Finite Group Databasebeta

← C3×#82552 #11872564

Subgroups — C3×#82552 #11872564

Order 1152.

873 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#519C211yesmaximal, characteristic, complemented
2C3×#5534C211yesmaximal, characteristic
3C3×#5228C211yesmaximal, characteristic, complemented
4C3×#5227C211yesmaximal, characteristic
5C3×#5030C211yesmaximal, characteristic, complemented
6C3×C4×#216C211yesmaximal, characteristic, complemented
7C3×#5028C211yesmaximal, characteristic, complemented
8C3×#5028C211yesmaximal, characteristic, complemented
9C3×#5026C211yesmaximal, characteristic, complemented
10C3×C4×#215C211yesmaximal, characteristic, complemented
11C3×#5021C211yesmaximal, characteristic, complemented
12C3×#5020C211yesmaximal, characteristic, complemented
13C3×#5003C211yesmaximal, characteristic
14C3×#5000C211yesmaximal, characteristic, complemented
15C3×#4996C211yesmaximal, characteristic, complemented
16C3×#3121—31nomaximal
17#82552C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic
19C32×C4×Q8—21no—
20C32×C4×Q8—21no—
21C32×C4×Q8C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic
23C32×C4×Q8C2211yescharacteristic
24C32×C4×Q8C2211yescharacteristic
25C32×#117—21no—
26C32×#117—21no—
27C32×#117C2211yescharacteristic
28C32×#117C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C2×C3×#215C2211yescharacteristic
33C3×#930C2211yescharacteristic
34C3×#924C2211yescharacteristic
35C3×#898—21no—
36C3×#896—21no—
37C3×#885—21no—
38C3×#883—21no—
39C3×#875C2211yescharacteristic
40C3×C4×D12C2211yescharacteristic
41C3×#869C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C3×#835C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#830C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic
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—31no—
62C3×#519—21no—
63C3×#519D311yescharacteristic, complemented
64C3×#519C2×C311yescharacteristic, complemented
65#5534C2×C311yescharacteristic
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#5228C2×C311yescharacteristic, complemented
80#5227C2×C311yescharacteristic
81#5030C2×C311yescharacteristic, complemented
82C4×#216C2×C311yescharacteristic, complemented
83#5028C2×C311yescharacteristic, complemented
84#5028C2×C311yescharacteristic, complemented
85#5026C2×C311yescharacteristic, complemented
86C4×#215C2×C311yescharacteristic, complemented
87#5021C2×C311yescharacteristic, complemented
88#5020C2×C311yescharacteristic, complemented
89#5003C2×C311yescharacteristic
90#5000C2×C311yescharacteristic, complemented
91#4996C2×C311yescharacteristic, complemented
92C2×C32×Q8—22no—
93C2×C32×Q8—22no—
94C2×C32×Q8—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2311yescharacteristic
104C32×C4⋊C4—21no—
105C32×C4⋊C4—21no—
106C32×C4⋊C4—21no—
107C32×C4⋊C4—21no—
108C32×C4⋊C4D411yescharacteristic
109C32×C4⋊C4D411yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C32×C22⋊C4D411yescharacteristic
114C32×C22⋊C4D411yescharacteristic
115C32×C42—21no—
116C32×C42—21no—
117C32×C42—21no—
118C32×C42—21no—
119C32×C42—21no—
120C32×C42C2311yescharacteristic
121C32×C42C2311yescharacteristic
122C3×#217—21no—
123C3×#216—22no—
124C3×#216—22no—
125C3×#215—22no—
126C3×#215—22no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—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—21no—
143C22×C3×Q8C2×D311yescharacteristic
144C22×C3×Q8C22×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×#124—31no—
152C3×#124—61no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—61no—
156C3×#121—31no—
157C3×C4×Q8—22no—
158C3×C4×Q8—22no—
159C3×C4×Q8—21no—
160C3×C4×Q8—21no—
161C3×C4×Q8—21no—
162C3×C4×Q8—21no—
163C3×C4×Q8—21no—
164C3×C4×Q8—21no—
165C3×C4×Q8—21no—
166C3×C4×Q8—21no—
167C3×C4×Q8—31no—
168C3×C4×Q8C2×D311yescharacteristic
169C3×C4×Q8C2×D311yescharacteristic
170C3×C4×Q8C2×D311yescharacteristic
171C3×C4×Q8C2×D311yescharacteristic
172C3×C4×Q8C22×C311yescharacteristic
173C3×C4×Q8C22×C311yescharacteristic
174C3×C4×Q8C22×C311yescharacteristic
175C3×C4×Q8C22×C311yescharacteristic
176C3×C4×D4—31no—
177C3×#117—22no—
178C3×#117—22no—
179C3×#117—21no—
180C3×#117—21no—
181C3×#117—21no—
182C3×#117—21no—
183C3×#117—21no—
184C3×#117—21no—
185C3×#117C2×D311yescharacteristic
186C3×#117C2×D311yescharacteristic
187C3×#117C22×C311yescharacteristic
188C3×#117C22×C311yescharacteristic
189C2×#216C22×C311yescharacteristic
190C2×#216C22×C311yescharacteristic
191C2×#215C22×C311yescharacteristic
192C2×#215C22×C311yescharacteristic
193#930C22×C311yescharacteristic
194#924C22×C311yescharacteristic
