Finite Group Databasebeta

← C3×#81748 #11888573

Subgroups — C3×#81748 #11888573

Order 1152.

833 conjugacy classes of subgroups.

The subgroup lattice has 785 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5726C211yesmaximal, characteristic, complemented
2C3×#5695C211yesmaximal, characteristic, complemented
3C32×#491C211yesmaximal, characteristic, complemented
4C3×#5083C211yesmaximal, characteristic, complemented
5C3×#5066C211yesmaximal, characteristic, complemented
6C3×#4815C211yesmaximal, characteristic, complemented
7C3×#4812C211yesmaximal, characteristic, complemented
8C3×#4810C211yesmaximal, characteristic, complemented
9C3×#4810C211yesmaximal, characteristic, complemented
10C3×#4807C211yesmaximal, characteristic, complemented
11C3×#4805C211yesmaximal, characteristic, complemented
12C3×#4804C211yesmaximal, characteristic, complemented
13C3×#4803C211yesmaximal, characteristic, complemented
14C3×#4711C211yesmaximal, characteristic, complemented
15C3×#4706C211yesmaximal, characteristic, complemented
16C3×#3307—31nomaximal
17#81748C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C32×C4⋊Q8C2211yescharacteristic
21C32×#125C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C2×C3×D24C2211yescharacteristic
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×#898—21no—
30C3×#895—21no—
31C3×#895—21no—
32C3×#895C2211yescharacteristic
33C3×#895C2211yescharacteristic
34C3×#894—21no—
35C3×#894—21no—
36C3×#894—21no—
37C3×#893—21no—
38C3×#892C2211yescharacteristic
39C3×D3×C4⋊C4—21no—
40C3×D3×C4⋊C4C2211yescharacteristic
41C3×C4×D12C2211yescharacteristic
42C3×C4×D12C2211yescharacteristic
43C3×C4×D12C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C32×#97C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#821C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic
54C3×(C2×D3)⋊C8C2211yescharacteristic
55C3×#817C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#553—31no—
62C3×#547—31no—
63#5726C2×C311yescharacteristic, complemented
64#5695C2×C311yescharacteristic, complemented
65C3×#491—21no—
66C3×#491D311yescharacteristic, complemented
67C3×#491C2×C311yescharacteristic, complemented
68C3×#485—31no—
69C3×#483—31no—
70C3×#478—31no—
71C3×#468—31no—
72C3×#465—31no—
73C3×#461—31no—
74C3×#449—31no—
75C3×#449—31no—
76C3×#442—31no—
77C3×#435—31no—
78C3×#417—31no—
79C3×#416—31no—
80#5083C2×C311yescharacteristic, complemented
81#5066C2×C311yescharacteristic, complemented
82#4815C2×C311yescharacteristic, complemented
83#4812C2×C311yescharacteristic, complemented
84#4810C2×C311yescharacteristic, complemented
85#4810C2×C311yescharacteristic, complemented
86#4807C2×C311yescharacteristic, complemented
87#4805C2×C311yescharacteristic, complemented
88#4804C2×C311yescharacteristic, complemented
89#4803C2×C311yescharacteristic, complemented
90#4711C2×C311yescharacteristic, complemented
91#4706C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C3×#239—22no—
95C3×#239—22no—
96C3×#239—41no—
97C3×#239—41no—
98C2×C3×D12—21no—
99C2×C3×D12—21no—
100C2×C3×D12—21no—
101C2×C3×D12—21no—
102C2×C3×D12D411yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4—21no—
115C32×C4⋊C4—21no—
116C32×C4⋊C4—21no—
117C32×C4⋊C4—21no—
118C32×C4⋊C4C2311yescharacteristic
119C32×C4⋊C4C2311yescharacteristic
120C32×C42C2311yescharacteristic
121C3×#215—41no—
122C3×#215—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4D411yescharacteristic
131C3×(C2×D3)⋊C4D411yescharacteristic
132C3×C4⋊Dic3D411yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×C4×Dic3—21no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×D24—22no—
142C3×ΓL(1,𝔽25)—41no—
143C3×D3×C8—41no—
144#3307—31noSylow
145C2×C3×#41—31no—
146C2×C3×#41—31no—
147C2×#239C22×C311yescharacteristic
148C2×#239C22×C311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C2×C3×D8—31no—
152C2×C3×M16—31no—
153C22×C3×C8—31no—
154C3×C4⋊Q8—21no—
155C3×C4⋊Q8C2×D311yescharacteristic
156C3×C4⋊Q8C22×C311yescharacteristic
157C3×#126—61no—
158C3×#125—21no—
159C3×#125C2×D311yescharacteristic
160C3×#125C22×C311yescharacteristic
161C3×#123—61no—
162C3×#123—61no—
163C3×#123—61no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—31no—
166C3×#121—31no—
167C3×#121—31no—
168C3×#121—61no—
169C3×#121—61no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172C3×C4×D4—31no—
173C3×C4×D4—61no—
174C3×#117—31no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—61no—
177#946C22×C311yescharacteristic
178#946C22×C311yescharacteristic
179C2×#215C22×C311yescharacteristic
180C2×#215C22×C311yescharacteristic
181C2×D24C22×C311yescharacteristic
182C2×ΓL(1,𝔽25)C22×C311yescharacteristic
183C2×D3×C8C22×C311yescharacteristic
184#898—21no—
185#895—21no—
