Finite Group Databasebeta

← C3×#82575 #11872410

Subgroups — C3×#82575 #11872410

Order 1152.

891 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#520C211yesmaximal, characteristic
2C3×#5518C211yesmaximal, characteristic, complemented
3C3×#5239C211yesmaximal, characteristic
4C3×#5239C211yesmaximal, characteristic
5C3×#5031C211yesmaximal, characteristic, complemented
6C3×#5030C211yesmaximal, characteristic, complemented
7C3×C4×#216C211yesmaximal, characteristic, complemented
8C3×#5022C211yesmaximal, characteristic, complemented
9C3×#5019C211yesmaximal, characteristic, complemented
10C3×#5018C211yesmaximal, characteristic, complemented
11C3×C4×#214C211yesmaximal, characteristic, complemented
12C3×#5009C211yesmaximal, characteristic, complemented
13C3×#5000C211yesmaximal, characteristic, complemented
14C3×#4971C211yesmaximal, characteristic, complemented
15C3×#4970C211yesmaximal, characteristic, complemented
16C3×#3120—31nomaximal
17#82575C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C32×C4×D4—21no—
22C32×C4×D4—21no—
23C32×C4×D4C2211yescharacteristic
24C32×C4×D4C2211yescharacteristic
25C32×#117—21no—
26C32×#117C2211yescharacteristic
27C2×C32×C4⋊C4—21no—
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C2×C3×#214C2211yescharacteristic
33C3×#924C2211yescharacteristic
34C3×#924C2211yescharacteristic
35C3×#889—21no—
36C3×#889—21no—
37C3×#879—21no—
38C3×#879—21no—
39C3×#870C2211yescharacteristic
40C3×#869C2211yescharacteristic
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×#541—31no—
62C3×#520—21no—
63C3×#520D311yescharacteristic
64C3×#520C2×C311yescharacteristic
65#5518C2×C311yescharacteristic, complemented
66C3×#484—31no—
67C3×#483—31no—
68C3×#479—31no—
69C3×#478—31no—
70C3×#462—31no—
71C3×#461—31no—
72C3×#452—31no—
73C3×#452—31no—
74C3×#441—31no—
75C3×#440—31no—
76C3×C4×Q16—31no—
77C3×C4×SD16—31no—
78C3×#433—31no—
79#5239C2×C311yescharacteristic
80#5239C2×C311yescharacteristic
81#5031C2×C311yescharacteristic, complemented
82#5030C2×C311yescharacteristic, complemented
83C4×#216C2×C311yescharacteristic, complemented
84#5022C2×C311yescharacteristic, complemented
85#5019C2×C311yescharacteristic, complemented
86#5018C2×C311yescharacteristic, complemented
87C4×#214C2×C311yescharacteristic, complemented
88#5009C2×C311yescharacteristic, complemented
89#5000C2×C311yescharacteristic, complemented
90#4971C2×C311yescharacteristic, complemented
91#4970C2×C311yescharacteristic, complemented
92C32×#41—22no—
93C32×#41—22no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4—21no—
99C22×C32×C4—21no—
100C22×C32×C4—21no—
101C22×C32×C4C2311yescharacteristic
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⋊C4D411yescharacteristic
114C32×C22⋊C4D411yescharacteristic
115C32×C42—21no—
116C32×C42—21no—
117C32×C42C2311yescharacteristic
118C32×C42C2311yescharacteristic
119C3×#217—21no—
120C3×#217—21no—
121C3×#216—22no—
122C3×#216—22no—
123C3×#214—22no—
124C3×#214—22no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—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#3120—31noSylow
142C2×C3×#41—21no—
143C2×C3×#41C2×D311yescharacteristic
144C2×C3×#41C22×C311yescharacteristic
145C2×C3×Q16—31no—
146C2×C3×Q16—31no—
147C2×C3×SD16—31no—
148C2×C3×SD16—31no—
149C3×C4⋊Q8—31no—
150C3×#126—61no—
151C3×#126—61no—
152C3×#125—31no—
153C3×#125—61no—
154C3×#125—61no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C4×Q8—21no—
158C3×C4×Q8—21no—
159C3×C4×Q8—31no—
160C3×C4×Q8—31no—
161C3×C4×Q8C2×D311yescharacteristic
162C3×C4×Q8C2×D311yescharacteristic
163C3×C4×Q8C22×C311yescharacteristic
164C3×C4×Q8C22×C311yescharacteristic
165C3×C4×D4—22no—
166C3×C4×D4—22no—
167C3×C4×D4—21no—
168C3×C4×D4—21no—
169C3×C4×D4—21no—
170C3×C4×D4—21no—
171C3×C4×D4—21no—
172C3×C4×D4—21no—
173C3×C4×D4C2×D311yescharacteristic
174C3×C4×D4C2×D311yescharacteristic
175C3×C4×D4C22×C311yescharacteristic
176C3×C4×D4C22×C311yescharacteristic
177C3×#117—22no—
178C3×#117—21no—
179C3×#117—21no—
180C3×#117—21no—
181C3×#117C2×D311yescharacteristic
182C3×#117C22×C311yescharacteristic
183C2×C3×C4⋊C4—22no—
184C2×C3×C4⋊C4—21no—
185C2×C3×C4⋊C4—21no—
186C2×C3×C4⋊C4—21no—
187C2×C3×C4⋊C4C2×D311yescharacteristic
188C2×C3×C4⋊C4C22×C311yescharacteristic
189C2×#216C22×C311yescharacteristic
190C2×#216C22×C311yescharacteristic
191C2×#214C22×C311yescharacteristic
192C2×#214C22×C311yescharacteristic
193#924C22×C311yescharacteristic
