Finite Group Databasebeta

← C3×#83603 #11889328

Subgroups — C3×#83603 #11889328

Order 1152.

859 conjugacy classes of subgroups.

The subgroup lattice has 777 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#552C211yesmaximal, characteristic
2C3×D4×Dic6C211yesmaximal, characteristic
3C3×#5069C211yesmaximal, characteristic, complemented
4C3×#5063C211yesmaximal, characteristic, complemented
5C3×#5052C211yesmaximal, characteristic, complemented
6C3×#5051C211yesmaximal, characteristic, complemented
7C3×#5050C211yesmaximal, characteristic, complemented
8C3×#5050C211yesmaximal, characteristic, complemented
9C3×#5031C211yesmaximal, characteristic, complemented
10C3×#5030C211yesmaximal, characteristic, complemented
11C3×#5011C211yesmaximal, characteristic
12C3×#5004C211yesmaximal, characteristic, complemented
13C3×#4996C211yesmaximal, characteristic, complemented
14C3×#4971C211yesmaximal, characteristic, complemented
15C2×C3×#810C211yesmaximal, characteristic, complemented
16C3×#3312—31nomaximal
17#83603C311yesmaximal, characteristic, direct product factor
18C22×C3×Dic6C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C32×#126—21no—
21C32×#125—21no—
22C32×#125C2211yescharacteristic
23C32×#123—21no—
24C32×C22⋊Q8C2211yescharacteristic
25C32×C22⋊Q8C2211yescharacteristic
26C32×C4×Q8C2211yescharacteristic
27C32×C4×D4C2211yescharacteristic
28C32×#117—21no—
29C32×#117C2211yescharacteristic
30C2×C32×C4⋊C4C2211yescharacteristic
31C2×C3×#216C2211yescharacteristic
32C2×C3×#216C2211yescharacteristic
33C2×C3×#216C2211yescharacteristic
34C3×D4×Dic3—21no—
35C3×#924C2211yescharacteristic
36C3×#924C2211yescharacteristic
37C2×C3×#208C2211yescharacteristic
38C22×C3×C3⋊C8C2211yescharacteristic
39C3×#888—21no—
40C3×#878—21no—
41C3×#878—21no—
42C3×#869C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#830C2211yescharacteristic
46C3×#830C2211yescharacteristic
47C3×#810C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#810C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#808C2211yescharacteristic
57C3×#808C2211yescharacteristic
58C3×#807C2211yescharacteristic
59C3×C4⋊(C3⋊C8)C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#552—21no—
62C3×#552D311yescharacteristic
63C3×#552C2×C311yescharacteristic
64C3×D4×Q8—31no—
65D4×Dic6C2×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#5069C2×C311yescharacteristic, complemented
80#5063C2×C311yescharacteristic, complemented
81#5052C2×C311yescharacteristic, complemented
82#5051C2×C311yescharacteristic, complemented
83#5050C2×C311yescharacteristic, complemented
84#5050C2×C311yescharacteristic, complemented
85#5031C2×C311yescharacteristic, complemented
86#5030C2×C311yescharacteristic, complemented
87#5011C2×C311yescharacteristic
88#5004C2×C311yescharacteristic, complemented
89#4996C2×C311yescharacteristic, complemented
90#4971C2×C311yescharacteristic, complemented
91C2×#810C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4D411yescharacteristic
94C22×C32×C4—21no—
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C2×C3×Dic6—22no—
100C2×C3×Dic6—22no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6—41no—
104C2×C3×Dic6—41no—
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
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⋊C4—21no—
114C32×C4⋊C4D411yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C32×C22⋊C4—21no—
120C32×C22⋊C4—21no—
121C32×C22⋊C4D411yescharacteristic
122C32×C22⋊C4D411yescharacteristic
123C32×C42—21no—
124C32×C42—21no—
125C32×C42C2311yescharacteristic
126C3×#217—21no—
127C3×#217—21no—
128C3×#216—22no—
129C3×#216—41no—
130C3×#216—41no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—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—31no—
146C22×C3×Q8—31no—
147C22×Dic6C22×C311yescharacteristic
148C22×Dic6C22×C311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C2×C3×Q16—31no—
152C2×C3×M16—31no—
153C22×C3×C8—31no—
154C3×C4⋊Q8—31no—
155C3×C4⋊Q8—61no—
156C3×#126—22no—
157C3×#126—21no—
158C3×#126—21no—
159C3×#125—22no—
160C3×#125—21no—
161C3×#125—21no—
162C3×#125—21no—
163C3×#125C2×D311yescharacteristic
164C3×#125C22×C311yescharacteristic
165C3×#123—22no—
166C3×#123—21no—
167C3×#123—21no—
168C3×C22⋊Q8—21no—
169C3×C22⋊Q8—21no—
170C3×C22⋊Q8—31no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—61no—
173C3×C22⋊Q8—61no—
174C3×C22⋊Q8C2×D311yescharacteristic
175C3×C22⋊Q8C2×D311yescharacteristic
176C3×C22⋊Q8C22×C311yescharacteristic
177C3×C22⋊Q8C22×C311yescharacteristic
178C3×C4×Q8—21no—
179C3×C4×Q8—31no—
180C3×C4×Q8C2×D311yescharacteristic
181C3×C4×Q8C22×C311yescharacteristic
182C3×C4×D4—21no—
183C3×C4×D4—61no—
184C3×C4×D4C2×D311yescharacteristic
185C3×C4×D4C22×C311yescharacteristic
186C3×#117—22no—
187C3×#117—21no—
188C3×#117—21no—
189C3×#117—21no—
190C3×#117C2×D311yescharacteristic
191C3×#117C22×C311yescharacteristic