186#895—21no—
187#895C22×C311yescharacteristic
188#895C22×C311yescharacteristic
189#894—21no—
190#894—21no—
191#894—21no—
192#893—21no—
193#892C22×C311yescharacteristic
194D3×C4⋊C4—21no—
195D3×C4⋊C4C22×C311yescharacteristic
196C4×D12C22×C311yescharacteristic
197C4×D12C22×C311yescharacteristic
198C4×D12C22×C311yescharacteristic
199C3×#107—31no—
200C3×#106—31no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×#103—21no—
204C3×#103—21no—
205C3×#103—21no—
206C3×#103—21no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103C2×D311yescharacteristic
210C3×#103C2×D311yescharacteristic
211C3×#103C2×D311yescharacteristic
212C3×#103C2×D311yescharacteristic
213C3×#103C22×C311yescharacteristic
214C3×#103C22×C311yescharacteristic
215C3×#103C22×C311yescharacteristic
216C3×#103C22×C311yescharacteristic
217C3×#102—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#102—31no—
221C3×C22⋊C8—31no—
222C3×C22⋊C8—31no—
223C3×#97—21no—
224C3×#97C2×D311yescharacteristic
225C3×#97C22×C311yescharacteristic
226#835C22×C311yescharacteristic
227#835C22×C311yescharacteristic
228#821C22×C311yescharacteristic
229#821C22×C311yescharacteristic
230(C2×D3)⋊C8C22×C311yescharacteristic
231(C2×D3)⋊C8C22×C311yescharacteristic
232#817C22×C311yescharacteristic
233#809C22×C311yescharacteristic
234#809C22×C311yescharacteristic
235#808C22×C311yescharacteristic
236#807C22×C311yescharacteristic
237C4⋊(C3⋊C8)C22×C311yescharacteristic
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C32×Q8—21no—
245C32×Q8—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—41no—
261C3×D12—42no—
262C3×D12—42no—
263C3×D12—42no—
264C3×D12—81no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272C3×C4×D3—42no—
273C3×C4×D3—81no—
274C3×C4×D3—81no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—31no—
280#547—31no—
281#491C3×D311yescharacteristic, complemented
282#485—31no—
283#483—31no—
284#478—31no—
285#468—31no—
286#465—31no—
287#461—31no—
288#449—31no—
289#449—31no—
290#442—31no—
291#435—31no—
292#417—31no—
293#416—31no—
294C3×#41—62no—
295C3×#41—62no—
296C3×#41—121no—
297C3×#41—121no—
298C2×C3×Q8—21no—
299C2×C3×Q8—21no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C23×C311yescharacteristic
303C2×C3×Q8C23×C311yescharacteristic
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318#239—22no—
319#239—22no—
320#239—41no—
321#239—41no—
322C2×D12—21no—
323C2×D12—21no—
324C2×D12—21no—
325C2×D12—21no—
326C2×D12C3×D411yescharacteristic
327C2×D12C23×C311yescharacteristic
328C2×D12C23×C311yescharacteristic
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3C23×C311yescharacteristic
335C2×C4×D3C23×C311yescharacteristic
336C3×SD16—121no—
337C3×SD16—121no—
338C3×D8—62no—
339C3×M16—121no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—121no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C23×C311yescharacteristic
348C2×C3×C8C23×C311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—41no—
363C3×C4⋊C4—41no—
364C3×C4⋊C4—41no—
365C3×C4⋊C4—41no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4C22×D311yescharacteristic
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C4⋊C4C23×C311yescharacteristic
372C3×C4⋊C4C23×C311yescharacteristic
373C3×C22⋊C4—31no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C42—21no—
383C3×C42—61no—
384C3×C42C22×D311yescharacteristic
385C3×C42C23×C311yescharacteristic
386#215—41no—
387#215—41no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4C3×D411yescharacteristic
396(C2×D3)⋊C4C3×D411yescharacteristic
397C4⋊Dic3C3×D411yescharacteristic
398C4⋊Dic3C23×C311yescharacteristic
399C4⋊Dic3C23×C311yescharacteristic
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402Dic3⋊C4—21no—
403C4×Dic3—21no—
404C2×C3⋊C8C23×C311yescharacteristic
405C2×C3⋊C8C23×C311yescharacteristic
406D24—22no—
407ΓL(1,𝔽25)—41no—
408D3×C8—41no—
409C22×C32C22×D411yescharacteristic
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—22no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—41no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C2×#41—31no—
435C2×#41—31no—
436C2×SD16—31no—
437C2×SD16—31no—
438C2×D8—31no—
439C2×M16—31no—
440C22×C8—31no—
441C4⋊Q8C2×C3×D311yescharacteristic
442#126—61no—
443#125C2×C3×D311yescharacteristic
444#123—61no—
445#123—61no—
446#123—61no—
447C22⋊Q8—31no—
448C22⋊Q8—31no—
449#121—31no—
450#121—31no—
451#121—61no—
452#121—61no—
453C4×D4—31no—
454C4×D4—31no—
455C4×D4—31no—
456C4×D4—61no—
457#117—31no—
458C2×C4⋊C4—31no—
459C2×C4⋊C4—61no—
460#107—31no—
461#106—31no—
462#106—31no—
463C4⋊C8—31no—
464#103—31no—
465#103—31no—
466#103C2×C3×D311yescharacteristic
467#103C2×C3×D311yescharacteristic
468#103C2×C3×D311yescharacteristic
