Finite Group Databasebeta

← #11887045

Subgroups — #11887045

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#10594512C211yesmaximal, characteristic, complemented
3#10592485C211yesmaximal, characteristic, complemented
4C3×#4774C211yesmaximal, characteristic, complemented
5C3×D3×#102C211yesmaximal, characteristic, complemented
6#10591449C211yesmaximal, characteristic, complemented
7#10591448C211yesmaximal, characteristic, complemented
8#10591402C211yesmaximal, characteristic, complemented
9#10590947C211yesmaximal, characteristic, complemented
10#10590832C211yesmaximal, characteristic, complemented
11#10590778C211yesmaximal, characteristic, complemented
12#10590717C211yesmaximal, characteristic, complemented
13D3×#809C211yesmaximal, characteristic, complemented
14#10590459C211yesmaximal, characteristic, complemented
15#10590422C211yesmaximal, characteristic, complemented
16#81302—31nomaximal
17#78757—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12C2211yescharacteristic
21C2×#3798—21no—
22#64149C2211yescharacteristic
23C2×#3753C2211yescharacteristic, complemented
24C2×#3745C2211yescharacteristic, complemented
25#64102C2211yescharacteristic, complemented
26C3×#938C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic, complemented
28C3×D3×C4⋊C4C2211yescharacteristic, complemented
29C3×D3×C4⋊C4C2211yescharacteristic, complemented
30#63983—21no—
31#63977—21no—
32#63971—21no—
33#63919C2211yescharacteristic, complemented
34#63909C2211yescharacteristic
35#63909C2211yescharacteristic, complemented
36#63909C2211yescharacteristic, complemented
37C4×#625C2211yescharacteristic
38#63898C2211yescharacteristic
39#63865—21no—
40#63850—21no—
41#63850—21no—
42C2×#3714C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45#63641C2211yescharacteristic, complemented
46#63636C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#818C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61D4×#67—31no—
62#5609—31no—
63#5507—31no—
64#5507—31no—
65C3×#480—31no—
66C2×C3×#102—31no—
67#5217—31no—
68#5115—31no—
69C8×#67—31no—
70#5038—31no—
71#4967—31no—
72C2×#809—31no—
73#4890—31no—
74#4883—31no—
75#4882—31no—
76#4872—31no—
77#4786—31no—
78#4786—31no—
79#4786—61no—
80#4775—31no—
81#4774D311yescharacteristic, complemented
82#4773—31no—
83#4773—31no—
84D3×#102—31no—
85D3×#102D311yescharacteristic, complemented
86#4760—31no—
87#4760—31no—
88#4759—31no—
89#4756—31no—
90#4732—31no—
91#67⋊C8—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C3×D3×D4—22no—
103C3×D3×D4—41no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109D3×#67—44no—
110C2×#627—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#625D411yescharacteristic
116C2×D3×Dic3—21no—
117D3×D12—22no—
118D3×D12—41no—
119#3798—44no—
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122#3753—41no—
123#3752—21no—
124C4×C3⋊Dic3C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126#3745—41no—
127C3×#217—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C3×D3×C8—41no—
136#3724—21no—
137#3724D411yescharacteristic
138#3722—21no—
139#3722—21no—
140#3722—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3D411yescharacteristic
143(C2×D3)⋊Dic3D411yescharacteristic
144#3714—22no—
145D3×C3⋊C8—41no—
146#3294—91noSylow
147C22×C3×D4—31no—
148C22×#67—61no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×D3×D4C2×D311yescharacteristic
152C2×#235—61no—
153C2×#235—61no—
154C22×D12—31no—
155C22×C3×C8—31no—
156C3×#121—31no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4—31no—
159#953—61no—
160#940—31no—
161#940—31no—
162#940—61no—
163#939—61no—
164#938C2×D311yescharacteristic
165#937—61no—
166#937—61no—
167D4×Dic3—31no—
168C2×#213—31no—
169C2×#213—31no—
170C2×#213—31no—
171C2×#213—61no—
172#930—31no—
173#930—31no—
174#930—31no—
175#929—61no—
176#929—61no—
177C4×#67—31no—
178C4×#67—31no—
