Finite Group Databasebeta

← C2×#10594756 #11918934

Subgroups — C2×#10594756 #11918934

Order 1152.

2945 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64315C211yesmaximal, characteristic, complemented
2C2×#64309C211yesmaximal, characteristic, complemented
3C2×#64124C211yesmaximal, characteristic, complemented
4C2×C3×#916C211yesmaximal, characteristic, complemented
5C2×C3×#915C211yesmaximal, characteristic, complemented
6C2×#63944C211yesmaximal, characteristic, complemented
7C2×#63943C211yesmaximal, characteristic, complemented
8C2×D3×#216C211yesmaximal, characteristic, complemented
9C2×#63936C211yesmaximal, characteristic, complemented
10C2×#63933C211yesmaximal, characteristic, complemented
11C2×#63929C211yesmaximal, characteristic, complemented
12#10594756C2116yesmaximal, direct product factor
13C2×#63811C211yesmaximal, characteristic, complemented
14C2×#63804C211yesmaximal, characteristic, complemented
15C2×#63800C211yesmaximal, characteristic, complemented
16C2×D3×Dic12C211yesmaximal, characteristic, complemented
17C2×#5779—31nomaximal
18C2×#5771—31nomaximal
19C2×Q8×C3⋊D3C2211yescharacteristic
20C2×#3830C2211yescharacteristic
21C2×C3×#239C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic
23C2×C3×#237C2211yescharacteristic
24C2×C3×#237C2211yescharacteristic
25C22×#627—21no—
26C2×#3805—21no—
27C2×#3804—21no—
28C2×#3804—21no—
29#64315—24no—
30#64315C2218yescomplemented
31#64309—24no—
32#64309C2218yescomplemented
33C2×#3798—21no—
34C2×#3798C2211yescharacteristic
35C2×#3797C2211yescharacteristic
36C2×#3796—21no—
37C2×#3796C2211yescharacteristic
38C2×#3795—21no—
39C2×#3795C2211yescharacteristic
40C2×D3×Dic6—21no—
41C2×D3×Dic6C2211yescharacteristic
42C2×D3×Dic6C2211yescharacteristic
43C2×D3×Dic6C2211yescharacteristic
44C2×C32×SD16C2211yescharacteristic
45C2×#3756C2211yescharacteristic
46C2×#3754C2211yescharacteristic
47#64124C2218yescomplemented
48C2×#3746C2211yescharacteristic
49C2×#3743C2211yescharacteristic
50C2×C3×#216C2211yescharacteristic
51C2×C3×#216C2211yescharacteristic
52C2×C3×#214C2211yescharacteristic
53C2×C3×#213C2211yescharacteristic
54C3×#916C2218yescomplemented
55C3×#915C2218yescomplemented
56C2×C3×Dic12C2211yescharacteristic
57C2×C3×#204C2211yescharacteristic
58C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
59C2×C3×D3×C8C2211yescharacteristic
60#63944C2218yescomplemented
61#63943C2218yescomplemented
62D3×#216C2218yescomplemented
63#63936C2218yescomplemented
64#63933C2218yescomplemented
65#63929C2218yescomplemented
66C2×#3719C2211yescharacteristic
