Finite Group Databasebeta

← #11887627

Subgroups — #11887627

Order 1152.

828 conjugacy classes of subgroups.

The subgroup lattice has 757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5511C211yesmaximal, characteristic
2Dic6×#67C211yesmaximal, characteristic
3#10592669C211yesmaximal, characteristic, complemented
4C2×C3×#810C211yesmaximal, characteristic, complemented
5#10591187C211yesmaximal, characteristic, complemented
6#10591185C211yesmaximal, characteristic, complemented
7C3⋊C8×#67C211yesmaximal, characteristic
8#10590604C211yesmaximal, characteristic, complemented
9D3×#810C211yesmaximal, characteristic, complemented
10#10590561C211yesmaximal, characteristic, complemented
11#10590560C211yesmaximal, characteristic, complemented
12#10590518C211yesmaximal, characteristic, complemented
13#10590517C211yesmaximal, characteristic, complemented
14#10590489C211yesmaximal, characteristic, complemented
15#10590476C211yesmaximal, characteristic, complemented
16#83640—31nomaximal
17#78806—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21#64133C2211yescharacteristic
22C3×C4×#67—21no—
23C3×C4×#67C2211yescharacteristic
24C3×#924—21no—
25C3×#924C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C3×#897C2211yescharacteristic
28C3×#896—21no—
29C3×D3×C4⋊C4C2211yescharacteristic
30C3×#889—21no—
31C3×#888C2211yescharacteristic
32C3×#887C2211yescharacteristic
33Dic3×#67—21no—
34#63964—21no—
35#63887—21no—
36#63866C2211yescharacteristic
37#63856C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39#63839—21no—
40C2×#3719C2211yescharacteristic
41C2×#3718C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63657C2211yescharacteristic
45#63637C2211yescharacteristic
46#63637C2211yescharacteristic
47#63634C2211yescharacteristic
48#63634C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53#63575C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#554—31no—
62Q8×#67—31no—
63D4×Dic6—31no—
64#5511D311yescharacteristic
65C2×C3×#103—31no—
66#5228—31no—
67#5116—31no—
68C8×#67—31no—
69#5093—31no—
70#5091—31no—
71#5051—31no—
72#5051—31no—
73#5050—31no—
74#5050—31no—
75#5031—31no—
76C4×#216—31no—
77D4×C3⋊C8—31no—
78#4970—31no—
79#4970—31no—
80#4970—31no—
81#4970—61no—
82C2×#810—31no—
83C2×#810D311yescharacteristic, complemented
84#4813—31no—
85#4811—31no—
86#4809—31no—
87D3×#103—31no—
88#4795—31no—
89#4793—31no—
90#4792—31no—
91#4790—31no—
92C22×C32×C4—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×#67D411yescharacteristic
96C22×C3×Dic3—21no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6—22no—
100C2×C3×Dic6—21no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6—41no—
103C2×C3×Dic6C2311yescharacteristic
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
113#3757—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4D411yescharacteristic
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8—41no—
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—41no—
141#3718—22no—
142#3718—41no—
143D3×C3⋊C8—41no—
144#3299—91noSylow
145C22×C3×Q8—31no—
146C2×D3×Q8—31no—
147C22×Dic6—31no—
148C22×Dic6C2×D311yescharacteristic
149C22×C3×C8—31no—
150C3×C4⋊Q8—31no—
151C3×#125—61no—
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—61no—
155C3×C22⋊Q8—61no—
156C3×C4×Q8—31no—
157C3×C4×D4—31no—
158C3×C4×D4—61no—
159C2×C3×C4⋊C4—21no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4C2×D311yescharacteristic
162C2×C3×C4⋊C4C2×D311yescharacteristic
163#946—31no—
164#946—61no—
165Q8×Dic3—31no—
166#944—31no—
167#944—61no—
168C2×#216—31no—
169C2×#216—31no—
170C2×#216—31no—
171C2×#216—31no—
172C2×#216—31no—
173D4×Dic3—61no—
174C4×#67—21no—
175C4×#67—61no—
176C4×#67C2×D311yescharacteristic
177#924—21no—
178#924—31no—
179#924—31no—
180#924—31no—
181#924—61no—
182#924—61no—
183#924C2×D311yescharacteristic
184C22×C3⋊C8—31no—
185C22×C3⋊C8C2×D311yescharacteristic
186C2×Dic12—31no—
187C2×D3×C8—31no—
188#897C2×D311yescharacteristic
189#896—21no—
190D3×C4⋊C4C2×D311yescharacteristic
191#889—21no—
192#888—61no—
193#888C2×D311yescharacteristic
194#887C2×D311yescharacteristic
195#878—61no—
196#878—61no—
197#869—31no—
198C4×Dic6—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#830—31no—
207#830—31no—
208#830—31no—
209#830—61no—
210(C2×D3)⋊C8—31no—
211#818—31no—
212#816—31no—
213#816—31no—
214Dic3⋊C8—31no—
