Finite Group Databasebeta

← #11889779

Subgroups — #11889779

Order 1152.

877 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595371C211yesmaximal, characteristic, complemented
2#10594630C211yesmaximal, characteristic
3#10592512C211yesmaximal, characteristic, complemented
4C3×#4817C211yesmaximal, characteristic, complemented
5C3×#4812C211yesmaximal, characteristic, complemented
6#10591655C211yesmaximal, characteristic, complemented
7#10591652C211yesmaximal, characteristic, complemented
8#10591604C211yesmaximal, characteristic, complemented
9#10590940C211yesmaximal, characteristic, complemented
10#10590895C211yesmaximal, characteristic, complemented
11#10590736C211yesmaximal, characteristic, complemented
12#10590670C211yesmaximal, characteristic, complemented
13#10590555C211yesmaximal, characteristic, complemented
14#10590444C211yesmaximal, characteristic, complemented
15#10590438C211yesmaximal, characteristic, complemented
16#80823—31nomaximal
17#79802—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20#64155C2211yescharacteristic
21C2×#3756C2211yescharacteristic, complemented
22C2×C8×C3⋊D3C2211yescharacteristic
23#64106C2211yescharacteristic
24C3×#946C2211yescharacteristic, complemented
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C2×C3×#215C2211yescharacteristic
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
29C3×#895C2211yescharacteristic
30C3×#893C2211yescharacteristic
31#63922—21no—
32D3×(C2×D3)⋊C4—21no—
33#63918C2211yescharacteristic, complemented
34#63908—21no—
35C4×#626C2211yescharacteristic
36#63900C2211yescharacteristic
37#63899—21no—
38#63895—21no—
39#63891—21no—
40D3×C4⋊Dic3C2211yescharacteristic, complemented
41#63880—21no—
42#63867—21no—
43#63860C2211yescharacteristic
44C32×#103C2211yescharacteristic, complemented
45#63643C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#815C2211yescharacteristic, complemented
50C3×#807C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63567C2211yescharacteristic, complemented
54#63567C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#5635—31no—
62#5612—31no—
63#5579—31no—
64#5554—31no—
65C3×#468—31no—
66C3×#440—31no—
67#5173—31no—
68#5169—31no—
69#5169—31no—
70#5166—31no—
71#5133—31no—
72#5127—31no—
73#5047—31no—
74#5033—31no—
75#5028—31no—
76#5007—31no—
77#4890—31no—
78#4884—31no—
79#4884—31no—
80#4882—31no—
81#4817D311yescharacteristic, complemented
82#4813—31no—
83#4813—31no—
84#4813—61no—
85#4812D311yescharacteristic, complemented
86#4771—31no—
87D3×#102—31no—
88D3×#102—31no—
89#4765—31no—
90#4714—31no—
91#4706—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×#627—21no—
102C2×#626D411yescharacteristic
103C2×#625—21no—
104C2×#625—21no—
105C2×#624—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3802—22no—
109#3802—41no—
110#3795—22no—
111#3795—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3756—41no—
115#3752—21no—
116#3752—21no—
117C4⋊(C3⋊Dic3)—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C8×C3⋊D3—41no—
122C3×#215—22no—
123C3×#215—41no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C3×ΓL(1,𝔽25)—41no—
136#3724—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3D411yescharacteristic
140#3722D411yescharacteristic
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3D411yescharacteristic
144#3314—91noSylow
145C2×#237—31no—
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×#235—31no—
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C2×C3×M16—31no—
152C3×C22⋊Q8—31no—
153C3×#121—31no—
154C3×C4×Q8—31no—
155C3×C4×D4—31no—
156#946—31no—
157#946—31no—
158#946—61no—
159#946C2×D311yescharacteristic, complemented
160Q8×Dic3C2×D311yescharacteristic, complemented
161C2×#216—31no—
162C2×#216—31no—
163C2×#216—61no—
164C2×#215C2×D311yescharacteristic
165C2×#215C2×D311yescharacteristic
166#938—61no—
167#937—61no—
168#936—31no—
169#930—61no—
170C4×#67—31no—
171C2×(C2×D3)⋊C4—61no—
172C2×C4⋊Dic3—31no—
173C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
174C2×D3×C8—31no—
175C2×D3×C8—31no—
176C2×D3×C8—61no—
177#897—31no—
178#897—31no—
179#897—61no—
180#897—61no—
181#896—61no—
182#896—61no—
183#895C2×D311yescharacteristic
184#893C2×D311yescharacteristic
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—31no—
188#889—61no—
189#888—31no—
190#886—61no—
191#883—61no—
192#882—61no—
193#67⋊C4—61no—
194D3×C22⋊C4—61no—
195#878—61no—
196#875—31no—
197C4×D12—31no—
198C4×D12—61no—
199#870—61no—
200#869—31no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#103—21no—
204C3×#103C2×D311yescharacteristic, complemented
205C3×#103C2×D311yescharacteristic, complemented
206C3×#102—31no—
207C3×#102—31no—
208C3×#97—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#830—31no—