469#103C2×C3×D311yescharacteristic
470#102—31no—
471#102—31no—
472#102—31no—
473#102—31no—
474C22⋊C8—31no—
475C22⋊C8—31no—
476#97C2×C3×D311yescharacteristic
477C23×C3—31no—
478C23×C3—31no—
479C23×C3—61no—
480C23×C3—61no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3C2×C3×D411yescharacteristic
484C22×D3C2×C3×D411yescharacteristic
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—41no—
494C3×Q8—41no—
495C3×Q8—41no—
496C3×Q8—41no—
497C3×D4—32no—
498C3×D4—61no—
499C3×D4—61no—
500C3×D4—61no—
501C3×D4—121no—
502C3×D4—122no—
503C3×D4—122no—
504C3×D4—122no—
505C3×D4—241no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—122no—
530C2×C3×C4—122no—
531C2×C3×C4—122no—
532C2×C3×C4—241no—
533C2×C3×C4—241no—
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4C2×C3×D411yescharacteristic
537C2×C3×C4C2×C3×D411yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C24×C311yescharacteristic
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3C2×C3×D411yescharacteristic
543C2×Dic3C2×C3×D411yescharacteristic
544D12—21no—
545D12—21no—
546D12—21no—
547D12—41no—
548D12—42no—
549D12—42no—
550D12—42no—
551D12—81no—
552D12C3×#4112yes—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—42no—
558C4×D3—42no—
559C4×D3—42no—
560C4×D3—81no—
561C4×D3—81no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—41no—
567C3×C8—41no—
568C3×C8—61no—
569C3×C8—61no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C2×C32#54611yescharacteristic
573C2×C32#57511yescharacteristic
574C2×C32#57711yescharacteristic
575C3×D3—41no—
576C3×D3—41no—
577C3×D3—42no—
578C3×D3—81no—
579#41—62no—
580#41—62no—
581#41—121no—
582#41—121no—
583C2×Q8C22×C3×D311yescharacteristic
584C2×Q8C22×C3×D311yescharacteristic
585C2×D4—31no—
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—61no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—61no—
599SD16—121no—
600SD16—121no—
601D8—62no—
602M16—121no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—121no—
606C2×C8C22×C3×D311yescharacteristic
607C2×C8C22×C3×D311yescharacteristic
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4C22×C3×D311yescharacteristic
619C4⋊C4C22×C3×D311yescharacteristic
620C22⋊C4—31no—
621C22⋊C4—31no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C42—61no—
630C42C22×C3×D311yescharacteristic
631C22×C3—21no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—62no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3C2×D3×D411yescharacteristic
645C22×C3C22×C3×D411yescharacteristic
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—22no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—81no—
677C3×C4—81no—
678C3×C4—81no—
679C3×C4—81no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4D3×#4111yescharacteristic
683C3×C4#100911yescharacteristic
684C3×C4C2×C3×#4111yescharacteristic
685C3×C4C3×H(5,𝔽2)11yescharacteristic
686Dic3—21no—
687Dic3—21no—
688Dic3—41no—
689Dic3—41no—
690C32#330711yescharacteristic, complemented, Sylow
691C23—31no—
692C23—31no—
693C23—61no—
694C23—61no—
695Q8—21no—
696Q8—21no—
697Q8—21no—
698Q8—21no—
699D4—32no—
700D4—61no—
701D4—61no—
702D4—61no—
703D4—121no—
704D4—122no—
705D4—122no—
706D4—122no—
707D4—241no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—31no—
713C2×C4—31no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—122no—
721C2×C4—122no—
722C2×C4—122no—
723C2×C4—241no—
724C2×C4—241no—
725C2×C4C3×D3×D411yescharacteristic
726C2×C4C3×D3×D411yescharacteristic
727C2×C4C23×C3×D311yescharacteristic
728C8—21no—
729C8—21no—
730C8—61no—
731C8—61no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—121no—
736C2×C3—121no—
737C2×C3—122no—
738C2×C3—241no—
739C2×C3#567611yescharacteristic
740C2×C3#577711yescharacteristic
741C2×C3#577811yescharacteristic
742C2×C3C3×#54611yescharacteristic
743C2×C3C3×#57511yescharacteristic
744C2×C3C3×#57711yescharacteristic
745D3—41no—
746D3—41no—
747D3—42no—
748D3—81no—
749C22—61no—
750C22—61no—
751C22—61no—
752C22—61no—
753C22—61no—
754C22—61no—
755C22—62no—
756C22—121no—
757C22—121no—
758C22—121no—
759C22—121no—
760C22—121no—
761C22C2×C3×D3×D411yescharacteristic
762C4—21no—
763C4—21no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—61no—
769C4—61no—
770C4—121no—
771C4—121no—
772C4C3×D3×#4111yescharacteristic
773C4C3×#100911yescharacteristic
774C3—21no—
775C3#8174811yescharacteristic, direct product factor
776C3C3×#330711yescharacteristic, complemented
777C2—121no—
778C2—121no—
779C2—122no—
780C2—241no—
781C2C3×#567611yescharacteristic
782C2C3×#577711yescharacteristic
783C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#491C2
socleC22×C32C22×D4
hypercenterC3×#491D3
hypocenterC3C3×#3307
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#491

