Finite Group Databasebeta

← C3×#83467 #11872546

Subgroups — C3×#83467 #11872546

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#542C211yesmaximal, characteristic
2C3×#5516C211yesmaximal, characteristic, complemented
3C3×#5094C211yesmaximal, characteristic, complemented
4C3×#5091C211yesmaximal, characteristic, complemented
5C3×#5054C211yesmaximal, characteristic, complemented
6C3×#5054C211yesmaximal, characteristic, complemented
7C3×#5050C211yesmaximal, characteristic, complemented
8C3×#5045C211yesmaximal, characteristic, complemented
9C3×#5040C211yesmaximal, characteristic
10C3×#5035C211yesmaximal, characteristic
11C3×#5030C211yesmaximal, characteristic, complemented
12C3×C4×#216C211yesmaximal, characteristic, complemented
13C3×#5018C211yesmaximal, characteristic, complemented
14C3×C4×#214C211yesmaximal, characteristic, complemented
15C3×#5000C211yesmaximal, characteristic, complemented
16C3×#3121—31nomaximal
17#83467C311yesmaximal, characteristic, direct product factor
18C22×C3×Dic6C2211yescharacteristic
19C32×C4⋊Q8C2211yescharacteristic
20C32×#126—21no—
21C32×#124—21no—
22C32×#124C2211yescharacteristic
23C32×#123—21no—
24C32×C22⋊Q8—21no—
25C32×C22⋊Q8C2211yescharacteristic
26C32×#121C2211yescharacteristic
27C32×C4×Q8C2211yescharacteristic
28C32×C4×D4C2211yescharacteristic
29C32×#117C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C2×C3×#216C2211yescharacteristic
32C2×C3×#214C2211yescharacteristic
33C2×C3×#214C2211yescharacteristic
34C3×#926C2211yescharacteristic
35C3×#887—21no—
36C3×#887—21no—
37C3×#877—21no—
38C3×#877—21no—
39C3×C4×Dic6C2211yescharacteristic
40C3×C4×Dic6C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C3×#835C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#830C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#808C2211yescharacteristic
54C3×#808C2211yescharacteristic
55C3×#807C2211yescharacteristic
56C3×#807C2211yescharacteristic
57C3×C4⋊(C3⋊C8)C2211yescharacteristic
58C3×C4⋊(C3⋊C8)C2211yescharacteristic
59C3×#803C2211yescharacteristic
60C3×C4×C3⋊C8C2211yescharacteristic
61C3×#542—21no—
62C3×#542D311yescharacteristic
63C3×#542C2×C311yescharacteristic
64C3×#519—31no—
65#5516C2×C311yescharacteristic, complemented
66C3×#485—31no—
67C3×#482—31no—
68C3×#477—31no—
69C3×#475—31no—
70C3×#464—31no—
71C3×#464—31no—
72C3×#451—31no—
73C3×#448—31no—
74C3×#441—31no—
75C3×#440—31no—
76C3×C4×Q16—31no—
77C3×C4×SD16—31no—
78C3×#433—31no—
79#5094C2×C311yescharacteristic, complemented
80#5091C2×C311yescharacteristic, complemented
81#5054C2×C311yescharacteristic, complemented
82#5054C2×C311yescharacteristic, complemented
83#5050C2×C311yescharacteristic, complemented
84#5045C2×C311yescharacteristic, complemented
85#5040C2×C311yescharacteristic
86#5035C2×C311yescharacteristic
87#5030C2×C311yescharacteristic, complemented
88C4×#216C2×C311yescharacteristic, complemented
89#5018C2×C311yescharacteristic, complemented
90C4×#214C2×C311yescharacteristic, complemented
91#5000C2×C311yescharacteristic, complemented
92C2×C32×Q8—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4—21no—
97C22×C32×C4C2311yescharacteristic
98C22×C3×Dic3—21no—
99C2×C3×Dic6—21no—
100C2×C3×Dic6—22no—
101C2×C3×Dic6—22no—
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C32×C4⋊C4—21no—
105C32×C4⋊C4—21no—
106C32×C4⋊C4—21no—
107C32×C4⋊C4D411yescharacteristic
108C32×C4⋊C4D411yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C22⋊C4—21no—
113C32×C22⋊C4—21no—
114C32×C22⋊C4—21no—
115C32×C22⋊C4—21no—
116C32×C22⋊C4D411yescharacteristic
117C32×C22⋊C4D411yescharacteristic
118C32×C42—21no—
119C32×C42C2311yescharacteristic
120C32×C42C2311yescharacteristic
121C3×#217—21no—
122C3×#216—22no—
123C3×#216—22no—
124C3×#214—22no—
125C3×#214—22no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3121—31noSylow
