Finite Group Databasebeta

← #11887042

Subgroups — #11887042

Order 1152.

1058 conjugacy classes of subgroups.

The subgroup lattice has 881 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595288C211yesmaximal, characteristic, complemented
2#10595134C211yesmaximal, characteristic, complemented
3#10592849C211yesmaximal, characteristic, complemented
4C3×#5157C211yesmaximal, characteristic, complemented
5C3×#5156C211yesmaximal, characteristic, complemented
6#10591515C211yesmaximal, characteristic, complemented
7#10591449C211yesmaximal, characteristic, complemented
8#10591435C211yesmaximal, characteristic, complemented
9#10591413C211yesmaximal, characteristic, complemented
10D3×#832C211yesmaximal, characteristic, complemented
11#10591402C211yesmaximal, characteristic, complemented
12D3×#821C211yesmaximal, characteristic, complemented
13#10590778C211yesmaximal, characteristic, complemented
14#10590717C211yesmaximal, characteristic, complemented
15#10590679C211yesmaximal, characteristic, complemented
16#80731—31nomaximal
17#80014—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3805—21no—
21C2×D3×D12C2211yescharacteristic
22C2×C32×D8C2211yescharacteristic, complemented
23#64149C2211yescharacteristic
24D4×C3⋊Dic3C2211yescharacteristic, complemented
25C2×#3753C2211yescharacteristic, complemented
26C3×#938C2211yescharacteristic
27C3×#938C2211yescharacteristic, complemented
28C3×#938C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic
30C2×C3×D3×C8C2211yescharacteristic, complemented
31#63983—21no—
32#63982—21no—
33#63977—21no—
34#63971—21no—
35#63969—21no—
36#63969—21no—
37#63919C2211yescharacteristic, complemented
38#63909C2211yescharacteristic
39C4×#625C2211yescharacteristic
40#63898C2211yescharacteristic
41D3×C4⋊Dic3C2211yescharacteristic, complemented
42D3×C4⋊Dic3C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic, complemented
45#63648C2211yescharacteristic, complemented
46#63641C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#818C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61D4×#67—31no—
62#5611—31no—
63#5611—31no—
64#5609—31no—
65C3×#466—31no—
66C3×#447—31no—
67C2×#832—31no—
68#5157D311yescharacteristic, complemented
69#5156—31no—
70#5156D311yescharacteristic, complemented
71#5150—31no—
72#5150—31no—
73#5150—61no—
74Dic3×D8—31no—
75C2×#821—31no—
76C8×#67—31no—
77#5038—31no—
78#5036—31no—
79#5033—31no—
80#4890—31no—
81#4882—31no—
82#4775—31no—
83#4774—31no—
84D3×#102—31no—
85D3×#102—31no—
86#4760—31no—
87#4760—31no—
88#4759—31no—
89#4756—31no—
90#4736—31no—
91#67⋊C8—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98C22×C3⋊Dic3—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C3×D3×D4—22no—
105C3×D3×D4—41no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109D3×#67—44no—
110C2×#627—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#625D411yescharacteristic
114#3805—44no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118D3×D12—22no—
119D3×D12—41no—
120C32×D8—41no—
121C2×C32×C8C2311yescharacteristic
122#3757—21no—
123#3753—41no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C4×C3⋊Dic3C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×#217—21no—
128C3×#217—21no—
129C3×#217—21no—
130C3×#213—22no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×D3×C8—41no—
137#3724—21no—
138#3724D411yescharacteristic
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141#3722—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3D411yescharacteristic
144(C2×D3)⋊Dic3D411yescharacteristic
145D3×C3⋊C8—41no—
146#3294—91noSylow