194#924C22×C311yescharacteristic
195#889—21no—
196#889—21no—
197#879—21no—
198#879—21no—
199#870C22×C311yescharacteristic
200#869C22×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#4112yes—
243C32×D4—24no—
244C32×D4—21no—
245C32×D4#4112yes—
246C2×C32×C4—24no—
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×C4—81no—
254C2×C32×C4—81no—
255C2×C32×C4C2×D411yescharacteristic
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—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×C3⋊C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272C3×C3⋊C8—21no—
273#541—31no—
274#520C3×D311yescharacteristic
275#484—31no—
276#483—31no—
277#479—31no—
278#478—31no—
279#462—31no—
280#461—31no—
281#452—31no—
282#452—31no—
283#441—31no—
284#440—31no—
285C4×Q16—31no—
286C4×SD16—31no—
287#433—31no—
288C3×#41—24no—
289C3×#41—24no—
290C3×#41—22no—
291C3×#41—22no—
292C3×#41—22no—
293C3×#41—22no—
294C2×C3×Q8—21no—
295C2×C3×Q8—31no—
296C2×C3×Q8—31no—
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—22no—
309C22×C3×C4—22no—
310C22×C3×C4—22no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C23×C311yescharacteristic
320C2×Dic6C23×C311yescharacteristic
321C2×Dic6C23×C311yescharacteristic
322C3×Q16—62no—
323C3×Q16—62no—
324C3×SD16—62no—
325C3×SD16—62no—
326C2×C3×C8—31no—
327C2×C3×C8—31no—
328C2×C3×C8—31no—
329C2×C3×C8—31no—
330C3×C4⋊C4—22no—
331C3×C4⋊C4—22no—
332C3×C4⋊C4—22no—
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—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4#6711yescharacteristic
354C3×C4⋊C4#6711yescharacteristic
355C3×C4⋊C4C3×D411yescharacteristic
356C3×C4⋊C4C3×D411yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C23×C311yescharacteristic
360C3×C4⋊C4C23×C311yescharacteristic
361C3×C22⋊C4—22no—
362C3×C22⋊C4—22no—
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—61no—
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—22no—
377C3×C42—21no—
378C3×C42—21no—
379C3×C42—21no—
380C3×C42—21no—
381C3×C42—21no—
382C3×C42—21no—
383C3×C42—61no—
384C3×C42—61no—
385C3×C42C22×D311yescharacteristic
386C3×C42C22×D311yescharacteristic
387C3×C42C23×C311yescharacteristic
388C3×C42C23×C311yescharacteristic
389#217—21no—
390#217—21no—
391#216—22no—
392#216—22no—
393#214—22no—
394#214—22no—
395C4⋊Dic3—21no—
396C4⋊Dic3—21no—
397C4⋊Dic3C23×C311yescharacteristic
398C4⋊Dic3C23×C311yescharacteristic
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405C4×Dic3—21no—
406C4×Dic3—21no—
407C2×C3⋊C8C23×C311yescharacteristic
408C2×C3⋊C8C23×C311yescharacteristic
409C2×C3⋊C8C23×C311yescharacteristic
410C2×C3⋊C8C23×C311yescharacteristic
411C22×C32—21no—
412C22×C32—22no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C32×C4—21no—
419C32×C4—22no—
420C32×C4—21no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—41no—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4C2×#4111yescharacteristic
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C2×#41C2×C3×D311yescharacteristic
433C2×Q16—31no—
434C2×Q16—31no—
435C2×SD16—31no—
436C2×SD16—31no—
437C4⋊Q8—31no—
438#126—61no—
439#126—61no—
440#125—31no—
441#125—61no—
442#125—61no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C4×Q8—31no—
446C4×Q8—31no—
447C4×Q8C2×C3×D311yescharacteristic
448C4×Q8C2×C3×D311yescharacteristic
449C4×D4—21no—
450C4×D4—21no—
451C4×D4C2×C3×D311yescharacteristic
452C4×D4C2×C3×D311yescharacteristic
453#117—21no—
454#117C2×C3×D311yescharacteristic
455C2×C4⋊C4—21no—
456C2×C4⋊C4C2×C3×D311yescharacteristic
457#107—31no—
458#107—31no—
459#106—31no—
460#106—31no—
461C4⋊C8—31no—
462C4⋊C8—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#103—31no—
467#103—31no—
468#103—31no—
469#102—31no—
470#102—31no—
471C22⋊C8—31no—
472C22⋊C8—31no—
473#97—31no—
474C4×C8—31no—
475C23×C3—22no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3C2×#6711yescharacteristic
480C23×C3C2×C3×D411yescharacteristic
481C3×Q8—22no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—22no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—61no—
489C3×Q8#23512yes—
490C3×Q8C3×#4112yes—
491C3×D4—28no—
492C3×D4—24no—
493C3×D4—24no—
494C3×D4—22no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—22no—
498C3×D4#23512yes—
499C3×D4C3×#4112yes—
500C2×C3×C4—22no—
501C2×C3×C4—28no—
502C2×C3×C4—24no—
503C2×C3×C4—24no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
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—22no—
