Finite Group Databasebeta

← C2×#10594770 #11918896

Subgroups — C2×#10594770 #11918896

Order 1152.

3049 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64320C211yesmaximal, characteristic, complemented
2C2×#64315C211yesmaximal, characteristic, complemented
3C2×#64127C211yesmaximal, characteristic, complemented
4C2×C3×#919C211yesmaximal, characteristic, complemented
5C2×C3×#918C211yesmaximal, characteristic, complemented
6C2×#63950C211yesmaximal, characteristic, complemented
7C2×#63947C211yesmaximal, characteristic, complemented
8C2×#63943C211yesmaximal, characteristic, complemented
9C2×#63940C211yesmaximal, characteristic, complemented
10C2×#63939C211yesmaximal, characteristic, complemented
11C2×D3×#215C211yesmaximal, characteristic, complemented
12#10594770C2116yesmaximal, direct product factor
13C2×#63804C211yesmaximal, characteristic, complemented
14C2×#63798C211yesmaximal, characteristic, complemented
15C2×#63795C211yesmaximal, characteristic, complemented
16C2×D3×#204C211yesmaximal, characteristic, complemented
17C2×#5778—31nomaximal
18C2×#5770—31nomaximal
19C2×#3832C2211yescharacteristic
20C2×Q8×C3⋊D3C2211yescharacteristic, complemented
21C2×C3×#239C2211yescharacteristic
22C2×C3×#239C2211yescharacteristic
23C2×C3×#239C2211yescharacteristic, complemented
24C2×C3×D3×Q8C2211yescharacteristic, complemented
25#64320—24no—
26#64320C2218yescomplemented
27#64315—24no—
28#64315C2218yescomplemented
29C2×#3802—21no—
30C2×#3802C2211yescharacteristic
31C2×D3×D12—21no—
32C2×D3×D12—21no—
33C2×D3×D12C2211yescharacteristic
34C2×D3×D12C2211yescharacteristic
35C2×#3798—21no—
36C2×#3798—21no—
37C2×#3798C2211yescharacteristic
38C2×#3796—21no—
39C2×#3796C2211yescharacteristic, complemented
40C2×#3795—21no—
41C2×#3795C2211yescharacteristic, complemented
42C2×D3×Dic6—21no—
43C2×D3×Dic6C2211yescharacteristic, complemented
44C2×C32×Q16C2211yescharacteristic, complemented
45C2×#3756C2211yescharacteristic, complemented
46C2×#3755C2211yescharacteristic, complemented
47#64127C2218yescomplemented
48C2×#3744C2211yescharacteristic, complemented
49C2×#3743C2211yescharacteristic, complemented
50C2×C3×#216C2211yescharacteristic, complemented
51C2×C3×#215C2211yescharacteristic, complemented
52C2×C3×#215C2211yescharacteristic, complemented
53C2×C3×#215C2211yescharacteristic, complemented
54C3×#919C2218yescomplemented
55C3×#918C2218yescomplemented
56C2×C3×D24C2211yescharacteristic, complemented
57C2×C3×#204C2211yescharacteristic, complemented
58C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
59C2×C3×D3×C8C2211yescharacteristic, complemented
60#63950C2218yescomplemented
61#63947C2218yescomplemented
62#63943C2218yescomplemented
63#63940C2218yescomplemented
64#63939C2218yescomplemented
65D3×#215C2218yescomplemented
66C2×#3717C2211yescharacteristic, complemented
67C2×#3716C2211yescharacteristic, complemented
68C2×#3716C2211yescharacteristic, complemented
69C2×#3715C2211yescharacteristic, complemented
70C2×#3714C2211yescharacteristic, complemented
71C2×#3713C2211yescharacteristic, complemented
72C2×#3711C2211yescharacteristic, complemented
73C2×#3710C2211yescharacteristic, complemented
74C2×D3×C3⋊C8C2211yescharacteristic, complemented
75#63804C2218yescomplemented
76#63798C2218yescomplemented
77#63795C2218yescomplemented
78D3×#204C2218yescomplemented
79C2×#1010—31no—
80C2×#1009—31no—
81C2×#1009—31no—
82C2×#1007—31no—
83C2×C3×#137—31no—
84C2×C3×#135—31no—
85C2×#951—31no—
86C2×#950—31no—
87C2×#949—31no—
88C22×#215—31no—
89#5778—316no—
