Finite Group Databasebeta

← #11887016

Subgroups — #11887016

Order 1152.

1055 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595069C211yesmaximal, characteristic, complemented
2#10594928C211yesmaximal, characteristic, complemented
3C8×#638C211yesmaximal, characteristic, complemented
4C3×#5115C211yesmaximal, characteristic, complemented
5C2×C3×#821C211yesmaximal, characteristic, complemented
6#10591160C211yesmaximal, characteristic, complemented
7#10591089C211yesmaximal, characteristic, complemented
8#10590945C211yesmaximal, characteristic, complemented
9#10590940C211yesmaximal, characteristic, complemented
10#10590885C211yesmaximal, characteristic, complemented
11#10590839C211yesmaximal, characteristic, complemented
12#10590778C211yesmaximal, characteristic, complemented
13#10590749C211yesmaximal, characteristic, complemented
14#10590740C211yesmaximal, characteristic, complemented
15#10590650C211yesmaximal, characteristic, complemented
16#80731—31nomaximal
17#78757—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3804—21no—
21C2×#3802C2211yescharacteristic
22C22×C32×C8C2211yescharacteristic, complemented
23C4×#638C2211yescharacteristic
24C2×C8×C3⋊D3C2211yescharacteristic, complemented
25C3×#930C2211yescharacteristic
26C3×#930C2211yescharacteristic, complemented
27C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
28C2×C3×D24C2211yescharacteristic, complemented
29#63976—21no—
30#63961—21no—
31#63922—21no—
32#63919C2211yescharacteristic, complemented
33#63916C2211yescharacteristic
34#63916C2211yescharacteristic, complemented
35#63914C2211yescharacteristic
36#63900C2211yescharacteristic, complemented
37#63899—21no—
38#63898C2211yescharacteristic
39#63898C2211yescharacteristic, complemented
40#63885—21no—
41#63854—21no—
42C2×#3713C2211yescharacteristic
43C2×#3713C2211yescharacteristic, complemented
44#63657C2211yescharacteristic, complemented
45#63647C2211yescharacteristic, complemented
46#63641C2211yescharacteristic, complemented
47C8×C3⋊Dic3C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic, complemented
52C3×#821C2211yescharacteristic, complemented
53C3×#821C2211yescharacteristic, complemented
54C3×#818C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56#63576C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61D4×#67—31no—
62#5611—31no—
63#5609—31no—
64#5507—31no—
65C3×#466—31no—
66C2×C3×#102—31no—
67#5217—31no—
68#5156—31no—
69#5150—31no—
70#5115D311yescharacteristic, complemented
71C2×#821D311yescharacteristic, complemented
72C8×#67—31no—
73C8×#67—31no—
74C8×#67—61no—
75#5036—31no—
76#5033—31no—
77#4967—31no—
78#4890—31no—
79#4882—31no—
80#4786—31no—
81#4775—31no—
82#4775—31no—
83#4774—31no—
84#4773—31no—
85D3×#102—31no—
86D3×#102—31no—
87#4760—31no—
88#4760—31no—
89#4759—31no—
90#4756—31no—
91#4756—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C22×C32×C4C2311yescharacteristic
95C2×#638D411yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C2×C3×D12—22no—
101C2×C3×D12—21no—
102C2×C3×D12—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107D3×#67—44no—
108C2×#627—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#625—21no—
112C2×#625—21no—
113C2×#625—21no—
114C2×#624—21no—
115#3804—44no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118#3802—22no—
119#3802—41no—
120C2×C32×C8—41no—
121C2×C32×C8C2311yescharacteristic
122C2×C32×C8C2311yescharacteristic
123#3757D411yescharacteristic
124#3752D411yescharacteristic
