Finite Group Databasebeta

← #11887683

Subgroups — #11887683

Order 1152.

833 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595371C211yesmaximal, characteristic
2#10594383C211yesmaximal, characteristic
3#10592512C211yesmaximal, characteristic, complemented
4C3×#4813C211yesmaximal, characteristic, complemented
5C3×#4790C211yesmaximal, characteristic, complemented
6#10591654C211yesmaximal, characteristic, complemented
7#10591653C211yesmaximal, characteristic, complemented
8#10591625C211yesmaximal, characteristic, complemented
9#10590890C211yesmaximal, characteristic, complemented
10C8×#626C211yesmaximal, characteristic
11#10590672C211yesmaximal, characteristic, complemented
12D3×#816C211yesmaximal, characteristic, complemented
13#10590557C211yesmaximal, characteristic, complemented
14#10590444C211yesmaximal, characteristic, complemented
15#10590440C211yesmaximal, characteristic, complemented
16#80781—31nomaximal
17#79735—31nomaximal
18C2×#3797C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20#64155C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C2×C8×C3⋊D3C2211yescharacteristic
23#64106C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×#897C2211yescharacteristic
30C3×#887C2211yescharacteristic
31#63918—21no—
32#63918C2211yescharacteristic
33C4×#626C2211yescharacteristic
34#63900C2211yescharacteristic
35#63899—21no—
36#63895—21no—
37#63895—21no—
38#63893—21no—
39D3×C4⋊Dic3C2211yescharacteristic
40#63880—21no—
41#63880—21no—
42#63867—21no—
43#63866C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63643C2211yescharacteristic
46#63634C2211yescharacteristic
47C3×#816C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×C8×Dic3C2211yescharacteristic
50C3×#807C2211yescharacteristic
51C3×#807C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5635—31no—
62#5632—31no—
63#5579—31no—
64Q8×D12—31no—
65C3×#467—31no—
66C3×C4×Q16—31no—
67#5186—31no—
68#5186—31no—
69#5186—31no—
70#5182—31no—
71C8×#67—31no—
72C2×#816—31no—
73#5050—31no—
74#5044—31no—
75#5031—31no—
76#5021—31no—
77#4884—31no—
78#4884—31no—
79#4884—31no—
80#4875—31no—
81#4813—31no—
82#4813—31no—
83#4813—61no—
84#4813D311yescharacteristic, complemented
85D3×#103—31no—
86D3×#103—31no—
87D3×#103—31no—
88#4792—31no—
89#4790D311yescharacteristic, complemented
90C8×D12—31no—
91#4681—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×#627—21no—
99C2×#627—21no—
100C2×#627—21no—
101C2×#626D411yescharacteristic
102C2×#624—21no—
103C2×#624—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106#3797—22no—
107#3797—41no—
108D3×Dic6—22no—
109D3×Dic6—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3756—41no—
113#3752—21no—
114#3752—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C8×C3⋊D3—41no—
120C3×#216—22no—
121C3×#216—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C3×D3×C8—41no—
136#3724—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3D411yescharacteristic
142#3722D411yescharacteristic
143(C2×D3)⋊Dic3D411yescharacteristic
144#3299—91noSylow
145C2×D3×Q8—31no—
146C2×D3×Q8—31no—
147C2×D3×Q8—31no—
148C22×Dic6—31no—
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C22×C3×C8—31no—
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156#946—31no—
157#946—31no—
158#946—61no—
159#946C2×D311yescharacteristic
160Q8×Dic3C2×D311yescharacteristic
161#944—31no—
162C2×#216—31no—
163C2×#216—31no—
164C2×#216—61no—
165C2×#216C2×D311yescharacteristic
166C2×#216C2×D311yescharacteristic
167C4×#67—31no—
168C2×C4⋊Dic3—31no—
169C2×D3×C8—31no—
170C2×D3×C8—31no—
171C2×D3×C8—61no—
172C2×D3×C8C2×D311yescharacteristic
173#897—31no—
174#897—31no—
175#897—61no—
176#897—61no—
177#897—61no—
178#897—61no—
179#897C2×D311yescharacteristic
180#896—61no—
181#896—61no—
182#896—61no—
183D3×C4⋊C4—31no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—31no—
186#889—61no—
187#888—31no—
188#888—61no—
189#887C2×D311yescharacteristic
190#67⋊C4—61no—
191#67⋊C4—61no—
192#878—61no—
193#878—61no—
194C4×D12—31no—
195C4×D12—61no—
196C4×D12—61no—
197#870—61no—
198#869—31no—
199#869—31no—
200#869—61no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#103—21no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103C2×D311yescharacteristic
207C3×#103C2×D311yescharacteristic
208C3×C4×C8—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#830—31no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217#816—31no—
218#816—31no—