90#5770—316no—
91C2×#919—31no—
92C2×#919D311yescharacteristic, complemented
93C2×#918—31no—
94C2×#918—31no—
95C2×#918—31no—
96C2×#918—61no—
97C2×#918D311yescharacteristic, complemented
98C2×#916—31no—
99C2×#916—31no—
100C2×#914—31no—
101C2×#914—31no—
102C2×D3×SD16—31no—
103C2×D3×SD16—31no—
104C2×D3×SD16—31no—
105C2×D3×SD16—31no—
106C2×#911—31no—
107C2×#911—31no—
108C2×#908—31no—
109C2×#907—31no—
110C22×#204—31no—
111C2×#901—31no—
112C22×D32—21no—
113C22×D32—21no—
114C22×D32—21no—
115C2×C32×Q8C2311yescharacteristic
116C2×C32×Q8C2311yescharacteristic
117#3832—22no—
118#3832C2314yes—
119Q8×C3⋊D3—22no—
120Q8×C3⋊D3C2314yescomplemented
121C2×C4⋊(C3⋊D3)—21no—
122C2×C4⋊(C3⋊D3)C2311yescharacteristic
123C2×C4×C3⋊D3—21no—
124C2×C4×C3⋊D3—21no—
125C2×C4×C3⋊D3C2311yescharacteristic
126C2×#634—21no—
127C2×#634C2311yescharacteristic
128C3×#239—22no—
129C3×#239—22no—
130C3×#239—22no—
131C3×#239C2314yes—
132C3×#239C2314yes—
133C3×#239C2314yescomplemented
134C3×D3×Q8—22no—
135C3×D3×Q8C2314yescomplemented
136C2×C3×D12—21no—
137C2×C3×D12—21no—
138C2×C3×D12—21no—
139C2×C3×D12C2311yescharacteristic
140C2×C3×D12C2311yescharacteristic
141C2×C3×D12C2311yescharacteristic
142C2×C3×C4×D3—21no—
143C2×C3×C4×D3—21no—
144C2×C3×C4×D3—21no—
145C2×C3×C4×D3—21no—
146C2×C3×C4×D3C2311yescharacteristic
147C2×C3×C4×D3C2311yescharacteristic
148C2×C3×Dic6—21no—
149C2×C3×Dic6C2311yescharacteristic
150C2×#627—21no—
151C2×#627D411yescharacteristic
152C2×#626—21no—
153C2×#626—21no—
154C2×#626—21no—
155C2×#626D411yescharacteristic
156C2×#626D411yescharacteristic
157C2×#625—21no—
158C2×#625—21no—
159C2×#625D411yescharacteristic
160C2×D3×Dic3—21no—
161C2×D3×Dic3—21no—
162C2×D3×Dic3—21no—
163#3802—22no—
164#3802—28no—
165#3802C2314yes—
166D3×D12—22no—
167D3×D12—22no—
168D3×D12—28no—
169D3×D12—28no—
170D3×D12C2314yes—
171D3×D12C2314yes—
172#3798—28no—
173#3798—28no—
174#3798D414yes—
175#3798C2314yes—
176#3796—22no—
177#3796—28no—
178#3796C2314yescomplemented
179#3795—22no—
180#3795—28no—
181#3795C2314yescomplemented
182D3×Dic6—22no—
183D3×Dic6—28no—
184D3×Dic6C2314yescomplemented
185C32×Q16C2314yescomplemented
186C2×C32×C8C2311yescharacteristic
187#3756C2314yescomplemented
188#3755C2314yescomplemented
189C2×C3⋊(C3⋊C8)C2311yescharacteristic
190#3744C2314yescomplemented
191#3743C2314yescomplemented
192C3×#216C2314yescomplemented
193C3×#215C2314yescomplemented
194C3×#215C2314yescomplemented
195C3×#215C2314yescomplemented
196C2×C3×C3⋊C8C2311yescharacteristic
197C2×C3×C3⋊C8C2311yescharacteristic
198C3×D24C2314yescomplemented
199C3×#204C2314yescomplemented
200C3×ΓL(1,𝔽25)C2314yescomplemented
201C3×D3×C8C2314yescomplemented
202#3717C2314yescomplemented
203#3716C2314yescomplemented
204#3716C2314yescomplemented
205#3715C2314yescomplemented
206#3714C2314yescomplemented
207#3713C2314yescomplemented
208#3711C2314yescomplemented
209#3710C2314yescomplemented
210D3×C3⋊C8C2314yescomplemented
211C2×#577—91noSylow
212C2×C3×#41—31no—
213C2×C3×#41—31no—
214C2×C3×#41—31no—
215C22×C3×Q8—31no—
216#1010—38no—
217#1010—64no—
218#1009—38no—
219#1009—38no—
220#1009—64no—
221#1009—64no—
222#1007—38no—
223#1007—64no—
224C2×#239—31no—
225C2×#239—31no—
226C2×#239—31no—
227C2×#239—61no—
228C2×#239—61no—
229C2×#239C2×D311yescharacteristic
230C2×#239C2×D311yescharacteristic
231C2×#239C2×D311yescharacteristic, complemented
232C2×D3×Q8—31no—
233C2×D3×Q8—31no—
234C2×D3×Q8—31no—
235C2×D3×Q8—61no—
236C2×D3×Q8—61no—
237C2×D3×Q8C2×D311yescharacteristic, complemented
238C2×#237—31no—
239C2×#237—31no—
240C2×#237—61no—
