Finite Group Databasebeta

← #11872125

Subgroups — #11872125

Order 1152.

920 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596074C211yesmaximal, characteristic, complemented
2#10594982C211yesmaximal, characteristic, complemented
3C3×#5036C211yesmaximal, characteristic
4C3×#5035C211yesmaximal, characteristic, complemented
5#10591436C211yesmaximal, characteristic, complemented
6#10591435C211yesmaximal, characteristic, complemented
7#10591434C211yesmaximal, characteristic, complemented
8#10591434C211yesmaximal, characteristic, complemented
9#10591172C211yesmaximal, characteristic, complemented
10#10591134C211yesmaximal, characteristic, complemented
11#10591062C211yesmaximal, characteristic, complemented
12#10590472C211yesmaximal, characteristic, complemented
13#10590471C211yesmaximal, characteristic, complemented
14#10590461C211yesmaximal, characteristic, complemented
15#10590460C211yesmaximal, characteristic, complemented
16#81352—31nomaximal
17#79992—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C32×#121C2211yescharacteristic
20#64145—21no—
21#64145C2211yescharacteristic, complemented
22#64144—21no—
23D4×C3⋊Dic3C2211yescharacteristic, complemented
24#64135C2211yescharacteristic
25#64133C2211yescharacteristic
26#64097C2211yescharacteristic, complemented
27#64096C2211yescharacteristic, complemented
28#64088—21no—
29#64087—21no—
30C2×C3×#213C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×#926C2211yescharacteristic
33D3×#217—21no—
34D3×#217—21no—
35#63898C2211yescharacteristic
36#63898C2211yescharacteristic
37#63898C2211yescharacteristic
38#63898C2211yescharacteristic
39Dic3×D12—21no—
40Dic3×D12—21no—
41C2×#3716C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C3×#832C2211yescharacteristic, complemented
44C3×#832C2211yescharacteristic, complemented
45C3×#830C2211yescharacteristic
46C3×#830C2211yescharacteristic
47C3×#809C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#808C2211yescharacteristic, complemented
50C3×#807C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63572C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63555C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61#5798—31no—
62#5603—31no—
63#5603—31no—
64#5603—61no—
65#5521—31no—
66C3×#482—31no—
67C3×#447—31no—
68#5218—31no—
69#5153—31no—
70#5153—31no—
71#5152—31no—
72Dic3×D8—31no—
73#5036D311yescharacteristic
74#5035D311yescharacteristic, complemented
75#4996—31no—
76#4890—31no—
77#4889—31no—
78#4870—31no—
79#4852—31no—
80#4787—31no—
81#4787—31no—
82#4785—31no—
83#4761—31no—
84#4759—31no—
85#4758—31no—
86#4757—31no—
87#4756—31no—
88#4731—31no—
89#4723—31no—
90#4720—31no—
91#4720—31no—
92C23×C3×D3—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C3⋊Dic3—21no—
97C2×#634—21no—
98C2×#634C2311yescharacteristic
99C2×C3×D12—21no—
100C2×C3×D12—22no—
101C2×C3×D12—22no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C22⋊C4—21no—
110#3757—21no—
111#3757—21no—
112#3757—21no—
113#3757—21no—
114#3757D411yescharacteristic
115#3757D411yescharacteristic
116C4⋊(C3⋊Dic3)D411yescharacteristic
117C4⋊(C3⋊Dic3)D411yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120#3750—21no—
121#3750—21no—
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C4×C3⋊Dic3C2311yescharacteristic
125C3×#217—21no—
126C3×#213—22no—
127C3×#213—22no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4×Dic3—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3716—22no—
140#3716—22no—
141#3118—91noSylow
142C22×C3×D4—31no—
143C22×D12C2×D311yescharacteristic
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C3×#121—21no—
