Finite Group Databasebeta

← #11860944

Subgroups — #11860944

Order 1152.

1029 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5546C211yesmaximal, characteristic, complemented
2C2×#63933C211yesmaximal, characteristic
3#10593887C211yesmaximal, characteristic, complemented
4C4×#3754C211yesmaximal, characteristic, complemented
5C3×#5014C211yesmaximal, characteristic, complemented
6#10591430C211yesmaximal, characteristic, complemented
7#10591414C211yesmaximal, characteristic, complemented
8#10591401C211yesmaximal, characteristic, complemented
9#10590607C211yesmaximal, characteristic, complemented
10D3×#808C211yesmaximal, characteristic, complemented
11#10590480C211yesmaximal, characteristic, complemented
12#10590453C211yesmaximal, characteristic, complemented
13#10590383C211yesmaximal, characteristic, complemented
14C4×#3715C211yesmaximal, characteristic, complemented
15#10590319C211yesmaximal, characteristic, complemented
16#82558—31nomaximal
17#79868—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#213C2211yescharacteristic
25C3×C4×#67—21no—
26C2×C3×Dic3⋊C4—21no—
27C3×D3×C4⋊C4C2211yescharacteristic
28C3×#887C2211yescharacteristic
29C3×#67⋊C4—21no—
30C3×#877—21no—
31C3×C4×D12C2211yescharacteristic
32C3×#872C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63933C418yescomplemented
35#63902—21no—
36Dic3×D12C2211yescharacteristic
37D3×C4⋊Dic3C2211yescharacteristic
38#63879—21no—
39#63878—21no—
40D3×Dic3⋊C4—21no—
41#63844C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C2×#3715C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46#63659C2211yescharacteristic
47#63637C2211yescharacteristic
48#63635C2211yescharacteristic
49C4×C3⋊(C3⋊C8)C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic
53C3×#803C2211yescharacteristic
54#63574C2211yescharacteristic
55#63573C2211yescharacteristic
56#63567C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59#63562C2211yescharacteristic
60#63554C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C3×#520—31no—
63C2×#950—31no—
64C2×#912—31no—
65#5546—31no—
66#5546D311yescharacteristic, complemented
67#5523—31no—
68C3×#442—31no—
69#5232—31no—
70#5152—31no—
71#5030—31no—
72#5030—31no—
73C4×#215—31no—
74C4×#215—31no—
75C4×#214—31no—
76C4×#214—31no—
77C4×#214—31no—
78C4×#214—31no—
79C4×#214—61no—
80#5014—31no—
81#5014D311yescharacteristic, complemented
82#4997—31no—
83#4966—31no—
84C2×#808—31no—
85D3×#106—31no—
86#4853—31no—
87#4771—31no—
88#4771—31no—
89#4758—31no—
90#4758—31no—
91#4716—31no—
92#4708—31no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C3×#237—22no—
100C3×#237C2×C414yescomplemented
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#625—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—22no—
111#3795C2×C414yescomplemented
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C42C2311yescharacteristic
115#3754C2×C414yescomplemented
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C4×C3⋊Dic3—21no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217—21no—
122C3×#213C2×C414yescomplemented
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3724—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3719C2×C414yescomplemented
143#3715C2×C414yescomplemented
144#3711—22no—
145D3×C3⋊C8C2×C414yescomplemented
146#2952—91noSylow
147C2×C3×#41—31no—
148C2×#237—31no—
149C2×#237C2×D311yescharacteristic
150C2×#235—31no—
151C2×C3×D8—31no—
152C3×C4×Q8—31no—
153C3×C4×Q8—31no—
154C3×C4×D4—21no—
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157C3×C4×D4—61no—
158C3×C4×D4—61no—
159C3×C4×D4C2×D311yescharacteristic
160C3×C4×D4C2×D311yescharacteristic
161C3×#117—31no—
