Finite Group Databasebeta

← C2×#10594751 #11918871

Subgroups — C2×#10594751 #11918871

Order 1152.

3069 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×#64316C211yesmaximal, characteristic, complemented
2C2×#64314C211yesmaximal, characteristic, complemented
3C2×#64123C211yesmaximal, characteristic, complemented
4C2×C3×#915C211yesmaximal, characteristic, complemented
5C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
6C2×#63950C211yesmaximal, characteristic, complemented
7C2×#63948C211yesmaximal, characteristic, complemented
8C2×D3×#215C211yesmaximal, characteristic, complemented
9C2×#63935C211yesmaximal, characteristic, complemented
10C2×#63934C211yesmaximal, characteristic, complemented
11C2×#63930C211yesmaximal, characteristic, complemented
12#10594751C2116yesmaximal, direct product factor
13C2×#63811C211yesmaximal, characteristic, complemented
14C2×#63808C211yesmaximal, characteristic, complemented
15C2×#63804C211yesmaximal, characteristic, complemented
16C2×#63794C211yesmaximal, characteristic, complemented
17C2×#5778—31nomaximal
18C2×#5762—31nomaximal
19C2×#3832C2211yescharacteristic, complemented
20C2×D4×C3⋊D3C2211yescharacteristic
21C2×C3×D3×Q8C2211yescharacteristic, complemented
22C2×C3×D3×Q8C2211yescharacteristic, complemented
23C2×C3×#237C2211yescharacteristic
24C2×C3×D3×D4C2211yescharacteristic
25C2×#3811—21no—
26C2×D3×#67—21no—
27C22×#626—21no—
28C2×#3804—21no—
29#64316—24no—
30#64316C2218yescomplemented
31#64314—24no—
32#64314C2218yescomplemented
33C2×D3×D12C2211yescharacteristic
34C2×#3799—21no—
35C2×#3799—21no—
36C2×#3799C2211yescharacteristic
37C2×#3799C2211yescharacteristic, complemented
38C2×#3799C2211yescharacteristic, complemented
39C2×#3798—21no—
40C2×#3798C2211yescharacteristic
41C2×#3797—21no—
42C2×#3797C2211yescharacteristic, complemented
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×#215C2211yescharacteristic, complemented
52C2×C3×#214C2211yescharacteristic, complemented
53C2×C3×#214C2211yescharacteristic, complemented
54C3×#915C2218yescomplemented
55C3×D3×SD16C2218yescomplemented
56C2×C3×Dic12C2211yescharacteristic, complemented
57C2×C3×#204C2211yescharacteristic, complemented
58C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
59C2×C3×D3×C8C2211yescharacteristic, complemented
60#63950C2218yescomplemented
61#63948C2218yescomplemented
62D3×#215C2218yescomplemented
63#63935C2218yescomplemented
64#63934C2218yescomplemented
65#63930C2218yescomplemented
66C2×#3718C2211yescharacteristic, complemented
67C2×#3717C2211yescharacteristic, complemented
68C2×#3717C2211yescharacteristic, complemented
69C2×#3717C2211yescharacteristic, complemented
70C2×#3715C2211yescharacteristic, complemented
71C2×#3714C2211yescharacteristic, complemented
72C2×#3711C2211yescharacteristic, complemented
