Finite Group Databasebeta

← #11889158

Subgroups — #11889158

Order 1152.

953 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594621C211yesmaximal, characteristic
2#10594457C211yesmaximal, characteristic, complemented
3#10592565C211yesmaximal, characteristic, complemented
4C3×#4871C211yesmaximal, characteristic, complemented
5C3×#4864C211yesmaximal, characteristic, complemented
6#10590943C211yesmaximal, characteristic, complemented
7D3×#821C211yesmaximal, characteristic, complemented
8#10590799C211yesmaximal, characteristic, complemented
9#10590727C211yesmaximal, characteristic, complemented
10#10590596C211yesmaximal, characteristic, complemented
11#10590594C211yesmaximal, characteristic, complemented
12#10590550C211yesmaximal, characteristic, complemented
13#10590522C211yesmaximal, characteristic, complemented
14#10590478C211yesmaximal, characteristic, complemented
15#10590438C211yesmaximal, characteristic, complemented
16#81189—31nomaximal
17#80685—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×D3×D12—21no—
20C2×D3×D12C2211yescharacteristic
21#64104C2211yescharacteristic
22#64101C2211yescharacteristic, complemented
23C2×C3×#204C2211yescharacteristic, complemented
24C2×C3×D3×C8C2211yescharacteristic, complemented
25C3×#897C2211yescharacteristic, complemented
26C3×#895C2211yescharacteristic
27C3×#893C2211yescharacteristic
28C3×#890C2211yescharacteristic, complemented
29#63923—21no—
30#63922—21no—
31#63911C2211yescharacteristic
32#63906—21no—
33C4×#626C2211yescharacteristic
34#63890—21no—
35D3×C4⋊Dic3C2211yescharacteristic, complemented
36#63878—21no—
37#63872—21no—
38#63871C2211yescharacteristic, complemented
39#63848—21no—
40Dic3×Dic6C2211yescharacteristic, complemented
41C2×#3717C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic
43C2×#3712C2211yescharacteristic, complemented
44C32×#106C2211yescharacteristic, complemented
45#63648C2211yescharacteristic, complemented
46#63647C2211yescharacteristic, complemented
47#63636C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic, complemented
54C3×#807C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61#5694—31no—
62#5642—31no—
63#5609—31no—
64D4×D12—31no—
65C3×#478—31no—
66C3×#465—31no—
67#5169—31no—
68#5163—31no—
69C2×#821—31no—
70#5111—31no—
71#5067—31no—
72#5046—31no—
73#5033—31no—
74#5018—31no—
75#4886—31no—
76#4882—31no—
77#4871D311yescharacteristic, complemented
78#4866—31no—
79#4866—31no—
80#4866—61no—
81#4864D311yescharacteristic, complemented
82#4848—31no—
83#4836—31no—
84#4817—31no—
85#4812—31no—
86#4776—31no—
87#4776—31no—
88#4770—31no—
89#4770—31no—
90D3×#102—31no—
91#4764—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C3×D12—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×#626—21no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#626D411yescharacteristic
107C2×#625—21no—
108C2×D3×Dic3—21no—
109#3802—22no—
110#3802—41no—
111D3×D12—22no—
112D3×D12—44no—
113D3×D12—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117#3752—21no—
118#3752—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4×C3⋊Dic3—21no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×#204—41no—
133C3×D3×C8—41no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3D411yescharacteristic
138#3722—21no—
139#3722D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3717—41no—
143#3715—22no—
144#3712—41no—
145#3310—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C22×D12—31no—
151C22×D12—61no—
152C2×C3×SD16—31no—
153C22×C3×C8—31no—
154C3×#125—31no—
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157C3×C4×D4—31no—
158#946—31no—
159Q8×Dic3—31no—
160C2×#215—31no—
161C2×#215—31no—
162#940—31no—
163#937—61no—
164C2×#214—31no—
165#930—61no—
166C4×#67—31no—
167C2×C4⋊Dic3—31no—
168C2×#204—31no—
169C2×#204C2×D311yescharacteristic, complemented
170C2×ΓL(1,𝔽25)—31no—
171C2×ΓL(1,𝔽25)—31no—
172C2×D3×C8C2×D311yescharacteristic, complemented