513C2×C3×C4—22no—
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—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
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—81no—
531C2×C3×C4—81no—
532C2×C3×C4—81no—
533C2×C3×C4—81no—
534C2×C3×C4—82no—
535C2×C3×C4—82no—
536C2×C3×C4—82no—
537C2×C3×C4C2×#6711yescharacteristic
538C2×C3×C4C2×#6711yescharacteristic
539C2×C3×C4C2×#6711yescharacteristic
540C2×C3×C4C2×#6711yescharacteristic
541C2×C3×C4C2×#6711yescharacteristic
542C2×C3×C4C2×C3×D411yescharacteristic
543C2×C3×C4C2×C3×D411yescharacteristic
544C2×C3×C4C2×C3×D411yescharacteristic
545C2×C3×C4C2×C3×D411yescharacteristic
546C2×C3×C4C2×C3×D411yescharacteristic
547C2×C3×C4C23×D311yescharacteristic
548C2×C3×C4C24×C311yescharacteristic
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553Dic6—21no—
554Dic6—21no—
555Dic6—21no—
556Dic6—21no—
557C3×C8—61no—
558C3×C8—61no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C3⋊C8—21no—
564C3⋊C8—21no—
565C2×C32—41no—
566C2×C32—42no—
567C2×C32#52511yescharacteristic
568C2×C32#57711yescharacteristic
569C2×C32#57811yescharacteristic
570#41—22no—
571#41—22no—
572C2×Q8—31no—
573C2×Q8—31no—
574C2×Q8C22×C3×D311yescharacteristic
575C2×D4—21no—
576C2×D4C22×C3×D311yescharacteristic
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4C22×C3×D311yescharacteristic
582Q16—62no—
583Q16—62no—
584SD16—62no—
585SD16—62no—
586C2×C8—31no—
587C2×C8—31no—
588C2×C8—31no—
589C2×C8—31no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4C3×#6711yescharacteristic
604C4⋊C4C3×#6711yescharacteristic
605C4⋊C4C22×C3×D311yescharacteristic
606C4⋊C4C22×C3×D311yescharacteristic
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4C3×#6711yescharacteristic
612C22⋊C4C3×#6711yescharacteristic
613C42—21no—
614C42—21no—
615C42—61no—
616C42—61no—
617C42C22×C3×D311yescharacteristic
618C42C22×C3×D311yescharacteristic
619C22×C3—22no—
620C22×C3—24no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—22no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—22no—
629C22×C3—21no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—42no—
633C22×C3—42no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3C22×#6711yescharacteristic
639C22×C3C22×C3×D411yescharacteristic
640C3×C4—22no—
641C3×C4—24no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—22no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—22no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—42no—
661C3×C4—42no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4C2×#23511yescharacteristic
671C3×C4C2×#23511yescharacteristic
672C3×C4C2×C3×#4111yescharacteristic
673C3×C4C2×C3×#4111yescharacteristic
674Dic3—41no—
675Dic3—41no—
676Dic3—41no—
677Dic3—41no—
678C32#312011yescharacteristic, complemented, Sylow
679C23—21no—
680C23C2×C3×#6711yescharacteristic
681Q8—21no—
682Q8—61no—
683Q8—61no—
684Q8—61no—
685Q8—61no—
686Q8C3×#23512yes—
687D4—24no—
688D4—21no—
689D4C3×#23512yes—
690C2×C4—24no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4C2×C3×#6711yescharacteristic
704C2×C4C2×C3×#6711yescharacteristic
705C2×C4C2×C3×#6711yescharacteristic
706C2×C4C2×C3×#6711yescharacteristic
707C2×C4C2×C3×#6711yescharacteristic
708C2×C4C23×C3×D311yescharacteristic
709C8—61no—
710C8—61no—
711C8—61no—
712C8—61no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—42no—
717C2×C3—44no—
718C2×C3—41no—
719C2×C3—42no—
720C2×C3—41no—
721C2×C3—42no—
722C2×C3#579111yescharacteristic
723C2×C3#583611yescharacteristic
724C2×C3#583811yescharacteristic
725C2×C3C3×#52511yescharacteristic
726C2×C3C3×#57711yescharacteristic
727C2×C3C3×#57811yescharacteristic
728C22—21no—
729C22—22no—
730C22—21no—
731C22—21no—
732C22—41no—
733C22—41no—
734C22C22×C3×#6711yescharacteristic
735C4—21no—
736C4—22no—
737C4—21no—
738C4—21no—
739C4—21no—
740C4—21no—
741C4—41no—
742C4—41no—
743C4—121no—
744C4—121no—
745C4—121no—
746C4—121no—
747C4C2×C3×#23511yescharacteristic
748C4C2×C3×#23511yescharacteristic
749C3—21no—
750C3#8257511yescharacteristic, direct product factor
751C3C3×#312011yescharacteristic, complemented
752C2—41no—
753C2—42no—
754C2C3×#579111yescharacteristic
755C2C3×#583611yescharacteristic
756C2C3×#583811yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#520C2
socleC22×C32C22×D4
prime radicalC2×C32×#41C22
hypercenterC3×#520D3
hypocenterC3C3×#3120
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#520

