Finite Group Databasebeta

← #11887047

Subgroups — #11887047

Order 1152.

1055 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595293C211yesmaximal, characteristic, complemented
2#10594517C211yesmaximal, characteristic, complemented
3#10592474C211yesmaximal, characteristic, complemented
4C3×D3×#102C211yesmaximal, characteristic, complemented
5C3×#4760C211yesmaximal, characteristic, complemented
6#10591448C211yesmaximal, characteristic, complemented
7#10591429C211yesmaximal, characteristic, complemented
8#10591417C211yesmaximal, characteristic, complemented
9#10590940C211yesmaximal, characteristic, complemented
10#10590826C211yesmaximal, characteristic, complemented
11#10590745C211yesmaximal, characteristic, complemented
12C8×#626C211yesmaximal, characteristic, complemented
13#10590598C211yesmaximal, characteristic, complemented
14#10590498C211yesmaximal, characteristic, complemented
15#10590463C211yesmaximal, characteristic, complemented
16#81576—31nomaximal
17#78757—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3802C2211yescharacteristic
21C2×#3799—21no—
22#64147C2211yescharacteristic
23C2×#3753C2211yescharacteristic, complemented
24C2×C8×C3⋊D3C2211yescharacteristic, complemented
25#64104C2211yescharacteristic, complemented
26C3×#940C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic, complemented
28C3×D3×C4⋊C4C2211yescharacteristic, complemented
29C3×#888C2211yescharacteristic, complemented
30#63983—21no—
31#63976—21no—
32#63970—21no—
33#63909C2211yescharacteristic, complemented
34#63908C2211yescharacteristic
35C4×#626C2211yescharacteristic
36#63900C2211yescharacteristic, complemented
37#63897—21no—
38#63894C2211yescharacteristic, complemented
39Dic3×D12C2211yescharacteristic
40#63888—21no—
41#63850—21no—
42C2×#3714C2211yescharacteristic
43C2×#3714C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45#63648C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×C8×Dic3C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61D4×#67—31no—
62#5726—31no—
63#5717—31no—
64#5507—31no—
65C3×#486—31no—
66C2×C3×#102—31no—
67#5217—31no—
68#5115—31no—
69C8×#67—31no—
70#5087—31no—
71#5072—31no—
72#4967—31no—
73#4786—31no—
74#4775—31no—
75#4775—31no—
76#4775—31no—
77#4775—61no—
78#4774—31no—
79#4774—31no—
80#4774—31no—
81#4773—31no—
82#4773—31no—
83#4773—31no—
84D3×#102—31no—
85D3×#102—31no—
86D3×#102D311yescharacteristic, complemented
87#4760D311yescharacteristic, complemented
88#4759—31no—
89#4756—31no—
90C4×D24—31no—
91C8×D12—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C3×D3×D4—22no—
103C3×D3×D4—41no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109D3×#67—44no—
110C2×#626—21no—
111C2×#626D411yescharacteristic
112C2×#625—21no—
113C2×#625—21no—
114C2×#624—21no—
115C2×#624—21no—
116C2×D3×Dic3—21no—
117#3802—22no—
118#3802—41no—
119#3799—44no—
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122#3757—21no—
123#3753—41no—
124#3752—21no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C8×C3⋊D3—41no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C3×D3×C8—41no—
136#3724—21no—
137Dic3⋊Dic3D411yescharacteristic
138#3722—21no—
139#3722—21no—
140#3722D411yescharacteristic
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3D411yescharacteristic