241C2×#237—61no—
242C2×D3×D4—31no—
243C2×D3×D4—31no—
244C2×D3×D4—31no—
245C2×D3×D4—31no—
246C2×D3×D4—61no—
247C2×D3×D4—61no—
248C2×D3×D4—61no—
249C2×D3×D4—61no—
250C2×#235—31no—
251C2×#235—31no—
252C2×#235—31no—
253C2×#235—61no—
254C2×#235—61no—
255C2×#235—61no—
256C2×#235—61no—
257C2×#235—61no—
258C22×D12—31no—
259C22×D12—31no—
260C22×D12—61no—
261C22×D12—61no—
262C22×Dic6—31no—
263C22×Dic6—61no—
264C3×#137—38no—
265C3×#135—38no—
266C2×C3×Q16—21no—
267C2×C3×Q16—31no—
268C2×C3×Q16C2×D311yescharacteristic, complemented
269C2×C3×Q16C2×D311yescharacteristic, complemented
270C2×C3×SD16—31no—
271C2×C3×SD16—31no—
272C2×C3×SD16—31no—
273C2×C3×SD16—31no—
274C2×C3×D8—31no—
275C2×C3×M16—31no—
276C22×C3×C8—31no—
277#951—38no—
278#950—38no—
279#949—38no—
280C2×#216—31no—
281C2×#216—31no—
282C2×#216—61no—
283C2×#216C2×D311yescharacteristic, complemented
284C2×#215—31no—
285C2×#215—31no—
286C2×#215—31no—
287C2×#215—38no—
288C2×#215—31no—
289C2×#215—61no—
290C2×#215C2×D311yescharacteristic, complemented
291C2×#215C2×D311yescharacteristic, complemented
292C2×#215C2×D311yescharacteristic, complemented
293C2×#214—31no—
294C2×#214—31no—
295C2×#214—31no—
296C2×#213—31no—
297C2×#213—31no—
298C2×#213—31no—
299C2×#208—31no—
300C22×C3⋊C8—31no—
301#919—38no—
302#919C2×D318yescomplemented
303#918—38no—
304#918—38no—
305#918—38no—
306#918—68no—
307#918C2×D318yescomplemented
308#916—38no—
309#916—38no—
310#914—38no—
311#914—38no—
312D3×SD16—38no—
313D3×SD16—38no—
314D3×SD16—38no—
315D3×SD16—38no—
316#911—38no—
317#911—38no—
318#908—38no—
319#907—38no—
320C2×D24—31no—
321C2×D24C2×D311yescharacteristic, complemented
322C2×#204—31no—
323C2×#204—31no—
324C2×#204—31no—
325C2×#204—31no—
326C2×#204—31no—
327C2×#204—38no—
328C2×#204—61no—
329C2×#204C2×D311yescharacteristic, complemented
330#901—38no—
331C2×ΓL(1,𝔽25)—31no—
332C2×ΓL(1,𝔽25)—31no—
333C2×ΓL(1,𝔽25)—31no—
334C2×ΓL(1,𝔽25)—61no—
335C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
336C2×D3×C8—31no—
337C2×D3×C8—31no—
338C2×D3×C8—31no—
339C2×D3×C8C2×D311yescharacteristic, complemented
340C22×C3⋊D3—21no—
341C22×C3⋊D3C2×D411yescharacteristic
342C22×C3×D3—21no—
343C22×C3×D3—21no—
344C22×C3×D3—21no—
345C22×C3×D3C2×D411yescharacteristic
346C22×C3×D3C2×D411yescharacteristic
347C2×D32—24no—
348C2×D32—24no—
349C2×D32—24no—
350C2×D32—82no—
351C2×D32—82no—
352C2×D32—82no—
353C32×Q8—21no—
354C32×Q8—21no—
355C32×Q8C2412yes—
356C32×Q8C2412yes—
357C2×C32×C4—21no—
358C2×C32×C4—21no—
359C2×C32×C4C2411yescharacteristic
360C2×C3⋊Dic3—21no—
361C2×C3⋊Dic3C2×D411yescharacteristic
362C4⋊(C3⋊D3)—24no—
363C4⋊(C3⋊D3)—21no—
364C4⋊(C3⋊D3)C2412yes—
365C4×C3⋊D3—24no—
366C4×C3⋊D3—24no—
367C4×C3⋊D3C2×D412yes—
368C4×C3⋊D3C2412yes—
369#634—21no—
370#634—24no—
371#634C2412yes—
372C2×C3×Dic3—21no—
373C2×C3×Dic3C2×D411yescharacteristic
374C2×C3×Dic3C2×D411yescharacteristic
375C3×D12—24no—
376C3×D12—24no—
377C3×D12—24no—
378C3×D12—21no—
379C3×D12—21no—
380C3×D12—21no—
381C3×D12C2412yes—
382C3×D12C2412yes—
383C3×D12C2412yes—
384C3×C4×D3—24no—
385C3×C4×D3—24no—
386C3×C4×D3—24no—
387C3×C4×D3—24no—
388C3×C4×D3C2×D412yes—
389C3×C4×D3C2×D412yes—
390C3×C4×D3C2412yes—
391C3×C4×D3C2412yes—
392C3×Dic6—21no—
393C3×Dic6—24no—
394C3×Dic6C2412yes—
395#627—24no—
396#627C2×D414yes—
397#626—24no—
398#626—24no—
399#626—24no—
400#626C2×D414yes—
401#626C2×D414yes—
402#625—24no—
403#625—24no—
404#625C2×D414yes—
405D3×Dic3—24no—
406D3×Dic3—24no—
407D3×Dic3—24no—
408C32×C8C2412yes—
409C3⋊(C3⋊C8)C2412yes—
410C3×C3⋊C8C2412yes—
411C3×C3⋊C8C2412yes—
