Finite Group Databasebeta

← C3×#83552 #11889346

Subgroups — C3×#83552 #11889346

Order 1152.

892 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×D4×Q8C211yesmaximal, characteristic
2C3×#5541C211yesmaximal, characteristic
3C3×#5228C211yesmaximal, characteristic, complemented
4C3×#5228C211yesmaximal, characteristic, complemented
5C3×#5225C211yesmaximal, characteristic, complemented
6C2×C3×#835C211yesmaximal, characteristic, complemented
7C3×#5090C211yesmaximal, characteristic, complemented
8C3×#5082C211yesmaximal, characteristic, complemented
9C3×#5052C211yesmaximal, characteristic, complemented
10C3×#5051C211yesmaximal, characteristic, complemented
11C3×#5045C211yesmaximal, characteristic, complemented
12C3×#5043C211yesmaximal, characteristic, complemented
13C3×#5030C211yesmaximal, characteristic, complemented
14C3×#5022C211yesmaximal, characteristic, complemented
15C3×#5011C211yesmaximal, characteristic
16C3×#3312—31nomaximal
17#83552C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic
19C22×C32×Q8C2211yescharacteristic
20C32×C4⋊Q8—21no—
21C32×C4⋊Q8C2211yescharacteristic
22C32×C22⋊Q8—21no—
23C32×C22⋊Q8—21no—
24C32×C22⋊Q8C2211yescharacteristic
25C32×C22⋊Q8C2211yescharacteristic
26C32×C4×Q8C2211yescharacteristic
27C32×C4×D4—21no—
28C32×C4×D4C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C2×C3×#216C2211yescharacteristic
32C3×#935—21no—
33C3×#926C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C3×#924C2211yescharacteristic
36C3×#924C2211yescharacteristic
37C2×C3×#208C2211yescharacteristic
38C22×C3×C3⋊C8C2211yescharacteristic
39C3×#889—21no—
40C3×#879—21no—
41C3×#877—21no—
42C3×#870C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#835C2211yescharacteristic
52C3×#835C2211yescharacteristic
53C3×#830C2211yescharacteristic
54C3×#830C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#808C2211yescharacteristic
57C3×#808C2211yescharacteristic
58C3×#807C2211yescharacteristic
59C3×C4⋊(C3⋊C8)C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#552—31no—
62C3×D4×Q8—21no—
63C3×D4×Q8D311yescharacteristic
64C3×D4×Q8C2×C311yescharacteristic
65#5541C2×C311yescharacteristic
66C3×#491—31no—
67C3×#485—31no—
68C3×#483—31no—
69C3×#479—31no—
70C3×#470—31no—
71C3×#467—31no—
72C3×#462—31no—
73C3×#451—31no—
74C3×#451—31no—
75C3×#441—31no—
76C3×#435—31no—
77C3×#419—31no—
78C2×C3×#103—31no—
79#5228C2×C311yescharacteristic, complemented
80#5228C2×C311yescharacteristic, complemented
81#5225C2×C311yescharacteristic, complemented
82C2×#835C2×C311yescharacteristic, complemented
83#5090C2×C311yescharacteristic, complemented
84#5082C2×C311yescharacteristic, complemented
85#5052C2×C311yescharacteristic, complemented
86#5051C2×C311yescharacteristic, complemented
87#5045C2×C311yescharacteristic, complemented
88#5043C2×C311yescharacteristic, complemented
89#5030C2×C311yescharacteristic, complemented
90#5022C2×C311yescharacteristic, complemented
91#5011C2×C311yescharacteristic
92C2×C32×Q8—21no—
93C2×C32×Q8—21no—
94C2×C32×Q8—22no—
95C2×C32×Q8—22no—
96C2×C32×Q8—41no—
97C2×C32×Q8—41no—
98C2×C32×Q8C2311yescharacteristic
99C2×C32×Q8C2311yescharacteristic
100C2×C32×Q8C2311yescharacteristic
101C2×C32×D4D411yescharacteristic
102C22×C32×C4—21no—
103C22×C32×C4—21no—
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C3×Dic3—21no—
107C2×C3×Dic6C2311yescharacteristic