214#821—31no—
215#821—31no—
216#821C2×D311yescharacteristic
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226#815C2×D311yescharacteristic, complemented
227Dic3⋊C8—31no—
228#810—31no—
229#810—31no—
230#809—31no—
231#809—31no—
232#807—31no—
233#807—31no—
234#807—61no—
235#807C2×D311yescharacteristic, complemented
236#807C2×D311yescharacteristic, complemented
237C4⋊(C3⋊C8)—31no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255#634—21no—
256#634—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—81no—
266C3×D12#4112yes—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—81no—
270#627—81no—
271#626—22no—
272#625—42no—
273#625—42no—
274#624—81no—
275D3×Dic3—42no—
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—91no—
290#452—91no—
291#450—91no—
292#440—31no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C2×C3×Q8—21no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C2×#67—31no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313#237—62no—
314#237—121no—
315D3×D4—62no—
316D3×D4—62no—
317D3×D4—121no—
318D3×D4—121no—
319#235—62no—
320#235—121no—
321C2×D12—21no—
322C2×D12—31no—
323C2×D12C22×D311yescharacteristic
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—21no—
326C2×C4×D3—31no—
327C2×C4×D3—31no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6—31no—
335C2×Dic6—31no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C3×SD16—62no—
340C3×SD16—121no—
341C3×M16—121no—
342C2×C3×C8—21no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—31no—
358C3×C42—61no—
359#217—31no—
360#217—61no—
361#217—61no—
362#216—121no—
363#216—121no—
364#216—122no—
365#215—22no—
366#215—41no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—121no—
380(C2×D3)⋊C4—121no—
381C4⋊Dic3—21no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—121no—
391C4⋊Dic3C22×D311yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393Dic3⋊C4—21no—
394Dic3⋊C4—31no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—121no—
402C4×Dic3—21no—
403C4×Dic3C22×D311yescharacteristic
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409ΓL(1,𝔽25)—41no—
410D3×C8—121no—
411D3×C8—121no—
412D3×C8—122no—
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3#13712yes—
417C2×C3×D3—22no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426D32—84no—
427C32×C4—41no—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3⋊Dic3—21no—
432C3⋊Dic3—41no—
433C3⋊Dic3—41no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—91no—
441C2×Q16—91no—
442C2×SD16—31no—
443C2×SD16—31no—
444C2×M16—31no—
445C22×C8—91no—
446C4⋊Q8—91no—
447#125—181no—
448#124—91no—
449#123—181no—
450C22⋊Q8—31no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453C22⋊Q8—181no—
454C22⋊Q8—181no—
455#121—31no—
456#121—181no—
457#120—181no—
458C4×Q8—31no—
459C4×D4—31no—
460C4×D4—91no—
461C4×D4—181no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—91no—
464C2×C22⋊C4—181no—
465#107—31no—
466#107—31no—
467#107—91no—
468C4⋊C8—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103D3211yescharacteristic, complemented
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—91no—
480C22⋊C8—91no—
481#97—31no—
482C23×C3—31no—
483C23×C3—61no—
484C23×C3—61no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—31no—
488C22×D3—31no—
489C22×D3—61no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—241no—
495C22×D3—241no—
496C22×D3D3×D411yescharacteristic
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—41no—
502C3×Q8—41no—
503C3×D4—32no—
504C3×D4—61no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—241no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—241no—
523C2×C3×C4C23×D311yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525#67—62no—
526#67—122no—
527#67—122no—
528#67—122no—
529#67—122no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—122no—
542C2×Dic3—241no—
543C2×Dic3D3×D411yescharacteristic
544C2×Dic3D3×D411yescharacteristic
545C2×Dic3D3×D411yescharacteristic
546D12—21no—
547D12—21no—
548D12—21no—
549D12—62no—
550D12—81no—
551D12#23512yes—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—61no—
555C4×D3—61no—
556C4×D3—61no—
557C4×D3—61no—
558C4×D3—81no—
559C4×D3—121no—
560C4×D3—121no—
561C4×D3—122no—
562C4×D3—241no—
563C4×D3—241no—
564C4×D3—241no—
565Dic6—61no—
566Dic6—61no—
567Dic6—61no—
568Dic6—61no—
569Dic6—121no—
570Dic6—121no—
571Dic6—241no—
572Dic6—241no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—41no—
576C3×C8—61no—
577C3×C8—61no—
578C3⋊C8—21no—
579C3⋊C8—21no—
580C3⋊C8—62no—
581C3⋊C8—61no—
582C3⋊C8—61no—
583C2×C32#54611yescharacteristic
584C2×C32C2×#13711yescharacteristic
585C2×C32#57611yescharacteristic
586C3⋊D3—22no—
587C3×D3—42no—
588C3×D3—41no—
589C3×D3—81no—
590C24—181no—
591#41—182no—
