Finite Group Databasebeta

← C3×#80247 #11887689

Subgroups — C3×#80247 #11887689

Order 1152.

848 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
1C3×#5831C211yesmaximal, characteristic
2C3×#5639C211yesmaximal, characteristic, complemented
3C32×#452C211yesmaximal, characteristic, complemented
4C3×#5233C211yesmaximal, characteristic, complemented
5C3×#5186C211yesmaximal, characteristic, complemented
6C3×Dic3×Q16C211yesmaximal, characteristic, complemented
7C3×#5171C211yesmaximal, characteristic, complemented
8C3×#5166C211yesmaximal, characteristic, complemented
9C3×#5051C211yesmaximal, characteristic, complemented
10C3×D3×#103C211yesmaximal, characteristic, complemented
11C3×#4799C211yesmaximal, characteristic, complemented
12C3×#4774C211yesmaximal, characteristic, complemented
13C3×#4768C211yesmaximal, characteristic, complemented
14C3×#67⋊C8C211yesmaximal, characteristic, complemented
15C3×#4723C211yesmaximal, characteristic, complemented
16C3×#3300—31nomaximal
17#80247C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C3×#938—21no—
28C3×#938C2211yescharacteristic
29C3×#936—21no—
30C3×#936C2211yescharacteristic
31C3×C4×#67—21no—
32C3×C4×#67C2211yescharacteristic
33C3×#926C2211yescharacteristic
34C3×#924—21no—
35C3×#924C2211yescharacteristic
36C22×C3×C3⋊C8C2211yescharacteristic
37C2×C3×D3×C8C2211yescharacteristic
38C3×#892—21no—
39C3×D3×C4⋊C4C2211yescharacteristic
40C3×#890C2211yescharacteristic
41C3×#889—21no—
42C3×#883—21no—
43C3×#879—21no—
44C32×#103C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×C22⋊C8C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#818C2211yescharacteristic
54C3×#817C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×#816C2211yescharacteristic
57C3×Dic3⋊C8C2211yescharacteristic
58C3×C8×Dic3C2211yescharacteristic
59C3×#810C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#552—31no—
62C3×#548—31no—
63#5831C2×C311yescharacteristic
64#5639C2×C311yescharacteristic, complemented
65C3×#488—31no—
66C3×#485—31no—
67C3×#480—31no—
68C3×#479—31no—
69C3×#467—31no—
70C3×#465—31no—
71C3×#464—31no—
72C3×#452—21no—
73C3×#452D311yescharacteristic, complemented
74C3×#452C2×C311yescharacteristic, complemented
75C3×#451—31no—
76C3×C4×Q16—31no—
77C3×C8×D4—31no—
78C3×#416—31no—
79C2×C3×#103—31no—
80#5233C2×C311yescharacteristic, complemented
81#5186C2×C311yescharacteristic, complemented
82Dic3×Q16C2×C311yescharacteristic, complemented
83#5171C2×C311yescharacteristic, complemented
84#5166C2×C311yescharacteristic, complemented
85#5051C2×C311yescharacteristic, complemented
86D3×#103C2×C311yescharacteristic, complemented
87#4799C2×C311yescharacteristic, complemented
88#4774C2×C311yescharacteristic, complemented
89#4768C2×C311yescharacteristic, complemented
90#67⋊C8C2×C311yescharacteristic, complemented
91#4723C2×C311yescharacteristic, complemented
92C32×#41—22no—
93C32×#41—41no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C3×D3×Q8—22no—
103C3×D3×Q8—41no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6—21no—
108C2×C3×Dic6C2311yescharacteristic
109C32×Q16—22no—
110C32×SD16—41no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217D411yescharacteristic
122C3×#216—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
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⋊C4D411yescharacteristic
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8—41no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D3×C8—41no—
144#3300—31noSylow
145C2×C3×#41—21no—
146C2×C3×#41C2×D311yescharacteristic
147C2×C3×#41C22×C311yescharacteristic
148C22×C3×Q8—31no—
149C2×D3×Q8C22×C311yescharacteristic
150C2×C3×Q16—21no—
151C2×C3×Q16—31no—
152C2×C3×Q16C2×D311yescharacteristic
153C2×C3×Q16C22×C311yescharacteristic
154C2×C3×SD16—21no—
155C2×C3×SD16C2×D311yescharacteristic
156C2×C3×SD16C22×C311yescharacteristic
157C22×C3×C8—31no—
158C22×C3×C8—31no—
159C3×#126—61no—
160C3×#125—31no—
161C3×#125—61no—
162C3×#124—31no—
163C3×#124—61no—
164C3×#123—61no—
165C3×C22⋊Q8—21no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—31no—
168C3×C22⋊Q8—61no—
169C3×C22⋊Q8C2×D311yescharacteristic
170C3×C22⋊Q8C22×C311yescharacteristic
171C3×#121—31no—
172C3×#121—61no—
173C3×C4×Q8—31no—
174C3×C4×Q8—31no—
175C3×C4×D4—31no—
176C3×C4×D4—61no—
177C3×#117—31no—
178C3×#117—61no—
179C2×C3×C4⋊C4—31no—
180#946C22×C311yescharacteristic
181Q8×Dic3C22×C311yescharacteristic
182Q8×Dic3C22×C311yescharacteristic
183C2×#216C22×C311yescharacteristic
184#938—21no—
185#938C22×C311yescharacteristic
186#936—21no—
187#936C22×C311yescharacteristic
188C4×#67—21no—
189C4×#67C22×C311yescharacteristic
190#926C22×C311yescharacteristic
191#924—21no—
192#924C22×C311yescharacteristic
193C22×C3⋊C8C22×C311yescharacteristic
194C2×D3×C8C22×C311yescharacteristic
195#892—21no—
196D3×C4⋊C4C22×C311yescharacteristic
197#890C22×C311yescharacteristic
