Finite Group Databasebeta

← #11887625

Subgroups — #11887625

Order 1152.

857 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5511C211yesmaximal, characteristic
2#10594915C211yesmaximal, characteristic
3C2×#63637C211yesmaximal, characteristic, complemented
4C3×#4970C211yesmaximal, characteristic, complemented
5#10591190C211yesmaximal, characteristic, complemented
6#10591188C211yesmaximal, characteristic, complemented
7#67⋊(C3⋊C8)C211yesmaximal, characteristic
8#10590604C211yesmaximal, characteristic, complemented
9D3×#810C211yesmaximal, characteristic, complemented
10#10590579C211yesmaximal, characteristic, complemented
11#10590561C211yesmaximal, characteristic, complemented
12#10590560C211yesmaximal, characteristic, complemented
13#10590488C211yesmaximal, characteristic, complemented
14#10590481C211yesmaximal, characteristic, complemented
15#10590427C211yesmaximal, characteristic, complemented
16#83640—31nomaximal
17#81490—31nomaximal
18C22×#634C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×#67—21no—
23C3×C4×#67C2211yescharacteristic
24C3×#924—21no—
25C3×#924C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C3×#897C2211yescharacteristic
28C3×#896—21no—
29C3×D3×C4⋊C4C2211yescharacteristic
30C3×#889—21no—
31C3×#888C2211yescharacteristic
32C3×#887C2211yescharacteristic
33#63982—21no—
34#67⋊Dic3—21no—
35#63896—21no—
36#63866C2211yescharacteristic
37#63857C2211yescharacteristic
38#63844C2211yescharacteristic
39#63840—21no—
40C2×#3719C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63637C2211yescharacteristic
45#63637C2211yescharacteristic
46#63637C2211yescharacteristic
47#63637C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63576C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#554—31no—
62#5632—31no—
63D4×Dic6—31no—
64#5511D311yescharacteristic
65C3×#484—31no—
66#5093—31no—
67#5091—31no—
68#5051—31no—
69#5051—31no—
70#5051—31no—
71#5050—31no—
72#5050—31no—
73#5031—31no—
74C4×#216—31no—
75D4×C3⋊C8—31no—
76#4970—31no—
77#4970D311yescharacteristic, complemented
78C2×#810—31no—
79C2×#810—31no—
80C2×#810—31no—
81C2×#810—61no—
82#4887—31no—
83#4884—31no—
84#4875—31no—
85#4873—31no—
86#4809—31no—
87D3×#103—31no—
88#4795—31no—
89#4792—31no—
90#4739—31no—
91#67⋊C8—31no—
92C22×C32×C4—21no—
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634—22no—
96C2×#634—21no—
97C2×#634—41no—
98C2×#634C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#627—21no—
107C2×D3×Dic3—21no—
108D3×Dic6—22no—
109D3×Dic6—41no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C2×C3⋊(C3⋊C8)—41no—
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#217—21no—
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140#3719—22no—
141#3719—41no—
142#3718—41no—
143D3×C3⋊C8—41no—
144#3299—91noSylow
145C2×D3×Q8—31no—
146C22×Dic6—31no—
147C22×Dic6—31no—
148C22×Dic6—31no—
149C22×Dic6—61no—
150C3×C4⋊Q8—31no—
151C3×#125—61no—
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—61no—
156C3×C22⋊Q8—61no—
157C3×C4×Q8—31no—
158C3×C4×D4—31no—
159C3×C4×D4—61no—
160C2×C3×C4⋊C4—21no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4C2×D311yescharacteristic
163C2×C3×C4⋊C4C2×D311yescharacteristic
164#944—31no—
165C2×#216—31no—
166C2×#216—31no—
167C2×#216—31no—
168C2×#216—31no—
169D4×Dic3—61no—