215C8×Dic3—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—61no—
224#810—61no—
225#810C2×D311yescharacteristic
226#810C2×D311yescharacteristic
227#810C2×D311yescharacteristic
228#810C2×D311yescharacteristic
229#807—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234#807—61no—
235#807—61no—
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—
249#634—21no—
250#634—21no—
251C3×#67Q1614yescomplemented
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—42no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—81no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—42no—
269C3×Dic6—81no—
270C3×Dic6#4112yes—
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—91no—
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—31no—
291C2×#103—91no—
292C2×C3×Q8—31no—
293C2×C3×Q8—31no—
294C2×C3×Q8—31no—
295C2×C3×Q8—61no—
296C2×C3×Q8—62no—
297C2×C3×Q8—61no—
298C2×C3×Q8—121no—
299C2×C3×D4—31no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—41no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67#6711yescharacteristic
310C22×Dic3—21no—
311C22×Dic3—61no—
312D3×Q8—62no—
313D3×Q8—121no—
314C2×C4×D3—21no—
315C2×C4×D3—61no—
316C2×C4×D3C22×D311yescharacteristic
317C2×Dic6—22no—
318C2×Dic6—21no—
319C2×Dic6—21no—
320C2×Dic6—31no—
321C2×Dic6—31no—
322C2×Dic6—41no—
323C2×Dic6—61no—
324C2×Dic6—62no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6—121no—
328C2×Dic6C22×D311yescharacteristic
329C2×Dic6C22×D311yescharacteristic
330C2×Dic6C22×D311yescharacteristic
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C2×C3×C8—121no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—41no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—31no—
351C3×C22⋊C4—31no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—31no—
355C3×C42—61no—
356#217—21no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—121no—
361#217#6711yescharacteristic
362#216—62no—
363#216—62no—
364#216—121no—
365#216—121no—
366#216—121no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4#6711yescharacteristic
370C4⋊Dic3—21no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—121no—
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—41no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—121no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405Dic12—121no—
406D3×C8—121no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32C2×Q1612yes—
410C22×C32C22×D411yescharacteristic
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3C2×Q1612yes—
414C32×C4—21no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4C2×#4111yescharacteristic
418C32×C4H(5,𝔽2)11yescharacteristic
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3×Dic3—22no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3C2×Q1612yes—
428C22×Q8—31no—
429C22×Q8—91no—
430C2×Q16—91no—
431C2×Q16—91no—
432C2×Q16—91no—
433C22×C8—31no—
434C22×C8—91no—
435C4⋊Q8—31no—
436C4⋊Q8—91no—
437C4⋊Q8—181no—
438#125—61no—
439C22⋊Q8—31no—
440C22⋊Q8—31no—
441C22⋊Q8—61no—
442C22⋊Q8—61no—
443C22⋊Q8—91no—
444C22⋊Q8—91no—
445C22⋊Q8—181no—
446C22⋊Q8—181no—
447C4×Q8—31no—
448C4×Q8—91no—
449C4×D4—31no—
450C4×D4—61no—
451C4×D4—181no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4D3211yescharacteristic
454#107—91no—
455#107—91no—
456#107—91no—
457C4⋊C8—91no—
458#103—31no—
459#103—31no—
460#103—31no—
461#103—31no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468C22⋊C8—91no—
469C22⋊C8—91no—
470C4×C8—91no—
471C23×C3—21no—
472C23×C3—31no—
473C23×C3D3×D411yescharacteristic
474C23×C3C2×#6711yescharacteristic
475C22×D3C2×#6711yescharacteristic
476C3×Q8—32no—
477C3×Q8—61no—
478C3×Q8—61no—
479C3×Q8—61no—
480C3×Q8—61no—
481C3×Q8—61no—
482C3×Q8—122no—
483C3×Q8—241no—
484C3×D4—34no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
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—31no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
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—122no—
512C2×C3×C4—241no—
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4C2×#6711yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67#21614yescomplemented
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—42no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—121no—
528C2×Dic3—121no—
529C2×Dic3—122no—
530C2×Dic3C2×#6711yescharacteristic
531C2×Dic3C2×#6711yescharacteristic
532C2×Dic3C2×#6711yescharacteristic