142C22×C3×Q8—31no—
143C22×Dic6C22×C311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×Q16—31no—
146C2×C3×SD16—31no—
147C2×C3×SD16—31no—
148C3×C4⋊Q8—21no—
149C3×C4⋊Q8C2×D311yescharacteristic
150C3×C4⋊Q8C22×C311yescharacteristic
151C3×#126—22no—
152C3×#126—21no—
153C3×#126—21no—
154C3×#124—22no—
155C3×#124—21no—
156C3×#124—21no—
157C3×#124—21no—
158C3×#124C2×D311yescharacteristic
159C3×#124C22×C311yescharacteristic
160C3×#123—22no—
161C3×#123—21no—
162C3×#123—21no—
163C3×C22⋊Q8—22no—
164C3×C22⋊Q8—21no—
165C3×C22⋊Q8—21no—
166C3×C22⋊Q8—21no—
167C3×C22⋊Q8C2×D311yescharacteristic
168C3×C22⋊Q8C22×C311yescharacteristic
169C3×#121—21no—
170C3×#121C2×D311yescharacteristic
171C3×#121C22×C311yescharacteristic
172C3×C4×Q8—21no—
173C3×C4×Q8—31no—
174C3×C4×Q8—31no—
175C3×C4×Q8—31no—
176C3×C4×Q8—31no—
177C3×C4×Q8—61no—
178C3×C4×Q8—61no—
179C3×C4×Q8C2×D311yescharacteristic
180C3×C4×Q8C22×C311yescharacteristic
181C3×C4×D4—21no—
182C3×C4×D4C2×D311yescharacteristic
183C3×C4×D4C22×C311yescharacteristic
184C3×#117—21no—
185C3×#117—31no—
186C3×#117—61no—
187C3×#117—61no—
188C3×#117C2×D311yescharacteristic
189C3×#117C22×C311yescharacteristic
190C2×#216C22×C311yescharacteristic
191C2×#216C22×C311yescharacteristic
192C2×#214C22×C311yescharacteristic
193C2×#214C22×C311yescharacteristic
194#926C22×C311yescharacteristic
195#887—21no—
196#887—21no—
197#877—21no—
198#877—21no—
199C4×Dic6C22×C311yescharacteristic
200C4×Dic6C22×C311yescharacteristic
201C4×Dic6C22×C311yescharacteristic
202C4×Dic6C22×C311yescharacteristic
203C3×#107—31no—
204C3×#107—31no—
205C3×#106—31no—
206C3×#106—31no—
207C3×C4⋊C8—31no—
208C3×C4⋊C8—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×C22⋊C8—31no—
218C3×C22⋊C8—31no—
219C3×#97—31no—
220C3×C4×C8—31no—
221#835C22×C311yescharacteristic
222#835C22×C311yescharacteristic
223#832C22×C311yescharacteristic
224#832C22×C311yescharacteristic
225#830C22×C311yescharacteristic
226#830C22×C311yescharacteristic
227#810C22×C311yescharacteristic
228#810C22×C311yescharacteristic
229#810C22×C311yescharacteristic
230#810C22×C311yescharacteristic
231#808C22×C311yescharacteristic
232#808C22×C311yescharacteristic
233#807C22×C311yescharacteristic
234#807C22×C311yescharacteristic
235C4⋊(C3⋊C8)C22×C311yescharacteristic
236C4⋊(C3⋊C8)C22×C311yescharacteristic
237#803C22×C311yescharacteristic
238C4×C3⋊C8C22×C311yescharacteristic
239C23×C32—21no—
240C23×C32C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—81no—
244C32×D4—21no—
245C32×D4—21no—
246C32×D4—81no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—81no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259C2×C3×Dic3—24no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C3×Dic6—24no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6#4112yes—
268C3×Dic6#4112yes—
269C3×C3⋊C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272C3×C3⋊C8—21no—
273#542C3×D311yescharacteristic
274#519—31no—
275#485—31no—
276#482—31no—
277#477—31no—
278#475—31no—
279#464—31no—
280#464—31no—
281#451—31no—
282#448—31no—
283#441—31no—
284#440—31no—
285C4×Q16—31no—
286C4×SD16—31no—
287#433—31no—
288C2×C3×Q8—22no—
289C2×C3×Q8—21no—
290C2×C3×Q8—21no—
291C2×C3×Q8—21no—
292C2×C3×Q8—31no—
293C2×C3×Q8—31no—
294C2×C3×Q8—62no—
295C2×C3×Q8—62no—
296C2×C3×Q8—61no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C23×C311yescharacteristic
299C2×C3×D4—22no—
300C2×C3×D4—21no—
301C2×C3×D4—21no—
302C2×C3×D4—21no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C23×C311yescharacteristic
305C22×C3×C4—22no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—61no—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C23×C311yescharacteristic
312C22×Dic3—21no—
313C2×Dic6—21no—
314C2×Dic6—22no—
315C2×Dic6—22no—
316C2×Dic6C23×C311yescharacteristic
317C2×Dic6C23×C311yescharacteristic
