Finite Group Databasebeta

← #11889778

Subgroups — #11889778

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595407C211yesmaximal, characteristic, complemented
2#10594633C211yesmaximal, characteristic
3#10592516C211yesmaximal, characteristic, complemented
4C3×#4813C211yesmaximal, characteristic, complemented
5C3×#4812C211yesmaximal, characteristic, complemented
6#10591657C211yesmaximal, characteristic, complemented
7#10591651C211yesmaximal, characteristic, complemented
8#10591612C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590866C211yesmaximal, characteristic, complemented
11#10590722C211yesmaximal, characteristic, complemented
12#10590671C211yesmaximal, characteristic, complemented
13#10590440C211yesmaximal, characteristic, complemented
14#10590438C211yesmaximal, characteristic, complemented
15#10590430C211yesmaximal, characteristic, complemented
16#80823—31nomaximal
17#80777—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic, complemented
21C2×#3755C2211yescharacteristic
22#64102C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#946C2211yescharacteristic, complemented
25C2×C3×#216C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
28C2×C3×D3×C8C2211yescharacteristic
29C3×#897C2211yescharacteristic
30C3×#895C2211yescharacteristic
31#63922—21no—
32#63921—21no—
33#63919C2211yescharacteristic, complemented
34#63916—21no—
35#63902—21no—
36C4×#625C2211yescharacteristic
37#63893—21no—
38#63893—21no—
39D3×C4⋊Dic3C2211yescharacteristic
40D3×C4⋊Dic3C2211yescharacteristic, complemented
41#63870—21no—
42#63863C2211yescharacteristic
43#63854—21no—
44C32×#103C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63642C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#816C2211yescharacteristic, complemented
50C3×#807C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52#63572C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#5635—31no—
62#5635—31no—
63#5630—31no—
64#5612—31no—
65C3×#468—31no—
66C3×#467—31no—
67#5187—31no—
68#5185—31no—
69#5169—31no—
70#5166—31no—
71#5133—31no—
72#5127—31no—
73C2×#821—31no—
74#5111—31no—
75#5047—31no—
76#5046—31no—
77#5044—31no—
78#5033—31no—
79#4890—31no—
80#4890—31no—
81#4884—31no—
82#4882—31no—
83#4817—31no—
84#4817—31no—
85#4817—61no—
86#4813D311yescharacteristic, complemented
87#4812D311yescharacteristic, complemented
88#4803—31no—
89#4794—31no—
90D3×#102—31no—
91#4765—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#627—21no—
102C2×#626—21no—
103C2×#626—21no—
104C2×#625D411yescharacteristic
105C2×#624—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108D3×D12—22no—
109D3×D12—41no—
110#3799—22no—
111#3799—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3755—22no—
115#3752—21no—
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#216—41no—
122C3×#215—41no—
123C3×(C2×D3)⋊C4—21no—
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×Dic3⋊C4—21no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×ΓL(1,𝔽25)—41no—
135C3×D3×C8—41no—
136#3724—21no—
137#3724D411yescharacteristic
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3D411yescharacteristic
143(C2×D3)⋊Dic3D411yescharacteristic
144#3314—91noSylow
145C2×#239—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C2×C3×M16—31no—
152C22×C3×C8—31no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157#947—31no—
158#946C2×D311yescharacteristic
159#946C2×D311yescharacteristic, complemented
160Q8×Dic3—31no—
161Q8×Dic3—31no—
162Q8×Dic3—61no—
163C2×#216C2×D311yescharacteristic, complemented
164C2×#215—31no—
165C2×#215—31no—
166C2×#215—61no—
167C2×#215C2×D311yescharacteristic
168#938—61no—
169#937—61no—
170#936—31no—
171C4×#67—31no—
172C4×#67—31no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—31no—
175C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
176C2×D3×C8C2×D311yescharacteristic
177#897—61no—
178#897—61no—
179#897C2×D311yescharacteristic
180#895—61no—
181#895C2×D311yescharacteristic
182#894—61no—
183#893—31no—
184#893—31no—
185#893—61no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—31no—
188#889—61no—
189#889—61no—
190#888—31no—
191#888—31no—
192#883—61no—
193#882—61no—
194#67⋊C4—61no—
195#67⋊C4—61no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198#878—61no—
199#878—61no—
200C3×#107—31no—
201C3×#107—31no—
202C3×#103—21no—
203C3×#103—31no—
204C3×#103C2×D311yescharacteristic, complemented
205C3×#103C2×D311yescharacteristic, complemented
206C3×#102—31no—
207#835—31no—
208#835—31no—
209#832—31no—
210#832—31no—
211#830—31no—
212#830—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—61no—
219#821C2×D311yescharacteristic