179C22×C3⋊C8—31no—
180C2×D24—31no—
181C2×D24—31no—
182C2×D24—31no—
183C2×D24—61no—
184C2×D3×C8—31no—
185C2×D3×C8C2×D311yescharacteristic, complemented
186#896—61no—
187#896—61no—
188#895—31no—
189#895—31no—
190#895—31no—
191#894—61no—
192#894—61no—
193#893—31no—
194#893—31no—
195#893—31no—
196#893—61no—
197D3×C4⋊C4C2×D311yescharacteristic, complemented
198D3×C4⋊C4C2×D311yescharacteristic, complemented
199#888—31no—
200#888—31no—
201#884—61no—
202#882—61no—
203C3×#107—31no—
204C3×#107—31no—
205C3×#102—21no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102C2×D311yescharacteristic, complemented
211C3×#102C2×D311yescharacteristic, complemented
212C3×C22⋊C8—31no—
213#832—31no—
214#832C2×D311yescharacteristic, complemented
215#832C2×D311yescharacteristic, complemented
216#830—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821C2×D311yescharacteristic
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8C2×D311yescharacteristic, complemented
223#818C2×D311yescharacteristic, complemented
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—61no—
236#809C2×D311yescharacteristic
237#807—31no—
238#807—31no—
239#807C2×D311yescharacteristic, complemented
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—81no—
247C22×C3×D3C2×D411yescharacteristic
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—
257#638—81no—
258C2×C3⋊Dic3C2×D411yescharacteristic
259C2×C3⋊Dic3C2×D411yescharacteristic
260C4⋊(C3⋊D3)—21no—
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)—21no—
263C4⋊(C3⋊D3)—21no—
264C4×C3⋊D3—42no—
265C3×#67—42no—
266C3×#67—42no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—21no—
273C3×D12#4112yescomplemented
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—42no—
279C3×C4×D3—42no—
280#627—42no—
281#626—42no—
282#626—42no—
283#626—42no—
284#626—42no—
285#625D814yescomplemented
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—31no—
295#480—91no—
296#474—91no—
297#466—91no—
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—21no—
311C2×C3×D4—31no—
312C2×C3×D4—61no—
313C2×C3×D4—62no—
314C2×C3×D4—61no—
315C2×C3×D4—121no—
316C2×C3×D4C22×D311yescharacteristic
317C2×C3×D4C22×D311yescharacteristic
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C2×#67—21no—
323C2×#67—21no—
324C2×#67—31no—
325C2×#67—31no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—121no—
335C2×#67—121no—
336C2×#67—124no—
337C22×Dic3—61no—
338D3×D4—22no—
339D3×D4—41no—
340D3×D4—62no—
341D3×D4—121no—
342D3×D4—124no—
343#235—124no—
344#235—124no—
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—31no—
348C2×D12—31no—
349C2×D12—61no—
350C2×D12—61no—
351C2×D12—62no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12—121no—
357C2×D12C22×D311yescharacteristic
358C2×C4×D3—21no—
359C2×C4×D3—21no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—121no—
364C2×C4×D3C22×D311yescharacteristic
365C2×C4×D3C22×D311yescharacteristic
366C2×Dic6—61no—
367C2×Dic6—61no—
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—31no—
377C3×C4⋊C4—31no—
378C3×C4⋊C4—61no—
379C3×C4⋊C4—61no—
380C3×C4⋊C4C22×D311yescharacteristic
381C3×C4⋊C4C22×D311yescharacteristic
382C3×C22⋊C4—61no—
383#217—21no—
384#217—31no—
385#217—31no—
386#217—61no—
387#213—62no—
388#213—121no—
389#213—121no—
390#213—122no—
391(C2×D3)⋊C4—31no—
392(C2×D3)⋊C4—31no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
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—
402(C2×D3)⋊C4—121no—
403C4⋊Dic3C22×D311yescharacteristic
404C4⋊Dic3C22×D311yescharacteristic
405C4⋊Dic3C22×D311yescharacteristic
406Dic3⋊C4—21no—
407Dic3⋊C4—21no—
408Dic3⋊C4—31no—
409Dic3⋊C4—31no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412C4×Dic3—31no—
413C4×Dic3—31no—
414C4×Dic3—61no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—61no—
418C2×C3⋊C8—121no—
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421D24—62no—