147C3×#121C2×D311yescharacteristic
148C3×#121C2×D311yescharacteristic
149C3×#117—31no—
150C2×#217—61no—
151C2×#217—61no—
152#936—31no—
153#936—31no—
154#936—61no—
155#936—61no—
156#936—61no—
157#936—62no—
158#935—61no—
159#935—61no—
160#935—62no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—31no—
167D4×Dic3—61no—
168D4×Dic3—61no—
169D4×Dic3—61no—
170C2×#214—31no—
171C2×#214—31no—
172C2×#213C2×D311yescharacteristic
173C2×#213C2×D311yescharacteristic
174#926—31no—
175#926—31no—
176#926—61no—
177#926C2×D311yescharacteristic
178#924—31no—
179#924—31no—
180#924—61no—
181C2×#204—31no—
182C2×#204—31no—
183#893—31no—
184#893—31no—
185#893—31no—
186#893—31no—
187#888—31no—
188#888—31no—
189#888—61no—
190#887—31no—
191#887—31no—
192#887—61no—
193D3×C22⋊C4—61no—
194D3×C22⋊C4—61no—
195#879—61no—
196#879—61no—
197#879—62no—
198#878—61no—
199#878—61no—
200#878—62no—
201C4×D12—61no—
202C4×D12—61no—
203C3×#107—31no—
204C3×#106—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8—31no—
211#832—31no—
212#832—31no—
213#832C2×D311yescharacteristic, complemented
214#832C2×D311yescharacteristic, complemented
215#830C2×D311yescharacteristic
216#830C2×D311yescharacteristic
217#821—31no—
218#821—31no—
219#818—31no—
220#817—31no—
221#816—31no—
222#816—31no—
223#815—31no—
224#815—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229C8×Dic3—31no—
230C8×Dic3—31no—
231#810—31no—
232#810—31no—
233#809C2×D311yescharacteristic
234#809C2×D311yescharacteristic
235#808—31no—
236#808C2×D311yescharacteristic, complemented
237#807—31no—
238#807C2×D311yescharacteristic, complemented
239C23×C32—21no—
240C23×C32C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—24no—
244C22×C3×D3—81no—
245C22×C3×D3—81no—
246C32×D4—21no—
247C32×D4—21no—
248C32×D4—81no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—81no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259C2×C3⋊Dic3C2×D411yescharacteristic
260C2×C3⋊Dic3C2×D411yescharacteristic
261#634—21no—
262#634—21no—
263#634—81no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C3×D12—24no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12#4112yes—
270C3×D12#4112yes—
271D3×Dic3—81no—
272D3×Dic3—81no—
273D3×Dic3—81no—
274D3×Dic3—81no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#542—91no—
280#518—91no—
281#485—91no—
282#482—31no—
283#476—91no—
284#474—91no—
285#463—91no—
286#463—91no—
287#450—91no—
288#447—31no—
289#442—91no—
290#440—91no—
291C4×SD16—91no—
292C4×D8—91no—
293#433—91no—
294C24×C3—61no—
295C23×D3—21no—
296C2×C3×D4—22no—
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—62no—
303C2×C3×D4—62no—
304C2×C3×D4—61no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—21no—
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—62no—
317C2×D12—21no—
318C2×D12—22no—
319C2×D12—22no—
320C2×D12C22×D311yescharacteristic
321C2×D12C22×D311yescharacteristic
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×Dic6—31no—
327C2×Dic6—31no—
328C2×Dic6—61no—
329C2×Dic6—61no—
330C2×Dic6—61no—
331C2×Dic6—62no—
332C3×D8—62no—
333C3×D8—62no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C22⋊C4—22no—
344C3×C22⋊C4—21no—
345C3×C22⋊C4—21no—
346C3×C22⋊C4—61no—
347C3×C42—61no—
348#217—21no—
349#217—31no—
350#217—31no—
351#217—31no—
352#217—31no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—62no—
366#217—62no—
367#217—62no—
368#217—62no—
369#217—61no—
370#217—61no—
371#214—62no—
372#214—62no—
373#213—22no—
374#213—22no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—62no—
395Dic3⋊C4—62no—
