Finite Group Databasebeta

← C2×#10594746 #11918754

Subgroups — C2×#10594746 #11918754

Order 1152.

3117 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C211yesmaximal, characteristic, complemented
2C2×#64312C211yesmaximal, characteristic, complemented
3C2×#64123C211yesmaximal, characteristic, complemented
4C2×C3×#916C211yesmaximal, characteristic, complemented
5C2×C3×#915C211yesmaximal, characteristic, complemented
6C2×#63949C211yesmaximal, characteristic, complemented
7C2×#63948C211yesmaximal, characteristic, complemented
8C2×#63945C211yesmaximal, characteristic, complemented
9C2×#63937C211yesmaximal, characteristic, complemented
10C2×#63935C211yesmaximal, characteristic, complemented
11C2×#63925C211yesmaximal, characteristic, complemented
12#10594746C2116yesmaximal, direct product factor
13C2×#63811C211yesmaximal, characteristic, complemented
14C2×#63808C211yesmaximal, characteristic, complemented
15C2×#63794C211yesmaximal, characteristic, complemented
16C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
17C2×#5777—31nomaximal
18C2×#5768—31nomaximal
19C2×#3832C2211yescharacteristic
20C2×D4×C3⋊D3C2211yescharacteristic, complemented
21C2×C3×#239C2211yescharacteristic, complemented
22C2×C3×D3×Q8C2211yescharacteristic, complemented
23C2×C3×#237C2211yescharacteristic
24C2×C3×#237C2211yescharacteristic, complemented
25C2×#3811—21no—
26C22×#624—21no—
27C2×#3804—21no—
28C2×#3804—21no—
29D3×#239—24no—
30D3×#239C2218yescomplemented
31#64312—24no—
32#64312C2218yescomplemented
33C2×D3×D12—21no—
34C2×D3×D12C2211yescharacteristic, complemented
35C2×C4×D32—21no—
36C2×C4×D32C2211yescharacteristic
37C2×#3799—21no—
38C2×#3799C2211yescharacteristic
39C2×#3799C2211yescharacteristic, complemented
40C2×#3799C2211yescharacteristic, complemented
41C2×#3797C2211yescharacteristic, complemented
42C2×#3796—21no—
43C2×#3796C2211yescharacteristic
44C2×C32×SD16C2211yescharacteristic, complemented
45C2×#3755C2211yescharacteristic, complemented
46C2×#3753C2211yescharacteristic, complemented
47#64123C2218yescomplemented
48C2×#3745C2211yescharacteristic, complemented
49C2×#3743C2211yescharacteristic, complemented
50C2×C3×#216C2211yescharacteristic, complemented
51C2×C3×#216C2211yescharacteristic, complemented
52C2×C3×#214C2211yescharacteristic, complemented
53C2×C3×#213C2211yescharacteristic, complemented
54C3×#916C2218yescomplemented
55C3×#915C2218yescomplemented
56C2×C3×Dic12C2211yescharacteristic, complemented
57C2×C3×#204C2211yescharacteristic, complemented
58C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
59C2×C3×D3×C8C2211yescharacteristic, complemented
60#63949C2218yescomplemented
61#63948C2218yescomplemented
62#63945C2218yescomplemented
63#63937C2218yescomplemented
64#63935C2218yescomplemented
65#63925C2218yescomplemented
66C2×#3718C2211yescharacteristic, complemented
67C2×#3717C2211yescharacteristic, complemented
68C2×#3717C2211yescharacteristic, complemented
69C2×#3717C2211yescharacteristic, complemented
70C2×#3715C2211yescharacteristic, complemented
71C2×#3714C2211yescharacteristic, complemented
72C2×#3712C2211yescharacteristic, complemented
73C2×#3711C2211yescharacteristic, complemented
74C2×D3×C3⋊C8C2211yescharacteristic, complemented
75#63811C2218yescomplemented
76#63808C2218yescomplemented
77#63794C2218yescomplemented
78D3×ΓL(1,𝔽25)C2218yescomplemented
79C2×D3×#41—31no—
80C2×D3×#41—31no—
81C2×D3×#41—31no—
82C22×#239—31no—
83C2×C3×#137—31no—
84C2×C3×#135—31no—
85C2×#950—31no—
86C2×#950—31no—
87C2×#949—31no—