73C2×#3710C2211yescharacteristic, complemented
74C2×D3×C3⋊C8C2211yescharacteristic, complemented
75#63811C2218yescomplemented
76#63808C2218yescomplemented
77#63804C2218yescomplemented
78#63794C2218yescomplemented
79C2×#1009—31no—
80C2×#1007—31no—
81C2×#1007—31no—
82C2×#1004—31no—
83C2×C3×#137—31no—
84C22×C3×SD16—31no—
85C2×#950—31no—
86C2×#942—31no—
87C22×#215—31no—
88C2×#932—31no—
89#5778—316no—
90C2×#919—31no—
91C2×#919—31no—
92C2×#918—31no—
93C2×#918—31no—
94#5762—316no—
95C2×#916—31no—
96C2×#916—31no—
97C2×#915—31no—
98C2×#915D311yescharacteristic, complemented
99C2×#914—31no—
100C2×#914—31no—
101C2×#914—31no—
102C2×#914—31no—
103C2×#914—61no—
104C2×D3×SD16—31no—
105C2×D3×SD16—31no—
106C2×D3×SD16—31no—
107C2×D3×SD16D311yescharacteristic, complemented
108C2×#908—31no—
109C2×#907—31no—
110C2×#904—31no—
111C2×#901—31no—
112C23×C3⋊D3—21no—
113C23×C3×D3—21no—
114C22×D32—21no—
115C2×C32×Q8C2311yescharacteristic
116C2×C32×D4C2311yescharacteristic
117C2×#638—21no—
118#3832—22no—
119#3832C2314yescomplemented
120D4×C3⋊D3—22no—
121D4×C3⋊D3C2314yes—
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—
130C3×D3×Q8—22no—
131C3×D3×Q8—22no—
132C3×D3×Q8C2314yescomplemented
133C3×D3×Q8C2314yescomplemented
134C3×#237—22no—
135C3×#237C2314yes—
136C3×D3×D4—22no—
137C3×D3×D4C2314yes—
138C2×C3×D12C2311yescharacteristic
139C2×C3×C4×D3—21no—
140C2×C3×C4×D3—21no—
141C2×C3×C4×D3C2311yescharacteristic
142C2×C3×C4×D3C2311yescharacteristic
143C2×C3×Dic6—21no—
144C2×C3×Dic6—21no—
145C2×C3×Dic6C2311yescharacteristic
146C2×C3×Dic6C2311yescharacteristic
147C2×C3×Dic6C2311yescharacteristic
148#3811—28no—
149D3×#67—28no—
150C2×#627—21no—
151C2×#627D411yescharacteristic
152C2×#626—21no—
153C2×#626—21no—
154C2×#626—21no—
155C2×#626—21no—
156C2×#626—21no—
157C2×#626—28no—
158C2×#626D411yescharacteristic
159C2×#626D411yescharacteristic
160C2×#625D411yescharacteristic
161C2×#624—21no—
162C2×#624—21no—
163C2×#624—21no—
164C2×#624—21no—
165#3804—28no—
166C2×D3×Dic3—21no—
167D3×D12—22no—
168D3×D12C2314yes—
169#3799—22no—
170#3799—22no—
171#3799—22no—
172#3799—28no—
173#3799—28no—
174#3799C2314yes—
175#3799C2314yescomplemented
176#3799C2314yescomplemented
177#3798—28no—
178#3798D414yes—
179#3798C2314yes—
180#3797—22no—
181#3797—28no—
182#3797C2314yescomplemented
183#3796—22no—
184#3796C2314yes—
185C32×SD16C2314yescomplemented
186C2×C32×C8C2311yescharacteristic
187#3755C2314yescomplemented
188#3753C2314yescomplemented
189C2×C3⋊(C3⋊C8)C2311yescharacteristic
190#3745C2314yescomplemented
191#3743C2314yescomplemented
192C3×#216C2314yescomplemented
193C3×#215C2314yescomplemented
194C3×#214C2314yescomplemented
195C3×#214C2314yescomplemented
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#3711C2314yescomplemented
209#3710C2314yescomplemented
