Finite Group Databasebeta

← #11887044

Subgroups — #11887044

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595293C211yesmaximal, characteristic, complemented
2#10594515C211yesmaximal, characteristic, complemented
3#10592473C211yesmaximal, characteristic, complemented
4C3×#4786C211yesmaximal, characteristic, complemented
5C3×D3×#102C211yesmaximal, characteristic, complemented
6#10591487C211yesmaximal, characteristic, complemented
7#10591455C211yesmaximal, characteristic, complemented
8#10591447C211yesmaximal, characteristic, complemented
9#10590945C211yesmaximal, characteristic, complemented
10#10590831C211yesmaximal, characteristic, complemented
11#10590762C211yesmaximal, characteristic, complemented
12#10590720C211yesmaximal, characteristic, complemented
13#10590593C211yesmaximal, characteristic, complemented
14#10590498C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#80352—31nomaximal
17#78757—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3802C2211yescharacteristic
21C2×#3798—21no—
22#64147C2211yescharacteristic
23C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
24C3×#940C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic, complemented
26C2×C3×D24C2211yescharacteristic, complemented
27C2×C3×D3×C8C2211yescharacteristic, complemented
28C3×#893C2211yescharacteristic, complemented
29C3×D3×C4⋊C4C2211yescharacteristic, complemented
30#63983—21no—
31#63976—21no—
32#63970—21no—
33#63918C2211yescharacteristic, complemented
34#63916C2211yescharacteristic, complemented
35#63908C2211yescharacteristic
36#63908C2211yescharacteristic, complemented
37#63905—21no—
38C4×#626C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40#63853—21no—
41#63851—21no—
42C2×#3713C2211yescharacteristic
43C2×#3710C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45#63659C2211yescharacteristic, complemented
46#63647C2211yescharacteristic, complemented
47#63645C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61D4×#67—31no—
62#5717—31no—
63#5551—31no—
64#5507—31no—
65C3×#459—31no—
66C2×C3×#102—31no—
67#5217—31no—
68#5157—31no—
69#5157—31no—
70#5156—31no—
71#5156—31no—
72#5115—31no—
73C8×#67—31no—
74#5070—31no—
75C4×#213—31no—
76#4967—31no—
77#4846—31no—
78#4834—31no—
79#4786D311yescharacteristic, complemented
80#4775—31no—
81#4774—31no—
82#4774—31no—
83#4774—31no—
84#4774—61no—
85#4773—31no—
86D3×#102—31no—
87D3×#102—31no—
88D3×#102D311yescharacteristic, complemented
89#4760—31no—
90#4759—31no—
91#4756—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×D3×D4—22no—
102C3×D3×D4—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109D3×#67—44no—
110C2×#627—21no—
111C2×#626—21no—
112C2×#626D411yescharacteristic
113C2×#625—21no—
114C2×#625—21no—
115C2×#625—21no—
116C2×D3×Dic3—21no—
117#3802—22no—
118#3802—41no—
119#3798—44no—
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122#3757—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×#213—41no—
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×D24—41no—
135C3×D3×C8—41no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3D411yescharacteristic
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3D411yescharacteristic
144#3713—22no—
145#3710—41no—
146#3294—91noSylow
147C22×C3×D4—31no—
148C22×#67—61no—
149C2×D3×D4—31no—
150C2×D3×D4—31no—
151C2×D3×D4—61no—