192C2×C3×C4⋊C4—21no—
193C2×C3×C4⋊C4C2×D311yescharacteristic
194C2×C3×C4⋊C4C22×C311yescharacteristic
195C2×#216C22×C311yescharacteristic
196C2×#216C22×C311yescharacteristic
197C2×#216C22×C311yescharacteristic
198D4×Dic3—21no—
199#924C22×C311yescharacteristic
200#924C22×C311yescharacteristic
201C2×#208C22×C311yescharacteristic
202C22×C3⋊C8C22×C311yescharacteristic
203#888—21no—
204#878—21no—
205#878—21no—
206#869C22×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#830C22×C311yescharacteristic
227#830C22×C311yescharacteristic
228#810C22×C311yescharacteristic
229#810C22×C311yescharacteristic
230#810C22×C311yescharacteristic
231#810C22×C311yescharacteristic
232#810C22×C311yescharacteristic
233#810C22×C311yescharacteristic
234#810C22×C311yescharacteristic
235#810C22×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×D4—22no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—42no—
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2411yescharacteristic
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—42no—
266C2×C3×Dic3—42no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—42no—
273C3×Dic6—42no—
274C3×Dic6#4112yes—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552C3×D311yescharacteristic
280D4×Q8—31no—
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—21no—
295C2×C3×Q8—31no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×Q8—62no—
299C2×C3×Q8—62no—
300C2×C3×Q8—61no—
301C2×C3×Q8—61no—
302C2×C3×Q8—121no—
303C2×C3×Q8—121no—
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×Q8C23×C311yescharacteristic
306C2×C3×D4—21no—
307C2×C3×D4#6711yescharacteristic
308C2×C3×D4C3×D411yescharacteristic
309C22×C3×C4—22no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C23×C311yescharacteristic
319C22×C3×C4C23×C311yescharacteristic
320C22×Dic3—21no—
321C22×Dic3—21no—
322C2×Dic6—22no—
323C2×Dic6—22no—
324C2×Dic6—21no—
325C2×Dic6—21no—
326C2×Dic6—41no—
327C2×Dic6—41no—
328C2×Dic6C23×C311yescharacteristic
329C2×Dic6C23×C311yescharacteristic
330C2×Dic6C23×C311yescharacteristic
331C3×Q16—62no—
332C3×Q16—121no—
333C3×Q16—121no—
334C3×M16—121no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8—121no—
340C3×C4⋊C4—22no—
341C3×C4⋊C4—22no—
342C3×C4⋊C4—22no—
343C3×C4⋊C4—22no—
344C3×C4⋊C4—22no—
345C3×C4⋊C4—22no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
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—21no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4#6711yescharacteristic
369C3×C4⋊C4C3×D411yescharacteristic
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C4⋊C4C22×D311yescharacteristic
372C3×C4⋊C4C22×D311yescharacteristic
373C3×C4⋊C4C23×C311yescharacteristic
374C3×C4⋊C4C23×C311yescharacteristic
375C3×C4⋊C4C23×C311yescharacteristic
376C3×C22⋊C4—22no—
377C3×C22⋊C4—22no—
378C3×C22⋊C4—22no—
379C3×C22⋊C4—21no—
380C3×C22⋊C4—21no—
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#6711yescharacteristic
390C3×C22⋊C4#6711yescharacteristic
391C3×C22⋊C4C3×D411yescharacteristic
392C3×C22⋊C4C3×D411yescharacteristic
393C3×C42—22no—
394C3×C42—22no—
395C3×C42—21no—
396C3×C42—21no—
397C3×C42—21no—
398C3×C42—21no—
399C3×C42—21no—
400C3×C42—61no—
401C3×C42C22×D311yescharacteristic
402C3×C42C23×C311yescharacteristic
403#217—21no—
404#217—21no—
405#216—22no—
406#216—41no—
407#216—41no—
408C4⋊Dic3—21no—
409C4⋊Dic3—21no—
410C4⋊Dic3C23×C311yescharacteristic
411Dic3⋊C4—21no—
412Dic3⋊C4—21no—
413Dic3⋊C4—21no—
414C4×Dic3—21no—
415#208—41no—
416C2×C3⋊C8—41no—
417C2×C3⋊C8C23×C311yescharacteristic
418C2×C3⋊C8C23×C311yescharacteristic
419C2×C3⋊C8C23×C311yescharacteristic
420C2×C3⋊C8C23×C311yescharacteristic
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32#13712yes—
427C22×C32C22×D411yescharacteristic
428C32×C4—21no—
429C32×C4—21no—
430C32×C4—21no—
431C32×C4—21no—
432C32×C4—41no—
433C32×C4—41no—
434C32×C4—41no—
435C32×C4—41no—
436C32×C4C2×#4111yescharacteristic
437C32×C4H(5,𝔽2)11yescharacteristic
438C3×Dic3—22no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C22×Q8—31no—
443C22×Q8—31no—
444C2×Q16—31no—
445C2×Q16—31no—
446C2×Q16—31no—
447C2×M16—31no—
448C22×C8—31no—
449C4⋊Q8—31no—
450C4⋊Q8—61no—
451#126—21no—
452#125—21no—
453#125C2×C3×D311yescharacteristic
454#123—21no—
455C22⋊Q8—31no—
456C22⋊Q8—31no—
457C22⋊Q8—61no—
458C22⋊Q8—61no—
459C22⋊Q8C2×C3×D311yescharacteristic
460C22⋊Q8C2×C3×D311yescharacteristic
461C4×Q8—31no—
462C4×Q8C2×C3×D311yescharacteristic
463C4×D4—61no—
464C4×D4C2×C3×D311yescharacteristic
465#117—21no—
466#117C2×C3×D311yescharacteristic
467C2×C4⋊C4C2×C3×D311yescharacteristic
468#107—31no—
469#106—31no—
470#106—31no—
471C4⋊C8—31no—
472#103—31no—
473#103—31no—
474#103—31no—
475#103—31no—
476#103—31no—
477#103—31no—
478#103—31no—
479#103—31no—
480#103—31no—
481#103—31no—
482C22⋊C8—31no—
483C22⋊C8—31no—
484#97—31no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3C2×#6711yescharacteristic