195#898—21no—
196#896—21no—
197#885—21no—
198#883—21no—
199#875C22×C311yescharacteristic
200C4×D12C22×C311yescharacteristic
201#869C22×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#835C22×C311yescharacteristic
224#835C22×C311yescharacteristic
225#830C22×C311yescharacteristic
226#830C22×C311yescharacteristic
227#810C22×C311yescharacteristic
228#810C22×C311yescharacteristic
229#809C22×C311yescharacteristic
230#809C22×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×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C32×Q8—24no—
242C32×Q8—21no—
243C32×Q8—21no—
244C32×Q8#4112yes—
245C32×Q8#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—21no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259C3×#67—81no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×C4×D3—81no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—81no—
269C3×C3⋊C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272C3×C3⋊C8—21no—
273#542—31no—
274#519C3×D311yescharacteristic, complemented
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—24no—
290C2×C3×Q8—24no—
291C2×C3×Q8—22no—
292C2×C3×Q8—22no—
293C2×C3×Q8—22no—
294C2×C3×Q8—22no—
295C2×C3×Q8—21no—
296C2×C3×Q8—21no—
297C2×C3×Q8—21no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8—61no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C23×C311yescharacteristic
304C2×C3×Q8C23×C311yescharacteristic
305C2×C3×D4—31no—
306C2×C3×D4—61no—
307C22×C3×C4—22no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—61no—
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C23×C311yescharacteristic
314C2×#67—21no—
315C2×D12C23×C311yescharacteristic
316C2×C4×D3—21no—
317C2×Dic6—21no—
318C2×Dic6C23×C311yescharacteristic
319C3×Q16—62no—
320C3×Q16—62no—
321C3×SD16—62no—
322C3×SD16—62no—
323C2×C3×C8—31no—
324C2×C3×C8—31no—
325C2×C3×C8—31no—
326C2×C3×C8—31no—
327C3×C4⋊C4—22no—
328C3×C4⋊C4—22no—
329C3×C4⋊C4—22no—
330C3×C4⋊C4—22no—
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—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#6711yescharacteristic
349C3×C4⋊C4#6711yescharacteristic
350C3×C4⋊C4C3×D411yescharacteristic
351C3×C4⋊C4C3×D411yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C23×C311yescharacteristic
355C3×C4⋊C4C23×C311yescharacteristic
356C3×C22⋊C4—22no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4#6711yescharacteristic
367C3×C22⋊C4#6711yescharacteristic
368C3×C22⋊C4C3×D411yescharacteristic
369C3×C22⋊C4C3×D411yescharacteristic
370C3×C42—22no—
371C3×C42—22no—
372C3×C42—22no—
373C3×C42—22no—
374C3×C42—22no—
375C3×C42—21no—
376C3×C42—21no—
377C3×C42—21no—
378C3×C42—21no—
379C3×C42—21no—
380C3×C42—21no—
381C3×C42—21no—
382C3×C42—21no—
383C3×C42—21no—
384C3×C42—21no—
385C3×C42—21no—
386C3×C42—21no—
387C3×C42—61no—
388C3×C42C22×D311yescharacteristic
389C3×C42C22×D311yescharacteristic
390C3×C42C23×C311yescharacteristic
391C3×C42C23×C311yescharacteristic
392#217—21no—
393#216—22no—
394#216—22no—
395#215—22no—
396#215—22no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—21no—
399(C2×D3)⋊C4—21no—
400(C2×D3)⋊C4—21no—
401C4⋊Dic3—21no—
402C4⋊Dic3C23×C311yescharacteristic
403C4⋊Dic3C23×C311yescharacteristic
404Dic3⋊C4—21no—
405Dic3⋊C4—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—21no—
413C22×C32—21no—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C32×C4—22no—
419C32×C4—22no—
420C32×C4—21no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4C2×#4111yescharacteristic
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C22×Q8C2×C3×D311yescharacteristic
433C2×Q16—31no—
434C2×Q16—31no—
435C2×SD16—31no—
436C2×SD16—31no—
437C4⋊Q8—31no—
438#126—61no—
439#124—31no—
440#124—61no—
441#123—61no—
442C22⋊Q8—31no—
443C22⋊Q8—61no—
444#121—31no—
445C4×Q8—21no—
446C4×Q8—21no—
447C4×Q8—31no—
448C4×Q8C2×C3×D311yescharacteristic
449C4×Q8C2×C3×D311yescharacteristic
450C4×Q8C2×C3×D311yescharacteristic
451C4×Q8C2×C3×D311yescharacteristic
452C4×D4—31no—
453#117—21no—
454#117—21no—
455#117C2×C3×D311yescharacteristic
456#117C2×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—21no—
476C23×C3—61no—
477C23×C3C2×#6711yescharacteristic
478C23×C3C2×C3×D411yescharacteristic
479C22×D3—21no—
480C3×Q8—28no—
481C3×Q8—24no—
482C3×Q8—24no—
483C3×Q8—22no—
484C3×Q8—22no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—22no—
490C3×Q8—22no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×Q8—241no—
494C3×Q8#23512yes—
495C3×Q8#23512yes—
496C3×Q8C3×#4112yes—
497C3×Q8C3×#4112yes—
498C3×D4—61no—
499C3×D4—61no—