210D3×C3⋊C8C2314yescomplemented
211C2×#577—91noSylow
212C2×C3×#41—31no—
213C22×C3×Q8—31no—
214C22×C3×Q8—31no—
215C22×C3×D4—31no—
216C22×#67—61no—
217C22×#67—61no—
218#1009—38no—
219#1009—64no—
220#1007—38no—
221#1007—38no—
222#1007—64no—
223#1007—64no—
224C2×#239—31no—
225C2×#239—31no—
226C2×#239—31no—
227C2×#239—31no—
228C2×#239—31no—
229C2×#239—31no—
230C2×#239—61no—
231C2×#239—61no—
232C2×#239—61no—
233C2×D3×Q8—31no—
234C2×D3×Q8—31no—
235C2×D3×Q8—61no—
236C2×D3×Q8—61no—
237C2×D3×Q8C2×D311yescharacteristic, complemented
238C2×D3×Q8C2×D311yescharacteristic, complemented
239#1004—38no—
240#1004—64no—
241C2×#237—31no—
242C2×#237—61no—
243C2×#237C2×D311yescharacteristic
244C2×D3×D4—31no—
245C2×D3×D4—31no—
246C2×D3×D4—31no—
247C2×D3×D4—61no—
248C2×D3×D4—61no—
249C2×D3×D4—61no—
250C2×D3×D4—61no—
251C2×D3×D4C2×D311yescharacteristic
252C2×#235—31no—
253C2×#235—31no—
254C2×#235—31no—
255C2×#235—31no—
256C2×#235—31no—
257C2×#235—61no—
258C2×#235—61no—
259C2×#235—61no—
260C2×#235—61no—
261C2×#235—61no—
262C22×D12—31no—
263C22×D12—61no—
264C3×#137—38no—
265C2×C3×Q16—31no—
266C2×C3×Q16—31no—
267C2×C3×SD16—21no—
268C2×C3×SD16—31no—
269C2×C3×SD16—31no—
270C2×C3×SD16—31no—
271C2×C3×SD16—38no—
272C2×C3×SD16—31no—
273C2×C3×SD16C2×D311yescharacteristic, complemented
274C2×C3×SD16C2×D311yescharacteristic, complemented
275C2×C3×M16—31no—
276C22×C3×C8—31no—
277#950—38no—
278C2×#216—31no—
279C2×#216—31no—
280C2×#216C2×D311yescharacteristic, complemented
281#942—38no—
282C2×#215—31no—
283C2×#215—31no—
284C2×#215—31no—
285C2×#215—38no—
286C2×#215—31no—
287C2×#215—31no—
288C2×#215—31no—
289C2×#215—61no—
290C2×#215C2×D311yescharacteristic, complemented
291C2×#214—31no—
292C2×#214C2×D311yescharacteristic, complemented
293C2×#214C2×D311yescharacteristic, complemented
294#932—38no—
295C2×#213—31no—
296C2×#213—31no—
297C2×#213—31no—
298C2×#213—61no—
299C2×#208—31no—
300C22×C3⋊C8—31no—
301#919—38no—
302#919—38no—
303#918—38no—
304#918—38no—
305#916—38no—
306#916—38no—
307#915—38no—
308#915C2×D318yescomplemented
309#914—38no—
310#914—38no—
311#914—38no—
312#914—38no—
313#914—68no—
314D3×SD16—38no—
315D3×SD16—38no—
316D3×SD16—38no—
317D3×SD16C2×D318yescomplemented
318#908—38no—
319#907—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
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
340C23×C32—21no—
341C22×C3⋊D3—21no—
342C22×C3⋊D3—21no—
343C22×C3⋊D3—24no—
344C22×C3⋊D3—82no—
345C22×C3⋊D3C2×D411yescharacteristic
346C22×C3×D3—21no—
347C22×C3×D3—24no—
348C22×C3×D3—82no—
349C22×C3×D3C2×D411yescharacteristic
350C22×C3×D3C2×D411yescharacteristic
351C2×D32—24no—
352C2×D32—82no—
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×Dic3C2×D411yescharacteristic
376C2×C3×Dic3C2×D411yescharacteristic
377C3×D12—21no—
378C3×D12C2412yes—
379C3×C4×D3—24no—