198#889—21no—
199#883—21no—
200#879—21no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#106—31no—
204C3×C4⋊C8—31no—
205C3×#103—21no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103C2×D311yescharacteristic
213C3×#103C22×C311yescharacteristic
214C3×#102—21no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102C2×D311yescharacteristic
218C3×#102C22×C311yescharacteristic
219C3×C22⋊C8—21no—
220C3×C22⋊C8—31no—
221C3×C22⋊C8C2×D311yescharacteristic
222C3×C22⋊C8C22×C311yescharacteristic
223C3×C4×C8—31no—
224#835C22×C311yescharacteristic
225#835C22×C311yescharacteristic
226#835C22×C311yescharacteristic
227#832C22×C311yescharacteristic
228#832C22×C311yescharacteristic
229(C2×D3)⋊C8C22×C311yescharacteristic
230#818C22×C311yescharacteristic
231#817C22×C311yescharacteristic
232#816C22×C311yescharacteristic
233#816C22×C311yescharacteristic
234Dic3⋊C8C22×C311yescharacteristic
235C8×Dic3C22×C311yescharacteristic
236#810C22×C311yescharacteristic
237#807C22×C311yescharacteristic
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C32×Q8#4112yes—
245C32×D4—21no—
246C32×D4—21no—
247C32×D4—42no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—42no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C3×#67—22no—
257C3×#67—42no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—42no—
268C3×C4×D3—42no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—42no—
272C32×C8—21no—
273C32×C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#552—31no—
277#548—31no—
278#488—31no—
279#485—31no—
280#480—31no—
281#479—31no—
282#467—31no—
283#465—31no—
284#464—31no—
285#452C3×D311yescharacteristic, complemented
286#451—31no—
287C4×Q16—31no—
288C8×D4—31no—
289#416—31no—
290C2×#103—31no—
291C3×#41—22no—
292C3×#41—22no—
293C3×#41—42no—
294C3×#41—41no—
295C3×#41—41no—
296C3×#41—42no—
297C2×C3×Q8—21no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8—61no—
301C2×C3×Q8—62no—
302C2×C3×Q8—121no—
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×Q8C23×C311yescharacteristic
306C2×C3×Q8C23×C311yescharacteristic
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—31no—
311C2×C3×D4—41no—
312C2×C3×D4—61no—
313C2×C3×D4C22×D311yescharacteristic
314C2×C3×D4C23×C311yescharacteristic
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—31no—
319C22×C3×C4—41no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C23×C311yescharacteristic
324C2×#67—21no—
325C2×#67C3×D411yescharacteristic
326D3×Q8—22no—
327D3×Q8—41no—
328C2×C4×D3—21no—
329C2×C4×D3—21no—
330C2×C4×D3C23×C311yescharacteristic
331C2×Dic6—21no—
332C2×Dic6C23×C311yescharacteristic
333C3×Q16—22no—
334C3×Q16—22no—
335C3×Q16—42no—
336C3×Q16—121no—
337C3×SD16—41no—
338C3×SD16—41no—
339C3×SD16—42no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—121no—
345C2×C3×C8—121no—
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C23×C311yescharacteristic
349C2×C3×C8C23×C311yescharacteristic
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—41no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C23×C311yescharacteristic
367C3×C22⋊C4—21no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—31no—
370C3×C22⋊C4—31no—
371C3×C22⋊C4—41no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C42—31no—
379C3×C42—61no—
380C3×C42—61no—
381C3×C42—61no—
382#217—21no—
383#217—21no—
384#217—21no—
385#217—21no—
386#217—21no—
387#217C3×D411yescharacteristic
388#216—41no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4C3×D411yescharacteristic
391C4⋊Dic3—21no—
392C4⋊Dic3—21no—
393C4⋊Dic3—21no—
394C4⋊Dic3C23×C311yescharacteristic
395C4⋊Dic3C23×C311yescharacteristic
396C4⋊Dic3C23×C311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4C3×D411yescharacteristic
402C4×Dic3—21no—
403C4×Dic3—21no—
404C4×Dic3—21no—
405C4×Dic3C23×C311yescharacteristic
406C2×C3⋊C8—41no—
407C2×C3⋊C8C23×C311yescharacteristic
408C2×C3⋊C8C23×C311yescharacteristic
409D3×C8—41no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3#13512yes—
420C32×C4—22no—
421C32×C4—21no—
422C32×C4—41no—
423C32×C4—41no—
424C32×C4C2×#4111yescharacteristic
425C32×C4H(5,𝔽2)11yescharacteristic
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C2×#41C2×C3×D311yescharacteristic
434C22×Q8—31no—
435C2×Q16—31no—
436C2×Q16C2×C3×D311yescharacteristic
437C2×SD16C2×C3×D311yescharacteristic
438C22×C8—31no—
439C22×C8—31no—
440#126—61no—
441#125—31no—
442#125—61no—
443#124—31no—
444#124—61no—
445#123—61no—
446C22⋊Q8—31no—
447C22⋊Q8—31no—
448C22⋊Q8—61no—
449C22⋊Q8C2×C3×D311yescharacteristic
450#121—31no—
451#121—61no—
452C4×Q8—31no—
453C4×Q8—31no—
454C4×D4—31no—
455C4×D4—61no—
456#117—31no—
457#117—61no—
458C2×C4⋊C4—31no—
459#107—31no—
460#107—31no—
461#106—31no—
462C4⋊C8—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103C2×C3×D311yescharacteristic
470#102—31no—
471#102—31no—
472#102C2×C3×D311yescharacteristic
473C22⋊C8—31no—
