Finite Group Databasebeta

← #11889758

Subgroups — #11889758

Order 1152.

914 conjugacy classes of subgroups.

The subgroup lattice has 819 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595371C211yesmaximal, characteristic, complemented
2#10595243C211yesmaximal, characteristic
3#10592868C211yesmaximal, characteristic, complemented
4C3×#5174C211yesmaximal, characteristic, complemented
5C3×#5166C211yesmaximal, characteristic, complemented
6#10591657C211yesmaximal, characteristic, complemented
7#10591601C211yesmaximal, characteristic, complemented
8#10591540C211yesmaximal, characteristic, complemented
9#10591488C211yesmaximal, characteristic, complemented
10#10591416C211yesmaximal, characteristic, complemented
11#10591413C211yesmaximal, characteristic, complemented
12#10590764C211yesmaximal, characteristic, complemented
13#10590738C211yesmaximal, characteristic, complemented
14#10590689C211yesmaximal, characteristic, complemented
15#10590671C211yesmaximal, characteristic, complemented
16#80823—31nomaximal
17#80619—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21#64155C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23C3×#946C2211yescharacteristic, complemented
24C3×Q8×Dic3C2211yescharacteristic, complemented
25C2×C3×#216C2211yescharacteristic, complemented
26C3×#938C2211yescharacteristic
27C3×#936C2211yescharacteristic
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
29#63981—21no—
30#63975—21no—
31#63974—21no—
32#63958—21no—
33#63918C2211yescharacteristic, complemented
34C4×#626C2211yescharacteristic
35#63900C2211yescharacteristic
36#63899—21no—
37#63895—21no—
38#63894C2211yescharacteristic
39D3×C4⋊Dic3C2211yescharacteristic, complemented
40#63880—21no—
41#63871C2211yescharacteristic
42#63867—21no—
43C2×#3710C2211yescharacteristic
44#63659C2211yescharacteristic
45#63648C2211yescharacteristic
46#63647C2211yescharacteristic
47C3×#835C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#818C2211yescharacteristic, complemented
51C3×#816C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61#5676—31no—
62#5635—31no—
63#5612—31no—
64#5579—31no—
65C3×#468—31no—
66C3×#464—31no—
67#5188—31no—
68#5187—31no—
69#5174D311yescharacteristic, complemented
70#5169—31no—
71#5169—31no—
72#5169—61no—
73#5166D311yescharacteristic, complemented
74#5133—31no—
75#5127—31no—
76#5055—31no—
77#5047—31no—
78#5033—31no—
79#5026—31no—
80#4890—31no—
81#4884—31no—
82#4846—31no—
83#4836—31no—
84#4817—31no—
85#4813—31no—
86#4811—31no—
87#4803—31no—
88#4774—31no—
89D3×#102—31no—
90D3×#102—31no—
91#4765—31no—
92C23×C3⋊D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96D4×C3⋊D3—22no—
97D4×C3⋊D3—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×#627—21no—
104C2×#626—21no—
105C2×#626D411yescharacteristic
106C2×#624—21no—
107C2×#624—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110#3799—22no—
111#3799—41no—
112C32×SD16—41no—
113C2×C32×C8C2311yescharacteristic
114#3755—22no—
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#216—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×ΓL(1,𝔽25)—41no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3D411yescharacteristic
139#3722—21no—
140#3722—21no—
141#3722D411yescharacteristic
142(C2×D3)⋊Dic3D411yescharacteristic
143#3710—41no—
144#3314—91noSylow
145C2×#239—31no—
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—61no—
149C2×#235—31no—
150C2×C3×Q16—31no—
151C2×C3×SD16—21no—
152C2×C3×SD16C2×D311yescharacteristic
153C2×C3×SD16C2×D311yescharacteristic
154C2×C3×M16—31no—
155C3×#124—31no—
156C3×C22⋊Q8—31no—
157C3×#121—31no—
158C3×C4×Q8—31no—
159#946—31no—
160#946—31no—
161#946—31no—
162#946—61no—
163#946C2×D311yescharacteristic, complemented
164Q8×Dic3C2×D311yescharacteristic, complemented