380C3×C4×D3—24no—
381C3×C4×D3C2×D412yes—
382C3×C4×D3C2×D412yes—
383C3×C4×D3C2412yes—
384C3×C4×D3C2412yes—
385C3×Dic6—21no—
386C3×Dic6—21no—
387C3×Dic6—21no—
388C3×Dic6—24no—
389C3×Dic6—24no—
390C3×Dic6C2412yes—
391C3×Dic6C2412yes—
392C3×Dic6C2412yes—
393#627—24no—
394#627C2×D414yes—
395#626—24no—
396#626—24no—
397#626—24no—
398#626—24no—
399#626—24no—
400#626C2×D414yes—
401#626C2×D414yes—
402#625C2×D414yes—
403#624—24no—
404#624—24no—
405#624—24no—
406#624—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—91no—
422C2×#135—91no—
423C2×#135—91no—
424C22×SD16—31no—
425C22×SD16—91no—
426C22×SD16—91no—
427C2×#131—91no—
428C24×C3—61no—
429C23×D3—21no—
430C23×D3—61no—
431C23×D3—61no—
432C23×D3—61no—
433C23×D3—61no—
434C23×D3—121no—
435C3×#41—34no—
436C3×#41—62no—
437C2×C3×Q8—21no—
438C2×C3×Q8—34no—
439C2×C3×Q8—34no—
440C2×C3×Q8—31no—
441C2×C3×Q8—31no—
442C2×C3×Q8—31no—
443C2×C3×Q8—61no—
444C2×C3×Q8—61no—
445C2×C3×Q8—62no—
446C2×C3×Q8—62no—
447C2×C3×Q8C22×D311yescharacteristic
448C2×C3×Q8C22×D311yescharacteristic
449C2×C3×D4—21no—
450C2×C3×D4—34no—
451C2×C3×D4—31no—
452C2×C3×D4—62no—
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—
462C2×#67—21no—
463C2×#67—21no—
464C2×#67—31no—
465C2×#67—31no—
466C2×#67—31no—
467C2×#67—31no—
468C2×#67—68no—
469C2×#67—61no—
470C2×#67—61no—
471C2×#67—61no—
472C2×#67—61no—
473C2×#67—61no—
474C2×#67—61no—
475C2×#67—68no—
476C2×#67—61no—
477C2×#67—121no—
478C22×Dic3—21no—
479C22×Dic3—61no—
480#239—34no—
481#239—34no—
482#239—34no—
483#239—34no—
484#239—34no—
485#239—34no—
486#239—64no—
487#239—68no—
488#239—68no—
489#239—62no—
490#239—62no—
491#239—62no—
492#239—62no—
493#239—62no—
494#239—62no—
495#239—122no—
496D3×Q8—22no—
497D3×Q8—22no—
498D3×Q8—34no—
499D3×Q8—34no—
500D3×Q8—68no—
501D3×Q8—68no—
502D3×Q8—62no—
503D3×Q8—62no—
504D3×Q8C22×D314yescomplemented
505D3×Q8C22×D314yescomplemented
506#237—22no—
507#237—34no—
508#237—62no—
509#237—68no—
510#237C22×D314yes—
511D3×D4—22no—
512D3×D4—34no—
513D3×D4—34no—
514D3×D4—34no—
515D3×D4—64no—
516D3×D4—62no—
517D3×D4—62no—
518D3×D4—68no—
519D3×D4—68no—
520D3×D4—68no—
521D3×D4—62no—
522D3×D4—122no—
523D3×D4C22×D314yes—
524#235—34no—
525#235—34no—
526#235—34no—
527#235—34no—
528#235—34no—
529#235—34no—
530#235—34no—
531#235—68no—
532#235—68no—
533#235—62no—
534#235—62no—
535#235—62no—
536#235—68no—
537#235—68no—
538#235—68no—
539C2×D12—31no—
540C2×D12—31no—
541C2×D12—31no—
542C2×D12—31no—
543C2×D12—31no—
544C2×D12—31no—
545C2×D12—34no—
546C2×D12—61no—
547C2×D12—61no—
548C2×D12—62no—
549C2×D12—68no—
550C2×D12—61no—
551C2×D12—61no—
552C2×D12—61no—
553C2×D12—61no—
554C2×D12—61no—
555C2×D12—61no—
556C2×D12—61no—
557C2×D12—121no—
558C2×D12C22×D311yescharacteristic
559C2×C4×D3—21no—
560C2×C4×D3—21no—
561C2×C4×D3—31no—
562C2×C4×D3—31no—
563C2×C4×D3—61no—