592#41—361no—
593C2×Q8—91no—
594C2×Q8—181no—
595C2×Q8C2×D3211yescharacteristic
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—61no—
599C2×D4—91no—
600C2×D4—181no—
601C2×D4—182no—
602C2×D4—181no—
603C2×D4—361no—
604C22×C4—31no—
605C22×C4—61no—
606C22×C4—91no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610Q16—361no—
611SD16—62no—
612SD16—121no—
613M16—121no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—91no—
617C2×C8—361no—
618C2×C8C2×D3211yescharacteristic
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—91no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—91no—
635C22⋊C4—91no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—31no—
641C42—61no—
642C22×C3—21no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—62no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3C2×D3×D411yescharacteristic
653C22×C3C2×D3×D411yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—22no—
657C2×D3—21no—
658C2×D3—32no—
659C2×D3—32no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—62no—
666C2×D3—61no—
667C2×D3—61no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—244no—
673C2×D3—244no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—81no—
684C3×C4—81no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4C2×#23511yescharacteristic
688C3×C4#100411yescharacteristic
689C3×C4D3×#4111yescharacteristic
690C3×C4#100911yescharacteristic
691Dic3—21no—
692Dic3—21no—
693Dic3—21no—
694Dic3—41no—
695Dic3—41no—
696Dic3—61no—
697Dic3—61no—
698Dic3—121no—
699Dic3—121no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—241no—
704Dic3—241no—
705C32#331411yescharacteristic, complemented, Sylow
706C23—31no—
707C23—61no—
708C23—61no—
709C23—91no—
710C23—362no—
711C23—362no—
712C23—721no—
713Q8—21no—
714Q8—21no—
715Q8—181no—
716Q8—181no—
717Q8—721no—
718D4—32no—
719D4—61no—
720D4—61no—
721D4—61no—
722D4—182no—
723D4—241no—
724D4—362no—
725D4—362no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—91no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—241no—
741C2×C4—362no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4C22×D3211yescharacteristic
745C8—21no—
746C8—61no—
747C8—61no—
748C8—181no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—122no—
753C2×C3—121no—
754C2×C3—241no—
755C2×C3#555011yescharacteristic
756C2×C3#561011yescharacteristic
757C2×C3#577411yescharacteristic
758C2×C3#577411yescharacteristic
759C2×C3D3×#13711yescharacteristic
760C2×C3D3×#13711yescharacteristic
761D3—41no—
762D3—42no—
763D3—62no—
764D3—62no—
765D3—81no—
766D3—122no—
767C22—61no—
768C22—61no—
769C22—61no—
770C22—62no—
771C22—92no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—181no—
778C22—181no—
779C22—724no—
780C22D32×D411yescharacteristic
781C4—41no—
782C4—41no—
783C4—61no—
784C4—61no—
785C4—61no—
786C4—121no—
787C4—121no—
788C4—181no—
789C4—361no—
790C4—361no—
791C4D3×#23511yescharacteristic
792C4#6431411yescharacteristic
793C3—21no—
794C3#7980211yescharacteristic, complemented
795C3#8082311yescharacteristic, complemented
796C2—121no—
797C2—122no—
798C2—182no—
799C2—241no—
800C2#1059428311yescharacteristic
801C2#1059475011yescharacteristic
802C2#1059476011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594630C2
hypercenter#103D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595371C2semidirect
3. #10592512C2semidirect
4. C3×#4817C2semidirect
5. C3×#4812C2semidirect
6. #10591655C2semidirect
7. #10591652C2semidirect
8. #10591604C2semidirect
9. #10590940C2semidirect
10. #10590895C2semidirect
11. #10590736C2semidirect
12. #10590670C2semidirect
13. #10590555C2semidirect
14. #10590444C2semidirect
15. #10590438C2semidirect
21. C2×#3756C22semidirect
24. C3×#946C22semidirect
25. C3×Q8×Dic3C22semidirect
28. C2×C3×ΓL(1,𝔽25)C22semidirect
33. #63918C22semidirect
40. D3×C4⋊Dic3C22semidirect
44. C32×#103C22semidirect
45. #63643C22semidirect
46. #63634C22semidirect
49. C3×#815C22semidirect
50. C3×#807C22semidirect
51. C3×#807C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63567C22semidirect
54. #63567C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
81. #4817D3semidirect
85. #4812D3semidirect
159. #946C2×D3semidirect
160. Q8×Dic3C2×D3semidirect
173. C2×ΓL(1,𝔽25)C2×D3semidirect
204. C3×#103C2×D3semidirect
205. C3×#103C2×D3semidirect
226. #815C2×D3semidirect
235. #807C2×D3semidirect
236. #807C2×D3semidirect
472. #103D32semidirect
705. C32#3314semidirect
794. C3#79802semidirect
795. C3#80823semidirect

Maximal subgroups

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

subgroupindex
#105953712
#105946302
#105925122
C3×#48172
C3×#48122
#105916552
#105916522
#105916042
#105909402
#105908952
#105907362
#105906702
#105905552
#105904442
#105904382
#808233
#798023