152C2×D3×D4C2×D311yescharacteristic
153C2×#235—61no—
154C2×#235—61no—
155C2×C3×D8—31no—
156C2×C3×D8—31no—
157C22×C3×C8—31no—
158C3×#127—31no—
159C3×C4×D4—31no—
160C2×C3×C4⋊C4—31no—
161#953—61no—
162#940C2×D311yescharacteristic
163#939—61no—
164#938—31no—
165#938—31no—
166#938—31no—
167#938—31no—
168#938—31no—
169#938—61no—
170#938—61no—
171#937—61no—
172#937—61no—
173#937—61no—
174D4×Dic3—31no—
175C2×#213—31no—
176C2×#213—31no—
177C2×#213C2×D311yescharacteristic, complemented
178#930—31no—
179#930—31no—
180#929—61no—
181C4×#67—31no—
182#924—61no—
183C2×D24C2×D311yescharacteristic, complemented
184C2×D3×C8—31no—
185C2×D3×C8—31no—
186C2×D3×C8C2×D311yescharacteristic, complemented
187#896—61no—
188#895—31no—
189#894—61no—
190#893C2×D311yescharacteristic, complemented
191D3×C4⋊C4—31no—
192D3×C4⋊C4—31no—
193D3×C4⋊C4—61no—
194D3×C4⋊C4C2×D311yescharacteristic, complemented
195#888—31no—
196#883—61no—
197#883—61no—
198C4×D12—31no—
199C4×D12—31no—
200#869—31no—
201C3×C4⋊C8—31no—
202C3×#102—21no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102C2×D311yescharacteristic, complemented
208C3×#102C2×D311yescharacteristic, complemented
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—61no—
216#832C2×D311yescharacteristic, complemented
217#830—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821C2×D311yescharacteristic
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225(C2×D3)⋊C8—61no—
226#818—31no—
227#818—31no—
228#818—31no—
229#818—61no—
230Dic3⋊C8C2×D311yescharacteristic, complemented
231C8×Dic3—31no—
232#809—31no—
233#809C2×D311yescharacteristic
234#809C2×D311yescharacteristic, complemented
235#807—31no—
236#807—31no—
237#807—31no—
238#807—61no—
239C4×C3⋊C8—31no—
240C23×C32—21no—
241C22×C3⋊D3C2×D411yescharacteristic
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—42no—
246C22×C3×D3—42no—
247C22×C3×D3—81no—
248C22×C3×D3C2×D411yescharacteristic
249C2×D32—42no—
250C2×D32—42no—
251C2×D32—81no—
252C32×D4—21no—
253C32×D4—21no—
254C2×C32×C4—21no—
255C2×C32×C4C2411yescharacteristic
256#638—42no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3C2×D411yescharacteristic
260C4×C3⋊D3—21no—
261C4×C3⋊D3—21no—
262C4×C3⋊D3—42no—
263C3×#67—42no—
264C3×#67—42no—
265C3×#67—81no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12#4112yescomplemented
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—42no—
279C3×C4×D3—42no—
280#627—42no—
281#626—42no—
282#626D814yescomplemented
283#625—42no—
284#625—42no—
285#625—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—31no—
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—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—121no—
319C2×C3×D4C22×D311yescharacteristic
320C2×C3×D4C22×D311yescharacteristic
321C22×C3×C4—31no—
322C22×C3×C4—61no—
323C22×C3×C4—61no—
324C2×#67—21no—
325C2×#67—21no—
326C2×#67—21no—
327C2×#67—31no—
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—61no—
337C2×#67—121no—
338C2×#67—124no—
339C22×Dic3—61no—
340D3×D4—22no—
341D3×D4—41no—
342D3×D4—62no—
343D3×D4—62no—
344D3×D4—121no—
345D3×D4—121no—
346D3×D4—124no—
347#235—124no—
348#235—124no—
349C2×D12—31no—
350C2×D12—61no—
351C2×D12C22×D311yescharacteristic
352C2×D12C22×D311yescharacteristic
353C2×D12C22×D311yescharacteristic
354C2×C4×D3—21no—
355C2×C4×D3—21no—
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—121no—
