Finite Group Databasebeta

← #11872745

Subgroups — #11872745

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#10596033C211yesmaximal, characteristic, complemented
2#10593996C211yesmaximal, characteristic, complemented
3C3×#5014C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic, complemented
5#10591516C211yesmaximal, characteristic, complemented
6#10591433C211yesmaximal, characteristic, complemented
7#10591433C211yesmaximal, characteristic, complemented
8#10591425C211yesmaximal, characteristic, complemented
9#10590598C211yesmaximal, characteristic, complemented
10#10590474C211yesmaximal, characteristic, complemented
11#10590473C211yesmaximal, characteristic, complemented
12#10590451C211yesmaximal, characteristic, complemented
13#10590346C211yesmaximal, characteristic, complemented
14C4×#3714C211yesmaximal, characteristic, complemented
15#10590298C211yesmaximal, characteristic, complemented
16#79874—31nomaximal
17#79596—31nomaximal
18C2×#3802C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic, complemented
20#64149C2211yescharacteristic, complemented
21#64147C2211yescharacteristic
22#64139—21no—
23#64138—21no—
24#64104C2211yescharacteristic
25#64099C2211yescharacteristic, complemented
26#64093—21no—
27#64092—21no—
28C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
29#64081C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C4×D12C2211yescharacteristic
34D3×(C2×D3)⋊C4—21no—
35D3×(C2×D3)⋊C4—21no—
36#63898C2211yescharacteristic
37#63898C2211yescharacteristic
38#63879—21no—
39#63879—21no—
40#63849C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C3×#832C2211yescharacteristic, complemented
44C3×#832C2211yescharacteristic, complemented
45C3×#809C2211yescharacteristic
46C3×#809C2211yescharacteristic
47C3×#808C2211yescharacteristic, complemented
48C3×#807C2211yescharacteristic, complemented
49C3×#803C2211yescharacteristic, complemented
50C3×C4×C3⋊C8C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63572C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63557C2211yescharacteristic
60#63557C2211yescharacteristic
61#5562—31no—
62#5562—31no—
63#5562—61no—
64#5545—31no—
65#5545—31no—
66C3×#442—31no—
67C3×C4×D8—31no—
68#5156—31no—
69#5156—31no—
70#5150—31no—
71#5150—31no—
72#5014—31no—
73#5014D311yescharacteristic, complemented
74C4×#213—31no—
75C4×#213D311yescharacteristic, complemented
76#4891—31no—
77#4885—31no—
78#4871—31no—
79#4866—31no—
80#4786—31no—
81#4786—31no—
82#4784—31no—
83#4779—31no—
84#4773—31no—
85#4773—31no—
86#4766—31no—
87#4763—31no—
88#4711—31no—
89#4709—31no—
90C4×D24—31no—
91#4690—31no—
92C22×D32—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×#638—21no—
96C2×#638—21no—
97C2×#638—21no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×#625—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109#3802—22no—
110#3802—22no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C32×C42C2311yescharacteristic
114#3757—21no—
115#3752—21no—
116#3752—21no—
117#3752D411yescharacteristic
118#3752D411yescharacteristic
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122#3750D411yescharacteristic
123#3750D411yescharacteristic
124C4×C3⋊Dic3C2311yescharacteristic
125C3×#213—22no—
126C3×#213—22no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3714—22no—
140#3714—22no—
141#3122—91noSylow
142C2×D3×D4—31no—
143C2×D3×D4—31no—
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C3×C4×D4—21no—
147C3×C4×D4—31no—
148C3×C4×D4—31no—
149C3×C4×D4C2×D311yescharacteristic, complemented
150C3×C4×D4C2×D311yescharacteristic, complemented
151#940—31no—
152#940—31no—
153#940—61no—
154#938—31no—
155#938—31no—
156#938—61no—
157D4×Dic3—31no—
158D4×Dic3—31no—