162C3×#117—61no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—61no—
165#950—38no—
166C2×#216—31no—
167C2×#215—31no—
168D4×Dic3—31no—
169D4×Dic3C2×D311yescharacteristic
170C2×#214—31no—
171C2×#214—31no—
172C2×#214—31no—
173C2×#214—61no—
174C2×#213C2×D311yescharacteristic
175C4×#67—21no—
176C4×#67—61no—
177C2×C4⋊Dic3—31no—
178C2×Dic3⋊C4—21no—
179C2×Dic3⋊C4—61no—
180C2×#208—31no—
181C22×C3⋊C8—31no—
182#912—38no—
183C2×Dic12—31no—
184C2×ΓL(1,𝔽25)—31no—
185C2×D3×C8—31no—
186#892—61no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—61no—
189D3×C4⋊C4C2×D311yescharacteristic
190#887—31no—
191#887C2×D311yescharacteristic
192#67⋊C4—21no—
193#67⋊C4—61no—
194#67⋊C4—61no—
195#67⋊C4—61no—
196#877—21no—
197#877—61no—
198C4×D12—31no—
199C4×D12C2×D311yescharacteristic
200#872C2×D311yescharacteristic
201C4×Dic6—31no—
202C4×Dic6—31no—
203C4×Dic6—31no—
204C4×Dic6—61no—
205C4×Dic6C2×D311yescharacteristic
206C3×#106—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#97—31no—
210#835—31no—
211#835—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—61no—
216#832C2×D311yescharacteristic
217#817—31no—
218#816—31no—
219#816—31no—
220#815—31no—
221C8×Dic3—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—61no—
227#809—31no—
228#809C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#808—31no—
232#808—31no—
233#808—31no—
234#808—61no—
235#808C2×D311yescharacteristic
236#803—31no—
237#803C2×D311yescharacteristic
238C4×C3⋊C8—31no—
239C4×C3⋊C8—31no—
240C4×C3⋊C8—31no—
241C4×C3⋊C8—61no—
242C23×C32—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4C22×C412yes—
247C2×C32×C4—21no—
248C2×C32×C4—81no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254#634—21no—
255#634C22×C412yes—
256C3×#67—24no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—24no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12C22×C412yes—
267C3×C4×D3—81no—
268C3×C4×D3—81no—
269C3×C4×D3C22×C412yes—
270C3×C4×D3#4112yes—
271C3×Dic6—21no—
272C3×Dic6C22×C412yes—
273#625—24no—
274D3×Dic3—24no—
275D3×Dic3—81no—
276D3×Dic3—81no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)C22×C412yes—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C2×#135—91no—
282#520—31no—
283#520—91no—
284#442—31no—
285#442—91no—
286#441—91no—
287#441—91no—
288C4×SD16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291C4×SD16—91no—
292C2×#106—91no—
293#417—91no—
294#417—91no—
295#405—91no—
296C3×#41—34no—
297C3×#41—62no—
298C2×C3×Q8—31no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—41no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C2×#67—21no—
313C2×#67—61no—
314C2×#67—61no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320#237—22no—
321#237—34no—
322#237—62no—
323#237C4×D314yescomplemented
324#235—34no—
325#235—62no—
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—21no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C2×Dic6C22×D311yescharacteristic
337C3×D8—34no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—41no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—21no—
358C3×C42—31no—
359C3×C42—61no—
360C3×C42—61no—
361C3×C42C22×D311yescharacteristic
362C3×C42C22×D311yescharacteristic
363#217—21no—
364#217—61no—
365#216—34no—
366#215—34no—
367#214—34no—
368#214—34no—
369#214—34no—
370#214—64no—
371#213C4×D314yescomplemented
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4#6711yescharacteristic
375(C2×D3)⋊C4#6711yescharacteristic
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—121no—
391Dic3⋊C4#6711yescharacteristic
392Dic3⋊C4#6711yescharacteristic
393C4×Dic3—21no—
394C4×Dic3—21no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—121no—
400C4×Dic3C22×D311yescharacteristic