165C2×#216C2×D311yescharacteristic, complemented
166C2×#215—31no—
167C2×#215—31no—
168C2×#215—61no—
169#938—61no—
170#938C2×D311yescharacteristic
171#937—61no—
172#936C2×D311yescharacteristic
173C4×#67—31no—
174C2×C4⋊Dic3—31no—
175C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178#897—31no—
179#897—61no—
180#896—61no—
181#896—61no—
182#893—31no—
183D3×C4⋊C4—31no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—31no—
186#889—61no—
187#888—31no—
188#884—61no—
189#883—61no—
190#883—61no—
191#882—61no—
192#67⋊C4—61no—
193D3×C22⋊C4—61no—
194D3×C22⋊C4—61no—
195#878—61no—
196C4×D12—31no—
197C4×D12—31no—
198C4×D12—61no—
199#870—61no—
200#869—31no—
201C3×#107—31no—
202C3×C4⋊C8—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#102—31no—
206C3×#102—31no—
207#835—31no—
208#835—31no—
209#835C2×D311yescharacteristic, complemented
210#832—31no—
211#832—31no—
212#832—61no—
213#832C2×D311yescharacteristic
214#832C2×D311yescharacteristic
215#830—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—61no—
225#818—31no—
226#818C2×D311yescharacteristic, complemented
227#816—31no—
228#816C2×D311yescharacteristic, complemented
229#815—31no—
230Dic3⋊C8C2×D311yescharacteristic, complemented
231#810—31no—
232#809—31no—
233#809—31no—
234#807—31no—
235#807—31no—
236#807—31no—
237#803—31no—
238C23×C32—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—42no—
241C22×C3⋊D3—42no—
242C22×C3⋊D3—81no—
243C22×C3⋊D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C32×D4—21no—
248C32×D4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2411yescharacteristic
251#638—42no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)#4112yes—
256C4×C3⋊D3—21no—
257C4×C3⋊D3—21no—
258C3×#67—81no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#627—81no—
271#626—22no—
272#626—42no—
273#624—42no—
274#624—81no—
275#624—81no—
276D3×Dic3—81no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282#546—91no—
283#489—91no—
284#484—91no—
285#480—91no—
286#474—91no—
287#468—31no—
288#467—91no—
289#464—31no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C23×D3—121no—
299C2×C3×Q8—21no—
300C2×C3×Q8—31no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×D4—21no—
304C2×C3×D4—61no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—31no—
308C2×#67—21no—
309C2×#67—31no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—121no—
314C22×Dic3—61no—
315#239—62no—
316#239—121no—
317D3×D4—62no—
318D3×D4—62no—
319D3×D4—122no—
320D3×D4—121no—
321D3×D4—121no—
322D3×D4—122no—
323#235—62no—
324#235—121no—
325C2×D12—31no—
326C2×D12—31no—
327C2×D12—31no—
328C2×D12—61no—
329C2×D12—61no—
330C2×C4×D3—31no—
331C2×C4×D3—31no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3C22×D311yescharacteristic
341C2×Dic6—61no—
342C2×Dic6—61no—
343C2×Dic6C22×D311yescharacteristic
344C3×Q16—121no—
345C3×SD16—41no—
346C3×SD16—41no—
347C3×SD16—42no—
348C3×M16—121no—
349C2×C3×C8—21no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C42—31no—
364C3×C42—61no—
365#217—21no—
366#217—21no—
367#217—21no—
368#217—31no—
369#216—41no—
370#215—62no—
371#215—62no—
372#215—122no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—121no—
384C4⋊Dic3—21no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—31no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—121no—
405C4×Dic3—21no—
406C4×Dic3C22×D311yescharacteristic
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412ΓL(1,𝔽25)—41no—
413D3×C8—121no—
414D3×C8—121no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—21no—
420C2×C3⋊D3—21no—
421C2×C3⋊D3—22no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—84no—
425C2×C3⋊D3#13712yes—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C32×C4—41no—
430C32×C4C2×#4111yescharacteristic
431C32×C4H(5,𝔽2)11yescharacteristic