412C2×2−1+4—91no—
413C2×H(5,𝔽2)—91no—
414#577—916no—
415C2×#137—31no—
416C2×#137—91no—
417C2×#137—91no—
418C2×AGL(1,ℤ/8)—91no—
419C2×AGL(1,ℤ/8)—91no—
420C2×AGL(1,ℤ/8)—91no—
421C2×#135—31no—
422C2×#135—91no—
423C2×#135—91no—
424C22×SD16—91no—
425C22×SD16—91no—
426C22×SD16—91no—
427C2×#131—91no—
428C23×D3—61no—
429C23×D3—61no—
430C23×D3—61no—
431C23×D3—61no—
432C23×D3—61no—
433C23×D3—61no—
434C3×#41—34no—
435C3×#41—34no—
436C3×#41—34no—
437C3×#41—62no—
438C3×#41—62no—
439C3×#41—62no—
440C2×C3×Q8—21no—
441C2×C3×Q8—21no—
442C2×C3×Q8—34no—
443C2×C3×Q8—31no—
444C2×C3×Q8—61no—
445C2×C3×Q8—62no—
446C2×C3×Q8C22×D311yescharacteristic
447C2×C3×Q8C22×D311yescharacteristic
448C2×C3×Q8C22×D311yescharacteristic
449C2×C3×Q8C22×D311yescharacteristic
450C2×C3×D4—31no—
451C2×C3×D4—31no—
452C2×C3×D4—31no—
453C2×C3×D4—61no—
454C2×C3×D4—61no—
455C2×C3×D4—61no—
456C22×C3×C4—31no—
457C22×C3×C4—31no—
458C22×C3×C4—61no—
459C22×C3×C4—61no—
460C22×C3×C4—61no—
461C22×C3×C4—61no—
462C2×#67—31no—
463C2×#67—31no—
464C2×#67—31no—
465C2×#67—31no—
466C2×#67—61no—
467C2×#67—61no—
468C2×#67—61no—
469C2×#67—61no—
470C2×#67—61no—
471C2×#67—61no—
472C2×#67—61no—
473C22×Dic3—61no—
474C22×Dic3—61no—
475C22×Dic3—61no—
476#239—22no—
477#239—22no—
478#239—22no—
479#239—34no—
480#239—34no—
481#239—34no—
482#239—64no—
483#239—62no—
484#239—62no—
485#239—62no—
486#239—68no—
487#239—122no—
488#239C22×D314yes—
489#239C22×D314yes—
490#239C22×D314yescomplemented
491D3×Q8—22no—
492D3×Q8—34no—
493D3×Q8—34no—
494D3×Q8—34no—
495D3×Q8—64no—
496D3×Q8—68no—
497D3×Q8—62no—
498D3×Q8—62no—
499D3×Q8—62no—
500D3×Q8—122no—
501D3×Q8C22×D314yescomplemented
502#237—34no—
503#237—34no—
504#237—62no—
505#237—68no—
506#237—68no—
507#237—62no—
508D3×D4—34no—
509D3×D4—34no—
510D3×D4—34no—
511D3×D4—34no—
512D3×D4—68no—
513D3×D4—68no—
514D3×D4—62no—
515D3×D4—62no—
516D3×D4—68no—
517D3×D4—68no—
518D3×D4—62no—
519D3×D4—62no—
520#235—34no—
521#235—34no—
522#235—34no—
523#235—34no—
524#235—34no—
525#235—68no—
526#235—68no—
527#235—68no—
528#235—68no—
529#235—68no—
530#235—62no—
531C2×D12—21no—
532C2×D12—21no—
533C2×D12—21no—
534C2×D12—31no—
535C2×D12—31no—
536C2×D12—31no—
537C2×D12—31no—
538C2×D12—34no—
539C2×D12—34no—
540C2×D12—61no—
541C2×D12—68no—
542C2×D12—68no—
543C2×D12—62no—
544C2×D12—62no—
545C2×D12—61no—
546C2×D12—61no—
547C2×D12—61no—
548C2×D12—61no—
549C2×D12—61no—
550C2×D12—121no—
551C2×D12C22×D311yescharacteristic
552C2×D12C22×D311yescharacteristic
553C2×D12C22×D311yescharacteristic
554C2×C4×D3—21no—
555C2×C4×D3—21no—
556C2×C4×D3—21no—
557C2×C4×D3—21no—
558C2×C4×D3—31no—
559C2×C4×D3—31no—
560C2×C4×D3—61no—
561C2×C4×D3—61no—
562C2×C4×D3—61no—
563C2×C4×D3—61no—
564C2×C4×D3—61no—
565C2×C4×D3—61no—
566C2×C4×D3—61no—
567C2×C4×D3—61no—
568C2×C4×D3—121no—
569C2×C4×D3—121no—
570C2×C4×D3C22×D311yescharacteristic
571C2×C4×D3C22×D311yescharacteristic
572C2×Dic6—21no—
573C2×Dic6—31no—
574C2×Dic6—31no—
575C2×Dic6—31no—
576C2×Dic6—31no—
577C2×Dic6—34no—
578C2×Dic6—61no—
579C2×Dic6—68no—
580C2×Dic6—62no—
581C2×Dic6—61no—
582C2×Dic6—61no—
583C2×Dic6—61no—
584C2×Dic6—61no—
585C2×Dic6—121no—
586C2×Dic6C22×D311yescharacteristic
587C3×Q16—24no—
588C3×Q16—34no—
589C3×Q16C22×D314yescomplemented
590C3×Q16C22×D314yescomplemented
591C3×SD16—34no—
592C3×SD16—34no—
593C3×SD16—34no—
594C3×SD16—34no—
595C3×D8—34no—
596C3×M16—34no—
597C2×C3×C8—21no—
598C2×C3×C8—31no—
599C2×C3×C8—31no—
600C2×C3×C8—34no—
601C2×C3×C8C22×D311yescharacteristic
602C2×C3×C8C22×D311yescharacteristic
603#216—34no—
604#216—34no—