125#3750D411yescharacteristic
126C4×C3⋊Dic3C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C8×C3⋊D3—41no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C3×D24—41no—
138#3724—21no—
139#3724—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144#3713—22no—
145#3713—41no—
146#3294—91noSylow
147C22×C3×D4—31no—
148C22×#67—61no—
149C2×#237—61no—
150C2×D3×D4—31no—
151C2×D3×D4—31no—
152C2×D3×D4—61no—
153C2×#235—61no—
154C22×D12C2×D311yescharacteristic
155C2×C3×D8—31no—
156C22×C3×C8—21no—
157C22×C3×C8C2×D311yescharacteristic, complemented
158C22×C3×C8C2×D311yescharacteristic, complemented
159C3×#121—31no—
160C3×#121—31no—
161C2×C3×C4⋊C4—31no—
162#953—61no—
163#940—31no—
164#940—31no—
165#939—61no—
166#938—31no—
167#938—31no—
168#937—61no—
169#937—61no—
170#935—61no—
171D4×Dic3—31no—
172D4×Dic3—31no—
173C2×#213—31no—
174C2×#213—31no—
175C2×#213—31no—
176C2×#213—31no—
177#930C2×D311yescharacteristic
178#930C2×D311yescharacteristic, complemented
179#929—61no—
180C4×#67—31no—
181C4×#67—31no—
182C4×#67—61no—
183C2×C4⋊Dic3C2×D311yescharacteristic, complemented
184C2×D24C2×D311yescharacteristic, complemented
185C2×D3×C8—31no—
186C2×D3×C8—31no—
187C2×D3×C8—61no—
188#896—61no—
189#895—31no—
190#895—31no—
191#894—61no—
192#893—31no—
193#893—31no—
194D3×C4⋊C4—31no—
195D3×C4⋊C4—31no—
196#888—31no—
197#888—31no—
198#884—61no—
199#883—61no—
200#882—61no—
201#878—61no—
202C3×#107—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#830—31no—
214#830—31no—
215#830—61no—
216#821C2×D311yescharacteristic
217#821C2×D311yescharacteristic
218#821C2×D311yescharacteristic, complemented
219#821C2×D311yescharacteristic, complemented
220#821C2×D311yescharacteristic, complemented
221#821C2×D311yescharacteristic, complemented
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—61no—
225#818C2×D311yescharacteristic, complemented
226Dic3⋊C8—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—61no—
229C8×Dic3—31no—
230C8×Dic3—31no—
231C8×Dic3—61no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#807—31no—
237#807—31no—
238#807—31no—
239#807—31no—
240C23×C32C2×D411yescharacteristic
241C22×C3⋊D3C2×D411yescharacteristic
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—42no—
247C22×C3×D3—42no—
248C22×C3×D3—81no—
249C2×D32—42no—
250C2×D32—42no—
251C2×D32—81no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256#638D814yescomplemented
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259C2×C3⋊Dic3C2×D411yescharacteristic
260C4×C3⋊D3—21no—
261C4×C3⋊D3—21no—
262C3×#67—42no—
263C3×#67—42no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—42no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—21no—
276C3×D12—42no—
277C3×D12#4112yescomplemented
278#627—42no—
279#626—42no—
280#626—42no—
281#625—42no—
282#625—42no—
283#625—81no—
284#624—42no—
285D3×Dic3—42no—
286D3×Dic3—42no—
287C32×C8—21no—
288C32×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—91no—
301#447—91no—
302C4×D8—91no—
303C8×D4—91no—
304C2×#102—31no—
305C2×#102—91no—
306C24×C3—61no—
307C23×D3—21no—
308C23×D3—61no—
309C23×D3—61no—
310C2×C3×D4—31no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—62no—
315C2×C3×D4—61no—
316C2×C3×D4—61no—
317C2×C3×D4—61no—
318C2×C3×D4—121no—
319C22×C3×C4—21no—
320C22×C3×C4—61no—
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C2×#67—21no—
324C2×#67—21no—
325C2×#67—31no—
326C2×#67—31no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—124no—
