Finite Group Databasebeta

← #11887446

Subgroups — #11887446

Order 1152.

902 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5558C211yesmaximal, characteristic, complemented
2#10594003C211yesmaximal, characteristic, complemented
3#10592715C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic, complemented
5#10591519C211yesmaximal, characteristic, complemented
6#10591515C211yesmaximal, characteristic, complemented
7#10591460C211yesmaximal, characteristic, complemented
8#10591449C211yesmaximal, characteristic, complemented
9#10590608C211yesmaximal, characteristic, complemented
10D3×#809C211yesmaximal, characteristic, complemented
11#10590427C211yesmaximal, characteristic, complemented
12#10590424C211yesmaximal, characteristic, complemented
13C3⋊C8×D12C211yesmaximal, characteristic, complemented
14#10590293C211yesmaximal, characteristic, complemented
15#10590270C211yesmaximal, characteristic, complemented
16#83614—31nomaximal
17#79609—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic, complemented
21C2×#3754C2211yescharacteristic, complemented
22C2×#3753C2211yescharacteristic
23#64084C2211yescharacteristic
24C3×#938C2211yescharacteristic
25C3×#938C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic
27C3×#929—21no—
28C3×C4×#67—21no—
29C3×#892C2211yescharacteristic, complemented
30C3×D3×C4⋊C4C2211yescharacteristic
31C3×#884—21no—
32C3×#879—21no—
33C3×C4×D12C2211yescharacteristic
34C3×C4×D12C2211yescharacteristic
35C3×#870C2211yescharacteristic, complemented
36#63922—21no—
37D3×(C2×D3)⋊C4—21no—
38#63909C2211yescharacteristic
39#63906—21no—
40#63890—21no—
41#63857C2211yescharacteristic
42C2×D3×C3⋊C8C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63637C2211yescharacteristic, complemented
45#63636C2211yescharacteristic
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic
49C3×#807C2211yescharacteristic, complemented
50C3×C4×C3⋊C8C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63574C2211yescharacteristic, complemented
53#63567C2211yescharacteristic, complemented
54#63567C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#553—31no—
62#5558D311yescharacteristic, complemented
63#5554—31no—
64#5550—31no—
65C3×C4×D8—31no—
66#5158—31no—
67#5156—31no—
68#5068—31no—
69#5066—31no—
70#5041—31no—
71#5038—31no—
72#5037—31no—
73#5036—31no—
74#5016—31no—
75#5016—31no—
76#5016—61no—
77C4×#213D311yescharacteristic, complemented
78D4×C3⋊C8—31no—
79#5009—31no—
80#5003—31no—
81#5002—31no—
82#4970—31no—
83C2×#809—31no—
84#4885—31no—
85#4884—31no—
86#4778—31no—
87#4775—31no—
88#4772—31no—
89D3×#102—31no—
90#4697—31no—
91C8×D12—31no—
92C22×D32—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×D12D411yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#625—21no—
108C2×D3×Dic3—21no—
109D3×D12—22no—
110D3×D12—41no—
111#3795—22no—
112#3795—41no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115C32×C42C2311yescharacteristic
116#3754—41no—
117#3753—41no—
118#3752—21no—
119#3752—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217—21no—
123C3×#217—21no—
124C3×#213—22no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3D411yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3—21no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139Dic3⋊Dic3—21no—
140#3722—21no—
141(C2×D3)⋊Dic3—21no—
142D3×C3⋊C8—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×#237—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C2×C3×D8—31no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#123—61no—
153C3×#121—31no—
154C3×#121—31no—
155C3×#121—61no—
156C3×C4×D4—21no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×C4×D4—61no—
160C3×C4×D4C2×D311yescharacteristic, complemented
161C3×C4×D4C2×D311yescharacteristic, complemented
162C3×#117—31no—
163C2×C3×C4⋊C4—31no—
164#938C2×D311yescharacteristic
165#938C2×D311yescharacteristic, complemented