159C2×#213—31no—
160C2×#213—31no—
161C2×#213C2×D311yescharacteristic
162C2×#213C2×D311yescharacteristic
163#930—61no—
164#930—61no—
165#930—62no—
166#929—61no—
167#929—61no—
168#929—62no—
169C4×#67—61no—
170C4×#67—61no—
171C2×(C2×D3)⋊C4—61no—
172C2×(C2×D3)⋊C4—61no—
173C2×D24—31no—
174C2×D24—31no—
175#895—31no—
176#895—31no—
177#895—61no—
178#893—31no—
179#893—31no—
180#892—31no—
181#892—31no—
182#890—31no—
183#890—31no—
184#890—61no—
185#884—61no—
186#884—61no—
187#884—62no—
188#883—61no—
189#883—61no—
190#883—62no—
191#67⋊C4—61no—
192#67⋊C4—61no—
193D3×C22⋊C4—61no—
194D3×C22⋊C4—61no—
195C4×D12—31no—
196C4×D12—31no—
197C4×D12—61no—
198C4×D12C2×D311yescharacteristic
199C4×D12C2×D311yescharacteristic
200#872—31no—
201#872—31no—
202#872—61no—
203C3×#107—31no—
204C3×#106—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#97—31no—
210C3×C4×C8—31no—
211#832—31no—
212#832—31no—
213#832C2×D311yescharacteristic, complemented
214#832C2×D311yescharacteristic, complemented
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223#818—31no—
224#817—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229#809—31no—
230#809—31no—
231#809C2×D311yescharacteristic
232#809C2×D311yescharacteristic
233#808—31no—
234#808C2×D311yescharacteristic, complemented
235#807—31no—
236#807C2×D311yescharacteristic, complemented
237#803C2×D311yescharacteristic, complemented
238C4×C3⋊C8C2×D311yescharacteristic, complemented
239C23×C32—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3C2×D411yescharacteristic
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C2×D32—24no—
245C2×D32—81no—
246C2×D32—81no—
247C32×D4—21no—
248C32×D4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—81no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254#638—81no—
255#638—81no—
256#638—81no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3C2×D411yescharacteristic
259C2×C3⋊Dic3C2×D411yescharacteristic
260C2×C3⋊Dic3C2×D411yescharacteristic
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)—21no—
263C4⋊(C3⋊D3)—81no—
264C4×C3⋊D3—21no—
265C4×C3⋊D3—21no—
266C4×C3⋊D3—81no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12#4112yes—
272C3×D12#4112yes—
273C3×C4×D3—81no—
274C3×C4×D3—81no—
275#625—24no—
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—91no—
285#482—91no—
286#478—91no—
287#478—91no—
288#459—91no—
289#459—91no—
290#447—91no—
291#447—91no—
292#442—31no—
293#442—91no—
294C4×D8—31no—
295C4×D8—91no—
296#433—91no—
297C23×D3—61no—
298C23×D3—61no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C22×C3×C4—22no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—62no—
318C2×#67—62no—
319C2×#67—62no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322D3×D4—62no—
323D3×D4—62no—
324D3×D4—62no—
325D3×D4—62no—
326C2×D12—31no—
327C2×D12—31no—
328C2×D12—61no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12—62no—
332C2×D12C22×D311yescharacteristic
333C2×D12C22×D311yescharacteristic
334C2×C4×D3—21no—
335C2×C4×D3—21no—
336C2×C4×D3—31no—
337C2×C4×D3—31no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—62no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
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×C22⋊C4—61no—
360C3×C42—21no—
361C3×C42C22×D311yescharacteristic
362C3×C42C22×D311yescharacteristic
363#217—61no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—62no—
368#213—22no—
369#213—22no—
370#213—62no—
371#213—62no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—31no—
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—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—62no—
387(C2×D3)⋊C4—62no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—62no—
396C4⋊Dic3C22×D311yescharacteristic