337C22×Dic3—21no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340#237—124no—
341D3×D4—62no—
342D3×D4—62no—
343D3×D4—121no—
344D3×D4—121no—
345D3×D4—124no—
346#235—124no—
347C2×D12—22no—
348C2×D12—21no—
349C2×D12—41no—
350C2×D12—61no—
351C2×D12—61no—
352C2×D12C22×D311yescharacteristic
353C2×D12C22×D311yescharacteristic
354C2×D12C22×D311yescharacteristic
355C2×D12C22×D311yescharacteristic
356C2×C4×D3—31no—
357C2×C4×D3—31no—
358C2×C4×D3—61no—
359C2×C4×D3—61no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×Dic6—61no—
364C2×Dic6—61no—
365C3×D8—121no—
366C2×C3×C8—21no—
367C2×C3×C8—21no—
368C2×C3×C8—41no—
369C2×C3×C8—41no—
370C2×C3×C8—42no—
371C2×C3×C8C22×D311yescharacteristic
372C2×C3×C8C22×D311yescharacteristic
373C2×C3×C8C22×D311yescharacteristic
374C2×C3×C8C22×D311yescharacteristic
375C3×C4⋊C4—31no—
376C3×C4⋊C4—31no—
377C3×C4⋊C4—31no—
378C3×C4⋊C4—31no—
379C3×C4⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382#217—31no—
383#217—31no—
384#217—61no—
385#217—61no—
386#217—61no—
387#217—61no—
388#217—61no—
389#213—62no—
390#213—62no—
391#213—121no—
392#213—121no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402C4⋊Dic3—21no—
403C4⋊Dic3C22×D311yescharacteristic
404C4⋊Dic3C22×D311yescharacteristic
405C4⋊Dic3C22×D311yescharacteristic
406C4⋊Dic3C22×D311yescharacteristic
407Dic3⋊C4—31no—
408Dic3⋊C4—31no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414C4×Dic3—31no—
415C4×Dic3—31no—
416C4×Dic3—61no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—31no—
419C2×C3⋊C8—31no—
420C2×C3⋊C8—31no—
421C2×C3⋊C8—61no—
422C2×C3⋊C8—61no—
423D24—41no—
424D3×C8—121no—
425D3×C8—121no—
426D3×C8—122no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32C2×D812yes—
430C22×C32C22×D411yescharacteristic
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3⋊D3C2×D812yes—
434C2×C3×D3—22no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—41no—
446C2×C3×D3—84no—
447D32—84no—
448C32×C4—21no—
449C32×C4C2×#4111yescharacteristic
450C32×C4H(5,𝔽2)11yescharacteristic
451C3⋊Dic3—21no—
452C3⋊Dic3—21no—
453C3⋊Dic3C2×D812yes—
454C3×Dic3—41no—
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×D8—91no—
465C22×C8—91no—
466C22×C8D3211yescharacteristic, complemented
467C4⋊Q8—91no—
468#127—91no—
469#123—181no—
470#123—181no—
471C22⋊Q8—181no—
472#121—31no—
473#121—31no—
474#121—91no—
475#121—91no—
476#121—181no—
477#120—181no—
478#120—181no—
479C4×D4—91no—
480C4×D4—91no—
481C4×D4—91no—
482C2×C4⋊C4—31no—
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—31no—
493#102—31no—
494#102—91no—
495#102—91no—
496#102—91no—
497#102—91no—
498C22⋊C8—91no—
499C22⋊C8—91no—
500C4×C8—91no—
501C23×C3—21no—
502C23×C3—61no—
503C23×C3—61no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3—122no—
507C23×C3—122no—
508C23×C3—241no—
509C23×C3D3×D411yescharacteristic
510C23×C3D3×D411yescharacteristic
511C22×D3—21no—
512C22×D3—21no—
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—31no—
516C22×D3—31no—
517C22×D3—42no—
518C22×D3—42no—
519C22×D3—61no—
520C22×D3—81no—
521C22×D3—122no—
522C22×D3—122no—
523C22×D3—122no—
524C22×D3—122no—
525C22×D3—241no—
526C22×D3—241no—
527C3×D4—32no—
528C3×D4—61no—
529C3×D4—61no—
530C3×D4—61no—
531C3×D4—61no—
532C3×D4—61no—
533C3×D4—61no—
534C3×D4—61no—
535C3×D4—122no—
536C3×D4—122no—
537C3×D4—122no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—122no—
551C2×C3×C4D3×D411yescharacteristic
552C2×C3×C4D3×D411yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555#67—34no—