144#3714—22no—
145#3714—41no—
146#3294—91noSylow
147C22×C3×D4—31no—
148C22×#67—61no—
149C2×#239—61no—
150C2×D3×D4—31no—
151C2×D3×D4—31no—
152C2×D3×D4—61no—
153C2×D3×D4C2×D311yescharacteristic
154C2×#235—61no—
155C22×C3×C8—31no—
156C3×C4⋊Q8—31no—
157C3×#127—31no—
158C2×C3×C4⋊C4—31no—
159#953—61no—
160#946—61no—
161#940C2×D311yescharacteristic
162#939—61no—
163#938—31no—
164#938—31no—
165#938—31no—
166#938—61no—
167#938—61no—
168#937—61no—
169#937—61no—
170#937—61no—
171D4×Dic3—31no—
172C2×#213—31no—
173C2×#213—31no—
174C2×#213—31no—
175C2×#213—31no—
176C2×#213—61no—
177#930—31no—
178#930—31no—
179#929—61no—
180C4×#67—31no—
181C2×D24—31no—
182C2×D24—31no—
183C2×D3×C8—31no—
184C2×D3×C8—31no—
185C2×D3×C8—61no—
186C2×D3×C8C2×D311yescharacteristic, complemented
187#896—61no—
188#895—31no—
189#895—31no—
190#895—31no—
191#895—61no—
192#894—61no—
193#894—61no—
194#894—61no—
195#893—31no—
196D3×C4⋊C4—31no—
197D3×C4⋊C4—31no—
198D3×C4⋊C4C2×D311yescharacteristic, complemented
199#888C2×D311yescharacteristic, complemented
200C4×D12—31no—
201C4×D12—31no—
202C4×D12—31no—
203C3×#102—21no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102C2×D311yescharacteristic, complemented
211C3×#102C2×D311yescharacteristic, complemented
212C3×C4×C8—31no—
213#832—31no—
214#832—31no—
215#832C2×D311yescharacteristic, complemented
216#832C2×D311yescharacteristic, complemented
217#830—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221#821C2×D311yescharacteristic
222#821C2×D311yescharacteristic, complemented
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225(C2×D3)⋊C8—31no—
226#818—31no—
227#818—31no—
228Dic3⋊C8—31no—
229C8×Dic3C2×D311yescharacteristic, complemented
230#809—31no—
231#809—31no—
232#809C2×D311yescharacteristic
233#809C2×D311yescharacteristic, complemented
234#807—31no—
235#807—31no—
236#807—31no—
237#807—31no—
238#807—61no—
239C4⋊(C3⋊C8)—31no—
240C23×C32—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3C2×D411yescharacteristic
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⋊Dic3C2×D411yescharacteristic
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261C4⋊(C3⋊D3)—42no—
262C4×C3⋊D3—21no—
263C4×C3⋊D3—21no—
264C3×#67—42no—
265C3×#67—42no—
266C3×#67—81no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
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×Dic6—42no—
280#626—42no—
281#626D814yescomplemented
282#625—42no—
283#625—42no—
284#624—42no—
285#624—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—31no—
294#480—91no—
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×Q8—61no—
311C2×C3×D4—21no—
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—
323C2×#67—21no—
324C2×#67—21no—
325C2×#67—21no—
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—121no—
335C2×#67—124no—
336C22×Dic3—61no—
337#239—124no—
338D3×D4—22no—
339D3×D4—41no—
340D3×D4—62no—
341D3×D4—62no—
342D3×D4—121no—
343D3×D4—121no—
344D3×D4—124no—
345#235—124no—
346C2×D12—31no—
347C2×D12—31no—
348C2×D12—31no—
349C2×D12—61no—
350C2×D12—61no—
351C2×D12—61no—
352C2×D12—61no—
353C2×D12—121no—
354C2×D12C22×D311yescharacteristic
355C2×D12C22×D311yescharacteristic
356C2×C4×D3—21no—
357C2×C4×D3—31no—
358C2×C4×D3—31no—