397C4⋊Dic3C22×D311yescharacteristic
398Dic3⋊C4—31no—
399Dic3⋊C4—31no—
400Dic3⋊C4—31no—
401Dic3⋊C4—31no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—62no—
407C4×Dic3—31no—
408C4×Dic3—31no—
409C4×Dic3—61no—
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—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32C22×D411yescharacteristic
422C2×C3⋊D3—21no—
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
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—
434D32—84no—
435C32×C4—21no—
436C32×C4—21no—
437C32×C4—41no—
438C32×C4C2×#4111yescharacteristic
439C32×C4C2×#4111yescharacteristic
440C3⋊Dic3—21no—
441C3⋊Dic3—21no—
442C3⋊Dic3—21no—
443C3⋊Dic3—41no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C22×D4—91no—
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—91no—
457#121—181no—
458#121—181no—
459C4×D4—31no—
460C4×D4—31no—
461C4×D4—91no—
462C4×D4—91no—
463C4×D4—91no—
464C4×D4—181no—
465C4×D4—181no—
466C4×D4D3211yescharacteristic, complemented
467#117—91no—
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—91no—
486C22⋊C8—91no—
487#97—31no—
488C4×C8—31no—
489C23×C3—22no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—61no—
493C23×C3—61no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—31no—
497C22×D3—31no—
498C22×D3—61no—
499C22×D3—64no—
500C22×D3—64no—
501C22×D3—62no—
502C22×D3—61no—
503C22×D3—61no—
504C22×D3—241no—
505C22×D3—241no—
506C22×D3—241no—
507C22×D3—241no—
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—61no—
517C3×D4—61no—
518C2×C3×C4—22no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—81no—
527C2×C3×C4—81no—
528C2×C3×C4—82no—
529C2×C3×C4—241no—
530C2×C3×C4—241no—
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4D3×D411yescharacteristic
533C2×C3×C4D3×D411yescharacteristic
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537#67—64no—
538#67—64no—
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—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—62no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—241no—
563C2×Dic3—241no—
564D12—21no—
565D12—21no—
566D12—61no—
567D12—61no—
568D12—61no—
569D12—61no—
570D12—121no—
571D12—121no—
572D12—241no—
573D12—241no—
574D12—242no—
575D12#23512yes—
576D12#23512yes—
577C4×D3—61no—
578C4×D3—61no—
579C4×D3—61no—
580C4×D3—61no—
581C4×D3—81no—
582C4×D3—81no—
583C4×D3—121no—
584C4×D3—121no—
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—81no—
599C2×C32#52511yescharacteristic
600C2×C32#57611yescharacteristic
601C2×C32#57611yescharacteristic
602C3⋊D3—41no—
603C3⋊D3—81no—
604C3×D3—42no—
605C3×D3—42no—
606C24—181no—
607C2×D4—31no—
608C2×D4—31no—
609C2×D4—91no—
610C2×D4—181no—
611C2×D4—181no—
612C2×D4—181no—
613C2×D4—181no—
614C2×D4—182no—
615C2×D4—182no—
616C2×D4—181no—
617C2×D4C2×D3211yescharacteristic
618C22×C4—21no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—91no—
622C22×C4—181no—
623C22×C4—181no—
624C22×C4—181no—
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—61no—
644C22⋊C4—91no—
645C22⋊C4—91no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C42—91no—
653C42—181no—
654C42C2×D3211yescharacteristic
655C22×C3—21no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—42no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—62no—
666C22×C3—62no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3C2×D3×D411yescharacteristic
672C22×C3C2×D3×D411yescharacteristic
673C2×D3—22no—
674C2×D3—22no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—61no—
682C2×D3—61no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—122no—
689C2×D3—122no—
690C2×D3—122no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—244no—
698C2×D3—244no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—42no—