432C3⋊Dic3—21no—
433C3⋊Dic3—41no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C2×#41—91no—
442C22×D4—91no—
443C2×Q16—31no—
444C2×SD16—91no—
445C2×SD16D3211yescharacteristic
446C2×M16—31no—
447C22×C8—91no—
448C4⋊Q8—91no—
449#125—181no—
450#124—31no—
451#123—181no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454C22⋊Q8—91no—
455C22⋊Q8—181no—
456C22⋊Q8—181no—
457#121—31no—
458#121—181no—
459#120—181no—
460C4×Q8—31no—
461C4×D4—91no—
462C4×D4—91no—
463C4×D4—181no—
464C2×C4⋊C4—91no—
465C2×C4⋊C4—91no—
466C2×C22⋊C4—181no—
467#107—31no—
468#107—91no—
469#107—91no—
470C4⋊C8—31no—
471#103—31no—
472#103—31no—
473#103—91no—
474#103—91no—
475#102—31no—
476#102—31no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481C22⋊C8—91no—
482C22⋊C8—91no—
483#97—91no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—31no—
487C23×C3—41no—
488C22×D3—31no—
489C22×D3—31no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—61no—
493C22×D3—121no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—122no—
497C22×D3—122no—
498C22×D3—124no—
499C22×D3—242no—
500C22×D3—241no—
501C22×D3—241no—
502C22×D3—242no—
503C22×D3D3×D411yescharacteristic
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—21no—
508C3×Q8—41no—
509C3×Q8—41no—
510C3×Q8—61no—
511C3×Q8—61no—
512C3×D4—22no—
513C3×D4—21no—
514C3×D4—21no—
515C3×D4—21no—
516C3×D4—21no—
517C3×D4—41no—
518C3×D4—241no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—41no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4C23×D311yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534#67—62no—
535#67—81no—
536#67—122no—
537#67—122no—
538#67—122no—
539#67—124no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—121no—
550C2×Dic3—241no—
551C2×Dic3D3×D411yescharacteristic
552C2×Dic3D3×D411yescharacteristic
553C2×Dic3D3×D411yescharacteristic
554D12—32no—
555D12—32no—
556D12—62no—
557D12—62no—
558D12—61no—
559D12—61no—
560D12—121no—
561D12—122no—
562C4×D3—21no—
563C4×D3—21no—
564C4×D3—61no—
565C4×D3—61no—
566C4×D3—61no—
567C4×D3—61no—
568C4×D3—121no—
569C4×D3—121no—
570C4×D3—122no—
571C4×D3—122no—
572C4×D3—241no—
573C4×D3—241no—
574C4×D3—241no—
575C4×D3—241no—
576C4×D3—241no—
577Dic6—21no—
578Dic6—21no—
579Dic6—241no—
580Dic6—241no—
581C3×C8—21no—
582C3×C8—21no—
583C3×C8—41no—
584C3×C8—61no—
585C3×C8—61no—
586C3⋊C8—21no—
587C3⋊C8—21no—
588C3⋊C8—61no—
589C3⋊C8—61no—
590C3⋊C8—121no—
591C2×C32—81no—
592C2×C32#54611yescharacteristic
593C2×C32C2×#13711yescharacteristic
594C2×C32#57611yescharacteristic
595C3⋊D3—22no—
596C3⋊D3—42no—
597C3×D3—41no—
598C24—181no—
599#41—182no—
600#41—361no—
601C2×Q8—31no—
602C2×Q8—181no—
603C2×Q8C2×D3211yescharacteristic
604C2×D4—61no—
605C2×D4—91no—
606C2×D4—91no—
607C2×D4—181no—
608C2×D4—181no—
609C2×D4—182no—
610C2×D4—361no—
611C2×D4C2×D3211yescharacteristic
612C22×C4—31no—
613C22×C4—91no—
614C22×C4—181no—
615C22×C4—181no—
616C22×C4—181no—
617C22×C4—181no—
618Q16—121no—
619SD16—41no—
620SD16—182no—
621M16—121no—
622C2×C8—31no—
623C2×C8—31no—
624C2×C8—91no—
625C2×C8—361no—
626C2×C8C2×D3211yescharacteristic
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4—91no—
633C4⋊C4—91no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C4⋊C4—181no—
638C4⋊C4—181no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—91no—
644C22⋊C4—91no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C42—31no—
649C42—61no—
650C22×C3—21no—
651C22×C3—42no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3C2×D3×D411yescharacteristic
664C22×C3C2×D3×D411yescharacteristic
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—32no—
669C2×D3—32no—
670C2×D3—62no—
671C2×D3—61no—
672C2×D3—61no—
673C2×D3—61no—
674C2×D3—61no—
675C2×D3—62no—
676C2×D3—62no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—122no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—241no—