401#208—62no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—34no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411Dic12—34no—
412ΓL(1,𝔽25)—62no—
413D3×C8—34no—
414C22×C32—22no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3C4×D412yes—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4C23×C411yescharacteristic
428C32×C4C2×#4111yescharacteristic
429C3⋊Dic3—22no—
430C3⋊Dic3—41no—
431C3×Dic3—22no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3C4×D412yes—
437C2×#41—31no—
438C2×#41—91no—
439#135—98no—
440C2×Q16—91no—
441C2×SD16—91no—
442C2×SD16—91no—
443C2×D8—31no—
444C2×M16—91no—
445C22×C8—91no—
446C4×Q8—31no—
447C4×Q8—31no—
448C4×Q8—91no—
449C4×Q8—91no—
450C4×D4—31no—
451C4×D4—31no—
452C4×D4—61no—
453C4×D4—61no—
454C4×D4—91no—
455C4×D4—181no—
456C4×D4—181no—
457C4×D4D3211yescharacteristic
458#117—31no—
459#117—61no—
460#117—181no—
461C2×C4⋊C4—31no—
462C2×C4⋊C4—61no—
463C2×C4⋊C4—91no—
464C2×C4⋊C4—181no—
465#106—31no—
466#106—91no—
467#106—91no—
468#106—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#97—31no—
478#97—91no—
479C4×C8—91no—
480C4×C8—91no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—41no—
485C23×C3—61no—
486C22×D3—21no—
487C22×D3C2×#6711yescharacteristic
488C3×Q8—32no—
489C3×Q8—61no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—22no—
493C3×D4—32no—
494C3×D4—41no—
495C3×D4—64no—
496C3×D4—61no—
497C3×D4C2×C4×D312yes—
498C3×D4C2×C4×D312yes—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—32no—
506C2×C3×C4—32no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—41no—
510C2×C3×C4—64no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—81no—
515C2×C3×C4—81no—
516C2×C3×C4—82no—
517C2×C3×C4—241no—
518C2×C3×C4—241no—
519C2×C3×C4—241no—
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4C2×#6711yescharacteristic
523C2×C3×C4C2×#6711yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526#67—24no—
527#67—64no—
528#67—64no—
529C2×Dic3—21no—
530C2×Dic3—24no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—64no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—81no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—241no—
542C2×Dic3—241no—
543C2×Dic3C2×#6711yescharacteristic
544C2×Dic3C2×#6711yescharacteristic
545C2×Dic3C2×#6711yescharacteristic
546D12—21no—
547D12C2×C4×D312yes—
548C4×D3—64no—
549C4×D3—81no—
550C4×D3—81no—
551C4×D3—241no—
552C4×D3—241no—
553C4×D3C2×C4×D312yes—
554C4×D3#23512yes—
555Dic6—21no—
556Dic6—32no—
557Dic6—32no—
558Dic6—62no—
559Dic6—61no—
560Dic6—61no—
561Dic6—121no—
562Dic6C2×C4×D312yes—
563C3×C8—32no—
564C3×C8—61no—
565C3⋊C8—21no—
566C3⋊C8—32no—
567C3⋊C8—32no—
568C3⋊C8—62no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—121no—
572C3⋊C8C2×C4×D312yes—
573C2×C32—42no—
574C2×C32C2×C4×D411yescharacteristic
575C2×C32#57711yescharacteristic
576C2×C32#57711yescharacteristic
577C3×D3—22no—
578C3×D3—42no—
579#41—34no—
580#41—62no—
581#41—94no—
582#41—182no—
583C2×Q8—31no—
584C2×Q8—91no—
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—181no—
588C2×D4C2×D3211yescharacteristic
589C22×C4—21no—
590C22×C4—31no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598Q16—94no—
599SD16—94no—
600SD16—94no—
601D8—34no—
602M16—182no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—94no—
606C2×C8—91no—
607C2×C8—91no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—91no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4C2×D3211yescharacteristic
620C22⋊C4—21no—
621C22⋊C4—31no—
622C22⋊C4—31no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—181no—
626C42—31no—
627C42—61no—
628C42—61no—
629C42—181no—
630C42—181no—
631C42C2×D3211yescharacteristic
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—21no—