359C2×C4×D3—61no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3C22×D311yescharacteristic
366C2×Dic6—21no—
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—31no—
376C3×C4⋊C4—61no—
377C3×C4⋊C4—61no—
378C3×C4⋊C4C22×D311yescharacteristic
379C3×C4⋊C4C22×D311yescharacteristic
380C3×C42—31no—
381#217—31no—
382#217—61no—
383#217—61no—
384#217—61no—
385#217—61no—
386#217—121no—
387#213—62no—
388#213—121no—
389#213—121no—
390#213—121no—
391#213—122no—
392(C2×D3)⋊C4—31no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
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—61no—
403(C2×D3)⋊C4—121no—
404C4⋊Dic3—31no—
405C4⋊Dic3—31no—
406C4⋊Dic3—31no—
407C4⋊Dic3—61no—
408C4⋊Dic3C22×D311yescharacteristic
409C4⋊Dic3C22×D311yescharacteristic
410Dic3⋊C4—21no—
411Dic3⋊C4—21no—
412Dic3⋊C4—31no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415C4×Dic3C22×D311yescharacteristic
416C2×C3⋊C8—31no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—61no—
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421D24—62no—
422D24—121no—
423D3×C8—41no—
424D3×C8—121no—
425D3×C8—121no—
426D3×C8—122no—
427C22×C32—41no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32C22×D411yescharacteristic
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3⋊D3—41no—
434C2×C3⋊D3—41no—
435C2×C3⋊D3—41no—
436C2×C3⋊D3C2×D812yes—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—22no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—84no—
446C2×C3×D3C2×D812yes—
447D32—84no—
448C32×C4—41no—
449C32×C4C2×#4111yescharacteristic
450C32×C4H(5,𝔽2)11yescharacteristic
451C3⋊Dic3—21no—
452C3⋊Dic3—41no—
453C3×Dic3—21no—
454C3×Dic3—21no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3C2×D812yes—
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—31no—
468#127—31no—
469#123—181no—
470#123—181no—
471C22⋊Q8—181no—
472#121—91no—
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—91no—
484#107—91no—
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#102D3211yescharacteristic, complemented
498C22⋊C8—91no—
499C22⋊C8—91no—
500C4×C8—31no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—31no—
504C23×C3—41no—
505C23×C3—61no—
506C23×C3—61no—
507C23×C3—122no—
508C23×C3—122no—
509C23×C3—241no—
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—31no—
513C22×D3—31no—
514C22×D3—42no—
515C22×D3—42no—
516C22×D3—61no—
517C22×D3—61no—
518C22×D3—61no—
519C22×D3—81no—
520C22×D3—121no—
521C22×D3—122no—
522C22×D3—122no—
523C22×D3—122no—
524C22×D3—122no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3D3×D411yescharacteristic
528C3×Q8—122no—
529C3×D4—21no—
530C3×D4—21no—
531C3×D4—21no—
532C3×D4—21no—
533C3×D4—32no—
534C3×D4—41no—
535C3×D4—41no—
536C3×D4—61no—
537C3×D4—61no—
538C3×D4—61no—
539C3×D4—122no—
540C3×D4—122no—
541C3×D4—241no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—31no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—41no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—122no—
554C2×C3×C4C23×D311yescharacteristic
555C2×C3×C4C23×D311yescharacteristic
556#67—34no—
557#67—42no—
558#67—42no—
559#67—81no—
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—21no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—121no—
576C2×Dic3—122no—