533C4×D3—21no—
534C4×D3—21no—
535C4×D3—81no—
536C4×D3—122no—
537Dic6—21no—
538Dic6—21no—
539Dic6—21no—
540Dic6—21no—
541Dic6—21no—
542Dic6—42no—
543Dic6—61no—
544Dic6—61no—
545Dic6—61no—
546Dic6—61no—
547Dic6—81no—
548Dic6—121no—
549Dic6—121no—
550Dic6—122no—
551Dic6—122no—
552Dic6#23512yes—
553C3×C8—61no—
554C3×C8—61no—
555C3⋊C8—21no—
556C3⋊C8—21no—
557C3⋊C8—61no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—121no—
562C3⋊C8—121no—
563C2×C32—22no—
564C2×C32#54611yescharacteristic
565C2×C32C22×Q1611yescharacteristic
566C2×C32#57711yescharacteristic
567C3×D3—22no—
568C2×Q8—31no—
569C2×Q8—31no—
570C2×Q8—31no—
571C2×Q8—61no—
572C2×Q8—62no—
573C2×Q8—61no—
574C2×Q8—91no—
575C2×Q8—121no—
576C2×Q8—181no—
577C2×Q8—182no—
578C2×Q8—361no—
579C2×D4—31no—
580C22×C4—21no—
581C22×C4—31no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—181no—
585C22×C4C2×D3211yescharacteristic
586Q16—182no—
587Q16—361no—
588Q16—361no—
589C2×C8—31no—
590C2×C8—31no—
591C2×C8—91no—
592C2×C8—91no—
593C2×C8—121no—
594C2×C8—361no—
595C4⋊C4—21no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—91no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4C2×D3211yescharacteristic
610C4⋊C4C2×D3211yescharacteristic
611C22⋊C4—31no—
612C22⋊C4—31no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C42—31no—
618C42—61no—
619C42—181no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—22no—
626C22×C3—32no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3D3×Q1612yes—
632C22×C3C2×#21612yes—
633C22×C3C2×D3×D411yescharacteristic
634C22×C3C22×#6711yescharacteristic
635C2×D3—21no—
636C2×D3—21no—
637C2×D3C2×#21612yes—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—32no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—61no—
649C3×C4—61no—
650C3×C4—62no—
651C3×C4—81no—
652C3×C4—81no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4C2×#23511yescharacteristic
657C3×C4#100411yescharacteristic
658C3×C4D3×#4111yescharacteristic
659C3×C4#100911yescharacteristic
660Dic3—22no—
661Dic3—21no—
662Dic3—21no—
663Dic3—41no—
664Dic3—41no—
665Dic3—41no—
666Dic3—121no—
667Dic3—121no—
668Dic3—121no—
669Dic3—121no—
670Dic3—241no—
671Dic3—241no—
672Dic3C2×#21612yes—
673C32#329911yescharacteristic, complemented, Sylow
674C23—31no—
675C23D3×#6711yescharacteristic
676Q8—32no—
677Q8—61no—
678Q8—61no—
679Q8—61no—
680Q8—61no—
681Q8—61no—
682Q8—122no—
683Q8—181no—
684Q8—181no—
685Q8—241no—
686Q8—362no—
687D4—34no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—81no—
702C2×C4—122no—
703C2×C4—181no—
704C2×C4—181no—
705C2×C4—241no—
706C2×C4—362no—
707C2×C4D3×#6711yescharacteristic
708C2×C4C22×D3211yescharacteristic
709C8—61no—
710C8—61no—
711C8—181no—
712C8—181no—
713C2×C3—22no—
714C2×C3—22no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—42no—
719C2×C3—62no—
720C2×C3#549011yescharacteristic
721C2×C3#576211yescharacteristic
722C2×C3C2×D3×Q1611yescharacteristic
723C2×C3C22×#21611yescharacteristic
724C2×C3#582911yescharacteristic
725C2×C3#583611yescharacteristic
726D3—22no—
727C22—21no—
728C22—21no—
729C22—32no—
730C22—61no—
731C22—61no—
732C22D3×#21612yes—
733C22C2×D3×#6711yescharacteristic
734C4—21no—
735C4—32no—
736C4—41no—
737C4—41no—
738C4—61no—
739C4—61no—
740C4—62no—
741C4—121no—
742C4—121no—
743C4—121no—
744C4—361no—
745C4—361no—
746C4D3×#23511yescharacteristic
747C4#6430711yescharacteristic
748C3—21no—
749C3#7880611yescharacteristic, complemented
750C3#8364011yescharacteristic, complemented
751C2—22no—
752C2—62no—
753C2#1059506511yescharacteristic
754C2#1059510511yescharacteristic
755C2C2×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. #10592669C2semidirect
4. C2×C3×#810C2semidirect
5. #10591187C2semidirect
6. #10591185C2semidirect
8. #10590604C2semidirect
9. D3×#810C2semidirect
10. #10590561C2semidirect
11. #10590560C2semidirect
12. #10590518C2semidirect
13. #10590517C2semidirect
14. #10590489C2semidirect
15. #10590476C2semidirect
83. C2×#810D3semidirect
251. C3×#67Q16semidirect
517. #67#216semidirect
673. C32#3299semidirect
749. C3#78806semidirect
750. C3#83640semidirect

Maximal subgroups

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

subgroupindex
C3×#55112
Dic6×#672
#105926692
C2×C3×#8102
#105911872
#105911852
C3⋊C8×#672
#105906042
D3×#8102
#105905612
#105905602
#105905182
#105905172
#105904892
#105904762
#836403
#788063