Finite Group Databasebeta

← #11872723

Subgroups — #11872723

Order 1152.

956 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596090C211yesmaximal, characteristic, complemented
2#10594982C211yesmaximal, characteristic, complemented
3C3×#5036C211yesmaximal, characteristic, complemented
4C3×#5035C211yesmaximal, characteristic, complemented
5#10591436C211yesmaximal, characteristic, complemented
6#10591435C211yesmaximal, characteristic, complemented
7#10591433C211yesmaximal, characteristic, complemented
8#10591433C211yesmaximal, characteristic, complemented
9#10591162C211yesmaximal, characteristic, complemented
10#10591136C211yesmaximal, characteristic, complemented
11#10591062C211yesmaximal, characteristic, complemented
12#10590474C211yesmaximal, characteristic, complemented
13#10590473C211yesmaximal, characteristic, complemented
14#10590462C211yesmaximal, characteristic, complemented
15#10590459C211yesmaximal, characteristic, complemented
16#81354—31nomaximal
17#79993—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C32×#121C2211yescharacteristic
20#64149C2211yescharacteristic, complemented
21#64148—21no—
22#64147—21no—
23D4×C3⋊Dic3C2211yescharacteristic, complemented
24#64139C2211yescharacteristic
25#64135C2211yescharacteristic
26#64102C2211yescharacteristic, complemented
27#64099C2211yescharacteristic, complemented
28#64095—21no—
29#64092—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×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
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#63564C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63555C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61#5798—31no—
62#5619—31no—
63#5619—31no—
64#5619—61no—
65#5521—31no—
66C3×#482—31no—
67C3×#447—31no—
68#5217—31no—
69#5152—31no—
70#5150—31no—
71#5150—31no—
72Dic3×D8—31no—
73#5036D311yescharacteristic, complemented
74#5035D311yescharacteristic, complemented
75#5003—31no—
76#4891—31no—
77#4872—31no—
78#4871—31no—
79#4869—31no—
80#4786—31no—
81#4786—31no—
82#4785—31no—
83#4785—31no—
84#4766—31no—
85#4763—31no—
86#4756—31no—
87#4756—31no—
88#4737—31no—
89#4732—31no—
90#4720—31no—
91#4720—31no—
92C23×C3×D3—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98C2×#638—21no—
99C22×C3⋊Dic3—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×C3×D12—21no—
103C2×C3×D12—22no—
104C2×C3×D12—22no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113#3757—21no—
114#3757D411yescharacteristic
115#3757D411yescharacteristic
116#3752—21no—
117#3752—21no—
118C4⋊(C3⋊Dic3)—21no—
119C4⋊(C3⋊Dic3)D411yescharacteristic
120C4⋊(C3⋊Dic3)D411yescharacteristic
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750—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#3714—22no—
140#3714—22no—
141#3122—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#940—31no—
153#940—31no—
154#940—61no—
155#939—61no—
156#939—61no—
157#939—62no—
158#938—61no—
159#938—61no—
160#938—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×#213—31no—
171C2×#213—31no—
172C2×#213C2×D311yescharacteristic
173C2×#213C2×D311yescharacteristic
174#930—31no—
175#930—31no—
176#930—61no—
177#926—31no—
178#926—31no—
179#926—61no—
180#926C2×D311yescharacteristic
181C2×D24—31no—
182C2×D24—31no—
183#893—31no—
184#893—31no—
185#893—31no—
186#893—31no—
187#893—31no—
188#893—31no—
189#893—61no—
190#890—31no—
191#890—31no—
192#890—61no—
193#886—61no—
194#886—61no—
195#886—62no—
196#883—61no—
197#883—61no—
198#883—62no—
199D3×C22⋊C4—61no—
200D3×C22⋊C4—61no—