556#67—34no—
557#67—42no—
558#67—42no—
559#67—64no—
560#67—122no—
561#67—122no—
562#67—122no—
563#67—122no—
564#67—122no—
565#67—122no—
566#67—241no—
567#67—241no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—31no—
578C2×Dic3—42no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—122no—
583C2×Dic3—122no—
584D12—21no—
585D12—21no—
586D12—21no—
587D12—21no—
588D12—21no—
589D12—21no—
590D12—21no—
591D12—42no—
592D12—122no—
593D12—122no—
594D12#23512yescomplemented
595C4×D3—61no—
596C4×D3—61no—
597C4×D3—61no—
598C4×D3—61no—
599C4×D3—121no—
600C4×D3—121no—
601C4×D3—122no—
602C4×D3—122no—
603C4×D3—122no—
604C4×D3—122no—
605Dic6—122no—
606Dic6—122no—
607C3×C8—22no—
608C3×C8—21no—
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—21no—
612C3×C8—41no—
613C3⋊C8—61no—
614C3⋊C8—61no—
615C3⋊C8—61no—
616C3⋊C8—61no—
617C3⋊C8—121no—
618C3⋊C8—121no—
619C2×C32—22no—
620C2×C32#54611yescharacteristic
621C2×C32C22×D811yescharacteristic
622C2×C32#57711yescharacteristic
623C3⋊D3—22no—
624C3×D3—42no—
625C3×D3—81no—
626C3×D3—81no—
627C3×D3—81no—
628C24—61no—
629C24—181no—
630#41—364no—
631C2×Q8—181no—
632C2×D4—31no—
633C2×D4—31no—
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—62no—
637C2×D4—61no—
638C2×D4—61no—
639C2×D4—61no—
640C2×D4—91no—
641C2×D4—121no—
642C2×D4—181no—
643C2×D4—181no—
644C2×D4—181no—
645C2×D4—181no—
646C2×D4—181no—
647C2×D4—182no—
648C2×D4—361no—
649C2×D4—364no—
650C22×C4—61no—
651C22×C4—91no—
652C22×C4—181no—
653C22×C4—181no—
654C22×C4—181no—
655C22×C4C2×D3211yescharacteristic
656D8—121no—
657D8—182no—
658D8—361no—
659C2×C8—41no—
660C2×C8—91no—
661C2×C8—91no—
662C2×C8—361no—
663C2×C8C2×D3211yescharacteristic
664C2×C8C2×D3211yescharacteristic
665C4⋊C4—31no—
666C4⋊C4—31no—
667C4⋊C4—31no—
668C4⋊C4—31no—
669C4⋊C4—61no—
670C4⋊C4—91no—
671C4⋊C4—181no—
672C4⋊C4—181no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—91no—
676C22⋊C4—91no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C42—91no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—22no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—62no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—121no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3—244no—
703C22×C3D3×D812yes—
704C22×C3D3×D812yes—
705C22×C3C2×D3×D411yescharacteristic
706C22×C3C2×D3×D411yescharacteristic
707C2×D3—22no—
708C2×D3—32no—
709C2×D3—32no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—41no—
716C2×D3—41no—
717C2×D3—41no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—41no—
721C2×D3—62no—
722C2×D3—61no—
723C2×D3—61no—
724C2×D3—61no—
725C2×D3—61no—
726C2×D3—84no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—244no—
730C2×D3—244no—
731C3×C4—21no—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—41no—
736C3×C4—121no—
737C3×C4—121no—
738C3×C4—121no—
739C3×C4—121no—
740C3×C4C2×#23511yescharacteristic
741C3×C4#100411yescharacteristic
742C3×C4#100411yescharacteristic
743C3×C4D3×#4111yescharacteristic
744Dic3—32no—
745Dic3—32no—
746Dic3—41no—
747Dic3—41no—
748Dic3—41no—
749Dic3—41no—
750Dic3—62no—
751Dic3—61no—
752Dic3—61no—
753Dic3—61no—
754Dic3—61no—
755Dic3—121no—
756Dic3—121no—
757C32#329411yescharacteristic, complemented, Sylow
758C23—61no—
759C23—61no—
760C23—61no—
761C23—61no—
762C23—91no—
763C23—122no—
764C23—122no—
765C23—241no—
766C23—362no—
767C23—362no—
768C23—721no—
769C23#380211yescharacteristic
770Q8—362no—
771D4—32no—
