Finite Group Databasebeta

← #11889713

Subgroups — #11889713

Order 1152.

987 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596277C211yesmaximal, characteristic
2#10594991C211yesmaximal, characteristic, complemented
3C3×#5218C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591496C211yesmaximal, characteristic, complemented
6#10591494C211yesmaximal, characteristic, complemented
7#10591466C211yesmaximal, characteristic, complemented
8#10591464C211yesmaximal, characteristic, complemented
9#10591446C211yesmaximal, characteristic, complemented
10#10591443C211yesmaximal, characteristic, complemented
11#10591418C211yesmaximal, characteristic, complemented
12#10591417C211yesmaximal, characteristic, complemented
13#10591187C211yesmaximal, characteristic, complemented
14#10591157C211yesmaximal, characteristic, complemented
15#10591135C211yesmaximal, characteristic, complemented
16#80163—31nomaximal
17#78763—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C2×#3830C2211yescharacteristic
20#64162—21no—
21C2×#3757—21no—
22#64148—21no—
23#64147C2211yescharacteristic
24#64145C2211yescharacteristic
25#64144—21no—
26D4×C3⋊Dic3C2211yescharacteristic
27C4×#638C2211yescharacteristic
28#64133C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C22×C3×C3⋊C8C2211yescharacteristic
34#63964—21no—
35#63952—21no—
36#63919C2211yescharacteristic, complemented
37#63900C2211yescharacteristic, complemented
38#63895—21no—
39#63871C2211yescharacteristic, complemented
40#63847—21no—
41#63843C2211yescharacteristic, complemented
42C2×#3719C2211yescharacteristic, complemented
43C2×#3712C2211yescharacteristic, complemented
44C3×#832C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51#63575C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61#5806—31no—
62#5806—31no—
63#5806—61no—
64#5635—31no—
65#5511—31no—
66C3×#450—31no—
67C2×C3×#102—31no—
68#5218D311yescharacteristic, complemented
69C2×#832D311yescharacteristic, complemented
70#5174—31no—
71#5173—31no—
72#5166—31no—
73#5164—31no—
74#5116—31no—
75#5111—31no—
76#5051—31no—
77#4970—31no—
78#4783—31no—
79#4780—31no—
80#4774—31no—
81#4774—31no—
82#4771—31no—
83#4771—31no—
84#4767—31no—
85#4765—31no—
86#4765—31no—
87#4759—31no—
88#4759—31no—
89#4757—31no—
90#4730—31no—
91#4722—31no—
92C24×C32—21no—
93C2×C32×D4—22no—
94C2×C32×D4—21no—
95C2×C32×D4—41no—
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×#638—21no—
100C2×#638—21no—
101C2×#638D411yescharacteristic
102C22×C3⋊Dic3—21no—
103C22×C3⋊Dic3—21no—
104#3830—22no—
105#3830—41no—
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×#634C2311yescharacteristic
108C22×C3×Dic3—21no—
109C2×C3×Dic6C2311yescharacteristic
110C2×#627—21no—
111C2×#624—21no—
112#3757—21no—
113#3757—21no—
114#3757—21no—
115#3757—21no—
116#3757—21no—
117#3757D411yescharacteristic
118#3752D411yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121#3750D411yescharacteristic
122C4×C3⋊Dic3C2311yescharacteristic
123C3×#217—21no—
124C3×#214—22no—
125C3×#214—41no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C2×C3×C3⋊C8—41no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3724—21no—
137#3724—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140#3722—21no—
141Dic32—21no—
142#3719—41no—
143#3712—41no—