166#937—61no—
167C2×#214—31no—
168C2×#214—31no—
169C2×#214—61no—
170C2×#213—31no—
171C2×#213—31no—
172C2×#213—61no—
173C2×#213C2×D311yescharacteristic
174#930—31no—
175#930—61no—
176#929—21no—
177C4×#67—21no—
178C2×(C2×D3)⋊C4—61no—
179#924—31no—
180C22×C3⋊C8—31no—
181C22×C3⋊C8—31no—
182C2×D3×C8—31no—
183C2×D3×C8—31no—
184#897—31no—
185#895—31no—
186#894—61no—
187#892C2×D311yescharacteristic, complemented
188D3×C4⋊C4C2×D311yescharacteristic
189#886—61no—
190#884—21no—
191#884—61no—
192#882—61no—
193D3×C22⋊C4—61no—
194#879—21no—
195#875—31no—
196#875—31no—
197#875—61no—
198C4×D12C2×D311yescharacteristic
199C4×D12C2×D311yescharacteristic
200#870C2×D311yescharacteristic, complemented
201C3×#107—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×C4×C8—31no—
205#832—31no—
206#832—31no—
207#832C2×D311yescharacteristic, complemented
208#830—31no—
209#830—31no—
210#821—31no—
211#821—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—31no—
214#816—31no—
215#816—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—61no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—61no—
228#809C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#807—31no—
232#807—31no—
233#807C2×D311yescharacteristic, complemented
234C4⋊(C3⋊C8)—31no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—61no—
237C4×C3⋊C8C2×D311yescharacteristic, complemented
238C23×C32—21no—
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C22×C3×D3C2×D411yescharacteristic
243C2×D32—42no—
244C2×D32—42no—
245C2×D32—81no—
246C32×D4—21no—
247C32×D4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—81no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256#634—21no—
257#634—21no—
258C3×#67—42no—
259C3×#67—81no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—22no—
266C3×D12—21no—
267C3×D12#4112yes—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—81no—
273C3×C4×D3—81no—
274#626—42no—
275#626—81no—
276#625—42no—
277D3×Dic3—42no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—31no—
283#546—91no—
284#488—91no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—31no—
294C8×D4—91no—
295#416—91no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C22×D311yescharacteristic
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—41no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C2×#67—21no—
314C2×#67—21no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C22×Dic3—61no—
320#237—62no—
321#237—121no—
322D3×D4—62no—
323D3×D4—121no—
324#235—62no—
325#235—121no—
326C2×D12—31no—
327C2×D12—31no—
328C2×D12—61no—
329C2×D12—62no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12—121no—
333C2×D12#6711yescharacteristic
334C2×D12C22×D311yescharacteristic
335C2×C4×D3—21no—
336C2×C4×D3—21no—
337C2×C4×D3—61no—
338C2×C4×D3C22×D311yescharacteristic
339C2×C4×D3C22×D311yescharacteristic
340C2×Dic6—31no—
341C2×Dic6—31no—
342C2×Dic6—61no—
343C3×D8—62no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—31no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—41no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C42—21no—
366C3×C42—61no—
367C3×C42C22×D311yescharacteristic
368C3×C42C22×D311yescharacteristic
369#217—21no—
370#217—21no—
371#217—61no—
372#214—121no—
373#214—121no—
374#214—122no—
375#213—22no—
376#213—121no—
377#213—121no—
378#213—122no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
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—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—121no—
389(C2×D3)⋊C4—121no—
390(C2×D3)⋊C4#6711yescharacteristic
391(C2×D3)⋊C4#6711yescharacteristic
392C4⋊Dic3—61no—
393C4⋊Dic3#6711yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—61no—
401C4×Dic3—21no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8—121no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412D3×C8—121no—
