Finite Group Databasebeta

← #11887020

Subgroups — #11887020

Order 1152.

1042 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#625C211yesmaximal, characteristic, complemented
2#10594370C211yesmaximal, characteristic, complemented
3#10592458C211yesmaximal, characteristic, complemented
4C3×#4773C211yesmaximal, characteristic, complemented
5C3×D3×#102C211yesmaximal, characteristic, complemented
6#10591447C211yesmaximal, characteristic, complemented
7#10591435C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10590831C211yesmaximal, characteristic, complemented
10#10590749C211yesmaximal, characteristic, complemented
11#10590717C211yesmaximal, characteristic, complemented
12#10590680C211yesmaximal, characteristic, complemented
13#10590552C211yesmaximal, characteristic, complemented
14#10590499C211yesmaximal, characteristic, complemented
15#10590498C211yesmaximal, characteristic, complemented
16#80014—31nomaximal
17#78757—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×#625—21no—
21C2×#3795—21no—
22D4×C3⋊Dic3C2211yescharacteristic
23#64097C2211yescharacteristic, complemented
24C2×C3×#213C2211yescharacteristic
25C2×C3×D24C2211yescharacteristic, complemented
26C2×C3×D3×C8C2211yescharacteristic, complemented
27C3×#895C2211yescharacteristic, complemented
28C3×D3×C4⋊C4C2211yescharacteristic, complemented
29#63980—21no—
30#63976—21no—
31#63976—21no—
32#63914C2211yescharacteristic
33#63908C2211yescharacteristic
34#63908C2211yescharacteristic
35#63908C2211yescharacteristic, complemented
36#63905—21no—
37C4×#625C2211yescharacteristic
38#63898C2211yescharacteristic, complemented
39#63896—21no—
40D3×C4⋊Dic3C2211yescharacteristic, complemented
41#63884—21no—
42C2×#3713C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63645C2211yescharacteristic, complemented
47#63641C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63563C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61D4×#67—31no—
62D4×#67—31no—
63#5611—31no—
64#5507—31no—
65C3×#447—31no—
66C2×C3×#102—31no—
67#5217—31no—
68C2×#832—31no—
69#5157—31no—
70#5156—31no—
71#5150—31no—
72Dic3×D8—31no—
73#5115—31no—
74C8×#67—31no—
75#5038—31no—
76#4967—31no—
77#4786—31no—
78#4775—31no—
79#4774—31no—
80#4774—31no—
81#4773D311yescharacteristic, complemented
82D3×#102—31no—
83D3×#102D311yescharacteristic, complemented
84#4760—31no—
85#4760—31no—
86#4759—31no—
87#4759—31no—
88#4759—61no—
89#4756—31no—
90#4736—31no—
91#67⋊C8—31no—
92C23×C3×D3—21no—
93C23×C3×D3—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×#634—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C3×D3×D4—22no—
100C3×D3×D4—22no—
101C3×D3×D4—41no—
102C3×D3×D4—41no—
103C2×C3×D12—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×#625—21no—
111C2×#625—21no—
112C2×#625—21no—
113C2×#625—21no—
114C2×#625—21no—
115C2×#625—44no—
116C2×#625D411yescharacteristic
117C2×D3×Dic3—21no—
118C2×D3×Dic3—21no—
119#3795—44no—
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122#3757—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126C4×C3⋊Dic3C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#213—22no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×D24—41no—
135C3×D3×C8—41no—
136#3724D411yescharacteristic
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3D411yescharacteristic
143(C2×D3)⋊Dic3D411yescharacteristic
144#3713—41no—
145D3×C3⋊C8—41no—
146#3294—91noSylow
147C22×C3×D4—31no—