577C2×Dic3D3×D411yescharacteristic
578C2×Dic3D3×D411yescharacteristic
579C2×Dic3D3×D411yescharacteristic
580D12—21no—
581D12—21no—
582D12—21no—
583D12—34no—
584D12—61no—
585D12—61no—
586D12—61no—
587D12—61no—
588D12—121no—
589D12—121no—
590D12—122no—
591D12—122no—
592D12—122no—
593D12—242no—
594D12#23512yescomplemented
595C4×D3—21no—
596C4×D3—21no—
597C4×D3—42no—
598C4×D3—61no—
599C4×D3—61no—
600C4×D3—61no—
601C4×D3—61no—
602C4×D3—121no—
603C4×D3—121no—
604C4×D3—122no—
605C4×D3—122no—
606C4×D3—122no—
607C4×D3—122no—
608C4×D3—122no—
609Dic6—42no—
610C3×C8—21no—
611C3×C8—21no—
612C3×C8—41no—
613C3×C8—61no—
614C3×C8—61no—
615C3⋊C8—21no—
616C3⋊C8—21no—
617C3⋊C8—62no—
618C3⋊C8—61no—
619C3⋊C8—61no—
620C2×C32—81no—
621C2×C32#54611yescharacteristic
622C2×C32C22×D811yescharacteristic
623C2×C32#57711yescharacteristic
624C3⋊D3—22no—
625C3⋊D3—81no—
626C3×D3—22no—
627C3×D3—42no—
628C3×D3—81no—
629C24—61no—
630C24—181no—
631#41—364no—
632C2×Q8—61no—
633C2×D4—31no—
634C2×D4—31no—
635C2×D4—61no—
636C2×D4—61no—
637C2×D4—61no—
638C2×D4—62no—
639C2×D4—91no—
640C2×D4—91no—
641C2×D4—121no—
642C2×D4—181no—
643C2×D4—181no—
644C2×D4—181no—
645C2×D4—182no—
646C2×D4—181no—
647C2×D4—181no—
648C2×D4—361no—
649C2×D4—364no—
650C2×D4C2×D3211yescharacteristic
651C22×C4—31no—
652C22×C4—61no—
653C22×C4—91no—
654C22×C4—181no—
655C22×C4—181no—
656C22×C4—181no—
657D8—182no—
658D8—361no—
659D8—361no—
660C2×C8—31no—
661C2×C8—31no—
662C2×C8—91no—
663C2×C8—121no—
664C2×C8—361no—
665C2×C8C2×D3211yescharacteristic
666C4⋊C4—31no—
667C4⋊C4—31no—
668C4⋊C4—61no—
669C4⋊C4—61no—
670C4⋊C4—91no—
671C4⋊C4—91no—
672C4⋊C4—181no—
673C4⋊C4C2×D3211yescharacteristic
674C22⋊C4—91no—
675C22⋊C4—91no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C22⋊C4—181no—
682C42—31no—
683C22×C3—21no—
684C22×C3—32no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—62no—
694C22×C3—81no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3—244no—
703C22×C3C2×D3×D411yescharacteristic
704C22×C3C2×D3×D411yescharacteristic
705C2×D3—21no—
706C2×D3—21no—
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—62no—
716C2×D3—61no—
717C2×D3—61no—
718C2×D3—61no—
719C2×D3—61no—
720C2×D3—84no—
721C2×D3—121no—
722C2×D3—121no—
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—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—32no—
738C3×C4—41no—
739C3×C4—41no—
740C3×C4—61no—
741C3×C4—61no—
742C3×C4—81no—
743C3×C4—121no—
744C3×C4—121no—
745C3×C4C2×#23511yescharacteristic
746C3×C4#100411yescharacteristic
747C3×C4D3×#4111yescharacteristic
748C3×C4#100911yescharacteristic
749Dic3—21no—
750Dic3—21no—
751Dic3—41no—
752Dic3—41no—
753Dic3—61no—
754Dic3—61no—
755Dic3—121no—
756Dic3—121no—
757Dic3—121no—
758Dic3—241no—
759Dic3D3×D812yes—
760C32#329411yescharacteristic, complemented, Sylow
761C23—21no—
762C23—31no—
763C23—61no—
764C23—61no—
765C23—91no—
766C23—122no—
767C23—122no—
768C23—181no—
769C23—241no—
770C23—362no—
771C23—362no—
772C23—721no—
773Q8—122no—
774D4—21no—
775D4—21no—
776D4—32no—
777D4—61no—
778D4—61no—
779D4—61no—
780D4—94no—
781D4—122no—
782D4—122no—
783D4—181no—
784D4—181no—
785D4—241no—
786D4—362no—
787D4—362no—
788D4—362no—
789D4—362no—
790D4—362no—
791C2×C4—21no—
792C2×C4—31no—
793C2×C4—31no—