108C32×C4⋊C4—21no—
109C32×C4⋊C4—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4D411yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C22⋊C4—21no—
117C32×C22⋊C4D411yescharacteristic
118C32×C22⋊C4D411yescharacteristic
119C32×C42—21no—
120C32×C42C2311yescharacteristic
121C3×#217—21no—
122C3×#217—21no—
123C3×#217—21no—
124C3×#216—22no—
125C3×#216—41no—
126C3×#216—41no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C3×#208—41no—
139C2×C3×C3⋊C8—41no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144#3312—31noSylow
145C22×C3×Q8—21no—
146C22×C3×Q8—21no—
147C22×C3×Q8C2×D311yescharacteristic
148C22×C3×Q8C2×D311yescharacteristic
149C22×C3×Q8C22×C311yescharacteristic
150C22×C3×Q8C22×C311yescharacteristic
151C2×C3×Q16—31no—
152C2×C3×Q16—31no—
153C2×C3×Q16—31no—
154C2×C3×M16—31no—
155C22×C3×C8—31no—
156C3×C4⋊Q8—22no—
157C3×C4⋊Q8—21no—
158C3×C4⋊Q8—21no—
159C3×C4⋊Q8—21no—
160C3×C4⋊Q8C2×D311yescharacteristic
161C3×C4⋊Q8C22×C311yescharacteristic
162C3×#126—61no—
163C3×#125—31no—
164C3×#125—61no—
165C3×#123—61no—
166C3×C22⋊Q8—22no—
167C3×C22⋊Q8—22no—
168C3×C22⋊Q8—21no—
169C3×C22⋊Q8—21no—
170C3×C22⋊Q8—21no—
171C3×C22⋊Q8—21no—
172C3×C22⋊Q8—21no—
173C3×C22⋊Q8—21no—
174C3×C22⋊Q8—31no—
175C3×C22⋊Q8—31no—
176C3×C22⋊Q8C2×D311yescharacteristic
177C3×C22⋊Q8C2×D311yescharacteristic
178C3×C22⋊Q8C22×C311yescharacteristic
179C3×C22⋊Q8C22×C311yescharacteristic
180C3×C4×Q8—21no—
181C3×C4×Q8—31no—
182C3×C4×Q8C2×D311yescharacteristic
183C3×C4×Q8C22×C311yescharacteristic
184C3×C4×D4—22no—
185C3×C4×D4—21no—
186C3×C4×D4—21no—
187C3×C4×D4—21no—
188C3×C4×D4C2×D311yescharacteristic
189C3×C4×D4C22×C311yescharacteristic
190C3×#117—31no—
191C3×#117—61no—
192C2×C3×C4⋊C4—31no—
193C2×#216C22×C311yescharacteristic
194C2×#216C22×C311yescharacteristic
195C2×#216C22×C311yescharacteristic
196#935—21no—
197#926C22×C311yescharacteristic
198C2×C4⋊Dic3C22×C311yescharacteristic
199#924C22×C311yescharacteristic
200#924C22×C311yescharacteristic
201C2×#208C22×C311yescharacteristic
202C22×C3⋊C8C22×C311yescharacteristic
203#889—21no—
204#879—21no—
205#877—21no—
206#870C22×C311yescharacteristic
207C4×Dic6C22×C311yescharacteristic
208C3×#107—31no—
209C3×#106—31no—
210C3×#106—31no—
211C3×C4⋊C8—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#103—31no—
217C3×#103—31no—
218C3×#103—31no—
219C3×#103—31no—
220C3×#103—31no—
221C3×#103—31no—
222C3×C22⋊C8—31no—
223C3×C22⋊C8—31no—
224C3×#97—31no—
225#835C22×C311yescharacteristic
226#835C22×C311yescharacteristic
227#835C22×C311yescharacteristic
228#835C22×C311yescharacteristic
229#835C22×C311yescharacteristic
230#835C22×C311yescharacteristic
231#835C22×C311yescharacteristic
232#835C22×C311yescharacteristic
233#835C22×C311yescharacteristic
234#830C22×C311yescharacteristic
235#830C22×C311yescharacteristic
236#810C22×C311yescharacteristic
237#808C22×C311yescharacteristic
238#808C22×C311yescharacteristic
239#807C22×C311yescharacteristic
240C4⋊(C3⋊C8)C22×C311yescharacteristic
241#803C22×C311yescharacteristic
242C23×C32C2×D411yescharacteristic
243C23×C32C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8—21no—
246C32×Q8—21no—
247C32×Q8—21no—
248C32×Q8—21no—
249C32×Q8—42no—
250C32×Q8—42no—
251C32×Q8#4112yes—
252C32×D4—22no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—42no—
262C2×C32×C4—42no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2×D411yescharacteristic