147C22×C3×D4—31no—
148C22×#67—61no—
149C2×#237—61no—
150C2×#237—61no—
151C2×D3×D4—31no—
152C2×D3×D4—61no—
153C2×D3×D4C2×D311yescharacteristic
154C22×D12—31no—
155C2×C3×D8—21no—
156C2×C3×D8—31no—
157C2×C3×D8C2×D311yescharacteristic, complemented
158C2×C3×D8C2×D311yescharacteristic, complemented
159C22×C3×C8—31no—
160C3×#121—31no—
161C3×#121—31no—
162C3×#121—31no—
163#953—61no—
164#940—31no—
165#940—31no—
166#940—61no—
167#939—61no—
168#938C2×D311yescharacteristic
169#938C2×D311yescharacteristic, complemented
170#938C2×D311yescharacteristic, complemented
171#937—61no—
172#937—61no—
173#935—61no—
174#935—61no—
175D4×Dic3—31no—
176D4×Dic3—31no—
177D4×Dic3—31no—
178D4×Dic3—61no—
179C2×#213—31no—
180C2×#213—31no—
181C2×#213—61no—
182C2×#213C2×D311yescharacteristic
183#930—31no—
184C4×#67—31no—
185C4×#67—31no—
186C2×C4⋊Dic3—31no—
187C2×C4⋊Dic3—31no—
188C22×C3⋊C8—31no—
189C2×D3×C8—31no—
190C2×D3×C8C2×D311yescharacteristic, complemented
191#895—31no—
192#893—31no—
193D3×C4⋊C4—31no—
194D3×C4⋊C4—31no—
195#888—31no—
196#888—31no—
197#884—61no—
198#883—61no—
199#883—61no—
200#882—61no—
201#878—61no—
202#878—61no—
203C3×#107—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×C22⋊C8—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—61no—
214#832C2×D311yescharacteristic, complemented
215#832C2×D311yescharacteristic, complemented
216#832C2×D311yescharacteristic, complemented
217#830—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—31no—
222#821—31no—
223#821—61no—
224#821C2×D311yescharacteristic
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8C2×D311yescharacteristic, complemented
227#818—31no—
228#818C2×D311yescharacteristic, complemented
229Dic3⋊C8—31no—
230Dic3⋊C8—31no—
231Dic3⋊C8—61no—
232C8×Dic3—31no—
233C8×Dic3—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#807—31no—
238#807—31no—
239#807—31no—
240C23×C32—21no—
241C23×C32—21no—
242C22×C3⋊D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—42no—
245C22×C3×D3—42no—
246C22×C3×D3—81no—
247C22×C3×D3C2×D411yescharacteristic
248C22×C3×D3C2×D411yescharacteristic
249C2×D32—42no—
250C2×D32—42no—
251C2×D32—81no—
252C32×D4—21no—
253C32×D4—21no—
254C32×D4—21no—
255C32×D4—21no—
256C2×C32×C4C2411yescharacteristic
257#638—42no—
258#638—81no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—42no—
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—21no—
265C3×#67—42no—
266C3×#67—42no—
267C3×#67—42no—
268C3×#67—42no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D411yescharacteristic
274C3×D12—21no—
275C3×D12#4112yescomplemented
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×C4×D3—21no—
280#627—42no—
281#626—42no—
282#626—42no—
283#625D814yescomplemented
284D3×Dic3—42no—
285D3×Dic3—42no—
286D3×Dic3—42no—
287C32×C8—21no—
288C3⋊(C3⋊C8)—21no—
289C3×C3⋊C8—21no—
290C3×C3⋊C8—21no—
291#547—91no—
292D42—91no—
293#486—91no—
294#480—91no—
295#480—91no—
296#474—91no—
297#466—31no—
298#466—91no—
299#459—91no—
300#447—31no—
301#447—91no—
302C4×D8—91no—
303C8×D4—91no—
304C2×#102—91no—
305C2×#102—91no—
306C24×C3—61no—
307C23×D3—21no—
308C23×D3—61no—
309C23×D3—61no—
310C2×C3×D4—21no—
311C2×C3×D4—21no—
312C2×C3×D4—31no—
313C2×C3×D4—61no—
314C2×C3×D4—62no—
315C2×C3×D4—61no—
316C2×C3×D4—61no—
317C2×C3×D4—61no—
318C2×C3×D4—121no—
319C2×C3×D4C22×D311yescharacteristic
320C2×C3×D4C22×D311yescharacteristic
321C2×C3×D4C22×D311yescharacteristic
322C2×C3×D4C22×D311yescharacteristic
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C2×#67—21no—
326C2×#67—21no—
327C2×#67—21no—
328C2×#67—21no—
329C2×#67—31no—