173#898—61no—
174#898—61no—
175#897—31no—
176#897C2×D311yescharacteristic, complemented
177#895—31no—
178#895—31no—
179#895—61no—
180#895C2×D311yescharacteristic
181#894—61no—
182#893C2×D311yescharacteristic
183#892—31no—
184#892—31no—
185#892—61no—
186#892—61no—
187D3×C4⋊C4—31no—
188#890—61no—
189#890—61no—
190#890C2×D311yescharacteristic, complemented
191#886—61no—
192#884—61no—
193#882—61no—
194#882—61no—
195#882—61no—
196#877—61no—
197#874—31no—
198C4×D12—31no—
199C4×Dic6—31no—
200C3×#107—31no—
201C3×#106—21no—
202C3×#106C2×D311yescharacteristic, complemented
203C3×#106C2×D311yescharacteristic, complemented
204C3×C4⋊C8—31no—
205C3×#103—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209#832—31no—
210#832—31no—
211#832—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(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—61no—
224#815—31no—
225Dic3⋊C8C2×D311yescharacteristic, complemented
226#810C2×D311yescharacteristic, complemented
227#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—61no—
232#809C2×D311yescharacteristic
233#809C2×D311yescharacteristic, complemented
234#807—31no—
235#807—31no—
236#807—61no—
237#807C2×D311yescharacteristic, complemented
238#803—31no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C2×D32—42no—
245C2×D32—42no—
246C2×D32—42no—
247C2×D32—42no—
248C2×D32—81no—
249C2×D32—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—42no—
258C4×C3⋊D3—21no—
259C4×C3⋊D3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—42no—
269C3×D12#4112yes—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—42no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275#626—22no—
276#626—42no—
277#626—42no—
278#626—81no—
279#625—42no—
280D3×Dic3—42no—
281C32×C8—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—91no—
286D42—91no—
287#490—91no—
288#482—91no—
289#480—91no—
290#478—31no—
291#468—91no—
292#465—31no—
293#460—91no—
294#450—91no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—91no—
299C2×#102—91no—
300C23×D3—61no—
301C23×D3—61no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×Q8—31no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—61no—
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C2×#67—31no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C22×Dic3—61no—
317D3×D4—62no—
318D3×D4—62no—
319D3×D4—62no—
320D3×D4—121no—
321D3×D4—124no—
322D3×D4—121no—
323D3×D4—121no—
324C2×D12—21no—
325C2×D12—31no—
326C2×D12—31no—
327C2×D12—31no—
328C2×D12—61no—
329C2×D12—62no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—121no—
336C2×D12—121no—
337C2×D12—124no—
338C2×D12C22×D311yescharacteristic
339C2×D12C22×D311yescharacteristic
340C2×C4×D3—21no—
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3C22×D311yescharacteristic
346C2×Dic6C22×D311yescharacteristic
347C3×SD16—121no—
348C2×C3×C8—21no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8—121no—
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C42—31no—
368#217—31no—
369#215—62no—
370#215—121no—
371#214—62no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—31no—
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—61no—
384(C2×D3)⋊C4—121no—
385(C2×D3)⋊C4—121no—
386C4⋊Dic3—21no—
387C4⋊Dic3—21no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—31no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—121no—
406C4×Dic3C22×D311yescharacteristic
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412#204—41no—
413#204—121no—
414ΓL(1,𝔽25)—121no—
415ΓL(1,𝔽25)—121no—
416D3×C8—41no—
417C22×C32C22×D411yescharacteristic
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—21no—
425C2×C3×D3—21no—
426C2×C3×D3—22no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3AGL(1,ℤ/8)12yes—
433D32—84no—
434D32—84no—
435C32×C4—41no—
436C32×C4—41no—
437C32×C4C2×#4111yescharacteristic
438C32×C4H(5,𝔽2)11yescharacteristic
439C3⋊Dic3—21no—
440C3⋊Dic3—41no—
441C3×Dic3—21no—
442C3×Dic3—21no—