413D3×C8—121no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—22no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3#13512yes—
430D32—84no—
431C32×C4—21no—
432C32×C4—21no—
433C32×C4—41no—
434C32×C4C2×#4111yescharacteristic
435C32×C4H(5,𝔽2)11yescharacteristic
436C3⋊Dic3—41no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—91no—
443C22×D4—91no—
444C2×SD16—91no—
445C2×D8—31no—
446C2×D8—91no—
447C22×C8—91no—
448C22×C8—91no—
449#126—61no—
450#125—31no—
451#124—91no—
452#123—61no—
453#123—181no—
454C22⋊Q8—91no—
455#121—31no—
456#121—31no—
457#121—61no—
458#121—91no—
459#121—181no—
460#120—181no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—61no—
464C4×D4D3211yescharacteristic, complemented
465#117—31no—
466C2×C4⋊C4—31no—
467C2×C22⋊C4—181no—
468#107—31no—
469#107—91no—
470#106—91no—
471C4⋊C8—91no—
472#103—91no—
473#103—91no—
474#103—91no—
475#102—31no—
476#102—31no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482C22⋊C8—91no—
483C22⋊C8—91no—
484C4×C8—31no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—31no—
488C23×C3—31no—
489C23×C3—41no—
490C23×C3—61no—
491C22×D3—21no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—121no—
495C22×D3—122no—
496C22×D3—122no—
497C22×D3—122no—
498C22×D3—122no—
499C22×D3—241no—
500C22×D3—241no—
501C22×D3C2×#6711yescharacteristic
502C22×D3C2×#6711yescharacteristic
503C3×D4—22no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—32no—
509C3×D4—41no—
510C3×D4—62no—
511C3×D4—61no—
512C3×D4—122no—
513C3×D4—241no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—41no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—81no—
530C2×C3×C4—81no—
531C2×C3×C4—82no—
532C2×C3×C4—241no—
533C2×C3×C4—241no—
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4C2×#6711yescharacteristic
537C2×C3×C4C2×#6711yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540#67—42no—
541#67—81no—
542#67—122no—
543#67—122no—
544#67—122no—
545#67—241no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—121no—
552C2×Dic3—122no—
553C2×Dic3C2×#6711yescharacteristic
554C2×Dic3C2×#6711yescharacteristic
555D12—22no—
556D12—21no—
557D12—61no—
558D12—61no—
559D12—61no—
560D12—61no—
561D12—121no—
562D12—121no—
563D12—122no—
564D12—241no—
565D12#23512yes—
566C4×D3—21no—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—21no—
570C4×D3—81no—
571C4×D3—81no—
572C4×D3—122no—
573Dic6—61no—
574Dic6—61no—
575Dic6—61no—
576Dic6—61no—
577Dic6—121no—
578Dic6—121no—
579C3×C8—61no—
580C3×C8—61no—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C3⋊C8—61no—
584C3⋊C8—61no—
585C3⋊C8—61no—
586C3⋊C8—61no—
587C3⋊C8—121no—
588C3⋊C8—121no—
589C2×C32—81no—
590C2×C32#54611yescharacteristic
591C2×C32C2×#13511yescharacteristic
592C2×C32#57611yescharacteristic
593C3⋊D3—81no—
594C3×D3—22no—
595C3×D3—42no—
596C3×D3—41no—
597C24—181no—
598#41—182no—
599#41—361no—
600C2×Q8—91no—
601C2×D4—31no—
602C2×D4—31no—
603C2×D4—61no—
604C2×D4—61no—
605C2×D4—91no—
606C2×D4—181no—
607C2×D4—182no—
608C2×D4—181no—
609C2×D4—181no—
610C2×D4—361no—
611C2×D4C2×D3211yescharacteristic
612C22×C4—21no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—181no—
618SD16—361no—
619D8—62no—
620D8—361no—
621C2×C8—31no—
622C2×C8—31no—
623C2×C8—91no—
624C2×C8—91no—
625C2×C8—361no—
626C2×C8—361no—
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—61no—
634C4⋊C4—181no—
635C4⋊C4C2×D3211yescharacteristic
636C22⋊C4—21no—
637C22⋊C4—31no—
638C22⋊C4—31no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C42—61no—
648C42C2×D3211yescharacteristic
649C22×C3—21no—
650C22×C3—32no—
651C22×C3—42no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—62no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3C2×D3×D411yescharacteristic
669C22×C3C22×#6711yescharacteristic
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—22no—
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—241no—