363C2×C4×D3C22×D311yescharacteristic
364C2×Dic6—61no—
365C2×Dic6—61no—
366C3×D8—121no—
367C3×D8—121no—
368C2×C3×C8—21no—
369C2×C3×C8—31no—
370C2×C3×C8—31no—
371C2×C3×C8—121no—
372C2×C3×C8C22×D311yescharacteristic
373C2×C3×C8C22×D311yescharacteristic
374C3×C4⋊C4—21no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—61no—
377C3×C4⋊C4C22×D311yescharacteristic
378C3×C4⋊C4C22×D311yescharacteristic
379C3×C22⋊C4—61no—
380C3×C42—31no—
381#217—31no—
382#217—61no—
383#217—61no—
384#217—61no—
385#217—61no—
386#217—61no—
387#217—61no—
388#217—121no—
389#213—41no—
390#213—62no—
391#213—62no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400C4⋊Dic3—31no—
401C4⋊Dic3—31no—
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404C4⋊Dic3—31no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3—61no—
408C4⋊Dic3C22×D311yescharacteristic
409Dic3⋊C4—21no—
410Dic3⋊C4—31no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—121no—
415C4×Dic3C22×D311yescharacteristic
416C2×C3⋊C8—31no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—61no—
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421D24—41no—
422D3×C8—41no—
423D3×C8—121no—
424D3×C8—121no—
425C22×C32—41no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32C22×D411yescharacteristic
429C2×C3⋊D3—21no—
430C2×C3⋊D3—21no—
431C2×C3⋊D3C2×D812yes—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
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—84no—
444C2×C3×D3C2×D812yes—
445D32—84no—
446C32×C4—41no—
447C32×C4C2×#4111yescharacteristic
448C32×C4H(5,𝔽2)11yescharacteristic
449C3⋊Dic3—21no—
450C3⋊Dic3—41no—
451C3⋊Dic3—41no—
452C3×Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3—41no—
455C3×Dic3C2×D812yes—
456C2×#41—181no—
457C22×D4—31no—
458C22×D4—91no—
459C22×D4—181no—
460C2×D8—31no—
461C2×D8—31no—
462C2×D8—91no—
463C22×C8—31no—
464C22×C8—91no—
465C4⋊Q8—91no—
466#127—31no—
467#123—181no—
468#123—181no—
469C22⋊Q8—181no—
470#121—91no—
471#121—91no—
472#121—91no—
473#121—91no—
474#121—181no—
475#120—181no—
476#120—181no—
477C4×D4—31no—
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—31no—
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, complemented
496C22⋊C8—91no—
497C22⋊C8—91no—
498C4×C8—91no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—31no—
502C23×C3—41no—
503C23×C3—61no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3—122no—
507C23×C3—122no—
508C23×C3—241no—
509C22×D3—21no—
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—31no—
513C22×D3—31no—
514C22×D3—42no—
515C22×D3—42no—
516C22×D3—61no—
517C22×D3—81no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—122no—
521C22×D3—122no—
522C22×D3—241no—
523C22×D3—241no—
524C22×D3D3×D411yescharacteristic
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—32no—
530C3×D4—41no—
531C3×D4—41no—
532C3×D4—61no—
533C3×D4—61no—
534C3×D4—61no—
535C3×D4—61no—
536C3×D4—61no—
537C3×D4—122no—
538C3×D4—122no—
539C3×D4—241no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—31no—
544C2×C3×C4—31no—
545C2×C3×C4—31no—
546C2×C3×C4—41no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—122no—
551C2×C3×C4—122no—
552C2×C3×C4C23×D311yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554#67—34no—
555#67—42no—
556#67—42no—
557#67—81no—
558#67—122no—
559#67—122no—
560#67—122no—
561#67—122no—
562#67—122no—