144#3314—91noSylow
145C22×C3×D4—21no—
146C22×C3×D4C2×D311yescharacteristic
147C22×C3×D4C2×D311yescharacteristic
148C2×#237—31no—
149C2×#237—31no—
150C2×#237—61no—
151C2×C3×SD16—31no—
152C2×C3×SD16—31no—
153C22×C3×C8—31no—
154C3×C22⋊Q8—31no—
155C2×C3×C4⋊C4—31no—
156#953—61no—
157#953—61no—
158#953—62no—
159C2×#217—61no—
160C2×#217—61no—
161C2×#217—62no—
162#946—31no—
163Q8×Dic3—31no—
164C2×#216—31no—
165#939—61no—
166#939—61no—
167#939—62no—
168#938—31no—
169#938—31no—
170#938—61no—
171#936—31no—
172#936—31no—
173#936—61no—
174#935—61no—
175#935—61no—
176#935—62no—
177D4×Dic3—31no—
178D4×Dic3—31no—
179D4×Dic3—61no—
180C2×#214C2×D311yescharacteristic
181C2×#214C2×D311yescharacteristic
182C4×#67—31no—
183C4×#67—31no—
184C4×#67—61no—
185C4×#67—61no—
186C2×C4⋊Dic3C2×D311yescharacteristic
187#924—31no—
188#924—31no—
189#924—61no—
190#924—61no—
191#924C2×D311yescharacteristic
192C22×C3⋊C8C2×D311yescharacteristic
193C2×Dic12—31no—
194C2×ΓL(1,𝔽25)—31no—
195C2×ΓL(1,𝔽25)—31no—
196#897—31no—
197#897—61no—
198#896—61no—
199D3×C4⋊C4—31no—
200D3×C4⋊C4—31no—
201#889—61no—
202#889—61no—
203#888—31no—
204#888—31no—
205#887—31no—
206#67⋊C4—61no—
207#878—61no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×C22⋊C8—31no—
215#835—31no—
216#832C2×D311yescharacteristic
217#832C2×D311yescharacteristic
218#832C2×D311yescharacteristic
219#832C2×D311yescharacteristic
220#832C2×D311yescharacteristic
221#832C2×D311yescharacteristic
222#830C2×D311yescharacteristic
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225#818—31no—
226#818—31no—
227#818—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232#815—31no—
233#815—31no—
234Dic3⋊C8—31no—
235Dic3⋊C8—31no—
236#810—31no—
237#810—31no—
238#810—31no—
239#807—31no—
240#807—31no—
241#807—31no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—42no—
245C23×C32—42no—
246C23×C32—81no—
247C23×C32C2×D411yescharacteristic
248C22×C3⋊D3C2×D411yescharacteristic
249C32×D4—21no—
250C32×D4—21no—
251C32×D4—21no—
252C32×D4—42no—
253C32×D4#4112yes—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2411yescharacteristic
258#638—22no—
259#638—42no—
260#638—81no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—42no—
264C2×C3⋊Dic3—81no—
265C2×C3⋊Dic3C2×D411yescharacteristic
266C2×C3⋊Dic3C2×D411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268C4×C3⋊D3—21no—
269C4×C3⋊D3—21no—
270#634—21no—
271#634—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—81no—
277C3×Dic6—21no—
278C3×Dic6—21no—
279#627—81no—
280#624—81no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#554—91no—
286#546—91no—
287#489—91no—
288#484—91no—
289#480—91no—
290#474—91no—
291#468—91no—
292#467—91no—
293#464—91no—
294#452—91no—
295#450—31no—
296#440—91no—
297#435—91no—
298#417—91no—
299C2×#102—31no—
300C24×C3—22no—
301C24×C3—21no—
302C24×C3—21no—
303C2×C3×Q8—31no—
304C2×C3×D4—22no—
305C2×C3×D4—22no—
306C2×C3×D4—22no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—42no—
312C2×C3×D4—41no—
313C2×C3×D4—41no—
314C2×C3×D4—42no—
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C22×D311yescharacteristic
317C2×C3×D4C22×D311yescharacteristic
318C2×C3×D4C22×D311yescharacteristic
319C22×C3×C4—21no—
320C22×C3×C4—61no—
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C2×#67—31no—