Complements

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

NH ≅ G/Ntype
2. C3×#5518C2semidirect
5. C3×#5031C2semidirect
6. C3×#5030C2semidirect
7. C3×C4×#216C2semidirect
8. C3×#5022C2semidirect
9. C3×#5019C2semidirect
10. C3×#5018C2semidirect
11. C3×C4×#214C2semidirect
12. C3×#5009C2semidirect
13. C3×#5000C2semidirect
14. C3×#4971C2semidirect
15. C3×#4970C2semidirect
17. #82575C3direct (N × H)
65. #5518C2×C3semidirect
81. #5031C2×C3semidirect
82. #5030C2×C3semidirect
83. C4×#216C2×C3semidirect
84. #5022C2×C3semidirect
85. #5019C2×C3semidirect
86. #5018C2×C3semidirect
87. C4×#214C2×C3semidirect
88. #5009C2×C3semidirect
89. #5000C2×C3semidirect
90. #4971C2×C3semidirect
91. #4970C2×C3semidirect
678. C32#3120semidirect
750. C3#82575direct (N × H)
751. C3C3×#3120semidirect

Maximal subgroups

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

subgroupindex
C32×#5202
C3×#55182
C3×#52392
C3×#50312
C3×#50302
C3×C4×#2162
C3×#50222
C3×#50192
C3×#50182
C3×C4×#2142
C3×#50092
C3×#50002
C3×#49712
C3×#49702
C3×#31203
#825753