318C3×Q16—62no—
319C3×Q16—62no—
320C3×SD16—62no—
321C3×SD16—62no—
322C2×C3×C8—31no—
323C2×C3×C8—31no—
324C2×C3×C8—31no—
325C2×C3×C8—31no—
326C3×C4⋊C4—22no—
327C3×C4⋊C4—22no—
328C3×C4⋊C4—22no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4#6711yescharacteristic
346C3×C4⋊C4#6711yescharacteristic
347C3×C4⋊C4C3×D411yescharacteristic
348C3×C4⋊C4C3×D411yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C23×C311yescharacteristic
352C3×C4⋊C4C23×C311yescharacteristic
353C3×C22⋊C4—22no—
354C3×C22⋊C4—22no—
355C3×C22⋊C4—22no—
356C3×C22⋊C4—22no—
357C3×C22⋊C4—22no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—21no—
367C3×C22⋊C4—21no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—21no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4#6711yescharacteristic
372C3×C22⋊C4#6711yescharacteristic
373C3×C22⋊C4C3×D411yescharacteristic
374C3×C22⋊C4C3×D411yescharacteristic
375C3×C42—22no—
376C3×C42—21no—
377C3×C42—21no—
378C3×C42—21no—
379C3×C42—21no—
380C3×C42—61no—
381C3×C42—61no—
382C3×C42—61no—
383C3×C42—61no—
384C3×C42—61no—
385C3×C42C22×D311yescharacteristic
386C3×C42C22×D311yescharacteristic
387C3×C42C23×C311yescharacteristic
388C3×C42C23×C311yescharacteristic
389#217—21no—
390#216—22no—
391#216—22no—
392#214—22no—
393#214—22no—
394C4⋊Dic3C23×C311yescharacteristic
395C4⋊Dic3C23×C311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400C4×Dic3—21no—
401C4×Dic3—21no—
402C4×Dic3—21no—
403C4×Dic3—21no—
404C4×Dic3—21no—
405C2×C3⋊C8C23×C311yescharacteristic
406C2×C3⋊C8C23×C311yescharacteristic
407C2×C3⋊C8C23×C311yescharacteristic
408C2×C3⋊C8C23×C311yescharacteristic
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32C22×D411yescharacteristic
416C32×C4—21no—
417C32×C4—21no—
418C32×C4—21no—
419C32×C4—21no—
420C32×C4—21no—
421C32×C4—41no—
422C32×C4—41no—
423C32×C4—41no—
424C32×C4C2×#4111yescharacteristic
425C32×C4C2×#4111yescharacteristic
426C3×Dic3—22no—
427C3×Dic3—22no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C22×Q8—31no—
431C2×Q16—31no—
432C2×Q16—31no—
433C2×SD16—31no—
434C2×SD16—31no—
435C4⋊Q8C2×C3×D311yescharacteristic
436#126—21no—
437#124—21no—
438#124C2×C3×D311yescharacteristic
439#123—21no—
440C22⋊Q8—21no—
441C22⋊Q8C2×C3×D311yescharacteristic
442#121C2×C3×D311yescharacteristic
443C4×Q8—31no—
444C4×Q8—31no—
445C4×Q8—31no—
446C4×Q8—31no—
447C4×Q8—61no—
448C4×Q8—61no—
449C4×Q8C2×C3×D311yescharacteristic
450C4×D4C2×C3×D311yescharacteristic
451#117—31no—
452#117—61no—
453#117—61no—
454#117C2×C3×D311yescharacteristic
455#107—31no—
456#107—31no—
457#106—31no—
458#106—31no—
459C4⋊C8—31no—
460C4⋊C8—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#103—31no—
467#102—31no—
468#102—31no—
469C22⋊C8—31no—
470C22⋊C8—31no—
471#97—31no—
472C4×C8—31no—
473C23×C3—22no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3C2×#6711yescharacteristic
478C23×C3C2×C3×D411yescharacteristic
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—32no—
484C3×Q8—32no—
485C3×Q8—41no—
486C3×Q8—41no—
487C3×Q8—64no—
488C3×Q8—61no—
489C3×Q8—61no—
490C3×Q8—81no—
491C3×Q8—81no—
492C3×Q8—82no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—41no—
498C3×D4—41no—
499C3×D4—81no—
500C3×D4—81no—
501C3×D4—82no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
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—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—64no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—81no—
529C2×C3×C4—81no—
530C2×C3×C4—82no—
531C2×C3×C4C2×#6711yescharacteristic
532C2×C3×C4C2×#6711yescharacteristic
533C2×C3×C4C2×#6711yescharacteristic
534C2×C3×C4C2×#6711yescharacteristic
535C2×C3×C4C2×#6711yescharacteristic
536C2×C3×C4C2×C3×D411yescharacteristic
537C2×C3×C4C2×C3×D411yescharacteristic
538C2×C3×C4C2×C3×D411yescharacteristic
539C2×C3×C4C2×C3×D411yescharacteristic