563#67—122no—
564#67—122no—
565#67—122no—
566#67—122no—
567#67—242no—
568C2×Dic3—21no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—121no—
577C2×Dic3—121no—
578C2×Dic3—122no—
579C2×Dic3D3×D411yescharacteristic
580C2×Dic3D3×D411yescharacteristic
581C2×Dic3D3×D411yescharacteristic
582D12—21no—
583D12—21no—
584D12—21no—
585D12—21no—
586D12—21no—
587D12—34no—
588D12—122no—
589D12#23512yescomplemented
590C4×D3—21no—
591C4×D3—21no—
592C4×D3—42no—
593C4×D3—42no—
594C4×D3—61no—
595C4×D3—61no—
596C4×D3—61no—
597C4×D3—61no—
598C4×D3—121no—
599C4×D3—121no—
600C4×D3—122no—
601C4×D3—122no—
602C4×D3—122no—
603C4×D3—242no—
604Dic6—122no—
605Dic6—122no—
606C3×C8—21no—
607C3×C8—21no—
608C3×C8—41no—
609C3×C8—61no—
610C3×C8—61no—
611C3⋊C8—21no—
612C3⋊C8—21no—
613C3⋊C8—61no—
614C3⋊C8—61no—
615C3⋊C8—121no—
616C2×C32—81no—
617C2×C32#54611yescharacteristic
618C2×C32C22×D811yescharacteristic
619C2×C32#57711yescharacteristic
620C3⋊D3—22no—
621C3×D3—22no—
622C3×D3—42no—
623C3×D3—81no—
624C3×D3—81no—
625C24—61no—
626C24—181no—
627#41—364no—
628C2×Q8—181no—
629C2×D4—31no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—61no—
633C2×D4—61no—
634C2×D4—61no—
635C2×D4—62no—
636C2×D4—91no—
637C2×D4—121no—
638C2×D4—181no—
639C2×D4—181no—
640C2×D4—182no—
641C2×D4—181no—
642C2×D4—181no—
643C2×D4—181no—
644C2×D4—361no—
645C2×D4—364no—
646C2×D4C2×D3211yescharacteristic
647C22×C4—31no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—91no—
651C22×C4—181no—
652C22×C4—181no—
653D8—121no—
654D8—121no—
655D8—182no—
656C2×C8—31no—
657C2×C8—31no—
658C2×C8—91no—
659C2×C8—121no—
660C2×C8—361no—
661C2×C8C2×D3211yescharacteristic
662C4⋊C4—31no—
663C4⋊C4—61no—
664C4⋊C4—91no—
665C4⋊C4—91no—
666C4⋊C4—91no—
667C4⋊C4—181no—
668C4⋊C4—181no—
669C4⋊C4C2×D3211yescharacteristic
670C22⋊C4—61no—
671C22⋊C4—91no—
672C22⋊C4—91no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C42—31no—
679C22×C3—21no—
680C22×C3—32no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—61no—
688C22×C3—61no—
689C22×C3—62no—
690C22×C3—81no—
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—244no—
702C22×C3C2×D3×D411yescharacteristic
703C22×C3C2×D3×D411yescharacteristic
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—22no—
707C2×D3—32no—
708C2×D3—32no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—41no—
716C2×D3—41no—
717C2×D3—62no—
718C2×D3—61no—
719C2×D3—61no—
720C2×D3—61no—
721C2×D3—61no—
722C2×D3—84no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3—244no—
726C2×D3—244no—
727C2×D3D3×D812yes—
728C3×C4—21no—
729C3×C4—21no—
730C3×C4—32no—
731C3×C4—41no—
732C3×C4—41no—
733C3×C4—61no—
734C3×C4—61no—
735C3×C4—81no—
736C3×C4—121no—
737C3×C4C2×#23511yescharacteristic
738C3×C4#100411yescharacteristic
739C3×C4#100411yescharacteristic
740C3×C4D3×#4111yescharacteristic
741Dic3—21no—
742Dic3—21no—
743Dic3—41no—
744Dic3—61no—
745Dic3—61no—
746Dic3—121no—
747Dic3—121no—
748Dic3—121no—
749Dic3—121no—
750Dic3—121no—
751Dic3—241no—
752Dic3—241no—
753Dic3D3×D812yes—
754C32#329411yescharacteristic, complemented, Sylow
755C23—21no—
756C23—31no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23—91no—
761C23—122no—
762C23—122no—
763C23—241no—
764C23—362no—
765C23—362no—
766C23—721no—
767Q8—362no—
768D4—21no—
769D4—21no—
770D4—32no—
771D4—61no—
772D4—61no—
773D4—61no—
774D4—61no—
775D4—61no—