564C2×C4×D3—61no—
565C2×C4×D3—61no—
566C2×C4×D3—61no—
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—121no—
576C2×C4×D3C22×D311yescharacteristic
577C2×C4×D3C22×D311yescharacteristic
578C2×Dic6—21no—
579C2×Dic6—21no—
580C2×Dic6—31no—
581C2×Dic6—31no—
582C2×Dic6—61no—
583C2×Dic6—61no—
584C2×Dic6C22×D311yescharacteristic
585C2×Dic6C22×D311yescharacteristic
586C2×Dic6C22×D311yescharacteristic
587C3×Q16—34no—
588C3×Q16—34no—
589C3×SD16—24no—
590C3×SD16—34no—
591C3×SD16—34no—
592C3×SD16—34no—
593C3×SD16—34no—
594C3×SD16C22×D314yescomplemented
595C3×SD16C22×D314yescomplemented
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#215—34no—
607#215—34no—
608#215—34no—
609#215—34no—
610#215—34no—
611#215—34no—
612#215—64no—
613#215C22×D314yescomplemented
614#214—34no—
615#214C22×D314yescomplemented
616#214C22×D314yescomplemented
617#213—34no—
618#213—34no—
619#213—34no—
620#213—64no—
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)—64no—
641ΓL(1,𝔽25)C22×D314yescomplemented
642D3×C8—34no—
643D3×C8—34no—
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—42no—
653C2×C3⋊D3—42no—
654C2×C3⋊D3—84no—
655C2×C3⋊D3C22×D412yes—
656C2×C3×D3—22no—
657C2×C3×D3—22no—
658C2×C3×D3—22no—
659C2×C3×D3—42no—
660C2×C3×D3—84no—
661C2×C3×D3C22×D412yes—
662C2×C3×D3C22×D412yes—
663D32—84no—
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—
6732−1+4—98no—
6742−1+4—184no—
675H(5,𝔽2)—98no—
676H(5,𝔽2)—184no—
677C2×#41—31no—
678C2×#41—91no—
679C2×#41—91no—
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—31no—
690C22×Q8—91no—
691C22×Q8—181no—
692C22×D4—31no—
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—98no—
705#135—98no—
706#135—98no—
707C2×Q16—31no—
708C2×Q16—31no—
709C2×Q16—91no—
710C2×SD16—31no—
711C2×SD16—31no—
712C2×SD16—31no—
713C2×SD16—38no—
714C2×SD16—31no—
715C2×SD16—91no—
716C2×SD16—91no—
717C2×SD16—91no—
718C2×SD16—98no—
719C2×SD16—98no—
720C2×SD16—91no—
721C2×SD16—91no—
722C2×SD16D3211yescharacteristic, complemented
723C2×D8—91no—
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—21no—
734C23×C3—21no—
735C23×C3—31no—
736C23×C3—31no—
737C23×C3—41no—
738C23×C3—64no—
739C23×C3—61no—
740C23×C3—242no—
741C22×D3—21no—
742C22×D3—24no—
743C22×D3—31no—
744C22×D3—31no—
745C22×D3—61no—
746C22×D3—64no—
747C22×D3—64no—
748C22×D3—64no—
749C22×D3—61no—
750C22×D3—61no—
751C22×D3—61no—
752C22×D3—61no—
753C22×D3—64no—
754C22×D3—82no—
755C22×D3—124no—
756C22×D3—121no—
757C22×D3—121no—
758C22×D3—242no—
759C22×D3—242no—
760C22×D3—242no—
761C22×D3—242no—
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—64no—
774C3×Q8—61no—
775C3×Q8—61no—
776C3×Q8—61no—
777C3×Q8C23×D312yes—
778C3×Q8C23×D312yes—
779C3×D4—21no—
780C3×D4—21no—
781C3×D4—22no—
782C3×D4—32no—
783C3×D4—41no—
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—61no—