267C2×C32×C4C2411yescharacteristic
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—42no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—31no—
280D4×Q8C3×D311yescharacteristic
281#491—31no—
282#485—31no—
283#483—31no—
284#479—31no—
285#470—31no—
286#467—31no—
287#462—31no—
288#451—31no—
289#451—31no—
290#441—31no—
291#435—31no—
292#419—31no—
293C2×#103—31no—
294C2×C3×Q8—22no—
295C2×C3×Q8—22no—
296C2×C3×Q8—21no—
297C2×C3×Q8—21no—
298C2×C3×Q8—21no—
299C2×C3×Q8—21no—
300C2×C3×Q8—22no—
301C2×C3×Q8—22no—
302C2×C3×Q8—22no—
303C2×C3×Q8—22no—
304C2×C3×Q8—21no—
305C2×C3×Q8—21no—
306C2×C3×Q8—21no—
307C2×C3×Q8—31no—
308C2×C3×Q8—42no—
309C2×C3×Q8—42no—
310C2×C3×Q8—41no—
311C2×C3×Q8—41no—
312C2×C3×Q8—41no—
313C2×C3×Q8—41no—
314C2×C3×Q8—42no—
315C2×C3×Q8—42no—
316C2×C3×Q8C22×D311yescharacteristic
317C2×C3×Q8C22×D311yescharacteristic
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×Q8C23×C311yescharacteristic
320C2×C3×Q8C23×C311yescharacteristic
321C2×C3×Q8C23×C311yescharacteristic
322C2×C3×D4—21no—
323C2×C3×D4#6711yescharacteristic
324C2×C3×D4C3×D411yescharacteristic
325C22×C3×C4—22no—
326C22×C3×C4—22no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—61no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C23×C311yescharacteristic
337C22×C3×C4C23×C311yescharacteristic
338C22×Dic3—21no—
339C2×Dic6C23×C311yescharacteristic
340C3×Q16—62no—
341C3×Q16—121no—
342C3×Q16—121no—
343C3×M16—121no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8—31no—
348C2×C3×C8—121no—
349C3×C4⋊C4—22no—
350C3×C4⋊C4—22no—
351C3×C4⋊C4—22no—
352C3×C4⋊C4—22no—
353C3×C4⋊C4—22no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4#6711yescharacteristic
376C3×C4⋊C4C3×D411yescharacteristic
377C3×C4⋊C4C22×D311yescharacteristic
378C3×C4⋊C4C23×C311yescharacteristic
379C3×C22⋊C4—22no—
380C3×C22⋊C4—22no—
381C3×C22⋊C4—21no—
382C3×C22⋊C4—21no—
383C3×C22⋊C4—21no—
384C3×C22⋊C4—21no—
385C3×C22⋊C4—21no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—61no—
388C3×C22⋊C4—61no—
389C3×C22⋊C4—61no—
390C3×C22⋊C4#6711yescharacteristic
391C3×C22⋊C4#6711yescharacteristic
392C3×C22⋊C4C3×D411yescharacteristic
393C3×C22⋊C4C3×D411yescharacteristic
394C3×C42—22no—
395C3×C42—21no—
396C3×C42—21no—
397C3×C42—21no—
398C3×C42—61no—
399C3×C42—61no—
400C3×C42C22×D311yescharacteristic
401C3×C42C23×C311yescharacteristic
402#217—21no—
403#217—21no—
404#217—21no—
405#216—22no—
406#216—41no—
407#216—41no—
408C4⋊Dic3—21no—
409C4⋊Dic3C23×C311yescharacteristic
410C4⋊Dic3C23×C311yescharacteristic
411C4⋊Dic3C23×C311yescharacteristic
412Dic3⋊C4—21no—
413Dic3⋊C4—21no—
414Dic3⋊C4—21no—
415Dic3⋊C4—21no—
416Dic3⋊C4—21no—
417C4×Dic3—21no—
418C4×Dic3—21no—
419#208—41no—
420C2×C3⋊C8—41no—
421C2×C3⋊C8C23×C311yescharacteristic
422C2×C3⋊C8C23×C311yescharacteristic
423C2×C3⋊C8C23×C311yescharacteristic
424C2×C3⋊C8C23×C311yescharacteristic
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32#13712yes—
431C22×C32C22×D411yescharacteristic
432C32×C4—22no—
433C32×C4—21no—
434C32×C4—21no—
435C32×C4—21no—
436C32×C4—21no—
437C32×C4—41no—
438C32×C4—41no—
439C32×C4—41no—
440C32×C4C2×#4111yescharacteristic
441C32×C4H(5,𝔽2)11yescharacteristic
442C3×Dic3—41no—
443C3×Dic3—41no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C22×Q8C2×C3×D311yescharacteristic
447C22×Q8C2×C3×D311yescharacteristic