88C2×#942—31no—
89#5777—316no—
90#5768—316no—
91C2×#919—31no—
92C2×#919—31no—
93C2×#918—31no—
94C2×#918—31no—
95C2×#918—31no—
96C2×#918—31no—
97C2×#916—31no—
98C2×#916D311yescharacteristic, complemented
99C2×#915—31no—
100C2×#915D311yescharacteristic, complemented
101C2×#914—31no—
102C2×#914—31no—
103C2×#914—31no—
104C2×#914—31no—
105C2×#914—61no—
106C2×#911—31no—
107C2×#911—31no—
108C2×#908—31no—
109C2×D3×M16—31no—
110C2×#904—31no—
111C22×ΓL(1,𝔽25)—31no—
112C23×C3⋊D3—21no—
113C22×D32—21no—
114C22×D32D411yescharacteristic
115C2×C32×Q8C2311yescharacteristic
116C2×C32×D4C2311yescharacteristic
117C2×#638—21no—
118#3832—22no—
119#3832C2314yes—
120D4×C3⋊D3—22no—
121D4×C3⋊D3C2314yescomplemented
122C2×C4⋊(C3⋊D3)—21no—
123C2×C4⋊(C3⋊D3)C2311yescharacteristic
124C2×C4⋊(C3⋊D3)C2311yescharacteristic
125C2×C4×C3⋊D3—21no—
126C2×C4×C3⋊D3C2311yescharacteristic
127C2×C3×#67—21no—
128C2×C3×#67—21no—
129C22×C3×Dic3—21no—
130C22×C3×Dic3—21no—
131C3×#239—22no—
132C3×#239C2314yescomplemented
133C3×D3×Q8—22no—
134C3×D3×Q8C2314yescomplemented
135C3×#237—22no—
136C3×#237—22no—
137C3×#237C2314yes—
138C3×#237C2314yescomplemented
139C2×C3×D12—21no—
140C2×C3×D12C2311yescharacteristic
141C2×C3×C4×D3—21no—
142C2×C3×C4×D3—21no—
143C2×C3×C4×D3C2311yescharacteristic
144C2×C3×C4×D3C2311yescharacteristic
145C2×C3×Dic6—21no—
146C2×C3×Dic6C2311yescharacteristic
147C2×C3×Dic6C2311yescharacteristic
148C2×C3×Dic6C2311yescharacteristic
149#3811—28no—
150C2×#627—21no—
151C2×#626—21no—
152C2×#626—21no—
153C2×#626—21no—
154C2×#626—21no—
155C2×#626—21no—
156C2×#624—21no—
157C2×#624—21no—
158C2×#624—21no—
159C2×#624—21no—
160C2×#624—28no—
161C2×#624D411yescharacteristic
162#3804—28no—
163#3804—28no—
164C2×D3×Dic3—21no—
165C2×D3×Dic3D411yescharacteristic
166C2×D3×Dic3D411yescharacteristic
167D3×D12—28no—
168D3×D12—22no—
169D3×D12C2314yescomplemented
170C4×D32—28no—
171C4×D32D414yes—
172C4×D32C2314yes—
173#3799—22no—
174#3799—22no—
175#3799—22no—
176#3799—28no—
177#3799C2314yes—
178#3799C2314yescomplemented
179#3799C2314yescomplemented
180#3797—22no—
181#3797C2314yescomplemented
182#3796—22no—
183#3796—28no—
184#3796C2314yes—
185C32×SD16C2314yescomplemented
186C2×C32×C8C2311yescharacteristic
187#3755C2314yescomplemented
188#3753C2314yescomplemented
189C2×C3⋊(C3⋊C8)C2311yescharacteristic
190#3745C2314yescomplemented
191#3743C2314yescomplemented
192C3×#216C2314yescomplemented
193C3×#216C2314yescomplemented
194C3×#214C2314yescomplemented
195C3×#213C2314yescomplemented
196C2×C3×C3⋊C8C2311yescharacteristic
197C2×C3×C3⋊C8C2311yescharacteristic
198C3×Dic12C2314yescomplemented
199C3×#204C2314yescomplemented
200C3×ΓL(1,𝔽25)C2314yescomplemented
201C3×D3×C8C2314yescomplemented
202#3718C2314yescomplemented
203#3717C2314yescomplemented
204#3717C2314yescomplemented
205#3717C2314yescomplemented
206#3715C2314yescomplemented
207#3714C2314yescomplemented
208#3712C2314yescomplemented
209#3711C2314yescomplemented
210D3×C3⋊C8C2314yescomplemented
211C2×#575—91noSylow
212C2×C3×#41—31no—
213C2×C3×#41—31no—
214C2×C3×#41—31no—
215C22×C3×Q8—31no—
216D3×#41—38no—
217D3×#41—38no—
218D3×#41—38no—
219D3×#41—64no—
220D3×#41—64no—
221D3×#41—64no—
222C2×#239—31no—
223C2×#239—31no—
224C2×#239—38no—
225C2×#239—31no—
226C2×#239—31no—
227C2×#239—31no—
228C2×#239—31no—
229C2×#239—61no—
230C2×#239—61no—
231C2×#239—61no—
232C2×#239—64no—
233C2×#239C2×D311yescharacteristic, complemented
234C2×D3×Q8—31no—
235C2×D3×Q8—31no—
236C2×D3×Q8C2×D311yescharacteristic, complemented
237C2×#237—31no—
238C2×#237—61no—