170C4×#67—21no—
171C4×#67C2×D311yescharacteristic
172#924—21no—
173#924—31no—
174#924C2×D311yescharacteristic
175#924C2×D311yescharacteristic
176C22×C3⋊C8—31no—
177C22×C3⋊C8—31no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—61no—
180C2×Dic12—31no—
181C2×Dic12—31no—
182C2×D3×C8—31no—
183#897—31no—
184#897C2×D311yescharacteristic
185#896—21no—
186#896—61no—
187D3×C4⋊C4C2×D311yescharacteristic
188#889—21no—
189#888—61no—
190#888—61no—
191#888C2×D311yescharacteristic
192#887—31no—
193#887C2×D311yescharacteristic
194#67⋊C4—61no—
195#878—61no—
196#878—61no—
197#878—61no—
198#869—31no—
199C4×Dic6—31no—
200C3×#107—31no—
201C3×#107—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×C22⋊C8—31no—
205#835—31no—
206#835—31no—
207#830—31no—
208#830C2×D311yescharacteristic
209(C2×D3)⋊C8—31no—
210#816—31no—
211#816—31no—
212Dic3⋊C8—31no—
213C8×Dic3—31no—
214#810—31no—
215#810—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—61no—
227#810—61no—
228#810—61no—
229#810—61no—
230#810C2×D311yescharacteristic
231#810C2×D311yescharacteristic
232#807—31no—
233#807—31no—
234#807C2×D311yescharacteristic
235#807C2×D311yescharacteristic
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—81no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—42no—
250#634—21no—
251#634—21no—
252#634—21no—
253#634—42no—
254#634#4112yes—
255C3×#67Q1614yescomplemented
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—81no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—81no—
271#627—42no—
272D3×Dic3—42no—
273C3⋊(C3⋊C8)—21no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#554—31no—
278D4×Q8—91no—
279#487—91no—
280#484—31no—
281#484—91no—
282#477—91no—
283#467—91no—
284#467—91no—
285#462—91no—
286#451—91no—
287#451—91no—
288C4×Q16—91no—
289C8×D4—91no—
290C2×#103—91no—
291C2×#103—91no—
292C2×C3×Q8—31no—
293C2×C3×Q8—31no—
294C2×C3×Q8—61no—
295C2×C3×D4—31no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—31no—
300C22×C3×C4—41no—
301C22×C3×C4—61no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C2×#67#6711yescharacteristic
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3—121no—
309D3×Q8—62no—
310D3×Q8—121no—
311C2×C4×D3—21no—
312C2×C4×D3—61no—
313C2×C4×D3C22×D311yescharacteristic
314C2×Dic6—21no—
315C2×Dic6—31no—
316C2×Dic6—31no—
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—61no—
320C2×Dic6—61no—
321C2×Dic6—62no—
322C2×Dic6—62no—
323C2×Dic6—62no—
324C2×Dic6—64no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C2×Dic6—121no—
330C2×Dic6—121no—
331C2×Dic6—121no—
332C2×Dic6—121no—
333C2×Dic6—122no—
334C2×Dic6C22×D311yescharacteristic
335C2×Dic6C22×D311yescharacteristic
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—41no—
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⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C22⋊C4—31no—
357C3×C22⋊C4—31no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C42—31no—
362C3×C42—61no—
363#217—21no—
364#217—21no—
365#217—61no—
366#217#6711yescharacteristic
367#216—62no—
368#216—121no—
369#216—121no—
370#216—121no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4#6711yescharacteristic
374C4⋊Dic3—21no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
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#6711yescharacteristic