474C22⋊C8C2×C3×D311yescharacteristic
475C4×C8—31no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—31no—
480C23×C3—41no—
481C23×C3D3×D411yescharacteristic
482C23×C3C2×C3×D411yescharacteristic
483C22×D3C2×C3×D411yescharacteristic
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—22no—
491C3×Q8—41no—
492C3×Q8—41no—
493C3×Q8—41no—
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—122no—
497C3×Q8#23712yes—
498C3×Q8C3×#4112yes—
499C3×D4—22no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—41no—
505C3×D4—42no—
506C3×D4—42no—
507C3×D4—44no—
508C3×D4—62no—
509C3×D4—122no—
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—21no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—42no—
531C2×C3×C4—42no—
532C2×C3×C4—44no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—122no—
540C2×C3×C4—122no—
541C2×C3×C4D3×D411yescharacteristic
542C2×C3×C4C2×C3×D411yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C24×C311yescharacteristic
545#67—22no—
546#67—42no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3C2×C3×D411yescharacteristic
552C2×Dic3C2×C3×D411yescharacteristic
553C2×Dic3C2×C3×D411yescharacteristic
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—42no—
557C4×D3—42no—
558Dic6—21no—
559Dic6—21no—
560Dic6—42no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—41no—
566C3×C8—41no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C2×C32—41no—
572C2×C32—81no—
573C2×C32#54611yescharacteristic
574C2×C32C2×#13511yescharacteristic
575C2×C32#57811yescharacteristic
576C3×D3—22no—
577#41—22no—
578#41—41no—
579C2×Q8—31no—
580C2×Q8—61no—
581C2×Q8—62no—
582C2×Q8—121no—
583C2×Q8C22×C3×D311yescharacteristic
584C2×Q8C22×C3×D311yescharacteristic
585C2×D4—21no—
586C2×D4—31no—
587C2×D4—61no—
588C2×D4C22×C3×D311yescharacteristic
589C22×C4—21no—
590C22×C4—31no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4C22×C3×D311yescharacteristic
594Q16—22no—
595Q16—121no—
596SD16—41no—
597C2×C8—31no—
598C2×C8—31no—
599C2×C8—121no—
600C2×C8—121no—
601C2×C8C22×C3×D311yescharacteristic
602C2×C8C22×C3×D311yescharacteristic
603C4⋊C4—21no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4C22×C3×D311yescharacteristic
616C22⋊C4—21no—
617C22⋊C4—31no—
618C22⋊C4—31no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C42—31no—
626C42—61no—
627C42—61no—
628C42—61no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—32no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—42no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3C2×D3×D411yescharacteristic
652C22×C3C22×C3×D411yescharacteristic
653C2×D3—21no—
654C2×D3—21no—
655C2×D3C3×#13512yes—
656C3×C4—21no—
657C3×C4—22no—
658C3×C4—22no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—41no—
663C3×C4—42no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—81no—
672C3×C4—81no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4C2×#23711yescharacteristic
678C3×C4#100411yescharacteristic
679C3×C4C2×C3×#4111yescharacteristic
680C3×C4C3×H(5,𝔽2)11yescharacteristic
681Dic3—21no—
682Dic3—21no—
683Dic3—21no—
684Dic3—41no—
685Dic3—41no—
686Dic3—41no—
687Dic3—41no—
688C32#330011yescharacteristic, complemented, Sylow
689C23—21no—
690C23—31no—
691C23C3×D3×D411yescharacteristic
692Q8—21no—
693Q8—21no—
694Q8—21no—
695Q8—61no—
696Q8—61no—
697Q8—122no—
698Q8C3×#23712yes—
699D4—21no—
700D4—21no—
701D4—42no—
702D4—62no—
703D4—122no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—31no—
710C2×C4—31no—
711C2×C4—31no—
712C2×C4—42no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—122no—
720C2×C4—122no—
721C2×C4C3×D3×D411yescharacteristic
722C2×C4C23×C3×D311yescharacteristic
723C8—21no—
724C8—21no—
725C8—61no—
726C8—61no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—41no—
731C2×C3—41no—
732C2×C3—62no—
733C2×C3—81no—
734C2×C3—82no—
735C2×C3—81no—
736C2×C3—81no—
737C2×C3#559111yescharacteristic
738C2×C3D3×#13511yescharacteristic
739C2×C3#577911yescharacteristic
740C2×C3C3×#54611yescharacteristic
741C2×C3C2×C3×#13511yescharacteristic
742C2×C3C3×#57811yescharacteristic
743D3—22no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—32no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—61no—
752C22—61no—
753C22C2×C3×D3×D411yescharacteristic
754C4—21no—
755C4—22no—
756C4—41no—
757C4—41no—
758C4—61no—
759C4—61no—
760C4—61no—
761C4—121no—
762C4—121no—
763C4—121no—
764C4—121no—
765C4C2×C3×#23711yescharacteristic
766C4C3×#100411yescharacteristic
767C3—21no—
768C3#8024711yescharacteristic, direct product factor
769C3C3×#330011yescharacteristic, complemented
770C2—41no—
771C2—62no—
772C2—81no—
773C2C3×#559111yescharacteristic
774C2C3×D3×#13511yescharacteristic
775C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#452C2
socleC22×C32C22×D4
prime radicalC3×#5831C2
hypercenterC3×#452D3
hypocenterC3C3×#3300
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#452