239C2×#237—61no—
240C2×#237—61no—
241C2×#237C2×D311yescharacteristic
242C2×#237C2×D311yescharacteristic, complemented
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—
256C22×D12—31no—
257C22×D12—61no—
258C22×C4×D3—31no—
259C22×C4×D3—31no—
260C22×C4×D3—61no—
261C22×C4×D3—61no—
262C22×C4×D3—61no—
263C22×C4×D3—61no—
264C3×#137—38no—
265C3×#135—38no—
266C2×C3×Q16—31no—
267C2×C3×Q16—31no—
268C2×C3×Q16—31no—
269C2×C3×SD16—21no—
270C2×C3×SD16—31no—
271C2×C3×SD16—31no—
272C2×C3×SD16C2×D311yescharacteristic, complemented
273C2×C3×SD16C2×D311yescharacteristic, complemented
274C2×C3×D8—31no—
275C2×C3×M16—31no—
276C22×C3×C8—31no—
277#950—38no—
278#950—38no—
279#949—38no—
280C2×#216—31no—
281C2×#216—31no—
282C2×#216C2×D311yescharacteristic, complemented
283C2×#216C2×D311yescharacteristic, complemented
284#942—38no—
285C2×#215—31no—
286C2×#215—31no—
287C2×#215—31no—
288C2×#215—31no—
289C2×#215—31no—
290C2×#215—31no—
291C2×#215—61no—
292C2×#214—31no—
293C2×#214C2×D311yescharacteristic, complemented
294C2×#213—31no—
295C2×#213—31no—
296C2×#213—31no—
297C2×#213—61no—
298C2×#213C2×D311yescharacteristic, complemented
299C2×#208—31no—
300C22×C3⋊C8—31no—
301#919—38no—
302#919—38no—
303#918—38no—
304#918—38no—
305#918—38no—
306#918—38no—
307#916—38no—
308#916C2×D318yescomplemented
309#915—38no—
310#915C2×D318yescomplemented
311#914—38no—
312#914—38no—
313#914—38no—
314#914—38no—
315#914—68no—
316#911—38no—
317#911—38no—
318#908—38no—
319D3×M16—38no—
320C2×Dic12C2×D311yescharacteristic, complemented
321#904—38no—
322C2×D24—31no—
323C2×D24—31no—
324C2×D24—31no—
325C2×D24—61no—
326C2×#204—31no—
327C2×#204—31no—
328C2×#204—31no—
329C2×#204C2×D311yescharacteristic, complemented
330C2×ΓL(1,𝔽25)—31no—
331C2×ΓL(1,𝔽25)—31no—
332C2×ΓL(1,𝔽25)—31no—
333C2×ΓL(1,𝔽25)—31no—
334C2×ΓL(1,𝔽25)—31no—
335C2×ΓL(1,𝔽25)—38no—
336C2×ΓL(1,𝔽25)—61no—
337C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
338C2×D3×C8—31no—
339C2×D3×C8C2×D311yescharacteristic, complemented
340C23×C32—21no—
341C22×C3⋊D3—21no—
342C22×C3⋊D3—21no—
343C22×C3⋊D3—24no—
344C22×C3⋊D3—44no—
345C22×C3⋊D3C2×D411yescharacteristic
346C22×C3×D3—21no—
347C22×C3×D3C2×D411yescharacteristic
348C22×C3×D3C2×D411yescharacteristic
349C2×D32—24no—
350C2×D32—42no—
351C2×D32—44no—
352C2×D32C2×D414yes—
353C32×Q8—21no—
354C32×Q8C2412yes—
355C32×D4—21no—
356C32×D4C2412yes—
357C2×C32×C4—21no—
358C2×C32×C4C2411yescharacteristic
359#638—24no—
360C2×C3⋊Dic3C2×D411yescharacteristic
361C4⋊(C3⋊D3)—24no—
362C4⋊(C3⋊D3)—21no—
363C4⋊(C3⋊D3)—21no—
364C4⋊(C3⋊D3)C2412yes—
365C4⋊(C3⋊D3)C2412yes—
366C4×C3⋊D3—24no—
367C4×C3⋊D3C2×D412yes—
368C4×C3⋊D3C2412yes—
369C3×#67—24no—
370C3×#67—24no—
371C2×C3×Dic3—21no—
372C2×C3×Dic3—21no—
373C2×C3×Dic3—21no—
374C2×C3×Dic3—24no—
375C2×C3×Dic3—24no—
376C2×C3×Dic3C2×D411yescharacteristic
377C2×C3×Dic3C2×D411yescharacteristic
378C3×D12—24no—
379C3×D12—21no—
380C3×D12C2412yes—
381C3×C4×D3—24no—
382C3×C4×D3—24no—
383C3×C4×D3C2×D412yes—
384C3×C4×D3C2×D412yes—
385C3×C4×D3C2412yes—
386C3×C4×D3C2412yes—
387C3×Dic6—21no—
388C3×Dic6—21no—
389C3×Dic6—21no—
390C3×Dic6—24no—
391C3×Dic6C2412yes—
392C3×Dic6C2412yes—
393C3×Dic6C2412yes—
394#627—24no—
395#626—24no—
396#626—24no—
397#626—24no—
398#626—24no—
399#626—24no—
400#624—24no—
401#624—24no—
402#624—24no—
403#624—24no—
404#624C2×D414yes—
405D3×Dic3—24no—
406D3×Dic3C2×D414yes—
407D3×Dic3C2×D414yes—
408C32×C8C2412yes—
409C3⋊(C3⋊C8)C2412yes—
410C3×C3⋊C8C2412yes—
411C3×C3⋊C8C2412yes—
412C22×#41—91no—
413C22×#41—91no—
414#575—916no—