540C2×C3×C4C2×C3×D411yescharacteristic
541C2×C3×C4C23×D311yescharacteristic
542C2×C3×C4C24×C311yescharacteristic
543C2×Dic3—24no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548Dic6—24no—
549Dic6—21no—
550Dic6—21no—
551Dic6C3×#4112yes—
552Dic6C3×#4112yes—
553C3×C8—61no—
554C3×C8—61no—
555C3×C8—61no—
556C3×C8—61no—
557C3⋊C8—21no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—21no—
561C2×C32—41no—
562C2×C32—81no—
563C2×C32#52511yescharacteristic
564C2×C32#57711yescharacteristic
565C2×C32#57811yescharacteristic
566C2×Q8—21no—
567C2×Q8—31no—
568C2×Q8—31no—
569C2×Q8—62no—
570C2×Q8—62no—
571C2×Q8—61no—
572C2×Q8C22×C3×D311yescharacteristic
573C2×D4—21no—
574C2×D4C22×C3×D311yescharacteristic
575C22×C4—21no—
576C22×C4—61no—
577C22×C4C22×C3×D311yescharacteristic
578Q16—62no—
579Q16—62no—
580SD16—62no—
581SD16—62no—
582C2×C8—31no—
583C2×C8—31no—
584C2×C8—31no—
585C2×C8—31no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—31no—
590C4⋊C4—31no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4C3×#6711yescharacteristic
596C4⋊C4C3×#6711yescharacteristic
597C4⋊C4C22×C3×D311yescharacteristic
598C4⋊C4C22×C3×D311yescharacteristic
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—61no—
605C22⋊C4C3×#6711yescharacteristic
606C22⋊C4C3×#6711yescharacteristic
607C42—21no—
608C42—61no—
609C42—61no—
610C42—61no—
611C42—61no—
612C42—61no—
613C42C22×C3×D311yescharacteristic
614C42C22×C3×D311yescharacteristic
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—42no—
626C22×C3—42no—
627C22×C3—42no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3C22×#6711yescharacteristic
635C22×C3C22×C3×D411yescharacteristic
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—42no—
654C3×C4—42no—
655C3×C4—42no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—62no—
663C3×C4—62no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4D3×#4111yescharacteristic
667C3×C4D3×#4111yescharacteristic
668C3×C4C2×C3×#4111yescharacteristic
669C3×C4C2×C3×#4111yescharacteristic
670Dic3—22no—
671Dic3—22no—
672Dic3—41no—
673Dic3—41no—
674C32#312111yescharacteristic, complemented, Sylow
675C23—21no—
676C23C2×C3×#6711yescharacteristic
677Q8—21no—
678Q8—21no—
679Q8—32no—
680Q8—32no—
681Q8—64no—
682Q8—61no—
683Q8—61no—
684Q8—81no—
685D4—21no—
686D4—21no—
687D4—81no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—64no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—81no—
699C2×C4C2×C3×#6711yescharacteristic
700C2×C4C2×C3×#6711yescharacteristic
701C2×C4C2×C3×#6711yescharacteristic
702C2×C4C2×C3×#6711yescharacteristic
703C2×C4C2×C3×#6711yescharacteristic
704C2×C4C23×C3×D311yescharacteristic
705C8—61no—
706C8—61no—
707C8—61no—
708C8—61no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—41no—
713C2×C3—41no—
714C2×C3—81no—
715C2×C3—82no—
716C2×C3—81no—
717C2×C3—81no—
718C2×C3#582811yescharacteristic
719C2×C3#583611yescharacteristic
720C2×C3#583811yescharacteristic
721C2×C3C3×#52511yescharacteristic
722C2×C3C3×#57711yescharacteristic
723C2×C3C3×#57811yescharacteristic
724C22—21no—
725C22—21no—
726C22—21no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22C22×C3×#6711yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—21no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—62no—
740C4—62no—
741C4—121no—
742C4—121no—
743C4C3×D3×#4111yescharacteristic
744C4C3×D3×#4111yescharacteristic
745C3—21no—
746C3#8346711yescharacteristic, direct product factor
747C3C3×#312111yescharacteristic, complemented
748C2—41no—
749C2—81no—
750C2C3×#582811yescharacteristic
751C2C3×#583611yescharacteristic
752C2C3×#583811yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#542C2
socleC22×C32C22×D4
prime radicalC32×#121C22
hypercenterC3×#542D3
hypocenterC3C3×#3121
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#542