500C3×D4—241no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—28no—
504C2×C3×C4—24no—
505C2×C3×C4—24no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
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—21no—
519C2×C3×C4—21no—
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—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—241no—
532C2×C3×C4C2×#6711yescharacteristic
533C2×C3×C4C2×#6711yescharacteristic
534C2×C3×C4C2×#6711yescharacteristic
535C2×C3×C4C2×#6711yescharacteristic
536C2×C3×C4C2×#6711yescharacteristic
537C2×C3×C4C2×C3×D411yescharacteristic
538C2×C3×C4C2×C3×D411yescharacteristic
539C2×C3×C4C2×C3×D411yescharacteristic
540C2×C3×C4C2×C3×D411yescharacteristic
541C2×C3×C4C2×C3×D411yescharacteristic
542C2×C3×C4C23×D311yescharacteristic
543C2×C3×C4C24×C311yescharacteristic
544#67—81no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548D12—21no—
549D12—21no—
550C4×D3—81no—
551Dic6—21no—
552Dic6—21no—
553Dic6—81no—
554C3×C8—61no—
555C3×C8—61no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—21no—
561C3⋊C8—21no—
562C2×C32—41no—
563C2×C32#52511yescharacteristic
564C2×C32#57711yescharacteristic
565C2×C32#57811yescharacteristic
566C3×D3—81no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—21no—
570C2×Q8—31no—
571C2×Q8—61no—
572C2×Q8C22×C3×D311yescharacteristic
573C2×Q8C22×C3×D311yescharacteristic
574C2×D4—31no—
575C2×D4—61no—
576C22×C4—21no—
577C22×C4—61no—
578C22×C4C22×C3×D311yescharacteristic
579Q16—62no—
580Q16—62no—
581SD16—62no—
582SD16—62no—
583C2×C8—31no—
584C2×C8—31no—
585C2×C8—31no—
586C2×C8—31no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4C3×#6711yescharacteristic
597C4⋊C4C3×#6711yescharacteristic
598C4⋊C4C22×C3×D311yescharacteristic
599C4⋊C4C22×C3×D311yescharacteristic
600C22⋊C4—21no—
601C22⋊C4—61no—
602C22⋊C4—61no—
603C22⋊C4—61no—
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4C3×#6711yescharacteristic
607C22⋊C4C3×#6711yescharacteristic
608C42—21no—
609C42—21no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42—61no—
614C42C22×C3×D311yescharacteristic
615C42C22×C3×D311yescharacteristic
616C22×C3—22no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—121no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3C22×#6711yescharacteristic
630C22×C3C22×C3×D411yescharacteristic
631C2×D3—41no—
632C2×D3—41no—
633C2×D3—41no—
634C3×C4—24no—
635C3×C4—24no—
636C3×C4—22no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—22no—
642C3×C4—22no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—22no—
649C3×C4—22no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—42no—
658C3×C4—42no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4C2×#23511yescharacteristic
667C3×C4C2×#23511yescharacteristic
668C3×C4C2×C3×#4111yescharacteristic
669C3×C4C2×C3×#4111yescharacteristic
670Dic3—41no—
671Dic3—41no—
672Dic3—41no—
673C32#312111yescharacteristic, complemented, Sylow
674C23—61no—
675C23C2×C3×#6711yescharacteristic
676Q8—24no—
677Q8—21no—
678Q8—21no—
679Q8—61no—
680Q8—61no—
681Q8—241no—
682Q8C3×#23512yes—
683Q8C3×#23512yes—
684D4—61no—
685D4—61no—
686D4—241no—
687C2×C4—24no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—241no—
698C2×C4C2×C3×#6711yescharacteristic
699C2×C4C2×C3×#6711yescharacteristic
700C2×C4C2×C3×#6711yescharacteristic
701C2×C4C2×C3×#6711yescharacteristic
702C2×C4C2×C3×#6711yescharacteristic
703C2×C4C23×C3×D311yescharacteristic
704C8—61no—
705C8—61no—
706C8—61no—
707C8—61no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—42no—
712C2×C3—41no—
713C2×C3—41no—
714C2×C3—241no—
715C2×C3#579111yescharacteristic
716C2×C3#583711yescharacteristic
717C2×C3#583811yescharacteristic
718C2×C3C3×#52511yescharacteristic
719C2×C3C3×#57711yescharacteristic
720C2×C3C3×#57811yescharacteristic
721D3—81no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—121no—
726C22—121no—
727C22—121no—
728C22C22×C3×#6711yescharacteristic
729C4—22no—
730C4—22no—
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—21no—
736C4—41no—
737C4—41no—
738C4—121no—
739C4—121no—
740C4—121no—
741C4C2×C3×#23511yescharacteristic
742C4C2×C3×#23511yescharacteristic
743C3—21no—
744C3#8255211yescharacteristic, direct product factor
745C3C3×#312111yescharacteristic, complemented
746C2—41no—
747C2—241no—
748C2C3×#579111yescharacteristic
749C2C3×#583711yescharacteristic
750C2C3×#583811yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#519C2
socleC22×C32C22×D4
prime radicalC3×#930C22
hypercenterC3×#519D3
hypocenterC3C3×#3121
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#519