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222#816—31no—
223#816C2×D311yescharacteristic, complemented
224#815—31no—
225#815—31no—
226#815—61no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229#810—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#807—31no—
234#807—31no—
235#807—61no—
236#807C2×D311yescharacteristic, complemented
237#807C2×D311yescharacteristic, complemented
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
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⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)#4112yes—
255C4×C3⋊D3—81no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—81no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#627—81no—
271#626—42no—
272#626—42no—
273#625—22no—
274#624—42no—
275D3×Dic3—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—31no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C2×#67—31no—
307C2×#67—31no—
308C2×#67—61no—
309C2×#67—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312#239—62no—
313#239—121no—
314D3×D4—62no—
315D3×D4—121no—
316#235—62no—
317#235—121no—
318C2×D12—21no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12—62no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—121no—
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—121no—
334C2×C4×D3C22×D311yescharacteristic
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6C22×D311yescharacteristic
339C3×Q16—121no—
340C3×SD16—121no—
341C3×M16—121no—
342C2×C3×C8—21no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8—121no—
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360#217—31no—
361#217—31no—
362#217—61no—
363#217—61no—
364#216—41no—
365#215—41no—
366#215—62no—
367#215—62no—
368#215—64no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—31no—
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—
380C4⋊Dic3—21no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—121no—
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—31no—
394Dic3⋊C4—31no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—121no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410ΓL(1,𝔽25)—41no—
411D3×C8—41no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—22no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
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#13712yes—
425D32—84no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—21no—
431C3⋊Dic3—21no—
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—91no—
439C22×D4—91no—
440C2×Q16—31no—
441C2×SD16—31no—
442C2×SD16—91no—
443C2×M16—31no—
444C22×C8—31no—
445C4⋊Q8—91no—
446#125—181no—
447#124—91no—
448#123—181no—
449C22⋊Q8—31no—
450C22⋊Q8—31no—
451C22⋊Q8—31no—
452C22⋊Q8—181no—
453C22⋊Q8—181no—
454#121—31no—
455#121—181no—
456#120—181no—
457C4×Q8—91no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—181no—
461C2×C4⋊C4—91no—
462C2×C4⋊C4—91no—
463C2×C22⋊C4—181no—
464#107—31no—
465#107—31no—
466#107—91no—
467C4⋊C8—91no—
468#103—31no—
469#103—91no—
470#103—91no—
471#103D3211yescharacteristic, complemented
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478C22⋊C8—91no—
479C22⋊C8—91no—
480#97—91no—
481C23×C3—31no—
482C23×C3—31no—
483C23×C3—61no—
484C22×D3—21no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—121no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—241no—
493C22×D3—241no—
494C22×D3D3×D411yescharacteristic
495C22×D3D3×D411yescharacteristic
496C3×Q8—22no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—41no—
502C3×Q8—61no—
503C3×Q8—61no—
504C3×D4—61no—
505C3×D4—61no—
506C3×D4—241no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4C23×D311yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525#67—62no—
526#67—62no—
527#67—122no—
528#67—122no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—121no—
541C2×Dic3—241no—
542C2×Dic3—241no—
543C2×Dic3D3×D411yescharacteristic
544C2×Dic3D3×D411yescharacteristic
545D12—21no—
546D12—21no—
547D12—32no—
548D12—32no—
549D12—62no—
550D12—61no—
551D12—61no—
552D12—81no—
553D12—121no—
554D12—122no—
555D12—122no—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—21no—
560C4×D3—122no—
561C4×D3—122no—
562C4×D3—241no—
563C4×D3—241no—
564C4×D3—242no—
565C4×D3—241no—
566C4×D3—241no—
567Dic6—21no—
568Dic6—21no—
569Dic6—241no—
570Dic6—241no—
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—41no—
574C3×C8—61no—
575C3×C8—61no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C3⋊C8—62no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C2×C32#54611yescharacteristic
582C2×C32C2×#13711yescharacteristic
583C2×C32#57611yescharacteristic
584C3⋊D3—42no—
585C3×D3—22no—
586C3×D3—41no—
587C3×D3—81no—
588C24—181no—
589#41—182no—