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#821—31no—
220#821—31no—
221#818—31no—
222#817—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#809—31no—
232#809—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—21no—
244C22×C3×D3—24no—
245C22×C3×D3—81no—
246C22×C3×D3—81no—
247C32×D4—21no—
248C32×D4—21no—
249C32×D4—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255#638—81no—
256#638—81no—
257#638—81no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—81no—
260C2×C3⋊Dic3C2×D411yescharacteristic
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C2×C3⋊Dic3C2×D411yescharacteristic
264C4⋊(C3⋊D3)—21no—
265C4⋊(C3⋊D3)—21no—
266C4×C3⋊D3—81no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C3×D12—24no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12#4112yes—
273C3×D12#4112yes—
274D3×Dic3—81no—
275D3×Dic3—81no—
276D3×Dic3—81no—
277D3×Dic3—81no—
278C3×C3⋊C8—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#540—91no—
283#518—91no—
284#482—31no—
285#482—91no—
286#478—91no—
287#478—91no—
288#459—91no—
289#459—91no—
290#447—31no—
291#447—91no—
292#442—91no—
293#442—91no—
294C4×D8—91no—
295C4×D8—91no—
296#433—91no—
297C24×C3—61no—
298C23×D3—21no—
299C2×C3×D4—22no—
300C2×C3×D4—21no—
301C2×C3×D4—21no—
302C2×C3×D4—21no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—62no—
306C2×C3×D4—62no—
307C2×C3×D4—61no—
308C2×C3×D4C22×D311yescharacteristic
309C2×C3×D4C22×D311yescharacteristic
310C22×C3×C4—21no—
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—62no—
318C2×#67—62no—
319C2×#67—62no—
320C2×#67—61no—
321C2×#67—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328C22×Dic3—62no—
329C2×D12—21no—
330C2×D12—22no—
331C2×D12—22no—
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—61no—
335C2×D12C22×D311yescharacteristic
336C2×D12C22×D311yescharacteristic
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—62no—
344C3×D8—62no—
345C3×D8—62no—
346C2×C3×C8—31no—
347C2×C3×C8—31no—
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C22⋊C4—22no—
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—61no—
359C3×C42—61no—
360#217—21no—
361#217—31no—
362#217—31no—
363#217—31no—
364#217—31no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—61no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217—62no—
374#213—22no—
375#213—22no—
376#213—62no—
377#213—62no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—62no—
385(C2×D3)⋊C4—62no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—31no—
393C4⋊Dic3—31no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3—61no—
399C4⋊Dic3—62no—
400C4⋊Dic3C22×D311yescharacteristic
401C4⋊Dic3C22×D311yescharacteristic
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—62no—
405C4×Dic3—21no—
406C4×Dic3—31no—
407C4×Dic3—31no—
408C4×Dic3—31no—
409C4×Dic3—31no—
410C4×Dic3—61no—
411C4×Dic3—61no—
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415C2×C3⋊C8C22×D311yescharacteristic
416D24—62no—
417D24—62no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32—41no—
424C22×C32C22×D411yescharacteristic
425C2×C3⋊D3—41no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—41no—
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—84no—
435C32×C4—21no—
436C32×C4—41no—
437C32×C4C2×#4111yescharacteristic
438C32×C4C2×#4111yescharacteristic
439C3⋊Dic3—21no—
440C3⋊Dic3—21no—
441C3⋊Dic3—21no—
442C3⋊Dic3—21no—
443C3⋊Dic3—41no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C22×D4—31no—
447C2×D8—31no—
448C2×D8—31no—
449C2×D8—91no—
450C2×D8—91no—
451#127—91no—
452#125—91no—
453#123—181no—
454#123—181no—