794C2×C4—31no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—91no—
800C2×C4—122no—
801C2×C4—181no—
802C2×C4—181no—
803C2×C4—181no—
804C2×C4—362no—
805C2×C4—362no—
806C2×C4—362no—
807C2×C4C22×D3211yescharacteristic
808C8—21no—
809C8—61no—
810C8—61no—
811C8—181no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—62no—
816C2×C3—81no—
817C2×C3—81no—
818C2×C3—122no—
819C2×C3—161no—
820C2×C3—241no—
821C2×C3#549011yescharacteristic
822C2×C3#567611yescharacteristic
823C2×C3C2×D3×D811yescharacteristic
824C2×C3C2×D3×D811yescharacteristic
825C2×C3#576211yescharacteristic
826C2×C3#576211yescharacteristic
827D3—22no—
828D3—42no—
829D3—62no—
830D3—62no—
831D3—81no—
832D3—122no—
833D3—241no—
834D3—241no—
835D3—481no—
836C22—32no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—61no—
841C22—61no—
842C22—62no—
843C22—92no—
844C22—121no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—181no—
850C22—181no—
851C22—244no—
852C22—361no—
853C22—361no—
854C22—361no—
855C22—724no—
856C22D32×D411yescharacteristic
857C4—32no—
858C4—41no—
859C4—61no—
860C4—61no—
861C4—121no—
862C4—121no—
863C4—181no—
864C4—361no—
865C4D3×#23511yescharacteristic
866C4#6431411yescharacteristic
867C3—21no—
868C3#7875711yescharacteristic, complemented
869C3#8157611yescharacteristic, complemented
870C2—62no—
871C2—81no—
872C2—122no—
873C2—182no—
874C2—241no—
875C2—721no—
876C2#1059428011yescharacteristic
877C2D32×D811yescharacteristic
878C2#1059474811yescharacteristic
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. #10594517C2semidirect
3. #10592474C2semidirect
4. C3×D3×#102C2semidirect
5. C3×#4760C2semidirect
6. #10591448C2semidirect
7. #10591429C2semidirect
8. #10591417C2semidirect
9. #10590940C2semidirect
10. #10590826C2semidirect
11. #10590745C2semidirect
12. C8×#626C2semidirect
13. #10590598C2semidirect
14. #10590498C2semidirect
15. #10590463C2semidirect
23. C2×#3753C22semidirect
24. C2×C8×C3⋊D3C22semidirect
25. #64104C22semidirect
27. C2×C3×D3×C8C22semidirect
28. C3×D3×C4⋊C4C22semidirect
29. C3×#888C22semidirect
33. #63909C22semidirect
36. #63900C22semidirect
38. #63894C22semidirect
43. C2×#3714C22semidirect
44. C32×#102C22semidirect
45. #63648C22semidirect
46. #63634C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
50. C3×#821C22semidirect
51. C3×C8×Dic3C22semidirect
53. C3×#809C22semidirect
54. #63575C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
58. #63562C22semidirect
59. #63557C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
86. D3×#102D3semidirect
87. #4760D3semidirect
186. C2×D3×C8C2×D3semidirect
198. D3×C4⋊C4C2×D3semidirect
199. #888C2×D3semidirect
210. C3×#102C2×D3semidirect
211. C3×#102C2×D3semidirect
215. #832C2×D3semidirect
216. #832C2×D3semidirect
222. #821C2×D3semidirect
229. C8×Dic3C2×D3semidirect
233. #809C2×D3semidirect
275. C3×D12#41semidirect
281. #626D8semidirect
497. #102D32semidirect
594. D12#235semidirect
760. C32#3294semidirect
868. C3#78757semidirect
869. C3#81576semidirect

Maximal subgroups

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

subgroupindex
#105952932
#105945172
#105924742
C3×D3×#1022
C3×#47602
#105914482
#105914292
#105914172
#105909402
#105908262
#105907452
C8×#6262
#105905982
#105904982
#105904632
#815763
#787573