219#816—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—61no—
224#816C2×D311yescharacteristic
225#816C2×D311yescharacteristic
226Dic3⋊C8—31no—
227C8×Dic3C2×D311yescharacteristic
228#810—31no—
229#810—31no—
230#810—31no—
231#810—31no—
232#807—31no—
233#807—31no—
234#807—61no—
235#807C2×D311yescharacteristic
236#807C2×D311yescharacteristic
237C4⋊(C3⋊C8)—31no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3C2×D411yescharacteristic
248C4×C3⋊D3—21no—
249C4×C3⋊D3—21no—
250#634—21no—
251#634—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×Dic6—21no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6#4112yes—
265#627—42no—
266#627—42no—
267#627—81no—
268#626Q1614yescomplemented
269#624—42no—
270#624—81no—
271D3×Dic3—42no—
272D3×Dic3—81no—
273C32×C8—21no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#554—91no—
278D4×Q8—91no—
279#487—91no—
280#484—91no—
281#484—91no—
282#477—91no—
283#467—31no—
284#467—91no—
285#462—91no—
286#451—91no—
287#451—91no—
288C4×Q16—31no—
289C8×D4—91no—
290C2×#103—91no—
291C2×#103—91no—
292C2×C3×Q8—21no—
293C2×C3×Q8—31no—
294C2×C3×Q8—31no—
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×Q8C22×D311yescharacteristic
297C22×C3×C4—31no—
298C2×#67—31no—
299C22×Dic3—61no—
300C22×Dic3—61no—
301D3×Q8—62no—
302D3×Q8—62no—
303D3×Q8—62no—
304D3×Q8—121no—
305D3×Q8—121no—
306D3×Q8—121no—
307C2×D12—31no—
308C2×C4×D3—31no—
309C2×C4×D3—31no—
310C2×C4×D3—61no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3C22×D311yescharacteristic
318C2×Dic6—31no—
319C2×Dic6—31no—
320C2×Dic6—61no—
321C2×Dic6—62no—
322C2×Dic6—61no—
323C2×Dic6—61no—
324C2×Dic6—61no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6—61no—
328C2×Dic6—121no—
329C2×Dic6C22×D311yescharacteristic
330C2×Dic6C22×D311yescharacteristic
331C3×Q16—62no—
332C3×Q16—121no—
333C2×C3×C8—21no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8—121no—
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—31no—
351C3×C42—61no—
352C3×C42—61no—
353#217—31no—
354#216—22no—
355#216—41no—
356#216—121no—
357#216—121no—
358#216—122no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—121no—
369(C2×D3)⋊C4—121no—
370C4⋊Dic3—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—121no—
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4—31no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—121no—
397C4×Dic3—21no—
398C4×Dic3—21no—
399C4×Dic3C22×D311yescharacteristic
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405D3×C8—41no—
406D3×C8—121no—
407D3×C8—121no—
408D3×C8—122no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3C2×Q1612yes—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3C2×Q1612yes—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4C2×#4111yescharacteristic
419C32×C4H(5,𝔽2)11yescharacteristic
420C3⋊Dic3—21no—
421C3⋊Dic3—41no—
422C3⋊Dic3—41no—
423C3×Dic3—22no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3C2×Q1612yes—
430C22×Q8—91no—
431C22×Q8—91no—
432C2×Q16—31no—
433C2×Q16—31no—
434C2×Q16—91no—
435C22×C8—31no—
436C22×C8—91no—
437C4⋊Q8—91no—
438C4⋊Q8—91no—
439C4⋊Q8—181no—
440#125—181no—
441C22⋊Q8—31no—
442C22⋊Q8—31no—
443C22⋊Q8—91no—
444C22⋊Q8—91no—
445C22⋊Q8—181no—
446C22⋊Q8—181no—
447C22⋊Q8—181no—
448C22⋊Q8—181no—
449C4×Q8—31no—
450C4×Q8—31no—
451C4×D4—91no—
452C4×D4—181no—
453C4×D4—181no—
454C2×C4⋊C4—91no—
455C2×C4⋊C4—91no—
456#107—31no—
457#107—31no—
458#107—91no—
459C4⋊C8—91no—
460#103—31no—
461#103—31no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103D3211yescharacteristic
470C22⋊C8—91no—
471C22⋊C8—91no—
472C4×C8—31no—
473C23×C3—31no—
474C22×D3—31no—
475C22×D3—31no—
476C22×D3—61no—
477C22×D3D3×D411yescharacteristic
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—32no—
483C3×Q8—41no—
484C3×Q8—41no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×Q8—61no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4C23×D311yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506#67—34no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—121no—
519C2×Dic3—121no—
520C2×Dic3—122no—
521C2×Dic3—241no—
522C2×Dic3D3×D411yescharacteristic
523C2×Dic3D3×D411yescharacteristic
524C2×Dic3D3×D411yescharacteristic
525D12—34no—
526C4×D3—21no—
527C4×D3—21no—
528C4×D3—61no—
529C4×D3—61no—
530C4×D3—61no—
531C4×D3—61no—
532C4×D3—121no—
533C4×D3—121no—
534C4×D3—122no—
535C4×D3—122no—
536C4×D3—122no—
537C4×D3—241no—
538C4×D3—241no—
539C4×D3—241no—
540Dic6—21no—
541Dic6—21no—
542Dic6—21no—