324C2×#67—31no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—62no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—62no—
332C22×Dic3—21no—
333C22×Dic3—61no—
334C22×Dic3—61no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337C22×Dic3—62no—
338C22×Dic3—62no—
339#237—62no—
340#237—62no—
341#237—122no—
342#237—121no—
343#237—121no—
344#237—122no—
345C2×C4×D3—31no—
346C2×C4×D3—31no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×Dic6—31no—
351C2×Dic6—31no—
352C2×Dic6—61no—
353C2×Dic6—61no—
354C2×Dic6—61no—
355C2×Dic6C22×D311yescharacteristic
356C3×SD16—62no—
357C3×SD16—121no—
358C2×C3×C8—31no—
359C2×C3×C8—31no—
360C2×C3×C8—31no—
361C2×C3×C8—31no—
362C2×C3×C8—121no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C22⋊C4—61no—
369#217—21no—
370#217—31no—
371#217—31no—
372#217—61no—
373#217—61no—
374#217—61no—
375#217—61no—
376#217—61no—
377#217—61no—
378#217—61no—
379#217—61no—
380#217—61no—
381#217—62no—
382#217—62no—
383#217—62no—
384#217—62no—
385#217—62no—
386#217—61no—
387#217—61no—
388#216—121no—
389#214—22no—
390#214—41no—
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—
396C4⋊Dic3—21no—
397C4⋊Dic3—31no—
398C4⋊Dic3—31no—
399C4⋊Dic3—61no—
400C4⋊Dic3—61no—
401C4⋊Dic3—61no—
402C4⋊Dic3C22×D311yescharacteristic
403C4⋊Dic3C22×D311yescharacteristic
404C4⋊Dic3C22×D311yescharacteristic
405Dic3⋊C4—21no—
406Dic3⋊C4—31no—
407Dic3⋊C4—31no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—62no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418C4×Dic3—31no—
419C4×Dic3—31no—
420C4×Dic3—61no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C2×C3⋊C8—41no—
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426C2×C3⋊C8C22×D311yescharacteristic
427C2×C3⋊C8C22×D311yescharacteristic
428Dic12—121no—
429ΓL(1,𝔽25)—121no—
430ΓL(1,𝔽25)—121no—
431C22×C32—22no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—41no—
435C22×C32—41no—
436C22×C32—41no—
437C22×C32—41no—
438C22×C32—41no—
439C22×C32—84no—
440C22×C32#13712yes—
441C22×C32C22×D411yescharacteristic
442C2×C3⋊D3—21no—
443C2×C3⋊D3—21no—
444C2×C3⋊D3—21no—
445C32×C4—21no—
446C32×C4C2×#4111yescharacteristic
447C32×C4H(5,𝔽2)11yescharacteristic
448C3⋊Dic3—21no—
449C3⋊Dic3—21no—
450C3⋊Dic3—21no—
451C3⋊Dic3—41no—
452C3⋊Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C2×#41—91no—
458C22×D4D3211yescharacteristic
459C2×Q16—91no—
460C2×SD16—31no—
461C2×SD16—31no—
462C2×M16—91no—
463C22×C8—31no—
464C4⋊Q8—91no—
465#125—181no—
466#124—91no—
467#123—181no—
468C22⋊Q8—31no—
469C22⋊Q8—91no—
470C22⋊Q8—91no—
471C22⋊Q8—181no—
472C22⋊Q8—181no—
473#121—91no—
474#121—181no—
475#120—181no—
476C4×Q8—91no—
477C4×D4—91no—
478C4×D4—91no—
479C4×D4—181no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—91no—
482C2×C22⋊C4—181no—
483#107—91no—
484#107—91no—
485#107—91no—
486C4⋊C8—91no—
487#103—91no—
488#103—91no—
489#103—91no—
490#103—91no—
491#102—31no—
492#102—31no—
493#102—31no—
494#102—31no—
495#102—31no—
496#102—31no—
497C22⋊C8—31no—
498C22⋊C8—91no—
499#97—91no—
500C23×C3—22no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—22no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—42no—
508C23×C3—42no—
509C23×C3—44no—
510C23×C3—44no—
511C23×C3—42no—
512C23×C3—42no—
513C23×C3—81no—