415C2×#137—31no—
416C2×#137—91no—
417C2×#137—91no—
418C2×#137—91no—
419C2×AGL(1,ℤ/8)—91no—
420C2×AGL(1,ℤ/8)—91no—
421C2×AGL(1,ℤ/8)—91no—
422C2×AGL(1,ℤ/8)—91no—
423C2×#135—31no—
424C2×#135—91no—
425C2×#135—91no—
426C2×#135—91no—
427C22×M16—91no—
428C23×D3—31no—
429C23×D3—31no—
430C23×D3—61no—
431C23×D3—61no—
432C23×D3—61no—
433C23×D3—61no—
434C23×D3—121no—
435C3×#41—34no—
436C3×#41—34no—
437C3×#41—34no—
438C3×#41—62no—
439C3×#41—62no—
440C3×#41—62no—
441C2×C3×Q8—21no—
442C2×C3×Q8—34no—
443C2×C3×Q8—31no—
444C2×C3×Q8—31no—
445C2×C3×Q8—31no—
446C2×C3×Q8—61no—
447C2×C3×Q8—62no—
448C2×C3×Q8C22×D311yescharacteristic
449C2×C3×Q8C22×D311yescharacteristic
450C2×C3×D4—21no—
451C2×C3×D4—31no—
452C2×C3×D4—61no—
453C2×C3×D4—61no—
454C2×C3×D4—61no—
455C2×C3×D4C22×D311yescharacteristic
456C2×C3×D4C22×D311yescharacteristic
457C22×C3×C4—31no—
458C22×C3×C4—31no—
459C22×C3×C4—61no—
460C22×C3×C4—61no—
461C22×C3×C4—61no—
462C22×C3×C4—61no—
463C2×#67—21no—
464C2×#67—21no—
465C2×#67—61no—
466C2×#67—61no—
467C2×#67—61no—
468C2×#67—61no—
469C2×#67—61no—
470C2×#67—61no—
471C2×#67—61no—
472C2×#67—121no—
473C22×Dic3—21no—
474C22×Dic3—21no—
475C22×Dic3—31no—
476C22×Dic3—31no—
477C22×Dic3—61no—
478#239—22no—
479#239—34no—
480#239—34no—
481#239—34no—
482#239—34no—
483#239—34no—
484#239—34no—
485#239—64no—
486#239—68no—
487#239—68no—
488#239—62no—
489#239—62no—
490#239—62no—
491#239—62no—
492#239—62no—
493#239—62no—
494#239—122no—
495#239C22×D314yescomplemented
496D3×Q8—22no—
497D3×Q8—34no—
498D3×Q8—34no—
499D3×Q8—62no—
500D3×Q8—62no—
501D3×Q8C22×D314yescomplemented
502#237—22no—
503#237—22no—
504#237—34no—
505#237—62no—
506#237—68no—
507#237—68no—
508#237—68no—
509#237C22×D314yes—
510#237C22×D314yescomplemented
511D3×D4—34no—
512D3×D4—34no—
513D3×D4—34no—
514D3×D4—64no—
515D3×D4—68no—
516D3×D4—62no—
517D3×D4—62no—
518D3×D4—68no—
519D3×D4—68no—
520D3×D4—62no—
521D3×D4—122no—
522#235—34no—
523#235—34no—
524#235—34no—
525#235—68no—
526#235—62no—
527#235—62no—
528#235—62no—
529#235—68no—
530#235—68no—
531C2×D12—21no—
532C2×D12—31no—
533C2×D12—31no—
534C2×D12—31no—
535C2×D12—31no—
536C2×D12—34no—
537C2×D12—61no—
538C2×D12—61no—
539C2×D12—62no—
540C2×D12—68no—
541C2×D12—61no—
542C2×D12—61no—
543C2×D12—61no—
544C2×D12—61no—
545C2×D12—61no—
546C2×D12—61no—
547C2×D12—61no—
548C2×D12—121no—
549C2×D12C22×D311yescharacteristic
550C2×C4×D3—21no—
551C2×C4×D3—21no—
552C2×C4×D3—31no—
553C2×C4×D3—31no—
554C2×C4×D3—31no—
555C2×C4×D3—31no—
556C2×C4×D3—31no—
557C2×C4×D3—31no—
558C2×C4×D3—34no—
559C2×C4×D3—34no—
560C2×C4×D3—34no—
561C2×C4×D3—34no—
562C2×C4×D3—61no—
563C2×C4×D3—68no—
564C2×C4×D3—68no—
565C2×C4×D3—68no—
566C2×C4×D3—68no—
567C2×C4×D3—61no—
568C2×C4×D3—61no—
569C2×C4×D3—61no—
570C2×C4×D3—61no—
571C2×C4×D3—61no—
572C2×C4×D3—61no—
573C2×C4×D3—61no—
574C2×C4×D3—61no—
575C2×C4×D3—61no—
576C2×C4×D3—61no—
577C2×C4×D3—61no—
578C2×C4×D3—121no—
579C2×C4×D3C22×D311yescharacteristic
580C2×C4×D3C22×D311yescharacteristic
581C2×Dic6—21no—
582C2×Dic6—61no—
583C2×Dic6—61no—
584C2×Dic6C22×D311yescharacteristic
585C2×Dic6C22×D311yescharacteristic
586C2×Dic6C22×D311yescharacteristic
587C3×Q16—34no—
588C3×Q16—34no—
589C3×Q16—34no—
590C3×SD16—24no—
591C3×SD16—34no—
592C3×SD16—34no—
593C3×SD16C22×D314yescomplemented
594C3×SD16C22×D314yescomplemented
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#216C22×D314yescomplemented
606#216C22×D314yescomplemented
607#215—34no—
608#215—34no—
609#215—34no—
610#215—34no—
611#215—34no—
612#215—34no—
613#215—64no—
614#214—34no—