391C4×Dic3—21no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3C22×D311yescharacteristic
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—121no—
402C2×C3⋊C8—121no—
403C2×C3⋊C8—121no—
404C2×C3⋊C8—122no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407Dic12—62no—
408Dic12—121no—
409D3×C8—121no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32C2×Q1612yes—
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3C2×Q1612yes—
417C32×C4—21no—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4C2×#4111yescharacteristic
421C32×C4H(5,𝔽2)11yescharacteristic
422C3⋊Dic3—22no—
423C3⋊Dic3—41no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3C2×Q1612yes—
431C22×Q8—91no—
432C22×Q8—91no—
433C2×Q16—91no—
434C2×Q16—91no—
435C2×Q16—91no—
436C22×C8—91no—
437C22×C8—91no—
438C4⋊Q8—31no—
439C4⋊Q8—91no—
440C4⋊Q8—181no—
441#125—61no—
442C22⋊Q8—31no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—61no—
446C22⋊Q8—61no—
447C22⋊Q8—91no—
448C22⋊Q8—181no—
449C22⋊Q8—181no—
450C4×Q8—31no—
451C4×Q8—91no—
452C4×D4—31no—
453C4×D4—61no—
454C4×D4—181no—
455C2×C4⋊C4—31no—
456C2×C4⋊C4D3211yescharacteristic
457#107—31no—
458#107—31no—
459#107—91no—
460C4⋊C8—91no—
461#103—31no—
462#103—31no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471C22⋊C8—31no—
472C22⋊C8—91no—
473C4×C8—91no—
474C23×C3—21no—
475C23×C3—31no—
476C23×C3D3×D411yescharacteristic
477C23×C3C2×#6711yescharacteristic
478C22×D3C2×#6711yescharacteristic
479C3×Q8—61no—
480C3×Q8—61no—
481C3×Q8—61no—
482C3×Q8—61no—
483C3×Q8—241no—
484C3×D4—34no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—81no—
509C2×C3×C4—81no—
510C2×C3×C4—82no—
511C2×C3×C4—241no—
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4C2×#6711yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516#67#21614yescomplemented
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—121no—
526C2×Dic3—121no—
527C2×Dic3—122no—
528C2×Dic3—122no—
529C2×Dic3—122no—
530C2×Dic3—124no—
531C2×Dic3C2×#6711yescharacteristic
532C2×Dic3C2×#6711yescharacteristic
533C2×Dic3C2×#6711yescharacteristic
534C4×D3—21no—
535C4×D3—21no—
536C4×D3—81no—
537C4×D3—122no—
538Dic6—21no—
539Dic6—21no—
540Dic6—21no—
541Dic6—21no—
542Dic6—32no—
543Dic6—32no—
544Dic6—62no—
545Dic6—61no—
546Dic6—61no—
547Dic6—62no—
548Dic6—61no—
549Dic6—61no—
550Dic6—61no—
551Dic6—61no—
552Dic6—81no—
553Dic6—121no—
554Dic6—121no—
555Dic6—122no—
556Dic6—122no—
557Dic6—122no—
558Dic6—122no—
559Dic6—124no—
560C3×C8—61no—
561C3×C8—61no—
562C3⋊C8—21no—
563C3⋊C8—21no—
564C3⋊C8—61no—
565C3⋊C8—61no—
566C3⋊C8—61no—
567C3⋊C8—61no—
568C3⋊C8—121no—
569C3⋊C8—121no—
570C2×C32—22no—
571C2×C32#54611yescharacteristic
572C2×C32C22×Q1611yescharacteristic
573C2×C32#57711yescharacteristic
574C3×D3—22no—
575C2×Q8—31no—
576C2×Q8—31no—
577C2×Q8—61no—
578C2×Q8—91no—
579C2×Q8—91no—
580C2×Q8—182no—
581C2×Q8—181no—
582C2×Q8—182no—
583C2×Q8—181no—
584C2×Q8—361no—
585C2×Q8—361no—
586C2×D4—31no—
587C22×C4—21no—
588C22×C4—31no—
589C22×C4—61no—
590C22×C4—181no—
591C22×C4—181no—
592C22×C4C2×D3211yescharacteristic
593Q16—182no—
594Q16—361no—
595Q16—361no—
596C2×C8—31no—
597C2×C8—31no—
598C2×C8—91no—
599C2×C8—91no—
600C2×C8—361no—
601C2×C8—361no—
602C4⋊C4—21no—
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4C2×D3211yescharacteristic