605#216—64no—
606#216C22×D314yescomplemented
607#215—34no—
608#215—34no—
609#215—34no—
610#215—34no—
611#215—64no—
612#215C22×D314yescomplemented
613#215C22×D314yescomplemented
614#215C22×D314yescomplemented
615#214—34no—
616#214—34no—
617#214—34no—
618#213—34no—
619#213—34no—
620#213—34no—
621#208—34no—
622C2×C3⋊C8—31no—
623C2×C3⋊C8—31no—
624C2×C3⋊C8—34no—
625C2×C3⋊C8—61no—
626C2×C3⋊C8C22×D311yescharacteristic
627C2×C3⋊C8C22×D311yescharacteristic
628D24—34no—
629D24C22×D314yescomplemented
630#204—34no—
631#204—34no—
632#204—34no—
633#204—34no—
634#204—34no—
635#204—64no—
636#204C22×D314yescomplemented
637ΓL(1,𝔽25)—34no—
638ΓL(1,𝔽25)—34no—
639ΓL(1,𝔽25)—34no—
640ΓL(1,𝔽25)—64no—
641ΓL(1,𝔽25)C22×D314yescomplemented
642D3×C8—34no—
643D3×C8—34no—
644D3×C8—34no—
645D3×C8C22×D314yescomplemented
646C22×C32C22×D411yescharacteristic
647C2×C3⋊D3—22no—
648C2×C3⋊D3—22no—
649C2×C3⋊D3—42no—
650C2×C3⋊D3C22×D412yes—
651C2×C3×D3—22no—
652C2×C3×D3—22no—
653C2×C3×D3—22no—
654C2×C3×D3—22no—
655C2×C3×D3—22no—
656C2×C3×D3—42no—
657C2×C3×D3—42no—
658C2×C3×D3—42no—
659C2×C3×D3C22×D412yes—
660C2×C3×D3C22×D412yes—
661D32—84no—
662D32—84no—
663D32—84no—
664C32×C4—22no—
665C32×C4—22no—
666C32×C4C22×D411yescharacteristic
667C32×C4C2511yescharacteristic
668C3⋊Dic3—22no—
669C3⋊Dic3C22×D412yes—
670C3×Dic3—22no—
671C3×Dic3C22×D412yes—
672C3×Dic3C22×D412yes—
6732−1+4—98no—
6742−1+4—184no—
675H(5,𝔽2)—98no—
676H(5,𝔽2)—184no—
677C2×#41—31no—
678C2×#41—31no—
679C2×#41—31no—
680C2×#41—91no—
681C2×#41—91no—
682C2×#41—91no—
683C2×#41—91no—
684C2×#41—181no—
685C2×#41—181no—
686C2×#41—181no—
687C2×#41—181no—
688C22×Q8—31no—
689C22×Q8—91no—
690C22×Q8—91no—
691C22×Q8—181no—
692C22×D4—91no—
693C22×D4—91no—
694C22×D4—91no—
695C22×D4—181no—
696C22×D4—181no—
697C22×D4—181no—
698#137—38no—
699#137—98no—
700#137—98no—
701AGL(1,ℤ/8)—98no—
702AGL(1,ℤ/8)—98no—
703AGL(1,ℤ/8)—98no—
704#135—38no—
705#135—98no—
706#135—98no—
707C2×Q16—31no—
708C2×Q16—91no—
709C2×Q16D3211yescharacteristic, complemented
710C2×SD16—31no—
711C2×SD16—31no—
712C2×SD16—31no—
713C2×SD16—31no—
714C2×SD16—98no—
715C2×SD16—91no—
716C2×SD16—91no—
717C2×SD16—91no—
718C2×SD16—98no—
719C2×SD16—98no—
720C2×SD16—91no—
721C2×SD16—91no—
722C2×SD16—91no—
723C2×D8—31no—
724C2×D8—91no—
725C2×D8—91no—
726#131—98no—
727C2×M16—31no—
728C2×M16—91no—
729C2×M16—91no—
730C22×C8—31no—
731C22×C8—91no—
732C22×C8—91no—
733C23×C3—31no—
734C23×C3—31no—
735C23×C3—61no—
736C23×C3—61no—
737C23×C3—61no—
738C22×D3—21no—
739C22×D3—21no—
740C22×D3—21no—
741C22×D3—31no—
742C22×D3—31no—
743C22×D3—61no—
744C22×D3—64no—
745C22×D3—64no—
746C22×D3—64no—
747C22×D3—64no—
748C22×D3—61no—
749C22×D3—61no—
750C22×D3—64no—
751C22×D3—64no—
752C22×D3—121no—
753C22×D3—242no—
754C22×D3—242no—
755C22×D3—242no—
756C22×D3—242no—
757C22×D3—242no—
758C22×D3—242no—
759C22×D3D3×D411yescharacteristic
760C22×D3D3×D411yescharacteristic
761C3×Q8—21no—
762C3×Q8—21no—
763C3×Q8—21no—
764C3×Q8—21no—
765C3×Q8—22no—
766C3×Q8—22no—
767C3×Q8—32no—
768C3×Q8—41no—
769C3×Q8—41no—
770C3×Q8—64no—
771C3×Q8—61no—
772C3×Q8C23×D312yes—
773C3×Q8C23×D312yes—
774C3×Q8C23×D312yes—
775C3×Q8C23×D312yes—
776C3×D4—32no—
777C3×D4—32no—
778C3×D4—32no—
779C3×D4—64no—
780C3×D4—64no—
781C3×D4—64no—
782C3×D4—61no—
783C3×D4—61no—
784C3×D4—61no—
785C2×C3×C4—21no—
786C2×C3×C4—21no—
787C2×C3×C4—21no—
788C2×C3×C4—21no—
789C2×C3×C4—21no—
790C2×C3×C4—31no—
791C2×C3×C4—31no—
792C2×C3×C4—32no—
793C2×C3×C4—32no—
794C2×C3×C4—32no—
795C2×C3×C4—32no—
796C2×C3×C4—41no—
797C2×C3×C4—41no—
798C2×C3×C4—64no—