615#214C22×D314yescomplemented
616#213—34no—
617#213—34no—
618#213—34no—
619#213—64no—
620#213C22×D314yescomplemented
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
628Dic12C22×D314yescomplemented
629D24—34no—
630D24—34no—
631D24—34no—
632D24—64no—
633#204—34no—
634#204—34no—
635#204—34no—
636#204C22×D314yescomplemented
637ΓL(1,𝔽25)—34no—
638ΓL(1,𝔽25)—34no—
639ΓL(1,𝔽25)—34no—
640ΓL(1,𝔽25)—34no—
641ΓL(1,𝔽25)—34no—
642ΓL(1,𝔽25)—64no—
643ΓL(1,𝔽25)C22×D314yescomplemented
644D3×C8—34no—
645D3×C8C22×D314yescomplemented
646C22×C32—22no—
647C22×C32—42no—
648C22×C32C22×D411yescharacteristic
649C2×C3⋊D3—22no—
650C2×C3⋊D3—22no—
651C2×C3⋊D3—22no—
652C2×C3⋊D3—48no—
653C2×C3⋊D3—42no—
654C2×C3⋊D3—42no—
655C2×C3⋊D3C22×D412yes—
656C2×C3×D3—22no—
657C2×C3×D3—22no—
658C2×C3×D3—22no—
659C2×C3×D3—42no—
660C2×C3×D3C22×D412yes—
661C2×C3×D3C22×D412yes—
662D32—44no—
663D32—48no—
664C32×C4—22no—
665C32×C4C22×D411yescharacteristic
666C32×C4C2511yescharacteristic
667C3⋊Dic3C22×D412yes—
668C3×Dic3—22no—
669C3×Dic3—22no—
670C3×Dic3—22no—
671C3×Dic3C22×D412yes—
672C3×Dic3C22×D412yes—
673C2×#41—31no—
674C2×#41—31no—
675C2×#41—31no—
676C2×#41—91no—
677C2×#41—91no—
678C2×#41—91no—
679C2×#41—91no—
680C2×#41—98no—
681C2×#41—98no—
682C2×#41—91no—
683C2×#41—181no—
684C2×#41—181no—
685C2×#41—181no—
686C2×#41—181no—
687C2×#41—184no—
688C2×#41—184no—
689C22×Q8—31no—
690C22×Q8—91no—
691C22×D4—91no—
692C22×D4—91no—
693C22×D4—181no—
694C22×D4—181no—
695C23×C4—91no—
696C23×C4—181no—
697C23×C4—181no—
698#137—38no—
699#137—98no—
700#137—98no—
701#137—98no—
702AGL(1,ℤ/8)—98no—
703AGL(1,ℤ/8)—98no—
704AGL(1,ℤ/8)—98no—
705AGL(1,ℤ/8)—98no—
706#135—38no—
707#135—98no—
708#135—98no—
709#135—98no—
710C2×Q16—31no—
711C2×Q16—31no—
712C2×Q16—31no—
713C2×Q16—91no—
714C2×SD16—31no—
715C2×SD16—31no—
716C2×SD16—91no—
717C2×SD16—91no—
718C2×SD16—91no—
719C2×SD16—91no—
720C2×SD16—91no—
721C2×SD16D3211yescharacteristic, complemented
722C2×D8—31no—
723C2×D8—91no—
724C2×D8—91no—
725C2×D8—91no—
726C2×M16—31no—
727C2×M16—91no—
728C2×M16—98no—
729C2×M16—91no—
730C2×M16—91no—
731C22×C8—31no—
732C22×C8—91no—
733C23×C3—21no—
734C23×C3—21no—
735C23×C3—31no—
736C23×C3—31no—
737C23×C3—41no—
738C23×C3—61no—
739C22×D3—21no—
740C22×D3—31no—
741C22×D3—31no—
742C22×D3—34no—
743C22×D3—34no—
744C22×D3—61no—
745C22×D3—64no—
746C22×D3—64no—
747C22×D3—64no—
748C22×D3—61no—
749C22×D3—61no—
750C22×D3—61no—
751C22×D3—61no—
752C22×D3—64no—
753C22×D3—124no—
754C22×D3—121no—
755C22×D3—121no—
756C22×D3—122no—
757C22×D3—122no—
758C22×D3—124no—
759C22×D3—124no—
760C22×D3—124no—
761C22×D3—124no—
762C22×D3—244no—
763C22×D3D3×D411yescharacteristic
764C22×D3D3×D411yescharacteristic
765C3×Q8—21no—
766C3×Q8—21no—
767C3×Q8—22no—
768C3×Q8—32no—
769C3×Q8—32no—
770C3×Q8—32no—
771C3×Q8—41no—
772C3×Q8—64no—
773C3×Q8—61no—
774C3×Q8—61no—
775C3×Q8—61no—
776C3×Q8C23×D312yes—
777C3×Q8C23×D312yes—
778C3×D4—21no—
779C3×D4—21no—
780C3×D4—22no—
781C3×D4—32no—
782C3×D4—41no—
783C3×D4—64no—
784C3×D4—64no—
785C3×D4—64no—
786C3×D4—61no—
787C3×D4C23×D312yes—
788C3×D4C23×D312yes—
789C2×C3×C4—21no—
790C2×C3×C4—21no—
791C2×C3×C4—21no—
792C2×C3×C4—31no—
793C2×C3×C4—31no—
794C2×C3×C4—32no—
795C2×C3×C4—32no—
796C2×C3×C4—32no—
797C2×C3×C4—32no—
798C2×C3×C4—41no—
799C2×C3×C4—64no—
800C2×C3×C4—64no—
801C2×C3×C4—64no—
802C2×C3×C4—64no—
803C2×C3×C4—61no—
804C2×C3×C4—61no—
805C2×C3×C4—61no—
806C2×C3×C4C23×D311yescharacteristic
807C2×C3×C4C23×D311yescharacteristic
808#67—24no—
809#67—24no—
810#67—64no—
811#67—64no—
812#67—64no—
813#67—64no—