772D4—61no—
773D4—61no—
774D4—61no—
775D4—61no—
776D4—61no—
777D4—61no—
778D4—61no—
779D4—94no—
780D4—122no—
781D4—122no—
782D4—122no—
783D4—362no—
784D4—362no—
785D4—362no—
786D4—362no—
787D4—721no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—91no—
795C2×C4—91no—
796C2×C4—91no—
797C2×C4—122no—
798C2×C4—181no—
799C2×C4—181no—
800C2×C4—362no—
801C2×C4—362no—
802C2×C4—362no—
803C2×C4#380211yescharacteristic
804C2×C4C22×D3211yescharacteristic
805C8—21no—
806C8—21no—
807C8—181no—
808C8—181no—
809C2×C3—22no—
810C2×C3—22no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—42no—
815C2×C3—122no—
816C2×C3—241no—
817C2×C3—241no—
818C2×C3—241no—
819C2×C3#549011yescharacteristic
820C2×C3#561011yescharacteristic
821C2×C3C2×D3×D811yescharacteristic
822C2×C3C2×D3×D811yescharacteristic
823C2×C3#576211yescharacteristic
824C2×C3#577011yescharacteristic
825D3—42no—
826D3—62no—
827D3—62no—
828D3—81no—
829D3—81no—
830D3—81no—
831D3—122no—
832C22—21no—
833C22—21no—
834C22—62no—
835C22—92no—
836C22—121no—
837C22—121no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—121no—
846C22—121no—
847C22—181no—
848C22—181no—
849C22—244no—
850C22—724no—
851C22#6379712yes—
852C22C2×#380211yescharacteristic
853C4—21no—
854C4—92no—
855C4—121no—
856C4—121no—
857C4—121no—
858C4—121no—
859C4—181no—
860C4—181no—
861C4D3×#23511yescharacteristic
862C4#6433011yescharacteristic
863C3—21no—
864C3#7875711yescharacteristic, complemented
865C3#8073111yescharacteristic, complemented
866C2—22no—
867C2—122no—
868C2—182no—
869C2—241no—
870C2—241no—
871C2—241no—
872C2C2×#6379711yescharacteristic
873C2#1059468611yescharacteristic
874C2#1059508311yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. #10595069C2semidirect
2. #10594928C2semidirect
3. C8×#638C2semidirect
4. C3×#5115C2semidirect
5. C2×C3×#821C2semidirect
6. #10591160C2semidirect
7. #10591089C2semidirect
8. #10590945C2semidirect
9. #10590940C2semidirect
10. #10590885C2semidirect
11. #10590839C2semidirect
12. #10590778C2semidirect
13. #10590749C2semidirect
14. #10590740C2semidirect
15. #10590650C2semidirect
22. C22×C32×C8C22semidirect
24. C2×C8×C3⋊D3C22semidirect
26. C3×#930C22semidirect
27. C2×C3×C4⋊Dic3C22semidirect
28. C2×C3×D24C22semidirect
32. #63919C22semidirect
34. #63916C22semidirect
36. #63900C22semidirect
39. #63898C22semidirect
43. C2×#3713C22semidirect
44. #63657C22semidirect
45. #63647C22semidirect
46. #63641C22semidirect
47. C8×C3⋊Dic3C22semidirect
50. C3×#821C22semidirect
51. C3×#821C22semidirect
52. C3×#821C22semidirect
53. C3×#821C22semidirect
54. C3×#818C22semidirect
55. #63576C22semidirect
56. #63576C22semidirect
58. #63562C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
70. #5115D3semidirect
71. C2×#821D3semidirect
157. C22×C3×C8C2×D3semidirect
158. C22×C3×C8C2×D3semidirect
178. #930C2×D3semidirect
183. C2×C4⋊Dic3C2×D3semidirect
184. C2×D24C2×D3semidirect
218. #821C2×D3semidirect
219. #821C2×D3semidirect
220. #821C2×D3semidirect
221. #821C2×D3semidirect
225. #818C2×D3semidirect
256. #638D8semidirect
277. C3×D12#41semidirect
466. C22×C8D32semidirect
594. D12#235semidirect
757. C32#3294semidirect
864. C3#78757semidirect
865. C3#80731semidirect

Maximal subgroups

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

subgroupindex
#105950692
#105949282
C8×#6382
C3×#51152
C2×C3×#8212
#105911602
#105910892
#105909452
#105909402
#105908852
#105908392
#105907782
#105907492
#105907402
#105906502
#807313
#787573