67C2×#3719C2211yescharacteristic
68C2×#3719C2211yescharacteristic
69C2×#3718C2211yescharacteristic
70C2×#3716C2211yescharacteristic
71C2×#3715C2211yescharacteristic
72C2×#3711C2211yescharacteristic
73C2×#3710C2211yescharacteristic
74C2×D3×C3⋊C8C2211yescharacteristic
75#63811C2218yescomplemented
76#63804C2218yescomplemented
77#63800C2218yescomplemented
78D3×Dic12C2218yescomplemented
79C2×#1010—31no—
80C2×#1010—31no—
81C2×#1010—31no—
82C2×#1007—31no—
83C2×C3×#137—31no—
84C2×C3×#135—31no—
85C2×#951—31no—
86C2×#951—31no—
87C2×#950—31no—
88C22×#216—31no—
89#5779—316no—
90#5771—316no—
91C2×#918—31no—
92C2×#918—31no—
93C2×D3×Q16—31no—
94C2×D3×Q16—31no—
95C2×D3×Q16—31no—
96C2×D3×Q16—31no—
97C2×#916—31no—
98C2×#916D311yescharacteristic, complemented
99C2×#915—31no—
100C2×#915—31no—
101C2×#915—31no—
102C2×#915—31no—
103C2×#915—31no—
104C2×#915—61no—
105C2×#915D311yescharacteristic, complemented
106C2×#912—31no—
107C2×#912—31no—
108C2×#909—31no—
109C2×#907—31no—
110C22×Dic12—31no—
111C2×#901—31no—
112C2×C32×Q8C2311yescharacteristic
113C2×C32×D4C2311yescharacteristic
114C2×#638—21no—
115C22×C3⋊Dic3—21no—
116Q8×C3⋊D3—22no—
117Q8×C3⋊D3C2314yes—
118#3830—22no—
119#3830C2314yes—
120C2×C4×C3⋊D3—21no—
121C2×C4×C3⋊D3C2311yescharacteristic
122C2×#634—21no—
123C2×#634C2311yescharacteristic
124C2×#634C2311yescharacteristic
125C2×C3×#67—21no—
126C2×C3×#67—21no—
127C22×C3×Dic3—21no—
128C22×C3×Dic3—21no—
129C3×#239—22no—
130C3×#239C2314yes—
131C3×D3×Q8—22no—
132C3×D3×Q8C2314yes—
133C3×#237—22no—
134C3×#237—22no—
135C3×#237C2314yes—
136C3×#237C2314yes—
137C2×C3×D12—21no—
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×Dic6C2311yescharacteristic
145C2×C3×Dic6C2311yescharacteristic
146C2×C3×Dic6C2311yescharacteristic
147C2×#627—21no—
148C2×#627—21no—
149C2×#627—21no—
150C2×#627—21no—
151C2×#627—28no—
152C2×#627D411yescharacteristic
153C2×#626—21no—
154C2×#626D411yescharacteristic
155C2×#626D411yescharacteristic
156C2×#625—21no—
157C2×#625D411yescharacteristic
158C2×#624—21no—
159#3805—28no—
160#3804—28no—
161#3804—28no—
162C2×D3×Dic3—21no—
163C2×D3×Dic3—21no—
164C2×D3×Dic3—21no—
165C2×D3×Dic3—21no—
166C2×D3×Dic3—21no—
167#3798—28no—
168#3798D414yes—
169#3798C2314yes—
170#3797—22no—
171#3797C2314yes—
172#3796—22no—
173#3796—28no—
174#3796C2314yes—
175#3795—22no—
176#3795—28no—
177#3795C2314yes—
178D3×Dic6—22no—
179D3×Dic6—22no—
180D3×Dic6—22no—
181D3×Dic6—28no—
182D3×Dic6C2314yes—
183D3×Dic6C2314yes—
184D3×Dic6C2314yes—
185C32×SD16C2314yes—
186C2×C32×C8C2311yescharacteristic
187#3756C2314yes—