814#67—64no—
815#67—64no—
816#67—64no—
817#67—124no—
818C2×Dic3—21no—
819C2×Dic3—21no—
820C2×Dic3—21no—
821C2×Dic3—24no—
822C2×Dic3—24no—
823C2×Dic3—31no—
824C2×Dic3—31no—
825C2×Dic3—34no—
826C2×Dic3—34no—
827C2×Dic3—61no—
828C2×Dic3—64no—
829C2×Dic3D3×D411yescharacteristic
830C2×Dic3D3×D411yescharacteristic
831D12—24no—
832D12—21no—
833D12—32no—
834D12—32no—
835D12—32no—
836D12—32no—
837D12—62no—
838D12—62no—
839D12—64no—
840D12—64no—
841D12—64no—
842D12—64no—
843D12—64no—
844D12—64no—
845D12—64no—
846D12—61no—
847D12—61no—
848D12—61no—
849D12—61no—
850D12—121no—
851D12—121no—
852D12—124no—
853D12C23×D312yes—
854C4×D3—24no—
855C4×D3—24no—
856C4×D3—34no—
857C4×D3—34no—
858C4×D3—32no—
859C4×D3—32no—
860C4×D3—32no—
861C4×D3—32no—
862C4×D3—34no—
863C4×D3—34no—
864C4×D3—62no—
865C4×D3—62no—
866C4×D3—64no—
867C4×D3—64no—
868C4×D3—64no—
869C4×D3—64no—
870C4×D3—64no—
871C4×D3—64no—
872C4×D3—64no—
873C4×D3—64no—
874C4×D3—64no—
875C4×D3—64no—
876C4×D3—64no—
877C4×D3—124no—
878C4×D3D3×D412yes—
879C4×D3D3×D412yes—
880C4×D3C23×D312yes—
881C4×D3C23×D312yes—
882Dic6—21no—
883Dic6—21no—
884Dic6—21no—
885Dic6—24no—
886Dic6—64no—
887Dic6—64no—
888Dic6C23×D312yes—
889Dic6C23×D312yes—
890Dic6C23×D312yes—
891C3×C8—22no—
892C3×C8—32no—
893C3×C8—32no—
894C3×C8C23×D312yes—
895C3×C8C23×D312yes—
896C3⋊C8—32no—
897C3⋊C8—32no—
898C3⋊C8—62no—
899C3⋊C8C23×D312yes—
900C3⋊C8C23×D312yes—
901C2×C32—42no—
902C2×C32#57512yescomplemented
903C2×C32C23×D411yescharacteristic
904C3⋊D3—22no—
905C3⋊D3—42no—
906C3⋊D3—42no—
907C3×D3—22no—
908C3×D3—22no—
909C3×D3—42no—
910C24—91no—
911C24—181no—
912C24—181no—
913#41—34no—
914#41—34no—
915#41—34no—
916#41—62no—
917#41—62no—
918#41—62no—
919#41—94no—
920#41—94no—
921#41—94no—
922#41—94no—
923#41—94no—
924#41—182no—
925#41—182no—
926#41—182no—
927#41—188no—
928#41—188no—
929#41—188no—
930#41—188no—
931#41—182no—
932#41—182no—
933C2×Q8—34no—
934C2×Q8—31no—
935C2×Q8—31no—
936C2×Q8—31no—
937C2×Q8—61no—
938C2×Q8—62no—
939C2×Q8—94no—
940C2×Q8—181no—
941C2×Q8—182no—
942C2×Q8C2×D3211yescharacteristic
943C2×D4—31no—
944C2×D4—61no—
945C2×D4—61no—
946C2×D4—61no—
947C2×D4—94no—
948C2×D4—94no—
949C2×D4—91no—
950C2×D4—91no—
951C2×D4—181no—
952C2×D4—182no—
953C2×D4—181no—
954C2×D4—188no—
955C2×D4—181no—
956C2×D4—181no—
957C2×D4—181no—
958C2×D4—181no—
959C2×D4—182no—
960C2×D4—181no—
961C2×D4—188no—
962C2×D4C2×D3211yescharacteristic
963C22×C4—31no—
964C22×C4—31no—
965C22×C4—61no—
966C22×C4—61no—
967C22×C4—61no—
968C22×C4—61no—
969C22×C4—94no—
970C22×C4—91no—
971C22×C4—94no—
972C22×C4—91no—
973C22×C4—91no—
974C22×C4—91no—
975C22×C4—181no—
976C22×C4—181no—
977C22×C4—181no—
978C22×C4—181no—
979C22×C4—188no—
980C22×C4—188no—
981C22×C4—181no—
982C22×C4—181no—
983Q16—34no—
984Q16—34no—
985Q16—34no—
986Q16—94no—
987SD16—34no—
988SD16—34no—
989SD16—94no—
990SD16—94no—
991SD16—94no—
992SD16—94no—
993SD16—94no—
994SD16C2×D3214yescomplemented
995D8—34no—
996D8—94no—
997D8—94no—
998D8—94no—
999M16—34no—
1000M16—94no—
1001M16—94no—
1002M16—94no—
1003C2×C8—31no—
1004C2×C8—31no—
1005C2×C8—34no—
1006C2×C8—94no—
1007C2×C8—91no—
1008C2×C8C2×D3211yescharacteristic
1009C22×C3—22no—
1010C22×C3—22no—
1011C22×C3—21no—
1012C22×C3—32no—
1013C22×C3—32no—
1014C22×C3—42no—
1015C22×C3—42no—
1016C22×C3—42no—
1017C22×C3—62no—
1018C22×C3—62no—
1019C22×C3—62no—
1020C22×C3—82no—
1021C22×C3—122no—
1022C22×C3C2×D3×D411yescharacteristic
1023C22×C3C2×D3×D411yescharacteristic
1024C2×D3—22no—
1025C2×D3—22no—
1026C2×D3—22no—
1027C2×D3—32no—
1028C2×D3—32no—