443C3×Dic3—21no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C22×D4—91no—
447C22×D4—91no—
448C22×D4—181no—
449C2×SD16—31no—
450C2×SD16—91no—
451C2×SD16—91no—
452C2×M16—91no—
453C22×C8—31no—
454#127—91no—
455#126—181no—
456#125—31no—
457#125—181no—
458#123—181no—
459C22⋊Q8—31no—
460C22⋊Q8—91no—
461#121—31no—
462#121—91no—
463#121—181no—
464#120—181no—
465#120—181no—
466C4×Q8—91no—
467C4×D4—31no—
468C4×D4—91no—
469#117—91no—
470#117—181no—
471C2×C4⋊C4—91no—
472#107—31no—
473#107—91no—
474#106D3211yescharacteristic, complemented
475C4⋊C8—31no—
476#103—31no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486C22⋊C8—91no—
487C22⋊C8—91no—
488#97—91no—
489C23×C3—31no—
490C23×C3—61no—
491C23×C3—61no—
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—31no—
495C22×D3—31no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—121no—
500C22×D3—122no—
501C22×D3—122no—
502C22×D3—122no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—241no—
509C22×D3—241no—
510C22×D3—241no—
511C22×D3—241no—
512C22×D3D3×D411yescharacteristic
513C3×Q8—61no—
514C3×Q8—61no—
515C3×D4—32no—
516C3×D4—61no—
517C3×D4—61no—
518C3×D4—61no—
519C3×D4—122no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—122no—
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537#67—62no—
538#67—122no—
539#67—122no—
540#67—122no—
541#67—122no—
542#67—241no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—121no—
551C2×Dic3—122no—
552C2×Dic3D3×D411yescharacteristic
553C2×Dic3D3×D411yescharacteristic
554C2×Dic3D3×D411yescharacteristic
555D12—21no—
556D12—21no—
557D12—21no—
558D12—42no—
559D12—62no—
560D12—61no—
561D12—61no—
562D12—61no—
563D12—61no—
564D12—121no—
565D12—121no—
566D12—122no—
567D12—122no—
568D12—122no—
569D12—122no—
570D12—242no—
571D12—241no—
572D12#23912yes—
573C4×D3—21no—
574C4×D3—21no—
575C4×D3—42no—
576C4×D3—61no—
577C4×D3—61no—
578C4×D3—61no—
579C4×D3—61no—
580C4×D3—121no—
581C4×D3—121no—
582C4×D3—122no—
583Dic6—21no—
584Dic6—21no—
585C3×C8—21no—
586C3×C8—21no—
587C3×C8—41no—
588C3×C8—61no—
589C3×C8—61no—
590C3⋊C8—21no—
591C3⋊C8—21no—
592C3⋊C8—61no—
593C3⋊C8—61no—
594C3⋊C8—121no—
595C2×C32#54611yescharacteristic
596C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
597C2×C32#57711yescharacteristic
598C3⋊D3—41no—
599C3⋊D3—81no—
600C3×D3—22no—
601C3×D3—42no—
602C3×D3—81no—
603C24—181no—
604C24—181no—
605C2×Q8—31no—
606C2×D4—31no—
607C2×D4—31no—
608C2×D4—61no—
609C2×D4—91no—
610C2×D4—91no—
611C2×D4—181no—
612C2×D4—181no—
613C2×D4—181no—
614C2×D4—181no—
615C2×D4—182no—
616C2×D4—181no—
617C2×D4—182no—
618C2×D4—361no—
619C2×D4—364no—
620C2×D4—361no—
621C22×C4—31no—
622C22×C4—61no—
623C22×C4—91no—
624C22×C4—181no—
625SD16—121no—
626SD16—182no—
627SD16—361no—
628M16—361no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—91no—
632C2×C8—121no—
633C2×C8C2×D3211yescharacteristic
634C4⋊C4—31no—
635C4⋊C4—61no—
636C4⋊C4—61no—
637C4⋊C4—61no—
638C4⋊C4—91no—
639C4⋊C4—91no—
640C4⋊C4—181no—
641C4⋊C4—181no—
642C4⋊C4—181no—
643C4⋊C4C2×D3211yescharacteristic
644C4⋊C4C2×D3211yescharacteristic
645C22⋊C4—61no—
646C22⋊C4—61no—
647C22⋊C4—61no—
648C22⋊C4—91no—
649C22⋊C4—91no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C42—31no—
654C42—181no—
655C42—181no—
656C22×C3—21no—
657C22×C3—32no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—62no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3C2×D3×D411yescharacteristic
667C22×C3C2×D3×D411yescharacteristic
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—22no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—61no—
677C2×D3—61no—
678C2×D3—61no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—61no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—241no—
692C2×D3—241no—
693C2×D3—241no—
694C2×D3—244no—
695C2×D3—244no—
696C2×D3—244no—
697C2×D3—244no—
698C2×D3#91412yes—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—61no—
706C3×C4—61no—
707C3×C4—61no—
708C3×C4—81no—