455#121—91no—
456#121—181no—
457#121—181no—
458#121D3211yescharacteristic
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—91no—
462C4×D4—91no—
463C4×D4—91no—
464C4×D4—91no—
465C4×D4—181no—
466C4×D4—181no—
467#117—31no—
468#117—91no—
469C2×C22⋊C4—181no—
470C2×C22⋊C4—181no—
471#107—31no—
472#107—91no—
473#106—31no—
474#106—91no—
475C4⋊C8—91no—
476C4⋊C8—91no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—31no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485C22⋊C8—31no—
486C22⋊C8—31no—
487#97—91no—
488C4×C8—91no—
489C23×C3—22no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—64no—
494C23×C3—61no—
495C23×C3—61no—
496C23×C3—241no—
497C23×C3—241no—
498C23×C3D3×D411yescharacteristic
499C23×C3D3×D411yescharacteristic
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—24no—
503C22×D3—62no—
504C22×D3—61no—
505C22×D3—61no—
506C22×D3—81no—
507C22×D3—81no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—32no—
513C3×D4—32no—
514C3×D4—41no—
515C3×D4—41no—
516C3×D4—64no—
517C3×D4—61no—
518C3×D4—61no—
519C3×D4—81no—
520C3×D4—81no—
521C3×D4—82no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—22no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539#67—241no—
540#67—241no—
541#67—241no—
542#67—241no—
543#67—241no—
544#67—241no—
545#67—242no—
546#67—242no—
547#67—242no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—31no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—31no—
554C2×Dic3—31no—
555C2×Dic3—31no—
556C2×Dic3—31no—
557C2×Dic3—31no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—62no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—241no—
566C2×Dic3—241no—
567C2×Dic3—241no—
568C2×Dic3—241no—
569C2×Dic3—241no—
570C2×Dic3—241no—
571C2×Dic3—242no—
572D12—24no—
573D12—21no—
574D12—21no—
575D12—61no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—121no—
580D12—121no—
581D12#23712yes—
582D12#23712yes—
583C4×D3—241no—
584C4×D3—241no—
585C4×D3—241no—
586C4×D3—241no—
587C4×D3—241no—
588C4×D3—241no—
589C4×D3—242no—
590C3×C8—61no—
591C3×C8—61no—
592C3×C8—61no—
593C3×C8—61no—
594C3⋊C8—21no—
595C3⋊C8—21no—
596C3⋊C8—21no—
597C3⋊C8—21no—
598C2×C32—41no—
599C2×C32—81no—
600C2×C32#52511yescharacteristic
601C2×C32#57611yescharacteristic
602C2×C32#57611yescharacteristic
603C3⋊D3—81no—
604C3×D3—42no—
605C3×D3—42no—
606C24—61no—
607C2×D4—21no—
608C2×D4—31no—
609C2×D4—31no—
610C2×D4—62no—
611C2×D4—62no—
612C2×D4—61no—
613C2×D4—91no—
614C2×D4—181no—
615C2×D4—181no—
616C2×D4—181no—
617C2×D4C2×D3211yescharacteristic
618C22×C4—181no—
619C22×C4—181no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—181no—
624C22×C4C2×D3211yescharacteristic
625D8—62no—
626D8—62no—
627D8—182no—
628D8—182no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—31no—
633C4⋊C4—31no—
634C4⋊C4—31no—
635C4⋊C4—91no—
636C4⋊C4—91no—
637C4⋊C4—91no—
638C4⋊C4—181no—
639C4⋊C4—181no—
640C4⋊C4C2×D3211yescharacteristic
641C22⋊C4—21no—
642C22⋊C4—61no—
643C22⋊C4—91no—
644C22⋊C4—91no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C42—61no—
653C42—91no—
654C42—91no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—62no—
675C22×C3—62no—
676C22×C3—121no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—244no—
681C22×C3C2×D3×D411yescharacteristic
682C22×C3C2×D3×D411yescharacteristic
683C2×D3—22no—
684C2×D3—22no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—84no—
690C2×D3—122no—
691C2×D3—122no—
692C2×D3—122no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—121no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—41no—