799C2×C3×C4—64no—
800C2×C3×C4—64no—
801C2×C3×C4—64no—
802C2×C3×C4—61no—
803C2×C3×C4C23×D311yescharacteristic
804C2×C3×C4C23×D311yescharacteristic
805#67—34no—
806#67—34no—
807#67—34no—
808#67—34no—
809#67—64no—
810#67—64no—
811#67—64no—
812#67—64no—
813#67—64no—
814#67—64no—
815#67—64no—
816C2×Dic3—21no—
817C2×Dic3—31no—
818C2×Dic3—31no—
819C2×Dic3—61no—
820C2×Dic3—64no—
821C2×Dic3—64no—
822C2×Dic3—61no—
823C2×Dic3—61no—
824C2×Dic3—64no—
825C2×Dic3—121no—
826C2×Dic3D3×D411yescharacteristic
827C2×Dic3D3×D411yescharacteristic
828D12—24no—
829D12—24no—
830D12—24no—
831D12—21no—
832D12—21no—
833D12—21no—
834D12—34no—
835D12—34no—
836D12—32no—
837D12—32no—
838D12—62no—
839D12—64no—
840D12—64no—
841D12—64no—
842D12—64no—
843D12—64no—
844D12—61no—
845D12—61no—
846D12—121no—
847D12—124no—
848D12C23×D312yes—
849D12C23×D312yes—
850D12C23×D312yes—
851C4×D3—24no—
852C4×D3—24no—
853C4×D3—24no—
854C4×D3—24no—
855C4×D3—32no—
856C4×D3—32no—
857C4×D3—32no—
858C4×D3—32no—
859C4×D3—62no—
860C4×D3—62no—
861C4×D3—64no—
862C4×D3—64no—
863C4×D3—64no—
864C4×D3—64no—
865C4×D3—64no—
866C4×D3—64no—
867C4×D3—64no—
868C4×D3—124no—
869C4×D3—124no—
870C4×D3D3×D412yes—
871C4×D3D3×D412yes—
872C4×D3C23×D312yes—
873C4×D3C23×D312yes—
874Dic6—21no—
875Dic6—24no—
876Dic6—34no—
877Dic6—34no—
878Dic6—32no—
879Dic6—32no—
880Dic6—62no—
881Dic6—64no—
882Dic6—64no—
883Dic6—64no—
884Dic6—61no—
885Dic6—61no—
886Dic6—64no—
887Dic6—124no—
888Dic6—121no—
889Dic6C23×D312yes—
890C3×C8—22no—
891C3×C8—32no—
892C3×C8—32no—
893C3×C8C23×D312yes—
894C3×C8C23×D312yes—
895C3⋊C8—32no—
896C3⋊C8—32no—
897C3⋊C8—62no—
898C3⋊C8C23×D312yes—
899C3⋊C8C23×D312yes—
900C2×C32#57712yescomplemented
901C2×C32C23×D411yescharacteristic
902C3⋊D3—22no—
903C3⋊D3—42no—
904C3×D3—22no—
905C3×D3—22no—
906C3×D3—42no—
907C3×D3—42no—
908C3×D3—42no—
909C24—181no—
910C24—181no—
911C24—181no—
912#41—34no—
913#41—34no—
914#41—34no—
915#41—62no—
916#41—62no—
917#41—62no—
918#41—94no—
919#41—94no—
920#41—94no—
921#41—94no—
922#41—94no—
923#41—182no—
924#41—188no—
925#41—188no—
926#41—188no—
927#41—182no—
928#41—182no—
929#41—188no—
930C2×Q8—34no—
931C2×Q8—31no—
932C2×Q8—61no—
933C2×Q8—62no—
934C2×Q8—91no—
935C2×Q8—94no—
936C2×Q8—94no—
937C2×Q8—91no—
938C2×Q8—181no—
939C2×Q8—181no—
940C2×Q8—182no—
941C2×Q8—188no—
942C2×Q8—182no—
943C2×Q8C2×D3211yescharacteristic
944C2×Q8C2×D3211yescharacteristic
945C2×D4—31no—
946C2×D4—31no—
947C2×D4—31no—
948C2×D4—61no—
949C2×D4—61no—
950C2×D4—61no—
951C2×D4—94no—
952C2×D4—94no—
953C2×D4—91no—
954C2×D4—91no—
955C2×D4—94no—
956C2×D4—91no—
957C2×D4—91no—
958C2×D4—181no—
959C2×D4—182no—
960C2×D4—182no—
961C2×D4—181no—
962C2×D4—181no—
963C2×D4—188no—
964C2×D4—188no—
965C2×D4—181no—
966C2×D4—182no—
967C2×D4—181no—
968C2×D4—188no—
969C2×D4—181no—
970C22×C4—31no—
971C22×C4—31no—
972C22×C4—61no—
973C22×C4—61no—
974C22×C4—61no—
975C22×C4—61no—
976C22×C4—91no—
977C22×C4—181no—
978C22×C4—181no—
979C22×C4—181no—
980C22×C4—181no—
981C22×C4—181no—
982Q16—34no—
983Q16—94no—
984Q16C2×D3214yescomplemented
985SD16—34no—
986SD16—34no—
987SD16—34no—
988SD16—34no—
989SD16—94no—
990SD16—94no—
991SD16—94no—
992SD16—94no—
993SD16—94no—
994SD16—94no—
995D8—34no—
996D8—94no—
997D8—94no—
998M16—34no—
999M16—94no—
1000M16—94no—
1001C2×C8—31no—
1002C2×C8—31no—
1003C2×C8—34no—
1004C2×C8—94no—
1005C2×C8—94no—
1006C2×C8—91no—
1007C2×C8C2×D3211yescharacteristic
1008C22×C3—21no—
1009C22×C3—32no—
1010C22×C3—32no—
1011C22×C3—62no—
1012C22×C3—62no—
1013C22×C3—62no—
1014C22×C3—62no—
1015C22×C3—62no—