709C3×C4—81no—
710C3×C4—121no—
711C3×C4—121no—
712C3×C4#100411yescharacteristic
713C3×C4C2×#23911yescharacteristic
714C3×C4D3×#4111yescharacteristic
715C3×C4#100911yescharacteristic
716Dic3—21no—
717Dic3—21no—
718Dic3—21no—
719Dic3—41no—
720Dic3—41no—
721Dic3—61no—
722Dic3—61no—
723Dic3—121no—
724Dic3—121no—
725Dic3—121no—
726Dic3—241no—
727C32#331011yescharacteristic, complemented, Sylow
728C23—31no—
729C23—61no—
730C23—61no—
731C23—91no—
732C23—181no—
733C23—362no—
734C23—362no—
735C23—362no—
736C23—362no—
737C23—721no—
738C23—721no—
739Q8—61no—
740Q8—61no—
741D4—32no—
742D4—61no—
743D4—61no—
744D4—61no—
745D4—122no—
746D4—182no—
747D4—181no—
748D4—181no—
749D4—362no—
750D4—362no—
751D4—362no—
752D4—362no—
753D4—721no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—31no—
757C2×C4—31no—
758C2×C4—31no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—91no—
764C2×C4—122no—
765C2×C4—181no—
766C2×C4—181no—
767C2×C4—181no—
768C2×C4—362no—
769C2×C4C22×D3211yescharacteristic
770C8—21no—
771C8—61no—
772C8—61no—
773C8—181no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—62no—
778C2×C3—122no—
779C2×C3—241no—
780C2×C3#561011yescharacteristic
781C2×C3#563011yescharacteristic
782C2×C3C2×#91411yescharacteristic
783C2×C3#577011yescharacteristic
784C2×C3#577011yescharacteristic
785C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
786D3—22no—
787D3—42no—
788D3—81no—
789D3—121no—
790D3—121no—
791D3—241no—
792D3—241no—
793D3—241no—
794D3—481no—
795C22—32no—
796C22—61no—
797C22—61no—
798C22—62no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22—121no—
803C22—121no—
804C22—181no—
805C22—181no—
806C22—181no—
807C22—361no—
808C22—361no—
809C22—361no—
810C22—724no—
811C22—724no—
812C22D32×D411yescharacteristic
813C4—41no—
814C4—41no—
815C4—61no—
816C4—61no—
817C4—61no—
818C4—121no—
819C4—121no—
820C4—181no—
821C4—361no—
822C4#6430711yescharacteristic
823C4D3×#23911yescharacteristic
824C3—21no—
825C3#8068511yescharacteristic, complemented
826C3#8118911yescharacteristic, complemented
827C2—62no—
828C2—122no—
829C2—241no—
830C2—361no—
831C2—721no—
832C2#1059462211yescharacteristic
833C2D3×#91411yescharacteristic
834C2#1059475711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radical#10594621C2
hypercenter#106D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594457C2semidirect
3. #10592565C2semidirect
4. C3×#4871C2semidirect
5. C3×#4864C2semidirect
6. #10590943C2semidirect
7. D3×#821C2semidirect
8. #10590799C2semidirect
9. #10590727C2semidirect
10. #10590596C2semidirect
11. #10590594C2semidirect
12. #10590550C2semidirect
13. #10590522C2semidirect
14. #10590478C2semidirect
15. #10590438C2semidirect
22. #64101C22semidirect
23. C2×C3×#204C22semidirect
24. C2×C3×D3×C8C22semidirect
25. C3×#897C22semidirect
28. C3×#890C22semidirect
35. D3×C4⋊Dic3C22semidirect
38. #63871C22semidirect
40. Dic3×Dic6C22semidirect
41. C2×#3717C22semidirect
43. C2×#3712C22semidirect
44. C32×#106C22semidirect
45. #63648C22semidirect
46. #63647C22semidirect
47. #63636C22semidirect
48. #63634C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#810C22semidirect
53. C3×#809C22semidirect
54. C3×#807C22semidirect
55. #63564C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
77. #4871D3semidirect
81. #4864D3semidirect
169. C2×#204C2×D3semidirect
172. C2×D3×C8C2×D3semidirect
176. #897C2×D3semidirect
190. #890C2×D3semidirect
202. C3×#106C2×D3semidirect
203. C3×#106C2×D3semidirect
225. Dic3⋊C8C2×D3semidirect
226. #810C2×D3semidirect
233. #809C2×D3semidirect
237. #807C2×D3semidirect
474. #106D32semidirect
727. C32#3310semidirect
825. C3#80685semidirect
826. C3#81189semidirect

Maximal subgroups

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

subgroupindex
#105946212
#105944572
#105925652
C3×#48712
C3×#48642
#105909432
D3×#8212
#105907992
#105907272
#105905962
#105905942
#105905502
#105905222
#105904782
#105904382
#811893
#806853