330C2×#67—31no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—121no—
338C2×#67—121no—
339C2×#67—124no—
340C22×Dic3—61no—
341C22×Dic3—61no—
342C22×Dic3—61no—
343C22×Dic3—61no—
344C22×Dic3—61no—
345C22×Dic3—121no—
346#237—124no—
347#237—124no—
348D3×D4—22no—
349D3×D4—41no—
350D3×D4—62no—
351D3×D4—121no—
352D3×D4—124no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—61no—
356C2×D12—62no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—121no—
360C2×D12C22×D311yescharacteristic
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3C22×D311yescharacteristic
365C2×C4×D3C22×D311yescharacteristic
366C2×Dic6—61no—
367C2×Dic6—61no—
368C3×D8—41no—
369C3×D8—41no—
370C3×D8—42no—
371C3×D8—62no—
372C2×C3×C8—21no—
373C2×C3×C8—31no—
374C2×C3×C8—31no—
375C2×C3×C8—121no—
376C2×C3×C8C22×D311yescharacteristic
377C2×C3×C8C22×D311yescharacteristic
378C3×C4⋊C4—31no—
379C3×C4⋊C4—31no—
380C3×C4⋊C4—31no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384#217—21no—
385#217—21no—
386#217—21no—
387#217—31no—
388#217—31no—
389#217—61no—
390#217—61no—
391#217—61no—
392#217—121no—
393#213—22no—
394#213—121no—
395#213—121no—
396#213—122no—
397(C2×D3)⋊C4—31no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3C22×D311yescharacteristic
408C4⋊Dic3C22×D311yescharacteristic
409C4⋊Dic3C22×D311yescharacteristic
410Dic3⋊C4—31no—
411Dic3⋊C4—31no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416C4×Dic3—31no—
417C4×Dic3—31no—
418C4×Dic3—61no—
419C2×C3⋊C8—31no—
420C2×C3⋊C8—31no—
421C2×C3⋊C8—61no—
422C2×C3⋊C8—121no—
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425D3×C8—41no—
426D3×C8—121no—
427C22×C32—41no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32—41no—
432C22×C32—41no—
433C22×C32C22×D411yescharacteristic
434C2×C3⋊D3—41no—
435C2×C3⋊D3—41no—
436C2×C3⋊D3—41no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3—21no—
441C2×C3×D3—22no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—84no—
445C2×C3×D3C2×D812yes—
446C2×C3×D3C2×D812yes—
447D32—84no—
448C32×C4C2×#4111yescharacteristic
449C32×C4H(5,𝔽2)11yescharacteristic
450C3⋊Dic3—21no—
451C3⋊Dic3—41no—
452C3⋊Dic3C2×D812yes—
453C3×Dic3—21no—
454C3×Dic3—21no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C2×#41—181no—
459C22×D4—31no—
460C22×D4—91no—
461C22×D4—181no—
462C2×D8—31no—
463C2×D8—91no—
464C2×D8D3211yescharacteristic, complemented
465C22×C8—31no—
466C22×C8—91no—
467C4⋊Q8—91no—
468#127—91no—
469#123—181no—
470#123—181no—
471C22⋊Q8—181no—
472#121—31no—
473#121—31no—
474#121—31no—
475#121—91no—
476#121—181no—
477#120—181no—
478#120—181no—
479C4×D4—91no—
480C4×D4—91no—
481C4×D4—91no—
482C2×C4⋊C4—91no—
483C2×C4⋊C4—91no—
484#107—31no—
485#107—91no—
486#107—91no—
487C4⋊C8—91no—
488#102—31no—
489#102—31no—
490#102—31no—
491#102—31no—
492#102—91no—
493#102—91no—
494#102—91no—
495#102—91no—
496#102—91no—
497#102—91no—
498C22⋊C8—31no—
499C22⋊C8—91no—
500C4×C8—91no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—31no—
506C23×C3—31no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—61no—
510C23×C3—122no—
511C23×C3—122no—
512C23×C3—241no—
513C22×D3—21no—
514C22×D3—42no—
515C22×D3—42no—
516C22×D3—61no—
517C22×D3—61no—
518C22×D3—81no—
519C22×D3—121no—
520C22×D3—122no—
521C22×D3—122no—
522C22×D3—122no—
523C22×D3—122no—
524C22×D3—241no—
525C22×D3—241no—
526C22×D3D3×D411yescharacteristic
527C22×D3D3×D411yescharacteristic
528C3×D4—22no—
529C3×D4—21no—
530C3×D4—21no—
531C3×D4—21no—
532C3×D4—21no—
533C3×D4—21no—
534C3×D4—21no—
535C3×D4—21no—
536C3×D4—21no—
537C3×D4—32no—
538C3×D4—41no—
539C3×D4—41no—
540C3×D4—41no—