188#3754C2314yes—
189C2×C3⋊(C3⋊C8)C2311yescharacteristic
190#3746C2314yes—
191#3743C2314yes—
192C3×#216C2314yes—
193C3×#216C2314yes—
194C3×#214C2314yes—
195C3×#213C2314yes—
196C2×C3×C3⋊C8C2311yescharacteristic
197C2×C3×C3⋊C8C2311yescharacteristic
198C3×Dic12C2314yes—
199C3×#204C2314yes—
200C3×ΓL(1,𝔽25)C2314yes—
201C3×D3×C8C2314yes—
202#3719C2314yes—
203#3719C2314yes—
204#3719C2314yes—
205#3718C2314yes—
206#3716C2314yes—
207#3715C2314yes—
208#3711C2314yes—
209#3710C2314yes—
210D3×C3⋊C8C2314yes—
211C2×#578—91noSylow
212C2×C3×#41—31no—
213C2×C3×#41—31no—
214C2×C3×#41—31no—
215C22×C3×Q8—31no—
216#1010—38no—
217#1010—38no—
218#1010—38no—
219#1010—64no—
220#1010—64no—
221#1010—64no—
222#1007—38no—
223#1007—64no—
224C2×#239—31no—
225C2×#239—61no—
226C2×#239C2×D311yescharacteristic
227C2×D3×Q8—31no—
228C2×D3×Q8—31no—
229C2×D3×Q8—31no—
230C2×D3×Q8—31no—
231C2×D3×Q8—31no—
232C2×D3×Q8—31no—
233C2×D3×Q8—31no—
234C2×D3×Q8—61no—
235C2×D3×Q8—61no—
236C2×D3×Q8C2×D311yescharacteristic
237C2×#237—31no—
238C2×#237—31no—
239C2×#237—31no—
240C2×#237—31no—
241C2×#237—61no—
242C2×#237—61no—
243C2×#237—61no—
244C2×#237—61no—
245C2×#237—61no—
246C2×#237—61no—
247C2×#237—61no—
248C2×#237C2×D311yescharacteristic
249C2×#237C2×D311yescharacteristic
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×Dic6—31no—
259C22×Dic6—31no—
260C22×Dic6—31no—
261C22×Dic6—61no—
262C22×Dic6—61no—
263C22×Dic6—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
273C2×C3×SD16C2×D311yescharacteristic
274C2×C3×D8—31no—
275C2×C3×M16—31no—
276C22×C3×C8—31no—
277#951—38no—
278#951—38no—
279#950—38no—
280C2×#216—31no—
281C2×#216—31no—
282C2×#216—31no—
283C2×#216—31no—
284C2×#216—38no—
285C2×#216—31no—
286C2×#216—31no—
287C2×#216—31no—
288C2×#216—61no—
289C2×#216C2×D311yescharacteristic
290C2×#216C2×D311yescharacteristic
291C2×#215—31no—
292C2×#214—31no—
293C2×#214—31no—
294C2×#214—31no—
295C2×#214—31no—
296C2×#214—61no—
297C2×#214C2×D311yescharacteristic
298C2×#213C2×D311yescharacteristic
299C2×#208—31no—
300C22×C3⋊C8—31no—
301#918—38no—
302#918—38no—
303D3×Q16—38no—
304D3×Q16—38no—
305D3×Q16—38no—
306D3×Q16—38no—
307#916—38no—
308#916C2×D318yescomplemented
309#915—38no—
310#915—38no—
311#915—38no—
312#915—38no—
313#915—38no—
314#915—68no—
315#915C2×D318yescomplemented
316#912—38no—
317#912—38no—
318#909—38no—
319#907—38no—
320C2×Dic12—31no—
321C2×Dic12—31no—
322C2×Dic12—31no—
323C2×Dic12—31no—
324C2×Dic12—31no—
325C2×Dic12—38no—
326C2×Dic12—61no—
327C2×Dic12C2×D311yescharacteristic
328C2×#204—31no—
329C2×#204C2×D311yescharacteristic