776D4—94no—
777D4—122no—
778D4—122no—
779D4—241no—
780D4—362no—
781D4—362no—
782D4—362no—
783D4—362no—
784D4—362no—
785C2×C4—21no—
786C2×C4—31no—
787C2×C4—31no—
788C2×C4—31no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—91no—
793C2×C4—122no—
794C2×C4—122no—
795C2×C4—181no—
796C2×C4—181no—
797C2×C4—181no—
798C2×C4—181no—
799C2×C4—362no—
800C2×C4—362no—
801C2×C4C22×D3211yescharacteristic
802C8—21no—
803C8—61no—
804C8—61no—
805C8—181no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—62no—
810C2×C3—81no—
811C2×C3—81no—
812C2×C3—122no—
813C2×C3—161no—
814C2×C3—241no—
815C2×C3—241no—
816C2×C3#549011yescharacteristic
817C2×C3#561211yescharacteristic
818C2×C3C2×D3×D811yescharacteristic
819C2×C3C2×D3×D811yescharacteristic
820C2×C3#576211yescharacteristic
821C2×C3#577511yescharacteristic
822D3—22no—
823D3—42no—
824D3—62no—
825D3—62no—
826D3—81no—
827D3—81no—
828D3—122no—
829C22—32no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—61no—
834C22—61no—
835C22—62no—
836C22—92no—
837C22—121no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—181no—
846C22—181no—
847C22—244no—
848C22—724no—
849C22D32×D411yescharacteristic
850C4—32no—
851C4—41no—
852C4—61no—
853C4—61no—
854C4—121no—
855C4—181no—
856C4—361no—
857C4—361no—
858C4D3×#23511yescharacteristic
859C4#6431311yescharacteristic
860C3—21no—
861C3#7875711yescharacteristic, complemented
862C3#8035211yescharacteristic, complemented
863C2—62no—
864C2—81no—
865C2—122no—
866C2—182no—
867C2—241no—
868C2—241no—
869C2#1059427811yescharacteristic
870C2D32×D811yescharacteristic
871C2#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. #10595293C2semidirect
2. #10594515C2semidirect
3. #10592473C2semidirect
4. C3×#4786C2semidirect
5. C3×D3×#102C2semidirect
6. #10591487C2semidirect
7. #10591455C2semidirect
8. #10591447C2semidirect
9. #10590945C2semidirect
10. #10590831C2semidirect
11. #10590762C2semidirect
12. #10590720C2semidirect
13. #10590593C2semidirect
14. #10590498C2semidirect
15. #10590452C2semidirect
23. C4⋊C4×C3⋊D3C22semidirect
25. C2×C3×#213C22semidirect
26. C2×C3×D24C22semidirect
27. C2×C3×D3×C8C22semidirect
28. C3×#893C22semidirect
29. C3×D3×C4⋊C4C22semidirect
33. #63918C22semidirect
34. #63916C22semidirect
36. #63908C22semidirect
43. C2×#3710C22semidirect
44. C32×#102C22semidirect
45. #63659C22semidirect
46. #63647C22semidirect
47. #63645C22semidirect
48. #63634C22semidirect
49. C3×#832C22semidirect
51. C3×Dic3⋊C8C22semidirect
53. C3×#809C22semidirect
54. #63575C22semidirect
56. #63563C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
79. #4786D3semidirect
88. D3×#102D3semidirect
177. C2×#213C2×D3semidirect
183. C2×D24C2×D3semidirect
186. C2×D3×C8C2×D3semidirect
190. #893C2×D3semidirect
194. D3×C4⋊C4C2×D3semidirect
207. C3×#102C2×D3semidirect
208. C3×#102C2×D3semidirect
216. #832C2×D3semidirect
230. Dic3⋊C8C2×D3semidirect
234. #809C2×D3semidirect
275. C3×D12#41semidirect
282. #626D8semidirect
495. #102D32semidirect
589. D12#235semidirect
754. C32#3294semidirect
861. C3#78757semidirect
862. C3#80352semidirect

Maximal subgroups

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

subgroupindex
#105952932
#105945152
#105924732
C3×#47862
C3×D3×#1022
#105914872
#105914552
#105914472
#105909452
#105908312
#105907622
#105907202
#105905932
#105904982
#105904522
#803523
#787573