1029C2×D3—42no—
1030C2×D3—62no—
1031C2×D3—62no—
1032C2×D3—62no—
1033C2×D3—62no—
1034C2×D3—62no—
1035C2×D3—62no—
1036C2×D3—62no—
1037C2×D3—122no—
1038C2×D3—122no—
1039C2×D3—122no—
1040C2×D3—124no—
1041C2×D3—124no—
1042C2×D3—128no—
1043C2×D3—128no—
1044C2×D3—128no—
1045C2×D3—128no—
1046C2×D3—122no—
1047C2×D3—122no—
1048C2×D3—122no—
1049C2×D3—122no—
1050C2×D3—248no—
1051C2×D3—242no—
1052C2×D3—242no—
1053C2×D3C2×D3×D412yes—
1054C2×D3C2×D3×D412yes—
1055C3×C4—22no—
1056C3×C4—22no—
1057C3×C4—21no—
1058C3×C4—21no—
1059C3×C4—32no—
1060C3×C4—32no—
1061C3×C4—42no—
1062C3×C4—62no—
1063C3×C4—62no—
1064C3×C4—62no—
1065C3×C4C2×D3×D411yescharacteristic
1066C3×C4C2×D3×D411yescharacteristic
1067C3×C4C24×D311yescharacteristic
1068C3×C4C24×D311yescharacteristic
1069Dic3—22no—
1070Dic3—22no—
1071Dic3—22no—
1072Dic3—32no—
1073Dic3—32no—
1074Dic3—62no—
1075Dic3C2×D3×D412yes—
1076Dic3C2×D3×D412yes—
1077C32C2×#57511yescharacteristic, complemented, Sylow
1078C23—21no—
1079C23—31no—
1080C23—31no—
1081C23—61no—
1082C23—94no—
1083C23—91no—
1084C23—184no—
1085C23—184no—
1086C23—181no—
1087C23—181no—
1088C23—364no—
1089C23—362no—
1090C23—364no—
1091Q8—21no—
1092Q8—32no—
1093Q8—32no—
1094Q8—32no—
1095Q8—64no—
1096Q8—61no—
1097Q8—61no—
1098Q8—61no—
1099Q8—184no—
1100Q8C22×D3212yes—
1101D4—21no—
1102D4—32no—
1103D4—64no—
1104D4—64no—
1105D4—64no—
1106D4—61no—
1107D4—92no—
1108D4—92no—
1109D4—184no—
1110D4—184no—
1111D4—184no—
1112D4—184no—
1113D4—184no—
1114D4—184no—
1115D4—184no—
1116D4—181no—
1117D4—181no—
1118D4C22×D3212yes—
1119C2×C4—21no—
1120C2×C4—31no—
1121C2×C4—31no—
1122C2×C4—32no—
1123C2×C4—32no—
1124C2×C4—32no—
1125C2×C4—32no—
1126C2×C4—64no—
1127C2×C4—64no—
1128C2×C4—64no—
1129C2×C4—64no—
1130C2×C4—61no—
1131C2×C4—61no—
1132C2×C4—61no—
1133C2×C4—94no—
1134C2×C4—94no—
1135C2×C4—94no—
1136C2×C4—91no—
1137C2×C4—92no—
1138C2×C4—92no—
1139C2×C4—184no—
1140C2×C4—184no—
1141C2×C4—184no—
1142C2×C4—184no—
1143C2×C4—184no—
1144C2×C4—184no—
1145C2×C4C22×D3211yescharacteristic
1146C8—32no—
1147C8—32no—
1148C8—92no—
1149C8C22×D3212yes—
1150C2×C3—21no—
1151C2×C3—22no—
1152C2×C3—42no—
1153C2×C3—42no—
1154C2×C3—62no—
1155C2×C3—62no—
1156C2×C3—82no—
1157C2×C3—122no—
1158C2×C3#576812yescomplemented
1159C2×C3#577712yescomplemented
1160C2×C3C22×D3×D411yescharacteristic
1161C2×C3C22×D3×D411yescharacteristic
1162D3—22no—
1163D3—22no—
1164D3—42no—
1165D3—62no—
1166D3—62no—
1167D3—122no—
1168D3—122no—
1169D3—122no—
1170D3—122no—
1171D3—122no—
1172D3—242no—
1173D3—242no—
1174C22—22no—
1175C22—32no—
1176C22—32no—
1177C22—42no—
1178C22—62no—
1179C22—62no—
1180C22—62no—
1181C22—92no—
1182C22—122no—
1183C22—182no—
1184C22—182no—
1185C22—182no—
1186C22—368no—
1187C22—364no—
1188C22—368no—
1189C22—362no—
1190C22—362no—
1191C22D32×D411yescharacteristic
1192C4—22no—
1193C4—32no—
1194C4—32no—
1195C4—62no—
1196C4—62no—
1197C4—62no—
1198C4—92no—
1199C4D32×D411yescharacteristic
1200C4C23×D3211yescharacteristic
1201C3—21no—
1202C3C2×#576811yescharacteristic, complemented
1203C3C2×#577711yescharacteristic, complemented
1204C2—42no—
1205C2—62no—
1206C2—62no—
1207C2—122no—
1208C2—182no—
1209C2—362no—
1210C2—362no—
1211C2#1059474612yesdirect product factor
1212C2C2×D32×D411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32C2×#575
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×D3×#239C2semidirect
2. C2×#64312C2semidirect
3. C2×#64123C2semidirect
4. C2×C3×#916C2semidirect
5. C2×C3×#915C2semidirect
6. C2×#63949C2semidirect
7. C2×#63948C2semidirect
8. C2×#63945C2semidirect