Complements

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

NH ≅ G/Ntype
2. C3×#5639C2semidirect
3. C32×#452C2semidirect
4. C3×#5233C2semidirect
5. C3×#5186C2semidirect
6. C3×Dic3×Q16C2semidirect
7. C3×#5171C2semidirect
8. C3×#5166C2semidirect
9. C3×#5051C2semidirect
10. C3×D3×#103C2semidirect
11. C3×#4799C2semidirect
12. C3×#4774C2semidirect
13. C3×#4768C2semidirect
14. C3×#67⋊C8C2semidirect
15. C3×#4723C2semidirect
17. #80247C3direct (N × H)
64. #5639C2×C3semidirect
73. C3×#452D3semidirect
74. C3×#452C2×C3semidirect
80. #5233C2×C3semidirect
81. #5186C2×C3semidirect
82. Dic3×Q16C2×C3semidirect
83. #5171C2×C3semidirect
84. #5166C2×C3semidirect
85. #5051C2×C3semidirect
86. D3×#103C2×C3semidirect
87. #4799C2×C3semidirect
88. #4774C2×C3semidirect
89. #4768C2×C3semidirect
90. #67⋊C8C2×C3semidirect
91. #4723C2×C3semidirect
285. #452C3×D3semidirect
688. C32#3300semidirect
768. C3#80247direct (N × H)
769. C3C3×#3300semidirect

Maximal subgroups

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

subgroupindex
C3×#58312
C3×#56392
C32×#4522
C3×#52332
C3×#51862
C3×Dic3×Q162
C3×#51712
C3×#51662
C3×#50512
C3×D3×#1032
C3×#47992
C3×#47742
C3×#47682
C3×#67⋊C82
C3×#47232
C3×#33003
#802473