541C3×D4—61no—
542C3×D4—122no—
543C3×D4—122no—
544C3×D4—122no—
545C3×D4—122no—
546C2×C3×C4—21no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4C23×D311yescharacteristic
557C2×C3×C4C23×D311yescharacteristic
558#67—34no—
559#67—34no—
560#67—42no—
561#67—42no—
562#67—42no—
563#67—42no—
564#67—122no—
565#67—122no—
566#67—122no—
567#67—122no—
568#67—242no—
569#67—241no—
570#67—241no—
571#67—242no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—31no—
578C2×Dic3—31no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—121no—
584C2×Dic3—122no—
585C2×Dic3—122no—
586C2×Dic3—122no—
587C2×Dic3—122no—
588C2×Dic3—122no—
589C2×Dic3—242no—
590C2×Dic3D3×D411yescharacteristic
591C2×Dic3D3×D411yescharacteristic
592D12—21no—
593D12—61no—
594D12—61no—
595D12—61no—
596D12—61no—
597D12—121no—
598D12—121no—
599D12—122no—
600D12—122no—
601D12#23712yescomplemented
602C4×D3—21no—
603C4×D3—21no—
604C4×D3—21no—
605C4×D3—21no—
606C4×D3—122no—
607C4×D3—122no—
608C4×D3—122no—
609Dic6—122no—
610Dic6—122no—
611C3×C8—21no—
612C3×C8—21no—
613C3×C8—41no—
614C3×C8—61no—
615C3×C8—61no—
616C3⋊C8—21no—
617C3⋊C8—21no—
618C3⋊C8—61no—
619C3⋊C8—61no—
620C3⋊C8—121no—
621C2×C32—81no—
622C2×C32—81no—
623C2×C32#54611yescharacteristic
624C2×C32C22×D811yescharacteristic
625C2×C32#57711yescharacteristic
626C3⋊D3—81no—
627C3×D3—22no—
628C3×D3—22no—
629C3×D3—42no—
630C24—61no—
631C24—181no—
632#41—364no—
633C2×Q8—181no—
634C2×D4—31no—
635C2×D4—61no—
636C2×D4—62no—
637C2×D4—61no—
638C2×D4—61no—
639C2×D4—61no—
640C2×D4—91no—
641C2×D4—91no—
642C2×D4—121no—
643C2×D4—181no—
644C2×D4—182no—
645C2×D4—181no—
646C2×D4—181no—
647C2×D4—181no—
648C2×D4—361no—
649C2×D4—364no—
650C2×D4C2×D3211yescharacteristic
651C2×D4C2×D3211yescharacteristic
652C22×C4—31no—
653C22×C4—31no—
654C22×C4—181no—
655C22×C4—181no—
656C22×C4—181no—
657C22×C4—181no—
658D8—41no—
659D8—62no—
660D8—361no—
661C2×C8—31no—
662C2×C8—31no—
663C2×C8—91no—
664C2×C8—121no—
665C2×C8—361no—
666C2×C8C2×D3211yescharacteristic
667C4⋊C4—31no—
668C4⋊C4—31no—
669C4⋊C4—31no—
670C4⋊C4—91no—
671C4⋊C4—91no—
672C4⋊C4—181no—
673C4⋊C4—181no—
674C4⋊C4—181no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C22⋊C4—61no—
678C22⋊C4—91no—
679C22⋊C4—91no—
680C22⋊C4—181no—
681C22⋊C4—181no—
682C22⋊C4—181no—
683C42—91no—
684C22×C3—21no—
685C22×C3—32no—
686C22×C3—32no—
687C22×C3—42no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—61no—
701C22×C3—61no—
702C22×C3—61no—
703C22×C3—61no—
704C22×C3—62no—
705C22×C3—81no—
706C22×C3—81no—
707C22×C3—81no—
708C22×C3—81no—
709C22×C3—81no—
710C22×C3—121no—
711C22×C3—121no—
712C22×C3—244no—
713C22×C3C2×D3×D411yescharacteristic
714C22×C3C2×D3×D411yescharacteristic
715C2×D3—21no—
716C2×D3—21no—
717C2×D3—21no—
718C2×D3—21no—
719C2×D3—22no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—84no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—241no—
730C2×D3—241no—
731C2×D3—241no—
732C2×D3—244no—
733C2×D3—244no—
734C2×D3D3×D812yes—
735C2×D3D3×D812yes—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—61no—
739C3×C4—61no—
740C3×C4—121no—
741C3×C4—121no—
742C3×C4—121no—
743C3×C4C2×#23711yescharacteristic
744C3×C4#100411yescharacteristic
745C3×C4#100411yescharacteristic
746C3×C4D3×#4111yescharacteristic
747Dic3—21no—
748Dic3—21no—
749Dic3—32no—
750Dic3—32no—
751Dic3—41no—
752Dic3—41no—
753Dic3—41no—
754Dic3—62no—
755Dic3—61no—
756Dic3—61no—
757Dic3—121no—
758Dic3—121no—
759Dic3—121no—
760Dic3—241no—
761C32#329411yescharacteristic, complemented, Sylow
762C23—21no—
763C23—21no—
764C23—31no—
765C23—31no—
766C23—61no—
