656C2×D4—31no—
657C2×D4—31no—
658C2×D4—61no—
659C2×D4—61no—
660C2×D4—61no—
661C2×D4C22×C3×D311yescharacteristic
662C22×C4—21no—
663C22×C4—31no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4C22×C3×D311yescharacteristic
669Q16—22no—
670Q16—62no—
671Q16—62no—
672Q16—121no—
673SD16—34no—
674SD16—41no—
675SD16—62no—
676SD16—62no—
677D8—62no—
678M16—62no—
679C2×C8—31no—
680C2×C8—31no—
681C2×C8—62no—
682C2×C8C22×C3×D311yescharacteristic
683C2×C8C22×C3×D311yescharacteristic
684C4⋊C4—21no—
685C4⋊C4—31no—
686C4⋊C4—31no—
687C4⋊C4—61no—
688C4⋊C4—61no—
689C4⋊C4—61no—
690C4⋊C4—61no—
691C4⋊C4—61no—
692C4⋊C4C22×C3×D311yescharacteristic
693C22⋊C4—21no—
694C22⋊C4—31no—
695C22⋊C4—31no—
696C22⋊C4—61no—
697C22⋊C4—61no—
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C42—31no—
703C42—61no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—42no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—62no—
725C22×C3—81no—
726C22×C3—81no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3C2×D3×D411yescharacteristic
730C22×C3C22×C3×D411yescharacteristic
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—21no—
734C2×D3—22no—
735C2×D3—41no—
736C2×D3—41no—
737C3×C4—21no—
738C3×C4—22no—
739C3×C4—22no—
740C3×C4—21no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—41no—
744C3×C4—42no—
745C3×C4—41no—
746C3×C4—41no—
747C3×C4—41no—
748C3×C4—41no—
749C3×C4—61no—
750C3×C4—61no—
751C3×C4—61no—
752C3×C4—81no—
753C3×C4—81no—
754C3×C4—121no—
755C3×C4—121no—
756C3×C4—121no—
757C3×C4C2×D3×D411yescharacteristic
758C3×C4#100411yescharacteristic
759C3×C4C22×C3×D411yescharacteristic
760C3×C4C3×H(5,𝔽2)11yescharacteristic
761Dic3—21no—
762Dic3—21no—
763Dic3—21no—
764Dic3—41no—
765Dic3—41no—
766Dic3—41no—
767C32#326911yescharacteristic, complemented, Sylow
768C23—21no—
769C23—31no—
770C23—61no—
771C23C3×D3×D411yescharacteristic
772Q8—21no—
773Q8—21no—
774Q8—21no—
775Q8—61no—
776Q8—61no—
777Q8—61no—
778Q8—61no—
779Q8—122no—
780Q8C3×D3×D412yes—
781D4—21no—
782D4—21no—
783D4—32no—
784D4—42no—
785D4—61no—
786D4—122no—
787D4—121no—
788D4—122no—
789D4—122no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—31no—
796C2×C4—31no—
797C2×C4—31no—
798C2×C4—42no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—122no—
805C2×C4—122no—
806C2×C4—122no—
807C2×C4—122no—
808C2×C4C3×D3×D411yescharacteristic
809C2×C4C23×C3×D311yescharacteristic
810C8—21no—
811C8—21no—
812C8—32no—
813C8—61no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—41no—
818C2×C3—41no—
819C2×C3—81no—
820C2×C3—82no—
821C2×C3—81no—
822C2×C3—81no—
823C2×C3—121no—
824C2×C3—122no—
825C2×C3#559011yescharacteristic
826C2×C3#576811yescharacteristic
827C2×C3#577911yescharacteristic
828C2×C3C3×D4211yescharacteristic
829C2×C3C3×#57511yescharacteristic
830C2×C3C3×#57811yescharacteristic
831D3—41no—
832D3—42no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—61no—
840C22—61no—
841C22—61no—
842C22—62no—
843C22—121no—
844C22—121no—
845C22C2×C3×D3×D411yescharacteristic
846C4—21no—
847C4—22no—
848C4—41no—
849C4—41no—
850C4—61no—
851C4—61no—
852C4—61no—
853C4—121no—
854C4—121no—
855C4—121no—
856C4C2×C3×D3×D411yescharacteristic
857C4C3×#100411yescharacteristic
858C3—21no—
859C3#8026711yescharacteristic, direct product factor
860C3C3×#326911yescharacteristic, complemented
861C2—41no—
862C2—81no—
863C2—121no—
864C2—122no—
865C2C3×#559011yescharacteristic
866C2C3×#576811yescharacteristic
867C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#452C2
socleC22×C32C22×D4
hypercenterC3×#452D3
hypocenterC3C3×#3269
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#452

Complements

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

NH ≅ G/Ntype
1. C3×#5831C2semidirect
2. C2×C3×#950C2semidirect
3. C2×C3×#918C2semidirect
4. C3×#5631C2semidirect
5. C32×#452C2semidirect
6. C3×#5182C2semidirect
7. C3×#5172C2semidirect
8. C3×#5167C2semidirect
9. C3×#5051C2semidirect
10. C3×#4817C2semidirect
11. C3×#4809C2semidirect
12. C3×#4787C2semidirect
13. C3×#4780C2semidirect
14. C3×#4733C2semidirect
15. C3×#4730C2semidirect
17. #80267C3direct (N × H)
67. #5831C2×C3semidirect
68. C2×#950C2×C3semidirect
69. C2×#918C2×C3semidirect
70. #5631C2×C3semidirect
78. C3×#452D3semidirect
79. C3×#452C2×C3semidirect
84. #5182C2×C3semidirect
85. #5172C2×C3semidirect
86. #5167C2×C3semidirect
87. #5051C2×C3semidirect
88. #4817C2×C3semidirect
89. #4809C2×C3semidirect
90. #4787C2×C3semidirect
91. #4780C2×C3semidirect
92. #4733C2×C3semidirect
93. #4730C2×C3semidirect
135. C3×#215D4semidirect
310. #452C3×D3semidirect
433. #215C3×D4semidirect
767. C32#3269semidirect
859. C3#80267direct (N × H)
860. C3C3×#3269semidirect

Maximal subgroups

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

subgroupindex
C3×#58312
C2×C3×#9502
C2×C3×#9182
C3×#56312
C32×#4522
C3×#51822
C3×#51722
C3×#51672
C3×#50512
C3×#48172
C3×#48092
C3×#47872
C3×#47802
C3×#47332
C3×#47302
C3×#32693
#802673