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
336C2×D3×C8—31no—
337C2×D3×C8—31no—
338C2×D3×C8—31no—
339C2×D3×C8C2×D311yescharacteristic
340C23×C32—21no—
341C22×C3⋊D3C2×D411yescharacteristic
342C22×C3×D3—21no—
343C22×C3×D3C2×D411yescharacteristic
344C22×C3×D3C2×D411yescharacteristic
345C32×Q8—21no—
346C32×Q8C2412yes—
347C32×D4—21no—
348C32×D4C2412yes—
349C2×C32×C4—21no—
350C2×C32×C4C2411yescharacteristic
351#638—24no—
352C2×C3⋊Dic3—21no—
353C2×C3⋊Dic3—21no—
354C2×C3⋊Dic3—24no—
355C2×C3⋊Dic3C2×D411yescharacteristic
356C4×C3⋊D3—24no—
357C4×C3⋊D3C2×D412yes—
358C4×C3⋊D3C2412yes—
359#634—21no—
360#634—21no—
361#634—24no—
362#634C2412yes—
363#634C2412yes—
364C3×#67—24no—
365C3×#67—24no—
366C2×C3×Dic3—21no—
367C2×C3×Dic3—21no—
368C2×C3×Dic3—21no—
369C2×C3×Dic3—24no—
370C2×C3×Dic3—24no—
371C2×C3×Dic3C2×D411yescharacteristic
372C2×C3×Dic3C2×D411yescharacteristic
373C3×D12—24no—
374C3×D12—21no—
375C3×D12C2412yes—
376C3×C4×D3—24no—
377C3×C4×D3—24no—
378C3×C4×D3C2×D412yes—
379C3×C4×D3C2×D412yes—
380C3×C4×D3C2412yes—
381C3×C4×D3C2412yes—
382C3×Dic6—21no—
383C3×Dic6—21no—
384C3×Dic6—21no—
385C3×Dic6—24no—
386C3×Dic6C2412yes—
387C3×Dic6C2412yes—
388C3×Dic6C2412yes—
389#627—24no—
390#627—24no—
391#627—24no—
392#627—24no—
393#627C2×D414yes—
394#626—24no—
395#626C2×D414yes—
396#626C2×D414yes—
397#625—24no—
398#625C2×D414yes—
399#624—24no—
400D3×Dic3—24no—
401D3×Dic3—24no—
402D3×Dic3—24no—
403D3×Dic3—24no—
404D3×Dic3—24no—
405C32×C8C2412yes—
406C3⋊(C3⋊C8)C2412yes—
407C3×C3⋊C8C2412yes—
408C3×C3⋊C8C2412yes—
409C2×2−1+4—91no—
410C2×2−1+4—91no—
411#578—916no—
412C2×#137—31no—
413C2×#137—91no—
414C2×#137—91no—
415C2×#137—91no—
416C2×#137—91no—
417C2×#137—91no—
418C2×#135—31no—
419C2×#135—91no—
420C2×#135—91no—
421C22×Q16—91no—
422C22×Q16—91no—
423C22×Q16—91no—
424C2×#131—91no—
425C3×#41—34no—
426C3×#41—34no—
427C3×#41—34no—
428C3×#41—62no—
429C3×#41—62no—
430C3×#41—62no—
431C2×C3×Q8—21no—
432C2×C3×Q8—34no—
433C2×C3×Q8—31no—
434C2×C3×Q8—31no—
435C2×C3×Q8—31no—
436C2×C3×Q8—61no—
437C2×C3×Q8—62no—
438C2×C3×Q8C22×D311yescharacteristic
439C2×C3×Q8C22×D311yescharacteristic
440C2×C3×D4—21no—
441C2×C3×D4—31no—
442C2×C3×D4—61no—
443C2×C3×D4—61no—
444C2×C3×D4—61no—
445C2×C3×D4C22×D311yescharacteristic
446C2×C3×D4C22×D311yescharacteristic
447C22×C3×C4—31no—
448C22×C3×C4—31no—
449C22×C3×C4—61no—
450C22×C3×C4—61no—
451C22×C3×C4—61no—
452C22×C3×C4—61no—
453C2×#67—21no—
454C2×#67—21no—
455C2×#67—31no—
456C2×#67—31no—
457C2×#67—31no—
458C2×#67—31no—
459C2×#67—61no—
460C2×#67—61no—
461C2×#67—61no—
462C2×#67—61no—