704C3×C4—42no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4C2×#23711yescharacteristic
710C3×C4C2×#23711yescharacteristic
711C3×C4D3×#4111yescharacteristic
712C3×C4D3×#4111yescharacteristic
713Dic3—41no—
714Dic3—41no—
715Dic3—61no—
716Dic3—61no—
717Dic3—61no—
718Dic3—61no—
719Dic3—61no—
720Dic3—61no—
721Dic3—61no—
722Dic3—61no—
723Dic3—121no—
724Dic3—121no—
725Dic3—121no—
726Dic3—121no—
727Dic3—122no—
728Dic3—121no—
729Dic3—121no—
730C32#312211yescharacteristic, complemented, Sylow
731C23—21no—
732C23—64no—
733C23—61no—
734C23—61no—
735C23—181no—
736C23—241no—
737C23—241no—
738C23#381111yescharacteristic
739D4—21no—
740D4—21no—
741D4—32no—
742D4—32no—
743D4—64no—
744D4—61no—
745D4—61no—
746D4—81no—
747D4—181no—
748D4—181no—
749D4—721no—
750D4—721no—
751D4—721no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—91no—
758C2×C4—91no—
759C2×C4—91no—
760C2×C4—91no—
761C2×C4—181no—
762C2×C4—721no—
763C2×C4—721no—
764C2×C4—721no—
765C2×C4—721no—
766C2×C4—721no—
767C2×C4—721no—
768C2×C4#381111yescharacteristic
769C2×C4C22×D3211yescharacteristic
770C8—61no—
771C8—61no—
772C8—61no—
773C8—61no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—41no—
778C2×C3—41no—
779C2×C3—81no—
780C2×C3—82no—
781C2×C3—81no—
782C2×C3—81no—
783C2×C3—122no—
784C2×C3—122no—
785C2×C3#558611yescharacteristic
786C2×C3#565611yescharacteristic
787C2×C3#575711yescharacteristic
788C2×C3#576911yescharacteristic
789C2×C3#577411yescharacteristic
790C2×C3#577411yescharacteristic
791D3—42no—
792D3—42no—
793D3—242no—
794D3—241no—
795D3—241no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—62no—
803C22—62no—
804C22—121no—
805C22—121no—
806C22—121no—
807C22—121no—
808C22—244no—
809C22—361no—
810C22—361no—
811C22—361no—
812C22C2×#381111yescharacteristic
813C4—21no—
814C4—41no—
815C4—121no—
816C4—121no—
817C4—181no—
818C4—181no—
819C4—181no—
820C4—181no—
821C4—361no—
822C4D3×#23711yescharacteristic
823C4D3×#23711yescharacteristic
824C3—21no—
825C3#7999311yescharacteristic, complemented
826C3#8135411yescharacteristic, complemented
827C2—41no—
828C2—81no—
829C2—122no—
830C2—122no—
831C2—721no—
832C2#1059510211yescharacteristic
833C2#1059516011yescharacteristic
834C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3122
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. #10596090C2semidirect
2. #10594982C2semidirect
3. C3×#5036C2semidirect
4. C3×#5035C2semidirect
5. #10591436C2semidirect
6. #10591435C2semidirect
7. #10591433C2semidirect
8. #10591433C2semidirect
9. #10591162C2semidirect
10. #10591136C2semidirect
11. #10591062C2semidirect
12. #10590474C2semidirect
13. #10590473C2semidirect
14. #10590462C2semidirect
15. #10590459C2semidirect
20. #64149C22semidirect
23. D4×C3⋊Dic3C22semidirect
26. #64102C22semidirect
27. #64099C22semidirect
43. C3×#832C22semidirect
44. C3×#832C22semidirect
49. C3×#808C22semidirect
50. C3×#807C22semidirect
51. #63575C22semidirect
52. #63573C22semidirect
53. #63572C22semidirect
54. #63572C22semidirect
55. #63564C22semidirect
56. #63564C22semidirect
59. #63555C22semidirect
60. #63553C22semidirect
73. #5036D3semidirect
74. #5035D3semidirect
213. #832C2×D3semidirect
214. #832C2×D3semidirect
236. #808C2×D3semidirect
238. #807C2×D3semidirect
730. C32#3122semidirect
825. C3#79993semidirect
826. C3#81354semidirect

Maximal subgroups

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

subgroupindex
#105960902
#105949822
C3×#50362
C3×#50352
#105914362
#105914352
#105914332
#105911622
#105911362
#105910622
#105904742
#105904732
#105904622
#105904592
#813543
#799933