803C2×C3×C4—61no—
804C2×C3×C4—61no—
805C2×C3×C4C23×D311yescharacteristic
806C2×C3×C4C23×D311yescharacteristic
807#67—24no—
808#67—24no—
809#67—34no—
810#67—34no—
811#67—34no—
812#67—34no—
813#67—64no—
814#67—64no—
815#67—64no—
816#67—64no—
817#67—64no—
818#67—64no—
819#67—64no—
820#67—124no—
821C2×Dic3—21no—
822C2×Dic3—21no—
823C2×Dic3—21no—
824C2×Dic3—24no—
825C2×Dic3—31no—
826C2×Dic3—31no—
827C2×Dic3—61no—
828C2×Dic3—64no—
829C2×Dic3D3×D411yescharacteristic
830C2×Dic3D3×D411yescharacteristic
831D12—21no—
832D12—34no—
833D12—34no—
834D12—32no—
835D12—32no—
836D12—32no—
837D12—32no—
838D12—62no—
839D12—62no—
840D12—64no—
841D12—64no—
842D12—64no—
843D12—64no—
844D12—64no—
845D12—64no—
846D12—64no—
847D12—61no—
848D12—61no—
849D12—61no—
850D12—61no—
851D12—121no—
852D12—121no—
853D12—124no—
854D12C23×D312yes—
855C4×D3—24no—
856C4×D3—24no—
857C4×D3—32no—
858C4×D3—32no—
859C4×D3—32no—
860C4×D3—32no—
861C4×D3—62no—
862C4×D3—62no—
863C4×D3—64no—
864C4×D3—64no—
865C4×D3—64no—
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—124no—
875C4×D3D3×D412yes—
876C4×D3D3×D412yes—
877C4×D3C23×D312yes—
878C4×D3C23×D312yes—
879Dic6—21no—
880Dic6—21no—
881Dic6—21no—
882Dic6—24no—
883Dic6—24no—
884Dic6—34no—
885Dic6—34no—
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#57712yescomplemented
903C2×C32C23×D411yescharacteristic
904C3⋊D3—22no—
905C3⋊D3—42no—
906C3⋊D3—42no—
907C3×D3—22no—
908C3×D3—22no—
909C3×D3—42no—
910C24—61no—
911C24—181no—
912C24—181no—
913#41—34no—
914#41—62no—
915#41—94no—
916#41—94no—
917#41—94no—
918#41—94no—
919#41—94no—
920#41—94no—
921#41—94no—
922#41—182no—
923#41—182no—
924#41—182no—
925#41—188no—
926#41—188no—
927#41—188no—
928#41—188no—
929#41—182no—
930#41—182no—
931C2×Q8—34no—
932C2×Q8—34no—
933C2×Q8—31no—
934C2×Q8—31no—
935C2×Q8—31no—
936C2×Q8—61no—
937C2×Q8—61no—
938C2×Q8—62no—
939C2×Q8—62no—
940C2×Q8—91no—
941C2×Q8—94no—
942C2×Q8—181no—
943C2×Q8—182no—
944C2×Q8—188no—
945C2×Q8C2×D3211yescharacteristic
946C2×D4—34no—
947C2×D4—31no—
948C2×D4—62no—
949C2×D4—61no—
950C2×D4—61no—
951C2×D4—94no—
952C2×D4—91no—
953C2×D4—91no—
954C2×D4—91no—
955C2×D4—94no—
956C2×D4—91no—
957C2×D4—91no—
958C2×D4—181no—
959C2×D4—182no—
960C2×D4—181no—
961C2×D4—188no—
962C2×D4—181no—
963C2×D4—181no—
964C2×D4—181no—
965C2×D4—181no—
966C2×D4—182no—
967C2×D4—181no—
968C2×D4—188no—
969C2×D4—188no—
970C2×D4C2×D3211yescharacteristic
971C22×C4—31no—
972C22×C4—31no—
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—
982C22×C4—181no—
983Q16—34no—
984Q16—34no—
985Q16—94no—
986SD16—34no—
987SD16—34no—
988SD16—34no—
989SD16—34no—
990SD16—94no—
991SD16—94no—
992SD16—94no—
993SD16—94no—
994SD16—94no—
995SD16C2×D3214yescomplemented
996D8—94no—
997D8—94no—
998D8—94no—
999M16—34no—
1000M16—94no—
1001M16—94no—
1002C2×C8—31no—