Complements

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

NH ≅ G/Ntype
1. C3×#5726C2semidirect
2. C3×#5695C2semidirect
3. C32×#491C2semidirect
4. C3×#5083C2semidirect
5. C3×#5066C2semidirect
6. C3×#4815C2semidirect
7. C3×#4812C2semidirect
8. C3×#4810C2semidirect
9. C3×#4810C2semidirect
10. C3×#4807C2semidirect
11. C3×#4805C2semidirect
12. C3×#4804C2semidirect
13. C3×#4803C2semidirect
14. C3×#4711C2semidirect
15. C3×#4706C2semidirect
17. #81748C3direct (N × H)
63. #5726C2×C3semidirect
64. #5695C2×C3semidirect
66. C3×#491D3semidirect
67. C3×#491C2×C3semidirect
80. #5083C2×C3semidirect
81. #5066C2×C3semidirect
82. #4815C2×C3semidirect
83. #4812C2×C3semidirect
84. #4810C2×C3semidirect
85. #4810C2×C3semidirect
86. #4807C2×C3semidirect
87. #4805C2×C3semidirect
88. #4804C2×C3semidirect
89. #4803C2×C3semidirect
90. #4711C2×C3semidirect
91. #4706C2×C3semidirect
281. #491C3×D3semidirect
690. C32#3307semidirect
775. C3#81748direct (N × H)
776. C3C3×#3307semidirect

Maximal subgroups

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

subgroupindex
C3×#57262
C3×#56952
C32×#4912
C3×#50832
C3×#50662
C3×#48152
C3×#48122
C3×#48102
C3×#48072
C3×#48052
C3×#48042
C3×#48032
C3×#47112
C3×#47062
C3×#33073
#817483