148C22×C3×D4—31no—
149C22×#67—61no—
150C22×#67—61no—
151C2×#237—61no—
152C2×D3×D4C2×D311yescharacteristic
153C2×D3×D4C2×D311yescharacteristic
154C2×#235—61no—
155C2×C3×D8—31no—
156C2×C3×D8—31no—
157C22×C3×C8—31no—
158C3×#121—31no—
159C2×C3×C4⋊C4—31no—
160#953—61no—
161#953—61no—
162#940—31no—
163#940—31no—
164#939—61no—
165#939—61no—
166#938—31no—
167#938—31no—
168#938—31no—
169#937—61no—
170#937—61no—
171#935—61no—
172D4×Dic3—31no—
173D4×Dic3—31no—
174D4×Dic3—31no—
175D4×Dic3—61no—
176C2×#213—31no—
177C2×#213—31no—
178C2×#213C2×D311yescharacteristic
179#930—31no—
180#930—31no—
181#930—31no—
182#929—61no—
183C4×#67—31no—
184C4×#67—31no—
185C2×C4⋊Dic3—31no—
186C22×C3⋊C8—31no—
187C2×D24C2×D311yescharacteristic, complemented
188C2×D3×C8—31no—
189C2×D3×C8C2×D311yescharacteristic, complemented
190#896—61no—
191#895C2×D311yescharacteristic, complemented
192#894—61no—
193#893—31no—
194D3×C4⋊C4—31no—
195D3×C4⋊C4C2×D311yescharacteristic, complemented
196#888—31no—
197#888—31no—
198#888—61no—
199#883—61no—
200#878—61no—
201C3×#102—21no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102C2×D311yescharacteristic
207C3×#102C2×D311yescharacteristic
208C3×C22⋊C8—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—61no—
216#832C2×D311yescharacteristic
217#830—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821C2×D311yescharacteristic, complemented
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8C2×D311yescharacteristic, complemented
224#818—31no—
225#818—31no—
226#818—31no—
227#818—61no—
228Dic3⋊C8—31no—
229Dic3⋊C8—31no—
230Dic3⋊C8—61no—
231C8×Dic3—31no—
232C8×Dic3—31no—
233#809—31no—
234#809C2×D311yescharacteristic, complemented
235#809C2×D311yescharacteristic, complemented
236#807—31no—
237#807—31no—
238#807—31no—
239#807—61no—
240C23×C32—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—42no—
245C22×C3×D3—42no—
246C22×C3×D3—42no—
247C22×C3×D3—42no—
248C22×C3×D3—81no—
249C22×C3×D3—81no—
250C22×C3×D3C2×D411yescharacteristic
251C22×C3×D3C2×D411yescharacteristic
252C32×D4—21no—
253C32×D4#4112yescomplemented
254C2×C32×C4—21no—
255C2×C32×C4C2411yescharacteristic
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—42no—
259C2×C3⋊Dic3C2×D411yescharacteristic
260C2×C3⋊Dic3C2×D411yescharacteristic
261#634—42no—
262C3×#67—42no—
263C3×#67—42no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12—42no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—42no—
279#625—42no—
280#625—42no—
281#625—42no—
282#625—42no—
283#625—81no—
284#625D814yescomplemented
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—91no—
298#466—91no—
299#459—91no—
300#447—31no—
301#447—91no—
302C4×D8—91no—
303C8×D4—91no—
304C2×#102—31no—
305C2×#102—91no—
306C24×C3—61no—
307C24×C3—61no—
308C23×D3—21no—
309C23×D3—21no—
310C2×C3×D4—21no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—61no—
315C2×C3×D4—61no—
316C2×C3×D4—61no—
317C2×C3×D4—62no—
318C2×C3×D4—62no—
319C2×C3×D4—121no—
320C2×C3×D4—121no—
321C2×C3×D4C22×D311yescharacteristic
322C2×C3×D4C22×D311yescharacteristic
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—61no—
326C2×#67—21no—
327C2×#67—21no—
328C2×#67—31no—
329C2×#67—31no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—124no—
341C2×#67—124no—
342C22×Dic3—61no—
343C22×Dic3—61no—
344C22×Dic3—61no—
345C22×Dic3—61no—
346C22×Dic3—121no—
347#237—124no—
348D3×D4—22no—
349D3×D4—22no—
350D3×D4—41no—
351D3×D4—41no—