Complements

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

NH ≅ G/Ntype
2. C3×#5516C2semidirect
3. C3×#5094C2semidirect
4. C3×#5091C2semidirect
5. C3×#5054C2semidirect
6. C3×#5054C2semidirect
7. C3×#5050C2semidirect
8. C3×#5045C2semidirect
11. C3×#5030C2semidirect
12. C3×C4×#216C2semidirect
13. C3×#5018C2semidirect
14. C3×C4×#214C2semidirect
15. C3×#5000C2semidirect
17. #83467C3direct (N × H)
65. #5516C2×C3semidirect
79. #5094C2×C3semidirect
80. #5091C2×C3semidirect
81. #5054C2×C3semidirect
82. #5054C2×C3semidirect
83. #5050C2×C3semidirect
84. #5045C2×C3semidirect
87. #5030C2×C3semidirect
88. C4×#216C2×C3semidirect
89. #5018C2×C3semidirect
90. C4×#214C2×C3semidirect
91. #5000C2×C3semidirect
674. C32#3121semidirect
746. C3#83467direct (N × H)
747. C3C3×#3121semidirect

Maximal subgroups

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

subgroupindex
C32×#5422
C3×#55162
C3×#50942
C3×#50912
C3×#50542
C3×#50502
C3×#50452
C3×#50402
C3×#50352
C3×#50302
C3×C4×#2162
C3×#50182
C3×C4×#2142
C3×#50002
C3×#31213
#834673