448C2×Q16—31no—
449C2×Q16—31no—
450C2×Q16—31no—
451C2×M16—31no—
452C22×C8—31no—
453C4⋊Q8—21no—
454C4⋊Q8C2×C3×D311yescharacteristic
455#126—61no—
456#125—31no—
457#125—61no—
458#123—61no—
459C22⋊Q8—21no—
460C22⋊Q8—21no—
461C22⋊Q8—31no—
462C22⋊Q8—31no—
463C22⋊Q8C2×C3×D311yescharacteristic
464C22⋊Q8C2×C3×D311yescharacteristic
465C4×Q8—31no—
466C4×Q8C2×C3×D311yescharacteristic
467C4×D4—21no—
468C4×D4C2×C3×D311yescharacteristic
469#117—31no—
470#117—61no—
471C2×C4⋊C4—31no—
472#107—31no—
473#106—31no—
474#106—31no—
475C4⋊C8—31no—
476#103—31no—
477#103—31no—
478#103—31no—
479#103—31no—
480#103—31no—
481#103—31no—
482#103—31no—
483#103—31no—
484#103—31no—
485#103—31no—
486C22⋊C8—31no—
487C22⋊C8—31no—
488#97—31no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3C2×#6711yescharacteristic
492C23×C3C2×#6711yescharacteristic
493C23×C3C2×C3×D411yescharacteristic
494C23×C3C2×C3×D411yescharacteristic
495C3×Q8—22no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—22no—
507C3×Q8—41no—
508C3×Q8—41no—
509C3×Q8—41no—
510C3×Q8—41no—
511C3×Q8—42no—
512C3×Q8—42no—
513C3×Q8—42no—
514C3×Q8—42no—
515C3×Q8—44no—
516C3×Q8—44no—
517C3×Q8—61no—
518C3×Q8—61no—
519C3×Q8#23712yes—
520C3×Q8C3×#4112yes—
521C3×D4—24no—
522C3×D4—22no—
523C3×D4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—42no—
554C2×C3×C4—42no—
555C2×C3×C4—42no—
556C2×C3×C4—42no—
557C2×C3×C4—44no—
558C2×C3×C4—44no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—122no—
564C2×C3×C4C2×#6711yescharacteristic
565C2×C3×C4C2×#6711yescharacteristic
566C2×C3×C4C2×#6711yescharacteristic
567C2×C3×C4C2×#6711yescharacteristic
568C2×C3×C4C2×C3×D411yescharacteristic
569C2×C3×C4C2×C3×D411yescharacteristic
570C2×C3×C4C2×C3×D411yescharacteristic
571C2×C3×C4C2×C3×D411yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573C2×C3×C4C24×C311yescharacteristic
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—42no—
579Dic6—21no—
580Dic6—21no—
581C3×C8—61no—
582C3×C8—61no—
583C3×C8—61no—
584C3×C8—61no—
585C3⋊C8—21no—
586C3⋊C8—21no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C2×C32—22no—
590C2×C32—41no—
591C2×C32#54611yescharacteristic
592C2×C32C2×#13711yescharacteristic
593C2×C32#57811yescharacteristic
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—22no—
597C2×Q8—22no—
598C2×Q8—31no—
599C2×Q8—41no—
600C2×Q8—41no—
601C2×Q8C22×C3×D311yescharacteristic
602C2×Q8C22×C3×D311yescharacteristic
603C2×Q8C22×C3×D311yescharacteristic
604C2×D4C3×#6711yescharacteristic
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—61no—
608C22×C4C22×C3×D311yescharacteristic
609C22×C4C22×C3×D311yescharacteristic
610Q16—62no—
611Q16—121no—
612Q16—121no—
613M16—121no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—121no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—31no—
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—61no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4C3×#6711yescharacteristic
634C4⋊C4C22×C3×D311yescharacteristic
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4C3×#6711yescharacteristic
641C22⋊C4C3×#6711yescharacteristic
642C42—21no—
643C42—61no—
644C42—61no—
645C42C22×C3×D311yescharacteristic
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—22no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—22no—
658C22×C3—21no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3#94212yes—