422D24—121no—
423D24—121no—
424D24—122no—
425D3×C8—41no—
426D3×C8—121no—
427C22×C32—41no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32C22×D411yescharacteristic
431C2×C3⋊D3—41no—
432C2×C3⋊D3—41no—
433C2×C3⋊D3—41no—
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×C4—41no—
449C32×C4C2×#4111yescharacteristic
450C32×C4H(5,𝔽2)11yescharacteristic
451C3⋊Dic3—21no—
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—91no—
463C2×D8—91no—
464C2×D8—91no—
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—91no—
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—31no—
484#107—31no—
485#107—31no—
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#102D3211yescharacteristic, complemented
498C22⋊C8—31no—
499C22⋊C8—91no—
500C4×C8—91no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—31no—
504C23×C3—31no—
505C23×C3—41no—
506C23×C3—61no—
507C23×C3—122no—
508C23×C3—122no—
509C23×C3—241no—
510C22×D3—21no—
511C22×D3—42no—
512C22×D3—42no—
513C22×D3—61no—
514C22×D3—61no—
515C22×D3—61no—
516C22×D3—61no—
517C22×D3—81no—
518C22×D3—121no—
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—21no—
529C3×D4—21no—
530C3×D4—21no—
531C3×D4—21no—
532C3×D4—32no—
533C3×D4—41no—
534C3×D4—41no—
535C3×D4—61no—
536C3×D4—122no—
537C3×D4—122no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—31no—
542C2×C3×C4—31no—
543C2×C3×C4—41no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—122no—
552C2×C3×C4—122no—
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555#67—34no—
556#67—34no—
557#67—42no—
558#67—42no—
559#67—122no—
560#67—122no—
561#67—122no—
562#67—122no—
563#67—122no—
564#67—122no—
565#67—242no—
566#67—241no—
567#67—241no—
568#67—242no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—122no—
579C2×Dic3D3×D411yescharacteristic
580C2×Dic3D3×D411yescharacteristic
581D12—21no—
582D12—62no—
583D12—61no—
584D12—61no—
585D12—61no—
586D12—61no—
587D12—61no—
588D12—61no—
589D12—61no—
590D12—61no—
591D12—121no—
592D12—121no—
593D12—121no—
594D12—122no—
595D12—122no—
596D12—122no—
597D12—122no—
598D12#23512yescomplemented
599C4×D3—21no—
600C4×D3—21no—
601C4×D3—21no—
602C4×D3—21no—
603C4×D3—42no—
604C4×D3—42no—
605C4×D3—122no—
606C4×D3—122no—
607C4×D3—122no—
608C4×D3—242no—
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#54611yescharacteristic
623C2×C32C22×D811yescharacteristic
624C2×C32#57711yescharacteristic
625C3⋊D3—81no—
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—91no—
639C2×D4—91no—
640C2×D4—91no—
641C2×D4—121no—
642C2×D4—181no—
643C2×D4—182no—
644C2×D4—181no—
645C2×D4—181no—
646C2×D4—181no—
647C2×D4—181no—
648C2×D4—181no—
649C2×D4—361no—
650C2×D4—364no—
651C2×D4C2×D3211yescharacteristic
652C22×C4—31no—
653C22×C4—31no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—181no—
657C22×C4—181no—
658D8—182no—
659D8—361no—
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—61no—
671C4⋊C4—61no—
672C4⋊C4—91no—
673C4⋊C4—181no—
674C4⋊C4C2×D3211yescharacteristic
675C22⋊C4—61no—
676C22⋊C4—91no—
677C22⋊C4—91no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C22⋊C4—181no—
682C22⋊C4—181no—
683C42—91no—
684C22×C3—21no—
685C22×C3—32no—
686C22×C3—32no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—61no—
697C22×C3—62no—
698C22×C3—81no—
699C22×C3—81no—
700C22×C3—81no—
701C22×C3—121no—
702C22×C3—121no—
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—22no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—84no—
714C2×D3—122no—
715C2×D3—121no—
716C2×D3—121no—
717C2×D3—121no—
718C2×D3—121no—
719C2×D3—121no—
720C2×D3—121no—
721C2×D3—121no—
722C2×D3—121no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—241no—
728C2×D3—241no—
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—41no—
739C3×C4—41no—
740C3×C4—61no—
741C3×C4—61no—
742C3×C4—81no—
743C3×C4—121no—
744C3×C4—121no—
745C3×C4—121no—
746C3×C4C2×#23511yescharacteristic