463C2×#67—61no—
464C2×#67—121no—
465C22×Dic3—21no—
466C22×Dic3—21no—
467C22×Dic3—61no—
468C22×Dic3—61no—
469C22×Dic3—61no—
470C22×Dic3—61no—
471C22×Dic3—61no—
472C22×Dic3—61no—
473C22×Dic3—61no—
474C22×Dic3—121no—
475#239—22no—
476#239—34no—
477#239—62no—
478#239—68no—
479#239C22×D314yes—
480D3×Q8—22no—
481D3×Q8—34no—
482D3×Q8—34no—
483D3×Q8—34no—
484D3×Q8—34no—
485D3×Q8—34no—
486D3×Q8—34no—
487D3×Q8—34no—
488D3×Q8—64no—
489D3×Q8—62no—
490D3×Q8—62no—
491D3×Q8—68no—
492D3×Q8—62no—
493D3×Q8—62no—
494D3×Q8—62no—
495D3×Q8—62no—
496D3×Q8—62no—
497D3×Q8—122no—
498D3×Q8C22×D314yes—
499#237—22no—
500#237—22no—
501#237—34no—
502#237—34no—
503#237—34no—
504#237—34no—
505#237—64no—
506#237—62no—
507#237—68no—
508#237—68no—
509#237—62no—
510#237—62no—
511#237—68no—
512#237—68no—
513#237—68no—
514#237—68no—
515#237—62no—
516#237—122no—
517#237C22×D314yes—
518#237C22×D314yes—
519#235—34no—
520#235—34no—
521#235—34no—
522#235—34no—
523#235—34no—
524#235—68no—
525#235—68no—
526#235—68no—
527#235—62no—
528#235—68no—
529#235—68no—
530C2×D12—21no—
531C2×D12—31no—
532C2×D12—31no—
533C2×D12—61no—
534C2×D12C22×D311yescharacteristic
535C2×C4×D3—21no—
536C2×C4×D3—21no—
537C2×C4×D3—31no—
538C2×C4×D3—31no—
539C2×C4×D3—61no—
540C2×C4×D3—61no—
541C2×C4×D3—61no—
542C2×C4×D3—61no—
543C2×C4×D3—61no—
544C2×C4×D3—61no—
545C2×C4×D3—61no—
546C2×C4×D3—61no—
547C2×C4×D3—61no—
548C2×C4×D3—61no—
549C2×C4×D3—121no—
550C2×C4×D3C22×D311yescharacteristic
551C2×C4×D3C22×D311yescharacteristic
552C2×Dic6—21no—
553C2×Dic6—31no—
554C2×Dic6—31no—
555C2×Dic6—31no—
556C2×Dic6—31no—
557C2×Dic6—31no—
558C2×Dic6—31no—
559C2×Dic6—34no—
560C2×Dic6—34no—
561C2×Dic6—34no—
562C2×Dic6—61no—
563C2×Dic6—61no—
564C2×Dic6—68no—
565C2×Dic6—62no—
566C2×Dic6—62no—
567C2×Dic6—62no—
568C2×Dic6—68no—
569C2×Dic6—68no—
570C2×Dic6—61no—
571C2×Dic6—61no—
572C2×Dic6—61no—
573C2×Dic6—61no—
574C2×Dic6—61no—
575C2×Dic6—61no—
576C2×Dic6—61no—
577C2×Dic6—61no—
578C2×Dic6—61no—
579C2×Dic6—61no—
580C2×Dic6—121no—
581C2×Dic6C22×D311yescharacteristic
582C2×Dic6C22×D311yescharacteristic
583C2×Dic6C22×D311yescharacteristic
584C3×Q16—34no—
585C3×Q16—34no—
586C3×Q16—34no—
587C3×SD16—24no—
588C3×SD16—34no—
589C3×SD16—34no—
590C3×SD16C22×D314yes—
591C3×SD16C22×D314yes—
592C3×D8—34no—
593C3×M16—34no—
594C2×C3×C8—21no—
595C2×C3×C8—31no—
596C2×C3×C8—31no—
597C2×C3×C8—34no—
598C2×C3×C8C22×D311yescharacteristic
599C2×C3×C8C22×D311yescharacteristic
600#216—34no—
601#216—34no—
602#216—34no—
603#216—34no—
604#216—34no—
605#216—34no—
606#216—34no—
607#216—64no—