543Dic6—61no—
544Dic6—61no—
545Dic6—61no—
546Dic6—61no—
547Dic6—121no—
548Dic6—121no—
549Dic6—122no—
550Dic6—122no—
551Dic6—122no—
552Dic6—122no—
553Dic6—241no—
554Dic6—241no—
555Dic6#23512yes—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—41no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C3⋊C8—62no—
564C3⋊C8—61no—
565C3⋊C8—61no—
566C2×C32#54611yescharacteristic
567C2×C32C22×Q1611yescharacteristic
568C2×C32#57711yescharacteristic
569C3⋊D3—22no—
570C3×D3—22no—
571C2×Q8—31no—
572C2×Q8—31no—
573C2×Q8—91no—
574C2×Q8—181no—
575C2×Q8—181no—
576C2×Q8—181no—
577C2×Q8—182no—
578C2×Q8—182no—
579C2×Q8—361no—
580C2×Q8—361no—
581C2×Q8C2×D3211yescharacteristic
582C2×D4—91no—
583C22×C4—31no—
584C22×C4—91no—
585C22×C4—181no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4—181no—
589Q16—62no—
590Q16—121no—
591Q16—361no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—91no—
595C2×C8—121no—
596C2×C8—361no—
597C2×C8C2×D3211yescharacteristic
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—91no—
605C4⋊C4—91no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C4⋊C4C2×D3211yescharacteristic
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—91no—
617C22⋊C4—91no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C42—31no—
621C42—61no—
622C42—61no—
623C22×C3—21no—
624C22×C3—32no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C2×D3×D411yescharacteristic
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—32no—
632C2×D3—32no—
633C2×D3—62no—
634C2×D3—61no—
635C2×D3—61no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3D3×Q1612yes—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—32no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—61no—
649C3×C4—61no—
650C3×C4—62no—
651C3×C4—81no—
652C3×C4—81no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4C2×#23511yescharacteristic
657C3×C4#100411yescharacteristic
658C3×C4D3×#4111yescharacteristic
659C3×C4#100911yescharacteristic
660Dic3—21no—
661Dic3—22no—
662Dic3—21no—
663Dic3—41no—
664Dic3—41no—
665Dic3—41no—
666Dic3—61no—
667Dic3—61no—
668Dic3—121no—
669Dic3—121no—
670Dic3—121no—
671Dic3—121no—
672Dic3—121no—
673Dic3—241no—
674Dic3—241no—
675Dic3D3×Q1612yes—
676C32#329911yescharacteristic, complemented, Sylow
677C23—31no—
678C23—91no—
679Q8—21no—
680Q8—21no—
681Q8—32no—
682Q8—61no—
683Q8—61no—
684Q8—61no—
685Q8—181no—
686Q8—181no—
687Q8—362no—
688Q8—362no—
689Q8—721no—
690D4—94no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—91no—
703C2×C4—181no—
704C2×C4—181no—
705C2×C4—181no—
706C2×C4—181no—
707C2×C4—362no—
708C2×C4—362no—
709C2×C4—721no—
710C2×C4—721no—
711C2×C4C22×D3211yescharacteristic
712C8—21no—
713C8—61no—
714C8—61no—
715C8—181no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—62no—
720C2×C3#555011yescharacteristic
721C2×C3#561011yescharacteristic
722C2×C3C2×D3×Q1611yescharacteristic
723C2×C3C2×D3×Q1611yescharacteristic
724C2×C3#577011yescharacteristic
725C2×C3#577011yescharacteristic
726D3—22no—
727D3—62no—
728D3—62no—
729D3—122no—
730C22—32no—
731C22—61no—
732C22—61no—
733C22—92no—
734C22—181no—
735C22—181no—
736C22D32×D411yescharacteristic
737C4—32no—
738C4—41no—
739C4—41no—
740C4—61no—
741C4—61no—
742C4—62no—
743C4—121no—
744C4—121no—
745C4—121no—
746C4—181no—
747C4—361no—
748C4—361no—
749C4D3×#23511yescharacteristic
750C4#6431411yescharacteristic
751C3—21no—
752C3#7973511yescharacteristic, complemented
753C3#8078111yescharacteristic, complemented
754C2—62no—
755C2—182no—
756C2#1059428311yescharacteristic
757C2#1059475711yescharacteristic
758C2D32×Q1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#626D4
hypercenter#103D32
hypocenterC32#3299
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
3. #10592512C2semidirect
4. C3×#4813C2semidirect
5. C3×#4790C2semidirect
6. #10591654C2semidirect
7. #10591653C2semidirect
8. #10591625C2semidirect
9. #10590890C2semidirect
11. #10590672C2semidirect
12. D3×#816C2semidirect
13. #10590557C2semidirect
14. #10590444C2semidirect
15. #10590440C2semidirect
84. #4813D3semidirect
89. #4790D3semidirect
268. #626Q16semidirect
676. C32#3299semidirect
752. C3#79735semidirect
753. C3#80781semidirect

Maximal subgroups

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

subgroupindex
#105953712
#105943832
#105925122
C3×#48132
C3×#47902
#105916542
#105916532
#105916252
#105908902
C8×#6262
#105906722
D3×#8162
#105905572
#105904442
#105904402
#807813
#797353