1016C22×C3—122no—
1017C22×C3—122no—
1018C22×C3—122no—
1019C22×C3C2×D3×D411yescharacteristic
1020C22×C3C2×D3×D411yescharacteristic
1021C2×D3—22no—
1022C2×D3—22no—
1023C2×D3—22no—
1024C2×D3—22no—
1025C2×D3—22no—
1026C2×D3—32no—
1027C2×D3—32no—
1028C2×D3—42no—
1029C2×D3—42no—
1030C2×D3—42no—
1031C2×D3—62no—
1032C2×D3—62no—
1033C2×D3—62no—
1034C2×D3—62no—
1035C2×D3—62no—
1036C2×D3—122no—
1037C2×D3—122no—
1038C2×D3—122no—
1039C2×D3—122no—
1040C2×D3—242no—
1041C2×D3—244no—
1042C2×D3—244no—
1043C2×D3—244no—
1044C2×D3—244no—
1045C2×D3—244no—
1046C2×D3—244no—
1047C2×D3C2×D3×D412yes—
1048C2×D3C2×D3×D412yes—
1049C3×C4—22no—
1050C3×C4—22no—
1051C3×C4—22no—
1052C3×C4—22no—
1053C3×C4—21no—
1054C3×C4—21no—
1055C3×C4—32no—
1056C3×C4—32no—
1057C3×C4—42no—
1058C3×C4—42no—
1059C3×C4—62no—
1060C3×C4C2×D3×D411yescharacteristic
1061C3×C4C2×D3×D411yescharacteristic
1062C3×C4C24×D311yescharacteristic
1063C3×C4C24×D311yescharacteristic
1064Dic3—22no—
1065Dic3—32no—
1066Dic3—32no—
1067Dic3—62no—
1068Dic3—62no—
1069Dic3—62no—
1070Dic3—122no—
1071Dic3C2×D3×D412yes—
1072Dic3C2×D3×D412yes—
1073C32C2×#57711yescharacteristic, complemented, Sylow
1074C23—31no—
1075C23—31no—
1076C23—61no—
1077C23—61no—
1078C23—61no—
1079C23—91no—
1080C23—184no—
1081C23—184no—
1082C23—184no—
1083C23—181no—
1084C23—722no—
1085C23—722no—
1086C23—722no—
1087Q8—21no—
1088Q8—21no—
1089Q8—32no—
1090Q8—64no—
1091Q8—61no—
1092Q8—94no—
1093Q8—92no—
1094Q8—184no—
1095Q8—184no—
1096Q8—181no—
1097Q8C22×D3212yes—
1098Q8C22×D3212yes—
1099D4—32no—
1100D4—32no—
1101D4—32no—
1102D4—64no—
1103D4—64no—
1104D4—64no—
1105D4—61no—
1106D4—61no—
1107D4—61no—
1108D4—94no—
1109D4—94no—
1110D4—94no—
1111D4—92no—
1112D4—184no—
1113D4—184no—
1114D4—184no—
1115D4—184no—
1116D4—184no—
1117D4—184no—
1118D4—181no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—31no—
1122C2×C4—31no—
1123C2×C4—32no—
1124C2×C4—32no—
1125C2×C4—32no—
1126C2×C4—32no—
1127C2×C4—64no—
1128C2×C4—64no—
1129C2×C4—64no—
1130C2×C4—64no—
1131C2×C4—61no—
1132C2×C4—91no—
1133C2×C4—92no—
1134C2×C4—92no—
1135C2×C4—184no—
1136C2×C4—184no—
1137C2×C4—184no—
1138C2×C4—184no—
1139C2×C4—184no—
1140C2×C4—181no—
1141C2×C4C22×D3211yescharacteristic
1142C8—32no—
1143C8—32no—
1144C8—92no—
1145C8C22×D3212yes—
1146C2×C3—21no—
1147C2×C3—22no—
1148C2×C3—62no—
1149C2×C3—62no—
1150C2×C3—122no—
1151C2×C3—122no—
1152C2×C3—122no—
1153C2×C3#577012yescomplemented
1154C2×C3#577812yescomplemented
1155C2×C3C22×D3×D411yescharacteristic
1156C2×C3C22×D3×D411yescharacteristic
1157D3—22no—
1158D3—22no—
1159D3—42no—
1160D3—42no—
1161D3—42no—
1162D3—62no—
1163D3—62no—
1164D3—122no—
1165D3—122no—
1166D3—122no—
1167D3—242no—
1168C22—32no—
1169C22—32no—
1170C22—62no—
1171C22—62no—
1172C22—62no—
1173C22—62no—
1174C22—62no—
1175C22—92no—
1176C22—122no—
1177C22—122no—
1178C22—122no—
1179C22—182no—
1180C22—182no—
1181C22—362no—
1182C22—724no—
1183C22—724no—
1184C22—724no—
1185C22D32×D411yescharacteristic
1186C4—22no—
1187C4—22no—
1188C4—32no—
1189C4—32no—
1190C4—62no—
1191C4—92no—
1192C4—182no—
1193C4D32×D411yescharacteristic
1194C4C23×D3211yescharacteristic
1195C3—21no—
1196C3C2×#577011yescharacteristic, complemented
1197C3C2×#577811yescharacteristic, complemented
1198C2—62no—
1199C2—62no—
1200C2—122no—
1201C2—122no—
1202C2—122no—
1203C2—182no—
1204C2—362no—
1205C2#1059477012yesdirect product factor
1206C2C2×D32×D411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
hypercenterC2×Q16D32
hypocenterC32C2×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#64320C2semidirect