9. C2×#63937C2semidirect
10. C2×#63935C2semidirect
11. C2×#63925C2semidirect
12. #10594746C2direct (N × H)
13. C2×#63811C2semidirect
14. C2×#63808C2semidirect
15. C2×#63794C2semidirect
16. C2×D3×ΓL(1,𝔽25)C2semidirect
20. C2×D4×C3⋊D3C22semidirect
21. C2×C3×#239C22semidirect
22. C2×C3×D3×Q8C22semidirect
24. C2×C3×#237C22semidirect
30. D3×#239C22semidirect
32. #64312C22semidirect
34. C2×D3×D12C22semidirect
39. C2×#3799C22semidirect
40. C2×#3799C22semidirect
41. C2×#3797C22semidirect
44. C2×C32×SD16C22semidirect
45. C2×#3755C22semidirect
46. C2×#3753C22semidirect
47. #64123C22semidirect
48. C2×#3745C22semidirect
49. C2×#3743C22semidirect
50. C2×C3×#216C22semidirect
51. C2×C3×#216C22semidirect
52. C2×C3×#214C22semidirect
53. C2×C3×#213C22semidirect
54. C3×#916C22semidirect
55. C3×#915C22semidirect
56. C2×C3×Dic12C22semidirect
57. C2×C3×#204C22semidirect
58. C2×C3×ΓL(1,𝔽25)C22semidirect
59. C2×C3×D3×C8C22semidirect
60. #63949C22semidirect
61. #63948C22semidirect
62. #63945C22semidirect
63. #63937C22semidirect
64. #63935C22semidirect
65. #63925C22semidirect
66. C2×#3718C22semidirect
67. C2×#3717C22semidirect
68. C2×#3717C22semidirect
69. C2×#3717C22semidirect
70. C2×#3715C22semidirect
71. C2×#3714C22semidirect
72. C2×#3712C22semidirect
73. C2×#3711C22semidirect
74. C2×D3×C3⋊C8C22semidirect
75. #63811C22semidirect
76. #63808C22semidirect
77. #63794C22semidirect
78. D3×ΓL(1,𝔽25)C22semidirect
98. C2×#916D3semidirect
100. C2×#915D3semidirect
121. D4×C3⋊D3C23semidirect
132. C3×#239C23semidirect
134. C3×D3×Q8C23semidirect
138. C3×#237C23semidirect
169. D3×D12C23semidirect
178. #3799C23semidirect
179. #3799C23semidirect
181. #3797C23semidirect
185. C32×SD16C23semidirect
187. #3755C23semidirect
188. #3753C23semidirect
190. #3745C23semidirect
191. #3743C23semidirect
192. C3×#216C23semidirect
193. C3×#216C23semidirect
194. C3×#214C23semidirect
195. C3×#213C23semidirect
198. C3×Dic12C23semidirect
199. C3×#204C23semidirect
200. C3×ΓL(1,𝔽25)C23semidirect
201. C3×D3×C8C23semidirect
202. #3718C23semidirect
203. #3717C23semidirect
204. #3717C23semidirect
205. #3717C23semidirect
206. #3715C23semidirect
207. #3714C23semidirect
208. #3712C23semidirect
209. #3711C23semidirect
210. D3×C3⋊C8C23semidirect
233. C2×#239C2×D3semidirect
236. C2×D3×Q8C2×D3semidirect
242. C2×#237C2×D3semidirect
272. C2×C3×SD16C2×D3semidirect
273. C2×C3×SD16C2×D3semidirect
282. C2×#216C2×D3semidirect
283. C2×#216C2×D3semidirect
293. C2×#214C2×D3semidirect
298. C2×#213C2×D3semidirect
308. #916C2×D3semidirect
310. #915C2×D3semidirect
320. C2×Dic12C2×D3semidirect
329. C2×#204C2×D3semidirect
337. C2×ΓL(1,𝔽25)C2×D3semidirect
339. C2×D3×C8C2×D3semidirect
495. #239C22×D3semidirect
501. D3×Q8C22×D3semidirect
510. #237C22×D3semidirect
593. C3×SD16C22×D3semidirect
594. C3×SD16C22×D3semidirect
605. #216C22×D3semidirect
606. #216C22×D3semidirect
615. #214C22×D3semidirect
620. #213C22×D3semidirect
628. Dic12C22×D3semidirect
636. #204C22×D3semidirect
643. ΓL(1,𝔽25)C22×D3semidirect
645. D3×C8C22×D3semidirect
721. C2×SD16D32semidirect
902. C2×C32#575semidirect
994. SD16C2×D32semidirect
1077. C32C2×#575semidirect
1158. C2×C3#5768semidirect
1159. C2×C3#5777semidirect
1202. C3C2×#5768semidirect
1203. C3C2×#5777semidirect
1211. C2#10594746direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C2×#643122
C2×#641232
C2×C3×#9162
C2×C3×#9152
C2×#639492
C2×#639482
C2×#639452
C2×#639372
C2×#639352
C2×#639252
#105947462
C2×#638112
C2×#638082
C2×#637942
C2×D3×ΓL(1,𝔽25)2
C2×#57773
C2×#57683