664C22×C3C3×#13712yes—
665C22×C3C22×#6711yescharacteristic
666C22×C3C22×C3×D411yescharacteristic
667C3×C4—24no—
668C3×C4—22no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—22no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—22no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—42no—
685C3×C4—42no—
686C3×C4—42no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—121no—
694C3×C4—121no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4C2×#23711yescharacteristic
698C3×C4#100411yescharacteristic
699C3×C4C2×C3×#4111yescharacteristic
700C3×C4C3×H(5,𝔽2)11yescharacteristic
701Dic3—41no—
702Dic3—41no—
703Dic3—41no—
704Dic3—41no—
705C32#331211yescharacteristic, complemented, Sylow
706C23C2×C3×#6711yescharacteristic
707C23C2×C3×#6711yescharacteristic
708Q8—21no—
709Q8—21no—
710Q8—21no—
711Q8—21no—
712Q8—21no—
713Q8—42no—
714Q8—42no—
715Q8—61no—
716Q8—61no—
717Q8C3×#23712yes—
718D4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—122no—
734C2×C4C2×C3×#6711yescharacteristic
735C2×C4C2×C3×#6711yescharacteristic
736C2×C4C2×C3×#6711yescharacteristic
737C2×C4C2×C3×#6711yescharacteristic
738C2×C4C23×C3×D311yescharacteristic
739C8—61no—
740C8—61no—
741C8—61no—
742C8—61no—
743C2×C3—22no—
744C2×C3—22no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—42no—
749C2×C3—42no—
750C2×C3—41no—
751C2×C3—41no—
752C2×C3#580611yescharacteristic
753C2×C3C2×#94211yescharacteristic
754C2×C3#583811yescharacteristic
755C2×C3C3×#54611yescharacteristic
756C2×C3C2×C3×#13711yescharacteristic
757C2×C3C3×#57811yescharacteristic
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22C3×#94212yes—
764C22C22×C3×#6711yescharacteristic
765C4—21no—
766C4—21no—
767C4—22no—
768C4—21no—
769C4—21no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—121no—
774C4—121no—
775C4—121no—
776C4—121no—
777C4C2×C3×#23711yescharacteristic
778C4C3×#100411yescharacteristic
779C3—21no—
780C3#8355211yescharacteristic, direct product factor
781C3C3×#331211yescharacteristic, complemented
782C2—22no—
783C2—41no—
784C2C3×#580611yescharacteristic
785C2C2×C3×#94211yescharacteristic
786C2C3×#583811yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×D4×Q8C2
socleC22×C32C22×D4
prime radicalC2×C32×D4D4
hypercenterC3×D4×Q8D3
hypocenterC3C3×#3312
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×D4×Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5228C2semidirect
4. C3×#5228C2semidirect
5. C3×#5225C2semidirect
6. C2×C3×#835C2semidirect
7. C3×#5090C2semidirect
8. C3×#5082C2semidirect
9. C3×#5052C2semidirect
10. C3×#5051C2semidirect
11. C3×#5045C2semidirect
12. C3×#5043C2semidirect
13. C3×#5030C2semidirect
14. C3×#5022C2semidirect
17. #83552C3direct (N × H)
79. #5228C2×C3semidirect
80. #5228C2×C3semidirect
81. #5225C2×C3semidirect
82. C2×#835C2×C3semidirect
83. #5090C2×C3semidirect
84. #5082C2×C3semidirect
85. #5052C2×C3semidirect
86. #5051C2×C3semidirect
87. #5045C2×C3semidirect
88. #5043C2×C3semidirect
89. #5030C2×C3semidirect
90. #5022C2×C3semidirect
705. C32#3312semidirect
780. C3#83552direct (N × H)
781. C3C3×#3312semidirect

Maximal subgroups

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

subgroupindex
C32×D4×Q82
C3×#55412
C3×#52282
C3×#52252
C2×C3×#8352
C3×#50902
C3×#50822
C3×#50522
C3×#50512
C3×#50452
C3×#50432
C3×#50302
C3×#50222
C3×#50112
C3×#33123
#835523