767C23—122no—
768C23—122no—
769C23—181no—
770C23—241no—
771C23—362no—
772C23—362no—
773C23—721no—
774Q8—362no—
775D4—21no—
776D4—21no—
777D4—21no—
778D4—21no—
779D4—32no—
780D4—61no—
781D4—94no—
782D4—122no—
783D4—122no—
784D4—122no—
785D4—122no—
786D4—181no—
787D4—181no—
788D4—362no—
789D4—362no—
790D4—362no—
791D4—721no—
792C2×C4—31no—
793C2×C4—31no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—91no—
802C2×C4—91no—
803C2×C4—181no—
804C2×C4—362no—
805C2×C4—362no—
806C2×C4—362no—
807C2×C4—362no—
808C2×C4C22×D3211yescharacteristic
809C8—21no—
810C8—61no—
811C8—61no—
812C8—181no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—62no—
817C2×C3—62no—
818C2×C3—82no—
819C2×C3—81no—
820C2×C3—81no—
821C2×C3—81no—
822C2×C3—81no—
823C2×C3—122no—
824C2×C3—161no—
825C2×C3#559111yescharacteristic
826C2×C3#561011yescharacteristic
827C2×C3C2×D3×D811yescharacteristic
828C2×C3C2×D3×D811yescharacteristic
829C2×C3#577011yescharacteristic
830C2×C3#577511yescharacteristic
831D3—22no—
832D3—22no—
833D3—42no—
834D3—241no—
835D3—241no—
836D3—481no—
837C22—32no—
838C22—32no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—61no—
846C22—61no—
847C22—61no—
848C22—61no—
849C22—62no—
850C22—121no—
851C22—121no—
852C22—244no—
853C22—361no—
854C22—361no—
855C22—361no—
856C22—724no—
857C22D32×D411yescharacteristic
858C4—61no—
859C4—61no—
860C4—92no—
861C4—121no—
862C4—121no—
863C4—121no—
864C4—181no—
865C4—361no—
866C4D3×#23711yescharacteristic
867C4#6433011yescharacteristic
868C3—21no—
869C3#8001411yescharacteristic, complemented
870C3#8073111yescharacteristic, complemented
871C2—62no—
872C2—62no—
873C2—81no—
874C2—81no—
875C2—122no—
876C2—721no—
877C2D32×D811yescharacteristic
878C2#1059473611yescharacteristic
879C2#1059529011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595288C2semidirect
2. #10595134C2semidirect
3. #10592849C2semidirect
4. C3×#5157C2semidirect
5. C3×#5156C2semidirect
6. #10591515C2semidirect
7. #10591449C2semidirect
8. #10591435C2semidirect
9. #10591413C2semidirect
10. D3×#832C2semidirect
11. #10591402C2semidirect
12. D3×#821C2semidirect
13. #10590778C2semidirect
14. #10590717C2semidirect
15. #10590679C2semidirect
22. C2×C32×D8C22semidirect
24. D4×C3⋊Dic3C22semidirect
25. C2×#3753C22semidirect
27. C3×#938C22semidirect
28. C3×#938C22semidirect
30. C2×C3×D3×C8C22semidirect
37. #63919C22semidirect
41. D3×C4⋊Dic3C22semidirect
42. D3×C4⋊Dic3C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63659C22semidirect
45. #63648C22semidirect
46. #63641C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
49. C3×#832C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#818C22semidirect
53. #63576C22semidirect
54. #63575C22semidirect
55. #63564C22semidirect
56. #63564C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63553C22semidirect
68. #5157D3semidirect
70. #5156D3semidirect
157. C2×C3×D8C2×D3semidirect
158. C2×C3×D8C2×D3semidirect
169. #938C2×D3semidirect
170. #938C2×D3semidirect
190. C2×D3×C8C2×D3semidirect
214. #832C2×D3semidirect
215. #832C2×D3semidirect
216. #832C2×D3semidirect
226. (C2×D3)⋊C8C2×D3semidirect
228. #818C2×D3semidirect
275. C3×D12#41semidirect
283. #625D8semidirect
464. C2×D8D32semidirect
601. D12#237semidirect
761. C32#3294semidirect
869. C3#80014semidirect
870. C3#80731semidirect

Maximal subgroups

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

subgroupindex
#105952882
#105951342
#105928492
C3×#51572
C3×#51562
#105915152
#105914492
#105914352
#105914132
D3×#8322
#105914022
D3×#8212
#105907782
#105907172
#105906792
#807313
#800143