514C23×C3—81no—
515C23×C3—82no—
516C23×C3D3×D411yescharacteristic
517C23×C3D3×D411yescharacteristic
518C22×D3—31no—
519C22×D3—31no—
520C22×D3—61no—
521C3×Q8—61no—
522C3×Q8—61no—
523C3×D4—22no—
524C3×D4—21no—
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—21no—
530C3×D4—22no—
531C3×D4—41no—
532C3×D4—41no—
533C3×D4—42no—
534C3×D4—42no—
535C3×D4—44no—
536C3×D4#23512yes—
537C3×D4#23712yes—
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—241no—
551C2×C3×C4D3×D411yescharacteristic
552C2×C3×C4D3×D411yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555#67—62no—
556#67—62no—
557#67—122no—
558#67—122no—
559#67—122no—
560#67—124no—
561#67—241no—
562#67—241no—
563#67—242no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—62no—
578C2×Dic3—62no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—81no—
584C2×Dic3—122no—
585C2×Dic3—122no—
586C2×Dic3—124no—
587C2×Dic3—241no—
588C2×Dic3—241no—
589C2×Dic3—242no—
590C4×D3—61no—
591C4×D3—61no—
592C4×D3—61no—
593C4×D3—61no—
594C4×D3—121no—
595C4×D3—121no—
596C4×D3—241no—
597C4×D3—241no—
598Dic6—21no—
599Dic6—21no—
600Dic6—61no—
601Dic6—61no—
602Dic6—61no—
603Dic6—61no—
604Dic6—121no—
605Dic6—121no—
606Dic6—241no—
607Dic6—241no—
608C3×C8—61no—
609C3×C8—61no—
610C3×C8—61no—
611C3×C8—61no—
612C3⋊C8—21no—
613C3⋊C8—21no—
614C3⋊C8—21no—
615C3⋊C8—21no—
616C2×C32—22no—
617C2×C32—42no—
618C2×C32—81no—
619C2×C32#54611yescharacteristic
620C2×C32C2×#13711yescharacteristic
621C2×C32#57611yescharacteristic
622C3⋊D3—41no—
623C24—21no—
624#41—182no—
625#41—361no—
626C2×Q8—31no—
627C2×Q8—91no—
628C2×Q8—181no—
629C2×D4—22no—
630C2×D4—21no—
631C2×D4—41no—
632C2×D4—91no—
633C2×D4—181no—
634C2×D4—181no—
635C2×D4C2×D3211yescharacteristic
636C2×D4C2×D3211yescharacteristic
637C22×C4—61no—
638C22×C4—91no—
639C22×C4—181no—
640C22×C4—181no—
641C22×C4—181no—
642C22×C4C2×D3211yescharacteristic
643Q16—361no—
644SD16—62no—
645SD16—121no—
646M16—361no—
647C2×C8—31no—
648C2×C8—31no—
649C2×C8—31no—
650C2×C8—31no—
651C2×C8—121no—
652C4⋊C4—31no—
653C4⋊C4—31no—
654C4⋊C4—31no—
655C4⋊C4—61no—
656C4⋊C4—61no—
657C4⋊C4—91no—
658C4⋊C4—91no—
659C4⋊C4—181no—
660C4⋊C4—181no—
661C4⋊C4—181no—
662C4⋊C4—181no—
663C4⋊C4—181no—
664C22⋊C4—61no—
665C22⋊C4—91no—
666C22⋊C4—91no—
667C22⋊C4—181no—
668C22⋊C4—181no—
669C22⋊C4—181no—
670C22⋊C4—181no—
671C22⋊C4—181no—
672C22⋊C4—181no—
673C42—91no—
674C42—181no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—24no—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—21no—
683C22×C3—22no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—42no—
687C22×C3—42no—
688C22×C3—42no—
689C22×C3—42no—
690C22×C3—42no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—84no—
702C22×C3—84no—
703C22×C3—88no—
704C22×C3#91512yes—
705C22×C3#91512yes—
706C22×C3C2×D3×D411yescharacteristic
707C22×C3C2×D3×D411yescharacteristic
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—61no—
712C2×D3—61no—
713C2×D3—61no—
714C2×D3—121no—
715C2×D3—121no—
716C2×D3—121no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—41no—
722C3×C4—121no—
723C3×C4—121no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4C2×#23511yescharacteristic
727C3×C4C2×#23711yescharacteristic
728C3×C4#100411yescharacteristic
729C3×C4#100411yescharacteristic
730Dic3—41no—