685C2×D3—241no—
686C2×D3—244no—
687C2×D3—244no—
688C2×D3—248no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—61no—
694C3×C4—61no—
695C3×C4—61no—
696C3×C4—81no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4—121no—
701C3×C4#100411yescharacteristic
702C3×C4#100411yescharacteristic
703C3×C4D3×#4111yescharacteristic
704C3×C4D3×#4111yescharacteristic
705Dic3—21no—
706Dic3—21no—
707Dic3—21no—
708Dic3—41no—
709Dic3—41no—
710Dic3—41no—
711Dic3—41no—
712Dic3—61no—
713Dic3—61no—
714Dic3—121no—
715Dic3—121no—
716Dic3—121no—
717Dic3—241no—
718C32#331411yescharacteristic, complemented, Sylow
719C23—21no—
720C23—31no—
721C23—91no—
722C23—181no—
723C23—362no—
724C23—362no—
725C23—721no—
726Q8—21no—
727Q8—21no—
728Q8—61no—
729Q8—61no—
730Q8—721no—
731D4—21no—
732D4—21no—
733D4—92no—
734D4—182no—
735D4—181no—
736D4—241no—
737D4—362no—
738D4—362no—
739C2×C4—21no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—91no—
750C2×C4—181no—
751C2×C4—181no—
752C2×C4—181no—
753C2×C4—362no—
754C2×C4—721no—
755C2×C4—721no—
756C2×C4—721no—
757C2×C4C22×D3211yescharacteristic
758C8—21no—
759C8—61no—
760C8—61no—
761C8—181no—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—82no—
766C2×C3—81no—
767C2×C3—81no—
768C2×C3—121no—
769C2×C3#561011yescharacteristic
770C2×C3#561211yescharacteristic
771C2×C3#576911yescharacteristic
772C2×C3#577411yescharacteristic
773C2×C3D3×#13711yescharacteristic
774C2×C3D3×#13711yescharacteristic
775D3—41no—
776D3—62no—
777D3—62no—
778D3—122no—
779D3—122no—
780D3—122no—
781D3—242no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—61no—
786C22—61no—
787C22—61no—
788C22—92no—
789C22—181no—
790C22—181no—
791C22—182no—
792C22—361no—
793C22—361no—
794C22—724no—
795C22D32×D411yescharacteristic
796C4—41no—
797C4—61no—
798C4—61no—
799C4—61no—
800C4—121no—
801C4—121no—
802C4—121no—
803C4—121no—
804C4—181no—
805C4—361no—
806C4#6431211yescharacteristic
807C4#6433011yescharacteristic
808C3—21no—
809C3#8061911yescharacteristic, complemented
810C3#8082311yescharacteristic, complemented
811C2—81no—
812C2—121no—
813C2—182no—
814C2—362no—
815C2#1059474211yescharacteristic
816C2#1059475511yescharacteristic
817C2#1059529611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595243C2
hypercenterC2×SD16D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #10595371C2semidirect
3. #10592868C2semidirect
4. C3×#5174C2semidirect
5. C3×#5166C2semidirect
6. #10591657C2semidirect
7. #10591601C2semidirect
8. #10591540C2semidirect
9. #10591488C2semidirect
10. #10591416C2semidirect
11. #10591413C2semidirect
12. #10590764C2semidirect
13. #10590738C2semidirect
14. #10590689C2semidirect
15. #10590671C2semidirect
23. C3×#946C22semidirect
24. C3×Q8×Dic3C22semidirect
25. C2×C3×#216C22semidirect
28. C2×C3×ΓL(1,𝔽25)C22semidirect
33. #63918C22semidirect
39. D3×C4⋊Dic3C22semidirect
47. C3×#835C22semidirect
50. C3×#818C22semidirect
51. C3×#816C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. #63576C22semidirect
54. #63575C22semidirect
55. #63566C22semidirect
56. #63565C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
69. #5174D3semidirect
73. #5166D3semidirect
163. #946C2×D3semidirect
164. Q8×Dic3C2×D3semidirect
165. C2×#216C2×D3semidirect
175. C2×ΓL(1,𝔽25)C2×D3semidirect
209. #835C2×D3semidirect
226. #818C2×D3semidirect
228. #816C2×D3semidirect
230. Dic3⋊C8C2×D3semidirect
718. C32#3314semidirect
809. C3#80619semidirect
810. C3#80823semidirect

Maximal subgroups

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

subgroupindex
#105953712
#105952432
#105928682
C3×#51742
C3×#51662
#105916572
#105916012
#105915402
#105914882
#105914162
#105914132
#105907642
#105907382
#105906892
#105906712
#808233
#806193