1003C2×C8—31no—
1004C2×C8—34no—
1005C2×C8—94no—
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×C3—244no—
1023C22×C3C2×D3×D411yescharacteristic
1024C22×C3C2×D3×D411yescharacteristic
1025C2×D3—22no—
1026C2×D3—22no—
1027C2×D3—22no—
1028C2×D3—32no—
1029C2×D3—32no—
1030C2×D3—42no—
1031C2×D3—62no—
1032C2×D3—62no—
1033C2×D3—62no—
1034C2×D3—62no—
1035C2×D3—62no—
1036C2×D3—62no—
1037C2×D3—62no—
1038C2×D3—84no—
1039C2×D3—122no—
1040C2×D3—122no—
1041C2×D3—122no—
1042C2×D3—122no—
1043C2×D3—122no—
1044C2×D3—122no—
1045C2×D3—122no—
1046C2×D3—242no—
1047C2×D3—242no—
1048C2×D3—244no—
1049C2×D3—244no—
1050C2×D3—244no—
1051C2×D3—244no—
1052C2×D3—248no—
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×#57711yescharacteristic, complemented, Sylow
1078C23—21no—
1079C23—31no—
1080C23—31no—
1081C23—64no—
1082C23—61no—
1083C23—91no—
1084C23—184no—
1085C23—184no—
1086C23—181no—
1087C23—181no—
1088C23—242no—
1089C23—722no—
1090C23—722no—
1091Q8—21no—
1092Q8—32no—
1093Q8—32no—
1094Q8—32no—
1095Q8—64no—
1096Q8—64no—
1097Q8—61no—
1098Q8—61no—
1099Q8—61no—
1100Q8—94no—
1101Q8—184no—
1102Q8C22×D3212yes—
1103D4—21no—
1104D4—32no—
1105D4—64no—
1106D4—64no—
1107D4—61no—
1108D4—94no—
1109D4—94no—
1110D4—94no—
1111D4—92no—
1112D4—92no—
1113D4—184no—
1114D4—184no—
1115D4—184no—
1116D4—184no—
1117D4—184no—
1118D4—184no—
1119D4—184no—
1120D4—181no—
1121D4—181no—
1122D4C22×D3212yes—
1123C2×C4—21no—
1124C2×C4—31no—
1125C2×C4—31no—
1126C2×C4—32no—
1127C2×C4—32no—
1128C2×C4—32no—
1129C2×C4—32no—
1130C2×C4—64no—
1131C2×C4—64no—
1132C2×C4—64no—
1133C2×C4—61no—
1134C2×C4—61no—
1135C2×C4—61no—
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#576212yescomplemented
1159C2×C3#577812yescomplemented
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—244no—
1187C22—362no—
1188C22—362no—
1189C22—724no—
1190C22—724no—
1191C22D32×D411yescharacteristic
1192C4—22no—
1193C4—32no—
1194C4—32no—
1195C4—62no—
1196C4—62no—
1197C4—62no—
1198C4—92no—
1199C4D32×D411yescharacteristic
1200C4C23×D3211yescharacteristic
1201C3—21no—
1202C3C2×#576211yescharacteristic, complemented
1203C3C2×#577811yescharacteristic, complemented
1204C2—42no—
1205C2—62no—
1206C2—62no—
1207C2—122no—
1208C2—182no—
1209C2—362no—
1210C2—362no—
1211C2#1059475112yesdirect product factor
1212C2C2×D32×D411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32C2×#577
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×#64316C2semidirect
2. C2×#64314C2semidirect
3. C2×#64123C2semidirect
4. C2×C3×#915C2semidirect
5. C2×C3×D3×SD16C2semidirect
6. C2×#63950C2semidirect
7. C2×#63948C2semidirect
8. C2×D3×#215C2semidirect
9. C2×#63935C2semidirect
10. C2×#63934C2semidirect
11. C2×#63930C2semidirect
12. #10594751C2direct (N × H)
13. C2×#63811C2semidirect
14. C2×#63808C2semidirect
15. C2×#63804C2semidirect