Complements

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

NH ≅ G/Ntype
1. C32×#519C2semidirect
3. C3×#5228C2semidirect
5. C3×#5030C2semidirect
6. C3×C4×#216C2semidirect
7. C3×#5028C2semidirect
8. C3×#5028C2semidirect
9. C3×#5026C2semidirect
10. C3×C4×#215C2semidirect
11. C3×#5021C2semidirect
12. C3×#5020C2semidirect
14. C3×#5000C2semidirect
15. C3×#4996C2semidirect
17. #82552C3direct (N × H)
63. C3×#519D3semidirect
64. C3×#519C2×C3semidirect
79. #5228C2×C3semidirect
81. #5030C2×C3semidirect
82. C4×#216C2×C3semidirect
83. #5028C2×C3semidirect
84. #5028C2×C3semidirect
85. #5026C2×C3semidirect
86. C4×#215C2×C3semidirect
87. #5021C2×C3semidirect
88. #5020C2×C3semidirect
90. #5000C2×C3semidirect
91. #4996C2×C3semidirect
274. #519C3×D3semidirect
673. C32#3121semidirect
744. C3#82552direct (N × H)
745. C3C3×#3121semidirect

Maximal subgroups

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

subgroupindex
C32×#5192
C3×#55342
C3×#52282
C3×#52272
C3×#50302
C3×C4×#2162
C3×#50282
C3×#50262
C3×C4×#2152
C3×#50212
C3×#50202
C3×#50032
C3×#50002
C3×#49962
C3×#31213
#825523