2. C2×#64315C2semidirect
3. C2×#64127C2semidirect
4. C2×C3×#919C2semidirect
5. C2×C3×#918C2semidirect
6. C2×#63950C2semidirect
7. C2×#63947C2semidirect
8. C2×#63943C2semidirect
9. C2×#63940C2semidirect
10. C2×#63939C2semidirect
11. C2×D3×#215C2semidirect
12. #10594770C2direct (N × H)
13. C2×#63804C2semidirect
14. C2×#63798C2semidirect
15. C2×#63795C2semidirect
16. C2×D3×#204C2semidirect
20. C2×Q8×C3⋊D3C22semidirect
23. C2×C3×#239C22semidirect
24. C2×C3×D3×Q8C22semidirect
26. #64320C22semidirect
28. #64315C22semidirect
39. C2×#3796C22semidirect
41. C2×#3795C22semidirect
43. C2×D3×Dic6C22semidirect
44. C2×C32×Q16C22semidirect
45. C2×#3756C22semidirect
46. C2×#3755C22semidirect
47. #64127C22semidirect
48. C2×#3744C22semidirect
49. C2×#3743C22semidirect
50. C2×C3×#216C22semidirect
51. C2×C3×#215C22semidirect
52. C2×C3×#215C22semidirect
53. C2×C3×#215C22semidirect
54. C3×#919C22semidirect
55. C3×#918C22semidirect
56. C2×C3×D24C22semidirect
57. C2×C3×#204C22semidirect
58. C2×C3×ΓL(1,𝔽25)C22semidirect
59. C2×C3×D3×C8C22semidirect
60. #63950C22semidirect
61. #63947C22semidirect
62. #63943C22semidirect
63. #63940C22semidirect
64. #63939C22semidirect
65. D3×#215C22semidirect
66. C2×#3717C22semidirect
67. C2×#3716C22semidirect
68. C2×#3716C22semidirect
69. C2×#3715C22semidirect
70. C2×#3714C22semidirect
71. C2×#3713C22semidirect
72. C2×#3711C22semidirect
73. C2×#3710C22semidirect
74. C2×D3×C3⋊C8C22semidirect
75. #63804C22semidirect
76. #63798C22semidirect
77. #63795C22semidirect
78. D3×#204C22semidirect
92. C2×#919D3semidirect
97. C2×#918D3semidirect
120. Q8×C3⋊D3C23semidirect
133. C3×#239C23semidirect
135. C3×D3×Q8C23semidirect
178. #3796C23semidirect
181. #3795C23semidirect
184. D3×Dic6C23semidirect
185. C32×Q16C23semidirect
187. #3756C23semidirect
188. #3755C23semidirect
190. #3744C23semidirect
191. #3743C23semidirect
192. C3×#216C23semidirect
193. C3×#215C23semidirect
194. C3×#215C23semidirect
195. C3×#215C23semidirect
198. C3×D24C23semidirect
199. C3×#204C23semidirect
200. C3×ΓL(1,𝔽25)C23semidirect
201. C3×D3×C8C23semidirect
202. #3717C23semidirect
203. #3716C23semidirect
204. #3716C23semidirect
205. #3715C23semidirect
206. #3714C23semidirect
207. #3713C23semidirect
208. #3711C23semidirect
209. #3710C23semidirect
210. D3×C3⋊C8C23semidirect
231. C2×#239C2×D3semidirect
237. C2×D3×Q8C2×D3semidirect
268. C2×C3×Q16C2×D3semidirect
269. C2×C3×Q16C2×D3semidirect
283. C2×#216C2×D3semidirect
290. C2×#215C2×D3semidirect
291. C2×#215C2×D3semidirect
292. C2×#215C2×D3semidirect
302. #919C2×D3semidirect
307. #918C2×D3semidirect
321. C2×D24C2×D3semidirect
329. C2×#204C2×D3semidirect
335. C2×ΓL(1,𝔽25)C2×D3semidirect
339. C2×D3×C8C2×D3semidirect
490. #239C22×D3semidirect
501. D3×Q8C22×D3semidirect
589. C3×Q16C22×D3semidirect
590. C3×Q16C22×D3semidirect
606. #216C22×D3semidirect
612. #215C22×D3semidirect
613. #215C22×D3semidirect
614. #215C22×D3semidirect
629. D24C22×D3semidirect
636. #204C22×D3semidirect
641. ΓL(1,𝔽25)C22×D3semidirect
645. D3×C8C22×D3semidirect
709. C2×Q16D32semidirect
900. C2×C32#577semidirect
984. Q16C2×D32semidirect
1073. C32C2×#577semidirect
1153. C2×C3#5770semidirect
1154. C2×C3#5778semidirect
1196. C3C2×#5770semidirect
1197. C3C2×#5778semidirect
1205. C2#10594770direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643202
C2×#643152
C2×#641272
C2×C3×#9192
C2×C3×#9182
C2×#639502
C2×#639472
C2×#639432
C2×#639402
C2×#639392
C2×D3×#2152
#105947702
C2×#638042
C2×#637982
C2×#637952
C2×D3×#2042
C2×#57783
C2×#57703