708C3×C4—41no—
709C3×C4—41no—
710C3×C4—121no—
711C3×C4—121no—
712C3×C4C2×#23511yescharacteristic
713C3×C4C2×#23511yescharacteristic
714C3×C4D3×#4111yescharacteristic
715C3×C4D3×#4111yescharacteristic
716Dic3—41no—
717Dic3—41no—
718Dic3—61no—
719Dic3—61no—
720Dic3—61no—
721Dic3—61no—
722Dic3—61no—
723Dic3—61no—
724Dic3—121no—
725Dic3—121no—
726Dic3—121no—
727Dic3—122no—
728Dic3—121no—
729Dic3—121no—
730C32#312211yescharacteristic, complemented, Sylow
731C23—21no—
732C23—61no—
733C23—61no—
734C23—91no—
735C23—184no—
736C23—181no—
737C23—721no—
738C23—721no—
739D4—21no—
740D4—21no—
741D4—32no—
742D4—32no—
743D4—61no—
744D4—61no—
745D4—184no—
746D4—181no—
747D4—181no—
748D4—721no—
749D4—721no—
750D4—721no—
751D4—721no—
752C2×C4—21no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—81no—
756C2×C4—91no—
757C2×C4—91no—
758C2×C4—91no—
759C2×C4—181no—
760C2×C4—181no—
761C2×C4—181no—
762C2×C4—241no—
763C2×C4—241no—
764C2×C4—721no—
765C2×C4—721no—
766C2×C4—721no—
767C2×C4#381111yescharacteristic
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—82no—
778C2×C3—81no—
779C2×C3—81no—
780C2×C3—122no—
781C2×C3—122no—
782C2×C3#554711yescharacteristic
783C2×C3#554711yescharacteristic
784C2×C3#575711yescharacteristic
785C2×C3#576911yescharacteristic
786C2×C3#577411yescharacteristic
787C2×C3#577411yescharacteristic
788D3—42no—
789D3—42no—
790D3—121no—
791D3—121no—
792D3—241no—
793D3—242no—
794D3—241no—
795D3—241no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—62no—
800C22—62no—
801C22—121no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—181no—
806C22—181no—
807C22—181no—
808C22—361no—
809C22—361no—
810C22—361no—
811C22—724no—
812C22C2×#381111yescharacteristic
813C4—21no—
814C4—21no—
815C4—41no—
816C4—121no—
817C4—121no—
818C4—181no—
819C4—181no—
820C4—181no—
821C4—361no—
822C4D3×#23511yescharacteristic
823C4D3×#23511yescharacteristic
824C3—21no—
825C3#7959611yescharacteristic, complemented
826C3#7987411yescharacteristic, complemented
827C2—81no—
828C2—122no—
829C2—122no—
830C2—361no—
831C2—721no—
832C2#1059507611yescharacteristic
833C2#1059510211yescharacteristic
834C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3122
LCSG ▷ C2×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. #10596033C2semidirect
2. #10593996C2semidirect
3. C3×#5014C2semidirect
4. C3×C4×#213C2semidirect
5. #10591516C2semidirect
6. #10591433C2semidirect
7. #10591433C2semidirect
8. #10591425C2semidirect
9. #10590598C2semidirect
10. #10590474C2semidirect
11. #10590473C2semidirect
12. #10590451C2semidirect
13. #10590346C2semidirect
14. C4×#3714C2semidirect
15. #10590298C2semidirect
19. C32×C4×D4C22semidirect
20. #64149C22semidirect
25. #64099C22semidirect
28. C4×C4⋊(C3⋊D3)C22semidirect
43. C3×#832C22semidirect
44. C3×#832C22semidirect
47. C3×#808C22semidirect
48. C3×#807C22semidirect
49. C3×#803C22semidirect
50. C3×C4×C3⋊C8C22semidirect
51. #63575C22semidirect
52. #63573C22semidirect
53. #63572C22semidirect
54. #63572C22semidirect
55. #63564C22semidirect
56. #63564C22semidirect
73. #5014D3semidirect
75. C4×#213D3semidirect
149. C3×C4×D4C2×D3semidirect
150. C3×C4×D4C2×D3semidirect
213. #832C2×D3semidirect
214. #832C2×D3semidirect
234. #808C2×D3semidirect
236. #807C2×D3semidirect
237. #803C2×D3semidirect
238. C4×C3⋊C8C2×D3semidirect
466. C4×D4D32semidirect
730. C32#3122semidirect
825. C3#79596semidirect
826. C3#79874semidirect

Maximal subgroups

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

subgroupindex
#105960332
#105939962
C3×#50142
C3×C4×#2132
#105915162
#105914332
#105914252
#105905982
#105904742
#105904732
#105904512
#105903462
C4×#37142
#105902982
#798743
#795963