617C4⋊C4C2×D3211yescharacteristic
618C22⋊C4—31no—
619C22⋊C4—31no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—181no—
624C42—31no—
625C42—61no—
626C42—181no—
627C22×C3—22no—
628C22×C3—22no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—22no—
635C22×C3—32no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3D3×Q1612yes—
639C22×C3C2×#21612yes—
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C22×#6711yescharacteristic
642C2×D3—21no—
643C2×D3—21no—
644C2×D3C2×#21612yes—
645C3×C4—22no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—32no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—81no—
658C3×C4—81no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4D3×#4111yescharacteristic
664C3×C4D3×#4111yescharacteristic
665C3×C4#100911yescharacteristic
666C3×C4#100911yescharacteristic
667Dic3—21no—
668Dic3—21no—
669Dic3—41no—
670Dic3—41no—
671Dic3—41no—
672Dic3—41no—
673Dic3—62no—
674Dic3—62no—
675Dic3—122no—
676Dic3—122no—
677Dic3—121no—
678Dic3—121no—
679Dic3C2×#21612yes—
680C32#329911yescharacteristic, complemented, Sylow
681C23—31no—
682C23D3×#6711yescharacteristic
683Q8—61no—
684Q8—61no—
685Q8—61no—
686Q8—61no—
687Q8—92no—
688Q8—181no—
689Q8—181no—
690Q8—181no—
691Q8—241no—
692Q8—362no—
693Q8—362no—
694D4—34no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—81no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—241no—
712C2×C4—362no—
713C2×C4—362no—
714C2×C4D3×#6711yescharacteristic
715C2×C4C22×D3211yescharacteristic
716C8—61no—
717C8—61no—
718C8—181no—
719C8—181no—
720C2×C3—24no—
721C2×C3—22no—
722C2×C3—22no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—62no—
727C2×C3#565411yescharacteristic
728C2×C3C2×D3×Q1611yescharacteristic
729C2×C3#577511yescharacteristic
730C2×C3C22×#21611yescharacteristic
731C2×C3#582911yescharacteristic
732C2×C3#583611yescharacteristic
733D3—22no—
734C22—21no—
735C22—21no—
736C22—32no—
737C22—61no—
738C22—61no—
739C22D3×#21612yes—
740C22C2×D3×#6711yescharacteristic
741C4—21no—
742C4—32no—
743C4—41no—
744C4—41no—
745C4—61no—
746C4—61no—
747C4—121no—
748C4—121no—
749C4—121no—
750C4—121no—
751C4—182no—
752C4—361no—
753C4#6430611yescharacteristic
754C4#6430811yescharacteristic
755C3—21no—
756C3#8149011yescharacteristic, complemented
757C3#8364011yescharacteristic, complemented
758C2—22no—
759C2—62no—
760C2#1059506811yescharacteristic
761C2#1059510611yescharacteristic
762C2C2×D3×#21611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×C3×#67D4
hypercenterC2×C4⋊C4D32
hypocenterC32#3299
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#63637C2semidirect
4. C3×#4970C2semidirect
5. #10591190C2semidirect
6. #10591188C2semidirect
8. #10590604C2semidirect
9. D3×#810C2semidirect
10. #10590579C2semidirect
11. #10590561C2semidirect
12. #10590560C2semidirect
13. #10590488C2semidirect
14. #10590481C2semidirect
15. #10590427C2semidirect
77. #4970D3semidirect
255. C3×#67Q16semidirect
516. #67#216semidirect
680. C32#3299semidirect
756. C3#81490semidirect
757. C3#83640semidirect

Maximal subgroups

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

subgroupindex
C3×#55112
#105949152
C2×#636372
C3×#49702
#105911902
#105911882
#67⋊(C3⋊C8)2
#105906042
D3×#8102
#105905792
#105905612
#105905602
#105904882
#105904812
#105904272
#836403
#814903