747C3×C4#100411yescharacteristic
748C3×C4D3×#4111yescharacteristic
749C3×C4#100911yescharacteristic
750Dic3—21no—
751Dic3—21no—
752Dic3—32no—
753Dic3—32no—
754Dic3—41no—
755Dic3—41no—
756Dic3—41no—
757Dic3—62no—
758Dic3—61no—
759Dic3—61no—
760Dic3—121no—
761C32#329411yescharacteristic, complemented, Sylow
762C23—21no—
763C23—31no—
764C23—31no—
765C23—61no—
766C23—122no—
767C23—122no—
768C23—181no—
769C23—181no—
770C23—241no—
771C23—362no—
772C23—362no—
773C23—721no—
774Q8—362no—
775D4—21no—
776D4—21no—
777D4—32no—
778D4—61no—
779D4—94no—
780D4—122no—
781D4—122no—
782D4—181no—
783D4—181no—
784D4—181no—
785D4—181no—
786D4—362no—
787D4—362no—
788D4—362no—
789D4—362no—
790D4—362no—
791D4—721no—
792C2×C4—21no—
793C2×C4—31no—
794C2×C4—31no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—91no—
803C2×C4—91no—
804C2×C4—122no—
805C2×C4—122no—
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—81no—
819C2×C3—81no—
820C2×C3—122no—
821C2×C3—161no—
822C2×C3#549011yescharacteristic
823C2×C3#565411yescharacteristic
824C2×C3C2×D3×D811yescharacteristic
825C2×C3C2×D3×D811yescharacteristic
826C2×C3#576211yescharacteristic
827C2×C3#577811yescharacteristic
828D3—22no—
829D3—22no—
830D3—42no—
831D3—242no—
832D3—241no—
833D3—241no—
834D3—241no—
835D3—241no—
836D3—481no—
837C22—32no—
838C22—32no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—61no—
843C22—61no—
844C22—61no—
845C22—61no—
846C22—62no—
847C22—121no—
848C22—121no—
849C22—244no—
850C22—361no—
851C22—361no—
852C22—361no—
853C22—361no—
854C22—361no—
855C22—361no—
856C22—724no—
857C22D32×D411yescharacteristic
858C4—41no—
859C4—61no—
860C4—61no—
861C4—92no—
862C4—121no—
863C4—121no—
864C4—121no—
865C4—181no—
866C4D3×#23511yescharacteristic
867C4#6431411yescharacteristic
868C3—21no—
869C3#7875711yescharacteristic, complemented
870C3#8130211yescharacteristic, complemented
871C2—62no—
872C2—62no—
873C2—81no—
874C2—122no—
875C2—721no—
876C2—721no—
877C2#1059427211yescharacteristic
878C2D32×D811yescharacteristic
879C2#1059475111yescharacteristic
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. #10595288C2semidirect
2. #10594512C2semidirect
3. #10592485C2semidirect
4. C3×#4774C2semidirect
5. C3×D3×#102C2semidirect
6. #10591449C2semidirect
7. #10591448C2semidirect
8. #10591402C2semidirect
9. #10590947C2semidirect
10. #10590832C2semidirect
11. #10590778C2semidirect
12. #10590717C2semidirect
13. D3×#809C2semidirect
14. #10590459C2semidirect
15. #10590422C2semidirect
23. C2×#3753C22semidirect
24. C2×#3745C22semidirect
25. #64102C22semidirect
27. C2×C3×D3×C8C22semidirect
28. C3×D3×C4⋊C4C22semidirect
29. C3×D3×C4⋊C4C22semidirect
33. #63919C22semidirect
35. #63909C22semidirect
36. #63909C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. C32×#102C22semidirect
45. #63641C22semidirect
46. #63636C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#818C22semidirect
53. C3×#807C22semidirect
54. #63576C22semidirect
55. #63564C22semidirect
56. #63564C22semidirect
57. #63564C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63553C22semidirect
81. #4774D3semidirect
85. D3×#102D3semidirect
185. C2×D3×C8C2×D3semidirect
197. D3×C4⋊C4C2×D3semidirect
198. D3×C4⋊C4C2×D3semidirect
210. C3×#102C2×D3semidirect
211. C3×#102C2×D3semidirect
214. #832C2×D3semidirect
215. #832C2×D3semidirect
222. (C2×D3)⋊C8C2×D3semidirect
223. #818C2×D3semidirect
239. #807C2×D3semidirect
273. C3×D12#41semidirect
285. #625D8semidirect
497. #102D32semidirect
598. D12#235semidirect
761. C32#3294semidirect
869. C3#78757semidirect
870. C3#81302semidirect

Maximal subgroups

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

subgroupindex
#105952882
#105945122
#105924852
C3×#47742
C3×D3×#1022
#105914492
#105914482
#105914022
#105909472
#105908322
#105907782
#105907172
D3×#8092
#105904592
#105904222
#813023
#787573