352#235—124no—
353C2×D12—21no—
354C2×D12C22×D311yescharacteristic
355C2×D12C22×D311yescharacteristic
356C2×D12C22×D311yescharacteristic
357C2×C4×D3—21no—
358C2×C4×D3—61no—
359C2×C4×D3—61no—
360C2×C4×D3C22×D311yescharacteristic
361C2×C4×D3C22×D311yescharacteristic
362C2×Dic6—61no—
363C2×Dic6—61no—
364C2×Dic6—121no—
365C3×D8—62no—
366C3×D8—121no—
367C2×C3×C8—21no—
368C2×C3×C8—31no—
369C2×C3×C8—31no—
370C2×C3×C8—121no—
371C2×C3×C8C22×D311yescharacteristic
372C2×C3×C8C22×D311yescharacteristic
373C3×C4⋊C4—21no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—61no—
376C3×C4⋊C4C22×D311yescharacteristic
377C3×C4⋊C4C22×D311yescharacteristic
378C3×C22⋊C4—61no—
379#217—31no—
380#217—31no—
381#217—61no—
382#217—61no—
383#217—61no—
384#217—61no—
385#217—61no—
386#217—61no—
387#217—121no—
388#213—22no—
389#213—121no—
390#213—121no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—31no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398C4⋊Dic3—31no—
399C4⋊Dic3—31no—
400C4⋊Dic3—31no—
401C4⋊Dic3—31no—
402C4⋊Dic3—61no—
403C4⋊Dic3—61no—
404C4⋊Dic3—61no—
405C4⋊Dic3C22×D311yescharacteristic
406Dic3⋊C4—21no—
407Dic3⋊C4—31no—
408Dic3⋊C4—31no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—121no—
413C4×Dic3—31no—
414C4×Dic3—31no—
415C4×Dic3—61no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—61no—
419C2×C3⋊C8—121no—
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422D24—41no—
423D3×C8—41no—
424D3×C8—121no—
425C22×C32—22no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32C22×D411yescharacteristic
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
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—84no—
443C2×C3×D3—84no—
444C2×C3×D3C2×D812yes—
445C2×C3×D3C2×D812yes—
446C32×C4—41no—
447C32×C4C2×#4111yescharacteristic
448C32×C4H(5,𝔽2)11yescharacteristic
449C3⋊Dic3—21no—
450C3⋊Dic3—41no—
451C3⋊Dic3—41no—
452C3⋊Dic3C2×D812yes—
453C3×Dic3—21no—
454C3×Dic3—21no—
455C3×Dic3—41no—
456C2×#41—181no—
457C22×D4—31no—
458C22×D4—31no—
459C22×D4—181no—
460C2×D8—31no—
461C2×D8—31no—
462C2×D8—91no—
463C22×C8—31no—
464C22×C8—91no—
465C4⋊Q8—91no—
466#127—91no—
467#123—181no—
468#123—181no—
469C22⋊Q8—181no—
470#121—31no—
471#121—91no—
472#121—91no—
473#121—91no—
474#121—181no—
475#120—181no—
476#120—181no—
477C4×D4—91no—
478C4×D4—91no—
479C4×D4—91no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—91no—
482#107—91no—
483#107—91no—
484#107—91no—
485C4⋊C8—91no—
486#102—31no—
487#102—31no—
488#102—31no—
489#102—31no—
490#102—91no—
491#102—91no—
492#102—91no—
493#102—91no—
494#102—91no—
495#102D3211yescharacteristic
496C22⋊C8—31no—
497C22⋊C8—91no—
498C4×C8—91no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—31no—
502C23×C3—31no—
503C23×C3—41no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3—61no—
507C23×C3—122no—
508C23×C3—122no—
509C23×C3—122no—
510C23×C3—122no—
511C23×C3—241no—
512C23×C3—241no—
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—42no—
517C22×D3—42no—
518C22×D3—42no—
519C22×D3—42no—
520C22×D3—81no—
521C22×D3—81no—
522C22×D3D3×D411yescharacteristic
523C22×D3D3×D411yescharacteristic
524C3×D4—21no—
525C3×D4—21no—
526C3×D4—22no—
527C3×D4—41no—
528C3×D4—61no—
529C3×D4—61no—
530C3×D4—61no—
531C3×D4—61no—
532C3×D4—61no—
533C3×D4—61no—
534C3×D4—122no—
535C3×D4—122no—
536C3×D4—122no—
537C3×D4#23512yescomplemented
538C3×D4#23712yescomplemented
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—31no—