488C23×C3C2×#6711yescharacteristic
489C23×C3C2×C3×D411yescharacteristic
490C23×C3C2×C3×D411yescharacteristic
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—32no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×Q8—61no—
499C3×Q8—61no—
500C3×Q8—61no—
501C3×Q8—61no—
502C3×Q8—61no—
503C3×Q8—122no—
504C3×Q8—122no—
505C3×D4—22no—
506C3×D4—22no—
507C3×D4—42no—
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—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
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—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—44no—
538C2×C3×C4—42no—
539C2×C3×C4—42no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—122no—
545C2×C3×C4—122no—
546C2×C3×C4C2×#6711yescharacteristic
547C2×C3×C4C2×#6711yescharacteristic
548C2×C3×C4C2×#6711yescharacteristic
549C2×C3×C4C2×#6711yescharacteristic
550C2×C3×C4C2×C3×D411yescharacteristic
551C2×C3×C4C2×C3×D411yescharacteristic
552C2×C3×C4C2×C3×D411yescharacteristic
553C2×C3×C4C2×C3×D411yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555C2×C3×C4C24×C311yescharacteristic
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—42no—
561C2×Dic3—42no—
562Dic6—21no—
563Dic6—21no—
564Dic6—21no—
565Dic6—21no—
566Dic6—21no—
567Dic6—42no—
568Dic6—42no—
569Dic6C3×#4112yes—
570C3×C8—61no—
571C3×C8—61no—
572C3×C8—61no—
573C3×C8—61no—
574C3⋊C8—21no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C2×C32—22no—
579C2×C32—41no—
580C2×C32#54611yescharacteristic
581C2×C32C2×#13711yescharacteristic
582C2×C32#57811yescharacteristic
583C2×Q8—31no—
584C2×Q8—31no—
585C2×Q8—31no—
586C2×Q8—62no—
587C2×Q8—62no—
588C2×Q8—61no—
589C2×Q8—61no—
590C2×Q8—121no—
591C2×Q8—121no—
592C2×Q8C22×C3×D311yescharacteristic
593C2×D4C3×#6711yescharacteristic
594C22×C4—21no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4C22×C3×D311yescharacteristic
598C22×C4C22×C3×D311yescharacteristic
599Q16—62no—
600Q16—121no—
601Q16—121no—
602M16—121no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—31no—
606C2×C8—31no—
607C2×C8—121no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—31no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4C3×#6711yescharacteristic
621C4⋊C4C22×C3×D311yescharacteristic
622C4⋊C4C22×C3×D311yescharacteristic
623C4⋊C4C22×C3×D311yescharacteristic
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4C3×#6711yescharacteristic
630C22⋊C4C3×#6711yescharacteristic
631C42—21no—
632C42—21no—
633C42—61no—
634C42C22×C3×D311yescharacteristic
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—22no—
646C22×C3—21no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3#95112yes—
653C22×C3C3×#13712yes—
654C22×C3C22×#6711yescharacteristic
655C22×C3C22×C3×D411yescharacteristic
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—42no—
671C3×C4—42no—
672C3×C4—42no—
673C3×C4—42no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—62no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4D3×#4111yescharacteristic
687C3×C4#100911yescharacteristic
688C3×C4C2×C3×#4111yescharacteristic
689C3×C4C3×H(5,𝔽2)11yescharacteristic
690Dic3—22no—
691Dic3—41no—
692Dic3—41no—
693Dic3—41no—
694C32#331211yescharacteristic, complemented, Sylow
695C23C2×C3×#6711yescharacteristic
696C23C2×C3×#6711yescharacteristic
697Q8—21no—
698Q8—21no—
699Q8—32no—
700Q8—61no—
701Q8—61no—
702Q8—61no—
703Q8—61no—
704Q8—61no—
705Q8—122no—
706Q8—122no—
707D4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—42no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—122no—
722C2×C4—122no—
723C2×C4C2×C3×#6711yescharacteristic
724C2×C4C2×C3×#6711yescharacteristic
725C2×C4C2×C3×#6711yescharacteristic
726C2×C4C2×C3×#6711yescharacteristic
727C2×C4C23×C3×D311yescharacteristic
728C8—61no—
729C8—61no—
730C8—61no—
731C8—61no—
732C2×C3—22no—
733C2×C3—22no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3—41no—
739C2×C3—41no—
740C2×C3—81no—
741C2×C3C2×#95111yescharacteristic
742C2×C3#582911yescharacteristic
743C2×C3#583811yescharacteristic
744C2×C3C3×#54611yescharacteristic
745C2×C3C2×C3×#13711yescharacteristic
746C2×C3C3×#57811yescharacteristic
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22C3×#95112yes—
753C22C22×C3×#6711yescharacteristic
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—62no—
763C4—121no—
764C4—121no—
765C4—121no—
766C4C3×D3×#4111yescharacteristic
767C4C3×#100911yescharacteristic
768C3—21no—
769C3#8360311yescharacteristic, direct product factor
770C3C3×#331211yescharacteristic, complemented
771C2—22no—
772C2—41no—
773C2C2×C3×#95111yescharacteristic
774C2C3×#582911yescharacteristic
775C2C3×#583811yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#552C2
socleC22×C32C22×D4
prime radicalC2×C32×D4D4
hypercenterC3×#552D3
hypocenterC3C3×#3312
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#552