396Dic3⋊C4—62no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399C4×Dic3—21no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—62no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413#204—62no—
414#204—62no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32C22×D411yescharacteristic
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—84no—
429C32×C4—21no—
430C32×C4—41no—
431C32×C4C2×#4111yescharacteristic
432C32×C4C2×#4111yescharacteristic
433C3⋊Dic3—21no—
434C3⋊Dic3—21no—
435C3⋊Dic3—21no—
436C3⋊Dic3—21no—
437C3⋊Dic3—41no—
438C3⋊Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C22×D4—31no—
442C2×SD16—91no—
443C2×SD16—91no—
444C2×D8—31no—
445C2×D8—31no—
446C4⋊Q8—91no—
447#126—181no—
448#124—91no—
449#124—181no—
450#123—181no—
451C22⋊Q8—91no—
452C22⋊Q8—181no—
453#121D3211yescharacteristic
454C4×Q8—91no—
455C4×D4—91no—
456C4×D4—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—181no—
461C4×D4—181no—
462#117—31no—
463#117—91no—
464C2×C22⋊C4—181no—
465C2×C22⋊C4—181no—
466#107—31no—
467#107—91no—
468#106—31no—
469#106—91no—
470C4⋊C8—91no—
471C4⋊C8—91no—
472#103—91no—
473#103—91no—
474#102—31no—
475#102—31no—
476#102—31no—
477#102—31no—
478#102—91no—
479#102—91no—
480C22⋊C8—31no—
481C22⋊C8—31no—
482#97—91no—
483C4×C8—91no—
484C23×C3—22no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—64no—
489C23×C3—61no—
490C23×C3—61no—
491C23×C3—241no—
492C23×C3—241no—
493C23×C3D3×D411yescharacteristic
494C23×C3D3×D411yescharacteristic
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—24no—
498C22×D3—81no—
499C22×D3—81no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—32no—
505C3×D4—32no—
506C3×D4—41no—
507C3×D4—41no—
508C3×D4—64no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4—81no—
512C3×D4—81no—
513C3×D4—82no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—22no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—62no—
546C2×Dic3—62no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—241no—
552C2×Dic3—241no—
553C2×Dic3—241no—
554C2×Dic3—241no—
555C2×Dic3—241no—
556C2×Dic3—241no—
557C2×Dic3—242no—
558D12—24no—
559D12—21no—
560D12—21no—
561D12#23712yes—
562D12#23712yes—
563C4×D3—241no—
564C4×D3—241no—
565C4×D3—241no—
566C4×D3—241no—
567Dic6—61no—
568Dic6—61no—
569Dic6—61no—
570Dic6—61no—
571Dic6—121no—
572Dic6—121no—
573Dic6—241no—
574Dic6—241no—
575Dic6—242no—
576C3×C8—61no—
577C3×C8—61no—
578C3×C8—61no—
579C3×C8—61no—
580C3⋊C8—21no—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C3⋊C8—21no—
584C2×C32—41no—
585C2×C32—81no—
586C2×C32#52511yescharacteristic
587C2×C32#57611yescharacteristic
588C2×C32#57711yescharacteristic
589C3×D3—42no—
590C3×D3—42no—
591C24—61no—
592C2×Q8—91no—
593C2×Q8—181no—
594C2×D4—21no—
595C2×D4—31no—
596C2×D4—31no—
597C2×D4—62no—
598C2×D4—62no—
599C2×D4—61no—
600C2×D4C2×D3211yescharacteristic
601C22×C4—181no—
602C22×C4—181no—
603C22×C4—181no—
604C22×C4—181no—
605C22×C4—181no—
606C22×C4C2×D3211yescharacteristic
607SD16—182no—
608SD16—182no—
609D8—62no—
610D8—62no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—31no—
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—91no—
618C4⋊C4—91no—
619C4⋊C4—91no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4C2×D3211yescharacteristic
624C22⋊C4—21no—
625C22⋊C4—61no—
626C22⋊C4—91no—
627C22⋊C4—91no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C42—61no—
637C42—91no—
638C42—91no—
639C42—181no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—62no—
660C22×C3—62no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—244no—
666C22×C3C2×D3×D411yescharacteristic
667C22×C3C2×D3×D411yescharacteristic
668C2×D3—22no—