608#216C22×D314yes—
609#216C22×D314yes—
610#215—34no—
611#214—34no—
612#214—34no—
613#214—34no—
614#214—34no—
615#214—64no—
616#214C22×D314yes—
617#213C22×D314yes—
618#208—34no—
619C2×C3⋊C8—31no—
620C2×C3⋊C8—31no—
621C2×C3⋊C8—34no—
622C2×C3⋊C8—61no—
623C2×C3⋊C8C22×D311yescharacteristic
624C2×C3⋊C8C22×D311yescharacteristic
625Dic12—34no—
626Dic12—34no—
627Dic12—34no—
628Dic12—34no—
629Dic12—34no—
630Dic12—64no—
631Dic12C22×D314yes—
632#204—34no—
633#204C22×D314yes—
634ΓL(1,𝔽25)—34no—
635ΓL(1,𝔽25)—34no—
636ΓL(1,𝔽25)—34no—
637ΓL(1,𝔽25)—64no—
638ΓL(1,𝔽25)C22×D314yes—
639D3×C8—34no—
640D3×C8—34no—
641D3×C8—34no—
642D3×C8C22×D314yes—
643C22×C32—22no—
644C22×C32—42no—
645C22×C32C22×D411yescharacteristic
646C2×C3⋊D3—22no—
647C2×C3⋊D3C22×D412yes—
648C2×C3×D3—22no—
649C2×C3×D3—22no—
650C2×C3×D3—22no—
651C2×C3×D3—42no—
652C2×C3×D3C22×D412yes—
653C2×C3×D3C22×D412yes—
654C32×C4—22no—
655C32×C4C22×D411yescharacteristic
656C32×C4C2511yescharacteristic
657C3⋊Dic3—22no—
658C3⋊Dic3—22no—
659C3⋊Dic3C22×D412yes—
660C3×Dic3—22no—
661C3×Dic3—22no—
662C3×Dic3—22no—
663C3×Dic3C22×D412yes—
664C3×Dic3C22×D412yes—
6652−1+4—98no—
6662−1+4—98no—
6672−1+4—184no—
6682−1+4—184no—
669C2×#41—31no—
670C2×#41—31no—
671C2×#41—31no—
672C2×#41—91no—
673C2×#41—91no—
674C2×#41—91no—
675C2×#41—91no—
676C2×#41—181no—
677C2×#41—181no—
678C2×#41—181no—
679C2×#41—181no—
680C2×#41—181no—
681C2×#41—181no—
682C22×Q8—31no—
683C22×Q8—91no—
684C22×Q8—91no—
685C22×Q8—91no—
686C22×Q8—91no—
687C22×Q8—91no—
688C22×Q8—181no—
689C22×Q8—181no—
690#137—38no—
691#137—98no—
692#137—98no—
693#137—98no—
694#137—98no—
695#137—98no—
696#135—38no—
697#135—98no—
698#135—98no—
699C2×Q16—31no—
700C2×Q16—31no—
701C2×Q16—31no—
702C2×Q16—98no—
703C2×Q16—91no—
704C2×Q16—91no—
705C2×Q16—91no—
706C2×Q16—98no—
707C2×Q16—98no—
708C2×Q16—91no—
709C2×Q16—91no—
710C2×Q16—91no—
711C2×SD16—31no—
712C2×SD16—31no—
713C2×SD16—91no—
714C2×SD16—91no—
715C2×SD16—91no—
716C2×SD16D3211yescharacteristic
717C2×D8—31no—
718#131—98no—
719C2×M16—31no—
720C2×M16—91no—
721C2×M16—91no—
722C22×C8—31no—
723C22×C8—91no—
724C22×C8—91no—
725C23×C3—21no—
726C23×C3—21no—
727C23×C3—31no—
728C23×C3—31no—
729C23×C3—41no—
730C23×C3—61no—
731C22×D3—21no—
732C22×D3—31no—
733C22×D3—31no—
734C22×D3—61no—
735C22×D3D3×D411yescharacteristic
736C22×D3D3×D411yescharacteristic
737C3×Q8—21no—
738C3×Q8—21no—
739C3×Q8—22no—
740C3×Q8—32no—
741C3×Q8—32no—
742C3×Q8—32no—
743C3×Q8—41no—
744C3×Q8—64no—
745C3×Q8—61no—
746C3×Q8—61no—
747C3×Q8—61no—
748C3×Q8C23×D312yes—
749C3×Q8C23×D312yes—
750C3×D4—21no—
751C3×D4—21no—