685C2×D3—241no—
686C2×D3—241no—
687C2×D3—244no—
688C2×D3—244no—
689C2×D3#95012yes—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—41no—
699C3×C4—41no—
700C3×C4—61no—
701C3×C4—61no—
702C3×C4—81no—
703C3×C4—121no—
704C3×C4—121no—
705C3×C4—121no—
706C3×C4C2×#23511yescharacteristic
707C3×C4D3×#4111yescharacteristic
708C3×C4#100911yescharacteristic
709C3×C4#100911yescharacteristic
710Dic3—21no—
711Dic3—21no—
712Dic3—41no—
713Dic3—41no—
714Dic3—41no—
715Dic3—121no—
716Dic3—121no—
717Dic3—241no—
718C32#329711yescharacteristic, complemented, Sylow
719C23—21no—
720C23—31no—
721C23—31no—
722C23—61no—
723C23—181no—
724C23—362no—
725C23—362no—
726C23—721no—
727Q8—181no—
728Q8—181no—
729D4—21no—
730D4—21no—
731D4—32no—
732D4—62no—
733D4—61no—
734D4—122no—
735D4—181no—
736D4—181no—
737D4—241no—
738D4—362no—
739D4—362no—
740D4—721no—
741C2×C4—21no—
742C2×C4—31no—
743C2×C4—31no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—81no—
752C2×C4—181no—
753C2×C4—241no—
754C2×C4—241no—
755C2×C4—362no—
756C2×C4D3×#6711yescharacteristic
757C2×C4D3×#6711yescharacteristic
758C2×C4C22×D3211yescharacteristic
759C8—61no—
760C8—61no—
761C8—181no—
762C8—181no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—62no—
767C2×C3—82no—
768C2×C3—81no—
769C2×C3—81no—
770C2×C3—122no—
771C2×C3—121no—
772C2×C3#555011yescharacteristic
773C2×C3#575711yescharacteristic
774C2×C3D3×#13511yescharacteristic
775C2×C3C2×#95011yescharacteristic
776C2×C3#582911yescharacteristic
777C2×C3#583511yescharacteristic
778D3—22no—
779D3—41no—
780D3—42no—
781D3—241no—
782D3—241no—
783D3—481no—
784C22—32no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—61no—
789C22—61no—
790C22—61no—
791C22—61no—
792C22—61no—
793C22—62no—
794C22—121no—
795C22—121no—
796C22—361no—
797C22—361no—
798C22—361no—
799C22—724no—
800C22C2×D3×#6711yescharacteristic
801C4—21no—
802C4—21no—
803C4—41no—
804C4—61no—
805C4—61no—
806C4—121no—
807C4—121no—
808C4—121no—
809C4—361no—
810C4D3×#23511yescharacteristic
811C4#6430811yescharacteristic
812C3—21no—
813C3#7960911yescharacteristic, complemented
814C3#8361411yescharacteristic, complemented
815C2—62no—
816C2—81no—
817C2—121no—
818C2—122no—
819C2—721no—
820C2#1059506711yescharacteristic
821C2#1059509611yescharacteristic
822C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3297
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. C3×#5558C2semidirect
2. #10594003C2semidirect
3. #10592715C2semidirect
4. C3×C4×#213C2semidirect
5. #10591519C2semidirect
6. #10591515C2semidirect
7. #10591460C2semidirect
8. #10591449C2semidirect
9. #10590608C2semidirect
10. D3×#809C2semidirect
11. #10590427C2semidirect
12. #10590424C2semidirect
13. C3⋊C8×D12C2semidirect
14. #10590293C2semidirect
15. #10590270C2semidirect
20. C32×C4×D4C22semidirect
21. C2×#3754C22semidirect
25. C3×#938C22semidirect
29. C3×#892C22semidirect
35. C3×#870C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63637C22semidirect
46. C4⋊(C3⋊(C3⋊C8))C22semidirect
47. C3×#832C22semidirect
49. C3×#807C22semidirect
50. C3×C4×C3⋊C8C22semidirect
51. #63576C22semidirect
52. #63574C22semidirect
53. #63567C22semidirect
54. #63567C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #5558D3semidirect
77. C4×#213D3semidirect
160. C3×C4×D4C2×D3semidirect
161. C3×C4×D4C2×D3semidirect
165. #938C2×D3semidirect
187. #892C2×D3semidirect
200. #870C2×D3semidirect
207. #832C2×D3semidirect
233. #807C2×D3semidirect
237. C4×C3⋊C8C2×D3semidirect
464. C4×D4D32semidirect
718. C32#3297semidirect
813. C3#79609semidirect
814. C3#83614semidirect

Maximal subgroups

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

subgroupindex
C3×#55582
#105940032
#105927152
C3×C4×#2132
#105915192
#105915152
#105914602
#105914492
#105906082
D3×#8092
#105904272
#105904242
C3⋊C8×D122
#105902932
#105902702
#836143
#796093