543C2×C3×C4—31no—
544C2×C3×C4—41no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—122no—
551C2×C3×C4C23×D311yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553#67—34no—
554#67—34no—
555#67—42no—
556#67—42no—
557#67—122no—
558#67—122no—
559#67—122no—
560#67—122no—
561#67—122no—
562#67—122no—
563#67—122no—
564#67—122no—
565#67—241no—
566#67—241no—
567C2×Dic3—21no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—121no—
579C2×Dic3—121no—
580C2×Dic3—122no—
581C2×Dic3—122no—
582C2×Dic3—122no—
583C2×Dic3—122no—
584C2×Dic3—242no—
585C2×Dic3D3×D411yescharacteristic
586C2×Dic3D3×D411yescharacteristic
587D12—21no—
588D12—21no—
589D12—21no—
590D12—21no—
591D12—21no—
592D12—21no—
593D12—42no—
594C4×D3—21no—
595C4×D3—21no—
596C4×D3—21no—
597C4×D3—21no—
598C4×D3—42no—
599C4×D3—122no—
600C4×D3—122no—
601Dic6—122no—
602Dic6—122no—
603Dic6—242no—
604C3×C8—21no—
605C3×C8—21no—
606C3×C8—41no—
607C3×C8—61no—
608C3×C8—61no—
609C3⋊C8—21no—
610C3⋊C8—21no—
611C3⋊C8—61no—
612C3⋊C8—61no—
613C3⋊C8—121no—
614C2×C32—42no—
615C2×C32#54611yescharacteristic
616C2×C32C22×D811yescharacteristic
617C2×C32#57711yescharacteristic
618C3×D3—22no—
619C3×D3—22no—
620C3×D3—81no—
621C3×D3—81no—
622C3×D3—81no—
623C24—61no—
624C24—61no—
625#41—364no—
626C2×Q8—181no—
627C2×D4—31no—
628C2×D4—31no—
629C2×D4—31no—
630C2×D4—61no—
631C2×D4—61no—
632C2×D4—61no—
633C2×D4—62no—
634C2×D4—62no—
635C2×D4—91no—
636C2×D4—121no—
637C2×D4—121no—
638C2×D4—181no—
639C2×D4—181no—
640C2×D4—181no—
641C2×D4—181no—
642C2×D4—181no—
643C2×D4—364no—
644C2×D4C2×D3211yescharacteristic
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—61no—
648C22×C4—181no—
649C22×C4—181no—
650C22×C4—181no—
651D8—62no—
652D8—121no—
653D8—361no—
654C2×C8—31no—
655C2×C8—31no—
656C2×C8—91no—
657C2×C8—121no—
658C2×C8—361no—
659C2×C8C2×D3211yescharacteristic
660C4⋊C4—31no—
661C4⋊C4—61no—
662C4⋊C4—91no—
663C4⋊C4—91no—
664C4⋊C4—91no—
665C4⋊C4—181no—
666C4⋊C4—181no—
667C4⋊C4C2×D3211yescharacteristic
668C22⋊C4—61no—
669C22⋊C4—91no—
670C22⋊C4—91no—
671C22⋊C4—181no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C42—91no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—21no—
680C22×C3—32no—
681C22×C3—32no—
682C22×C3—42no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—61no—
688C22×C3—61no—
689C22×C3—61no—
690C22×C3—61no—
691C22×C3—81no—
692C22×C3—81no—
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×C3—244no—
704C22×C3C2×D3×D411yescharacteristic
705C22×C3C2×D3×D411yescharacteristic
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—21no—
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—84no—
720C2×D3—84no—
721C2×D3D3×D812yes—
722C2×D3D3×D812yes—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—61no—
728C3×C4—61no—
729C3×C4—81no—
730C3×C4—121no—
731C3×C4C2×#23511yescharacteristic
732C3×C4C2×#23711yescharacteristic
733C3×C4#100411yescharacteristic
734C3×C4#100411yescharacteristic
735Dic3—21no—
736Dic3—21no—
737Dic3—32no—
738Dic3—32no—
739Dic3—41no—
740Dic3—62no—
741Dic3—61no—
742Dic3—61no—
743Dic3—121no—
744Dic3—121no—
745Dic3—121no—
746Dic3—121no—
747Dic3—121no—
748Dic3—241no—
749Dic3—241no—
750C32#329411yescharacteristic, complemented, Sylow
751C23—21no—
752C23—31no—
753C23—31no—
754C23—61no—
755C23—61no—
756C23—61no—
757C23—122no—
758C23—122no—
759C23—122no—
760C23—122no—
761C23—241no—
762C23—241no—
763Q8—362no—
764D4—21no—
765D4—61no—