731Dic3—41no—
732Dic3—41no—
733Dic3—41no—
734Dic3—61no—
735Dic3—61no—
736Dic3—61no—
737Dic3—61no—
738Dic3—61no—
739Dic3—61no—
740Dic3—121no—
741Dic3—121no—
742Dic3—121no—
743Dic3—122no—
744Dic3—122no—
745Dic3—121no—
746Dic3—121no—
747Dic3—121no—
748Dic3—121no—
749C32#331411yescharacteristic, complemented, Sylow
750C23—21no—
751C23—21no—
752C23—42no—
753C23—42no—
754C23—81no—
755C23—91no—
756C23#381111yescharacteristic
757Q8—61no—
758Q8—61no—
759Q8—181no—
760Q8—181no—
761Q8—721no—
762D4—21no—
763D4—21no—
764D4—21no—
765D4—42no—
766D4—182no—
767D4—362no—
768D4—721no—
769D4#380412yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—91no—
777C2×C4—91no—
778C2×C4—91no—
779C2×C4—181no—
780C2×C4—181no—
781C2×C4—181no—
782C2×C4—181no—
783C2×C4—241no—
784C2×C4—362no—
785C2×C4—721no—
786C2×C4—721no—
787C2×C4#381111yescharacteristic
788C2×C4C22×D3211yescharacteristic
789C8—61no—
790C8—61no—
791C8—61no—
792C8—61no—
793C2×C3—22no—
794C2×C3—22no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—42no—
799C2×C3—44no—
800C2×C3—42no—
801C2×C3—42no—
802C2×C3—82no—
803C2×C3—81no—
804C2×C3—81no—
805C2×C3#549011yescharacteristic
806C2×C3#559111yescharacteristic
807C2×C3#575711yescharacteristic
808C2×C3C2×#91511yescharacteristic
809C2×C3C2×#91511yescharacteristic
810C2×C3#577411yescharacteristic
811D3—121no—
812D3—121no—
813D3—241no—
814C22—21no—
815C22—21no—
816C22—22no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—84no—
823C22—181no—
824C22—181no—
825C22—181no—
826C22#6393112yes—
827C22C2×#381111yescharacteristic
828C4—21no—
829C4—121no—
830C4—121no—
831C4—121no—
832C4—121no—
833C4—181no—
834C4—181no—
835C4—181no—
836C4—361no—
837C4—361no—
838C4C2×#380411yescharacteristic
839C4#6433011yescharacteristic
840C3—21no—
841C3#7876311yescharacteristic, complemented
842C3#8016311yescharacteristic, complemented
843C2—22no—
844C2—42no—
845C2—81no—
846C2—361no—
847C2#1059510211yescharacteristic
848C2C2×#6393111yescharacteristic
849C2#1059550011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radical#10596277C2
hypercenterC22×D4D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10594991C2semidirect
3. C3×#5218C2semidirect
4. C2×C3×#832C2semidirect
5. #10591496C2semidirect
6. #10591494C2semidirect
7. #10591466C2semidirect
8. #10591464C2semidirect
9. #10591446C2semidirect
10. #10591443C2semidirect
11. #10591418C2semidirect
12. #10591417C2semidirect
13. #10591187C2semidirect
14. #10591157C2semidirect
15. #10591135C2semidirect
36. #63919C22semidirect
37. #63900C22semidirect
39. #63871C22semidirect
41. #63843C22semidirect
42. C2×#3719C22semidirect
43. C2×#3712C22semidirect
51. #63575C22semidirect
52. #63575C22semidirect
53. #63575C22semidirect
54. #63572C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
57. #63567C22semidirect
58. #63566C22semidirect
59. #63557C22semidirect
60. #63555C22semidirect
68. #5218D3semidirect
69. C2×#832D3semidirect
749. C32#3314semidirect
841. C3#78763semidirect
842. C3#80163semidirect

Maximal subgroups

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

subgroupindex
#105962772
#105949912
C3×#52182
C2×C3×#8322
#105914962
#105914942
#105914662
#105914642
#105914462
#105914432
#105914182
#105914172
#105911872
#105911572
#105911352
#801633
#787633