16. C2×#63794C2semidirect
19. C2×#3832C22semidirect
21. C2×C3×D3×Q8C22semidirect
22. C2×C3×D3×Q8C22semidirect
30. #64316C22semidirect
32. #64314C22semidirect
37. C2×#3799C22semidirect
38. C2×#3799C22semidirect
42. 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×#215C22semidirect
52. C2×C3×#214C22semidirect
53. C2×C3×#214C22semidirect
54. C3×#915C22semidirect
55. C3×D3×SD16C22semidirect
56. C2×C3×Dic12C22semidirect
57. C2×C3×#204C22semidirect
58. C2×C3×ΓL(1,𝔽25)C22semidirect
59. C2×C3×D3×C8C22semidirect
60. #63950C22semidirect
61. #63948C22semidirect
62. D3×#215C22semidirect
63. #63935C22semidirect
64. #63934C22semidirect
65. #63930C22semidirect
66. C2×#3718C22semidirect
67. C2×#3717C22semidirect
68. C2×#3717C22semidirect
69. C2×#3717C22semidirect
70. C2×#3715C22semidirect
71. C2×#3714C22semidirect
72. C2×#3711C22semidirect
73. C2×#3710C22semidirect
74. C2×D3×C3⋊C8C22semidirect
75. #63811C22semidirect
76. #63808C22semidirect
77. #63804C22semidirect
78. #63794C22semidirect
98. C2×#915D3semidirect
107. C2×D3×SD16D3semidirect
119. #3832C23semidirect
132. C3×D3×Q8C23semidirect
133. C3×D3×Q8C23semidirect
175. #3799C23semidirect
176. #3799C23semidirect
182. #3797C23semidirect
185. C32×SD16C23semidirect
187. #3755C23semidirect
188. #3753C23semidirect
190. #3745C23semidirect
191. #3743C23semidirect
192. C3×#216C23semidirect
193. C3×#215C23semidirect
194. C3×#214C23semidirect
195. C3×#214C23semidirect
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. #3711C23semidirect
209. #3710C23semidirect
210. D3×C3⋊C8C23semidirect
237. C2×D3×Q8C2×D3semidirect
238. C2×D3×Q8C2×D3semidirect
273. C2×C3×SD16C2×D3semidirect
274. C2×C3×SD16C2×D3semidirect
280. C2×#216C2×D3semidirect
290. C2×#215C2×D3semidirect
292. C2×#214C2×D3semidirect
293. C2×#214C2×D3semidirect
308. #915C2×D3semidirect
317. D3×SD16C2×D3semidirect
320. C2×Dic12C2×D3semidirect
329. C2×#204C2×D3semidirect
335. C2×ΓL(1,𝔽25)C2×D3semidirect
339. C2×D3×C8C2×D3semidirect
504. D3×Q8C22×D3semidirect
505. D3×Q8C22×D3semidirect
594. C3×SD16C22×D3semidirect
595. C3×SD16C22×D3semidirect
605. #216C22×D3semidirect
613. #215C22×D3semidirect
615. #214C22×D3semidirect
616. #214C22×D3semidirect
628. Dic12C22×D3semidirect
636. #204C22×D3semidirect
641. ΓL(1,𝔽25)C22×D3semidirect
645. D3×C8C22×D3semidirect
722. C2×SD16D32semidirect
902. C2×C32#577semidirect
995. SD16C2×D32semidirect
1077. C32C2×#577semidirect
1158. C2×C3#5762semidirect
1159. C2×C3#5778semidirect
1202. C3C2×#5762semidirect
1203. C3C2×#5778semidirect
1211. C2#10594751direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643162
C2×#643142
C2×#641232
C2×C3×#9152
C2×C3×D3×SD162
C2×#639502
C2×#639482
C2×D3×#2152
C2×#639352
C2×#639342
C2×#639302
#105947512
C2×#638112
C2×#638082
C2×#638042
C2×#637942
C2×#57783
C2×#57623