766D4—61no—
767D4—61no—
768D4—61no—
769D4—61no—
770D4—61no—
771D4—94no—
772D4—122no—
773D4—122no—
774D4—122no—
775D4—362no—
776D4—362no—
777D4—362no—
778D4—362no—
779D4—721no—
780D4#379512yescomplemented
781C2×C4—21no—
782C2×C4—31no—
783C2×C4—31no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—91no—
790C2×C4—91no—
791C2×C4—122no—
792C2×C4—181no—
793C2×C4—181no—
794C2×C4—362no—
795C2×C4—362no—
796C2×C4—362no—
797C2×C4C22×D3211yescharacteristic
798C8—21no—
799C8—61no—
800C8—61no—
801C8—181no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—42no—
806C2×C3—42no—
807C2×C3—62no—
808C2×C3—62no—
809C2×C3—82no—
810C2×C3—241no—
811C2×C3—241no—
812C2×C3—241no—
813C2×C3#549011yescharacteristic
814C2×C3#559111yescharacteristic
815C2×C3C2×D3×D811yescharacteristic
816C2×C3C2×D3×D811yescharacteristic
817C2×C3#576211yescharacteristic
818C2×C3#577511yescharacteristic
819D3—22no—
820D3—22no—
821D3—81no—
822D3—81no—
823D3—81no—
824C22—22no—
825C22—32no—
826C22—32no—
827C22—41no—
828C22—41no—
829C22—61no—
830C22—61no—
831C22—61no—
832C22—61no—
833C22—121no—
834C22—121no—
835C22—121no—
836C22—121no—
837C22—121no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—244no—
843C22—244no—
844C22D32×D411yescharacteristic
845C4—41no—
846C4—61no—
847C4—61no—
848C4—92no—
849C4—121no—
850C4—181no—
851C4—361no—
852C4—361no—
853C4C2×#379511yescharacteristic
854C4#6431311yescharacteristic
855C3—21no—
856C3#7875711yescharacteristic, complemented
857C3#8001411yescharacteristic, complemented
858C2—42no—
859C2—62no—
860C2—62no—
861C2—241no—
862C2—241no—
863C2—241no—
864C2#1059418411yescharacteristic
865C2D32×D811yescharacteristic
866C2#1059474911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. D4×#625C2semidirect
2. #10594370C2semidirect
3. #10592458C2semidirect
4. C3×#4773C2semidirect
5. C3×D3×#102C2semidirect
6. #10591447C2semidirect
7. #10591435C2semidirect
8. D3×#832C2semidirect
9. #10590831C2semidirect
10. #10590749C2semidirect
11. #10590717C2semidirect
12. #10590680C2semidirect
13. #10590552C2semidirect
14. #10590499C2semidirect
15. #10590498C2semidirect
23. #64097C22semidirect
25. C2×C3×D24C22semidirect
26. C2×C3×D3×C8C22semidirect
27. C3×#895C22semidirect
28. C3×D3×C4⋊C4C22semidirect
35. #63908C22semidirect
38. #63898C22semidirect
40. D3×C4⋊Dic3C22semidirect
42. C2×#3713C22semidirect
43. C2×D3×C3⋊C8C22semidirect
46. #63645C22semidirect
47. #63641C22semidirect
48. #63634C22semidirect
50. C3×#821C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#809C22semidirect
53. C3×#809C22semidirect
54. #63575C22semidirect
55. #63563C22semidirect
56. #63563C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63553C22semidirect
81. #4773D3semidirect
83. D3×#102D3semidirect
187. C2×D24C2×D3semidirect
189. C2×D3×C8C2×D3semidirect
191. #895C2×D3semidirect
195. D3×C4⋊C4C2×D3semidirect
221. #821C2×D3semidirect
223. (C2×D3)⋊C8C2×D3semidirect
234. #809C2×D3semidirect
235. #809C2×D3semidirect
253. C32×D4#41semidirect
284. #625D8semidirect
537. C3×D4#235semidirect
538. C3×D4#237semidirect
750. C32#3294semidirect
780. D4#3795semidirect
856. C3#78757semidirect
857. C3#80014semidirect

Maximal subgroups

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

subgroupindex
D4×#6252
#105943702
#105924582
C3×#47732
C3×D3×#1022
#105914472
#105914352
D3×#8322
#105908312
#105907492
#105907172
#105906802
#105905522
#105904992
#105904982
#800143
#787573