635C22×C3—32no—
636C22×C3—42no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—62no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3C2×D3×D411yescharacteristic
649C22×C3C22×#6711yescharacteristic
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—22no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3C4×#6712yes—
656C3×C4—22no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—32no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—61no—
668C3×C4—61no—
669C3×C4—62no—
670C3×C4—81no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4C22×C4×D311yescharacteristic
674C3×C4C22×C4×D311yescharacteristic
675C3×C4C2×#23511yescharacteristic
676C3×C4D3×#4111yescharacteristic
677Dic3—22no—
678Dic3—21no—
679Dic3—21no—
680Dic3—41no—
681Dic3—41no—
682Dic3—62no—
683Dic3—62no—
684Dic3—122no—
685Dic3—121no—
686Dic3—121no—
687Dic3—241no—
688Dic3C4×#6712yes—
689C32#295211yescharacteristic, complemented, Sylow
690C23—21no—
691C23—31no—
692C23—61no—
693Q8—32no—
694Q8—61no—
695Q8—92no—
696Q8—181no—
697D4—21no—
698D4—32no—
699D4—64no—
700D4—61no—
701D4—184no—
702D4C4×D3212yes—
703C2×C4—21no—
704C2×C4—31no—
705C2×C4—32no—
706C2×C4—32no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—64no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—81no—
714C2×C4—184no—
715C2×C4—181no—
716C2×C4—181no—
717C2×C4—241no—
718C2×C4—241no—
719C2×C4—241no—
720C2×C4—721no—
721C2×C4—721no—
722C2×C4D3×#6711yescharacteristic
723C2×C4D3×#6711yescharacteristic
724C2×C4C22×D3211yescharacteristic
725C8—32no—
726C8—61no—
727C8—92no—
728C8—181no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—42no—
733C2×C3—42no—
734C2×C3—62no—
735C2×C3—82no—
736C2×C3—122no—
737C2×C3C4×D3×D411yescharacteristic
738C2×C3#577511yescharacteristic
739C2×C3#577511yescharacteristic
740C2×C3C2×C4×#6711yescharacteristic
741C2×C3#583611yescharacteristic
742C2×C3#583711yescharacteristic
743D3—22no—
744D3—42no—
745C22—22no—
746C22—32no—
747C22—41no—
748C22—41no—
749C22—61no—
750C22—61no—
751C22—62no—
752C22—121no—
753C22—121no—
754C22C2×D3×#6711yescharacteristic
755C4—21no—
756C4—21no—
757C4—32no—
758C4—41no—
759C4—61no—
760C4—61no—
761C4—62no—
762C4—121no—
763C4—121no—
764C4—182no—
765C4—361no—
766C4C2×C4×D3211yescharacteristic
767C4D3×#23511yescharacteristic
768C3—21no—
769C3#7986811yescharacteristic, complemented
770C3#8255811yescharacteristic, complemented
771C2—42no—
772C2—62no—
773C2—122no—
774C2C4×D3×#6711yescharacteristic
775C2#1059510611yescharacteristic
776C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×#63933C2
cosocleC2×C32×C4C24
hypercenterC4×D4D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5546C2semidirect
3. #10593887C2semidirect
4. C4×#3754C2semidirect
5. C3×#5014C2semidirect
6. #10591430C2semidirect
7. #10591414C2semidirect
8. #10591401C2semidirect
9. #10590607C2semidirect
10. D3×#808C2semidirect
11. #10590480C2semidirect
12. #10590453C2semidirect
13. #10590383C2semidirect
14. C4×#3715C2semidirect
15. #10590319C2semidirect
34. #63933C4semidirect
66. #5546D3semidirect
81. #5014D3semidirect
100. C3×#237C2×C4semidirect
111. #3795C2×C4semidirect
115. #3754C2×C4semidirect
122. C3×#213C2×C4semidirect
142. #3719C2×C4semidirect
143. #3715C2×C4semidirect
145. D3×C3⋊C8C2×C4semidirect
323. #237C4×D3semidirect
371. #213C4×D3semidirect
689. C32#2952semidirect
769. C3#79868semidirect
770. C3#82558semidirect

Maximal subgroups

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

subgroupindex
C3×#55462
C2×#639332
#105938872
C4×#37542
C3×#50142
#105914302
#105914142
#105914012
#105906072
D3×#8082
#105904802
#105904532
#105903832
C4×#37152
#105903192
#825583
#798683