669C2×D3—22no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—84no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—41no—
680C3×C4—42no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4C2×#23711yescharacteristic
686C3×C4C2×#23711yescharacteristic
687C3×C4D3×#4111yescharacteristic
688C3×C4D3×#4111yescharacteristic
689Dic3—41no—
690Dic3—41no—
691Dic3—61no—
692Dic3—61no—
693Dic3—61no—
694Dic3—61no—
695Dic3—61no—
696Dic3—61no—
697Dic3—61no—
698Dic3—61no—
699Dic3—121no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—122no—
704Dic3—122no—
705Dic3—121no—
706Dic3—121no—
707Dic3—121no—
708Dic3—121no—
709C32#311811yescharacteristic, complemented, Sylow
710C23—21no—
711C23—64no—
712C23—61no—
713C23—61no—
714C23—241no—
715C23—241no—
716C23#381111yescharacteristic
717Q8—181no—
718Q8—181no—
719Q8—721no—
720D4—21no—
721D4—21no—
722D4—32no—
723D4—32no—
724D4—64no—
725D4—61no—
726D4—61no—
727D4—81no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—91no—
734C2×C4—91no—
735C2×C4—91no—
736C2×C4—91no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—721no—
740C2×C4—721no—
741C2×C4—721no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4#381111yescharacteristic
745C2×C4C22×D3211yescharacteristic
746C8—61no—
747C8—61no—
748C8—61no—
749C8—61no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—41no—
754C2×C3—41no—
755C2×C3—81no—
756C2×C3—82no—
757C2×C3—81no—
758C2×C3—81no—
759C2×C3—122no—
760C2×C3—122no—
761C2×C3#558611yescharacteristic
762C2×C3#565611yescharacteristic
763C2×C3#575711yescharacteristic
764C2×C3#577011yescharacteristic
765C2×C3#577411yescharacteristic
766C2×C3#577511yescharacteristic
767D3—42no—
768D3—42no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—62no—
776C22—62no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22—244no—
782C22C2×#381111yescharacteristic
783C4—21no—
784C4—41no—
785C4—121no—
786C4—121no—
787C4—181no—
788C4—181no—
789C4—181no—
790C4—181no—
791C4—361no—
792C4—361no—
793C4D3×#23711yescharacteristic
794C4D3×#23711yescharacteristic
795C3—21no—
796C3#7999211yescharacteristic, complemented
797C3#8135211yescharacteristic, complemented
798C2—41no—
799C2—81no—
800C2—122no—
801C2—122no—
802C2#1059510211yescharacteristic
803C2#1059516011yescharacteristic
804C2#1059546211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radicalC3×#5036C2
hypercenter#121D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #10596074C2semidirect
2. #10594982C2semidirect
4. C3×#5035C2semidirect
5. #10591436C2semidirect
6. #10591435C2semidirect
7. #10591434C2semidirect
8. #10591434C2semidirect
9. #10591172C2semidirect
10. #10591134C2semidirect
11. #10591062C2semidirect
12. #10590472C2semidirect
13. #10590471C2semidirect
14. #10590461C2semidirect
15. #10590460C2semidirect
21. #64145C22semidirect
23. D4×C3⋊Dic3C22semidirect
26. #64097C22semidirect
27. #64096C22semidirect
43. C3×#832C22semidirect
44. C3×#832C22semidirect
49. C3×#808C22semidirect
50. C3×#807C22semidirect
51. #63575C22semidirect
52. #63573C22semidirect
53. #63572C22semidirect
54. #63572C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
59. #63555C22semidirect
60. #63553C22semidirect
74. #5035D3semidirect
213. #832C2×D3semidirect
214. #832C2×D3semidirect
236. #808C2×D3semidirect
238. #807C2×D3semidirect
709. C32#3118semidirect
796. C3#79992semidirect
797. C3#81352semidirect

Maximal subgroups

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

subgroupindex
#105960742
#105949822
C3×#50362
C3×#50352
#105914362
#105914352
#105914342
#105911722
#105911342
#105910622
#105904722
#105904712
#105904612
#105904602
#813523
#799923