Complements

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

NH ≅ G/Ntype
3. C3×#5069C2semidirect
4. C3×#5063C2semidirect
5. C3×#5052C2semidirect
6. C3×#5051C2semidirect
7. C3×#5050C2semidirect
8. C3×#5050C2semidirect
9. C3×#5031C2semidirect
10. C3×#5030C2semidirect
12. C3×#5004C2semidirect
13. C3×#4996C2semidirect
14. C3×#4971C2semidirect
15. C2×C3×#810C2semidirect
17. #83603C3direct (N × H)
79. #5069C2×C3semidirect
80. #5063C2×C3semidirect
81. #5052C2×C3semidirect
82. #5051C2×C3semidirect
83. #5050C2×C3semidirect
84. #5050C2×C3semidirect
85. #5031C2×C3semidirect
86. #5030C2×C3semidirect
88. #5004C2×C3semidirect
89. #4996C2×C3semidirect
90. #4971C2×C3semidirect
91. C2×#810C2×C3semidirect
694. C32#3312semidirect
769. C3#83603direct (N × H)
770. C3C3×#3312semidirect

Maximal subgroups

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

subgroupindex
C32×#5522
C3×D4×Dic62
C3×#50692
C3×#50632
C3×#50522
C3×#50512
C3×#50502
C3×#50312
C3×#50302
C3×#50112
C3×#50042
C3×#49962
C3×#49712
C2×C3×#8102
C3×#33123
#836033