590#41—361no—
591C2×Q8—31no—
592C2×Q8—181no—
593C2×Q8C2×D3211yescharacteristic
594C2×D4—31no—
595C2×D4—61no—
596C2×D4—91no—
597C2×D4—91no—
598C2×D4—181no—
599C2×D4—182no—
600C2×D4—181no—
601C2×D4—361no—
602C22×C4—31no—
603C22×C4—31no—
604C22×C4—181no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4—181no—
608Q16—121no—
609SD16—121no—
610SD16—182no—
611M16—121no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—91no—
615C2×C8—121no—
616C2×C8C2×D3211yescharacteristic
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—91no—
623C4⋊C4—91no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4C2×D3211yescharacteristic
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—91no—
634C22⋊C4—91no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—91no—
639C42—181no—
640C22×C3—21no—
641C22×C3—32no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C2×D3×D411yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—62no—
661C2×D3—62no—
662C2×D3—122no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—241no—
668C2×D3—241no—
669C2×D3—244no—
670C2×D3—244no—
671C2×D3#91812yes—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—42no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—81no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4#100411yescharacteristic
686C3×C4#100411yescharacteristic
687C3×C4D3×#4111yescharacteristic
688C3×C4D3×#4111yescharacteristic
689Dic3—21no—
690Dic3—21no—
691Dic3—41no—
692Dic3—41no—
693Dic3—41no—
694Dic3—61no—
695Dic3—61no—
696Dic3—61no—
697Dic3—61no—
698Dic3—121no—
699Dic3—121no—
700Dic3—121no—
701Dic3—121no—
702Dic3—241no—
703C32#331411yescharacteristic, complemented, Sylow
704C23—31no—
705C23—31no—
706C23—61no—
707C23—181no—
708C23—362no—
709C23—362no—
710C23—721no—
711Q8—21no—
712Q8—21no—
713Q8—61no—
714Q8—61no—
715Q8—721no—
716D4—61no—
717D4—61no—
718D4—92no—
719D4—182no—
720D4—181no—
721D4—241no—
722D4—362no—
723D4—362no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—91no—
736C2×C4—91no—
737C2×C4—181no—
738C2×C4—362no—
739C2×C4—721no—
740C2×C4—721no—
741C2×C4—721no—
742C2×C4C22×D3211yescharacteristic
743C8—21no—
744C8—61no—
745C8—61no—
746C8—181no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—62no—
751C2×C3—121no—
752C2×C3—241no—
753C2×C3#561011yescharacteristic
754C2×C3#561011yescharacteristic
755C2×C3C2×#91811yescharacteristic
756C2×C3#576911yescharacteristic
757C2×C3#577411yescharacteristic
758C2×C3D3×#13711yescharacteristic
759D3—22no—
760D3—41no—
761D3—81no—
762D3—122no—
763D3—122no—
764D3—242no—
765C22—32no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—182no—
775C22—361no—
776C22—361no—
777C22—724no—
778C22D32×D411yescharacteristic
779C4—41no—
780C4—41no—
781C4—61no—
782C4—61no—
783C4—121no—
784C4—121no—
785C4—121no—
786C4—181no—
787C4—181no—
788C4—361no—
789C4#6430611yescharacteristic
790C4#6431311yescharacteristic
791C3—21no—
792C3#8077711yescharacteristic, complemented
793C3#8082311yescharacteristic, complemented
794C2—62no—
795C2—121no—
796C2—241no—
797C2—362no—
798C2#1059427611yescharacteristic
799C2#1059475511yescharacteristic
800C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594633C2
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. #10595407C2semidirect
3. #10592516C2semidirect
4. C3×#4813C2semidirect
5. C3×#4812C2semidirect
6. #10591657C2semidirect
7. #10591651C2semidirect
8. #10591612C2semidirect
9. D3×#821C2semidirect
10. #10590866C2semidirect
11. #10590722C2semidirect
12. #10590671C2semidirect
13. #10590440C2semidirect
14. #10590438C2semidirect
15. #10590430C2semidirect
20. Q8×C3⋊Dic3C22semidirect
24. C3×#946C22semidirect
25. C2×C3×#216C22semidirect
27. C2×C3×ΓL(1,𝔽25)C22semidirect
33. #63919C22semidirect
40. D3×C4⋊Dic3C22semidirect
44. C32×#103C22semidirect
46. #63642C22semidirect
47. #63634C22semidirect
49. C3×#816C22semidirect
50. C3×#807C22semidirect
51. C3×#807C22semidirect
52. #63572C22semidirect
53. #63566C22semidirect
54. #63565C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
86. #4813D3semidirect
87. #4812D3semidirect
159. #946C2×D3semidirect
163. C2×#216C2×D3semidirect
175. C2×ΓL(1,𝔽25)C2×D3semidirect
204. C3×#103C2×D3semidirect
205. C3×#103C2×D3semidirect
223. #816C2×D3semidirect
236. #807C2×D3semidirect
237. #807C2×D3semidirect
471. #103D32semidirect
703. C32#3314semidirect
792. C3#80777semidirect
793. C3#80823semidirect

Maximal subgroups

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

subgroupindex
#105954072
#105946332
#105925162
C3×#48132
C3×#48122
#105916572
#105916512
#105916122
D3×#8212
#105908662
#105907222
#105906712
#105904402
#105904382
#105904302
#808233
#807773