752C3×D4—22no—
753C3×D4—32no—
754C3×D4—41no—
755C3×D4—64no—
756C3×D4—64no—
757C3×D4—64no—
758C3×D4—61no—
759C3×D4C23×D312yes—
760C3×D4C23×D312yes—
761C2×C3×C4—21no—
762C2×C3×C4—21no—
763C2×C3×C4—21no—
764C2×C3×C4—31no—
765C2×C3×C4—31no—
766C2×C3×C4—32no—
767C2×C3×C4—32no—
768C2×C3×C4—32no—
769C2×C3×C4—32no—
770C2×C3×C4—41no—
771C2×C3×C4—64no—
772C2×C3×C4—64no—
773C2×C3×C4—64no—
774C2×C3×C4—64no—
775C2×C3×C4—61no—
776C2×C3×C4—61no—
777C2×C3×C4—61no—
778C2×C3×C4C23×D311yescharacteristic
779C2×C3×C4C23×D311yescharacteristic
780#67—24no—
781#67—24no—
782#67—34no—
783#67—34no—
784#67—34no—
785#67—34no—
786#67—64no—
787#67—64no—
788#67—64no—
789#67—64no—
790#67—64no—
791#67—124no—
792C2×Dic3—21no—
793C2×Dic3—21no—
794C2×Dic3—21no—
795C2×Dic3—24no—
796C2×Dic3—24no—
797C2×Dic3—31no—
798C2×Dic3—31no—
799C2×Dic3—61no—
800C2×Dic3—64no—
801C2×Dic3—64no—
802C2×Dic3—64no—
803C2×Dic3—64no—
804C2×Dic3—64no—
805C2×Dic3—64no—
806C2×Dic3—61no—
807C2×Dic3—61no—
808C2×Dic3—61no—
809C2×Dic3—61no—
810C2×Dic3—64no—
811C2×Dic3—124no—
812C2×Dic3—121no—
813C2×Dic3—121no—
814C2×Dic3D3×D411yescharacteristic
815C2×Dic3D3×D411yescharacteristic
816D12—24no—
817D12—21no—
818D12—34no—
819D12—34no—
820D12—64no—
821D12C23×D312yes—
822C4×D3—24no—
823C4×D3—24no—
824C4×D3—32no—
825C4×D3—32no—
826C4×D3—32no—
827C4×D3—32no—
828C4×D3—62no—
829C4×D3—62no—
830C4×D3—64no—
831C4×D3—64no—
832C4×D3—64no—
833C4×D3—64no—
834C4×D3—64no—
835C4×D3—64no—
836C4×D3—64no—
837C4×D3—64no—
838C4×D3—64no—
839C4×D3—124no—
840C4×D3D3×D412yes—
841C4×D3D3×D412yes—
842C4×D3C23×D312yes—
843C4×D3C23×D312yes—
844Dic6—21no—
845Dic6—21no—
846Dic6—21no—
847Dic6—24no—
848Dic6—34no—
849Dic6—34no—
850Dic6—32no—
851Dic6—32no—
852Dic6—32no—
853Dic6—32no—
854Dic6—62no—
855Dic6—62no—
856Dic6—64no—
857Dic6—64no—
858Dic6—64no—
859Dic6—64no—
860Dic6—64no—
861Dic6—64no—
862Dic6—64no—
863Dic6—61no—
864Dic6—61no—
865Dic6—61no—
866Dic6—61no—
867Dic6—64no—
868Dic6—64no—
869Dic6—64no—
870Dic6—124no—
871Dic6—121no—
872Dic6—121no—
873Dic6C23×D312yes—
874Dic6C23×D312yes—
875Dic6C23×D312yes—
876C3×C8—22no—
877C3×C8—32no—
878C3×C8—32no—
879C3×C8C23×D312yes—
880C3×C8C23×D312yes—
881C3⋊C8—32no—
882C3⋊C8—32no—
883C3⋊C8—62no—
884C3⋊C8C23×D312yes—
885C3⋊C8C23×D312yes—
886C2×C32—42no—
887C2×C32#57812yescomplemented
888C2×C32C23×D411yescharacteristic
889C3⋊D3—22no—
890C3×D3—22no—
891C3×D3—22no—
892C3×D3—42no—
893#41—34no—
894#41—34no—
895#41—34no—
896#41—62no—
897#41—62no—
898#41—62no—
899#41—94no—
900#41—94no—
901#41—94no—
902#41—94no—
903#41—94no—
904#41—182no—
905#41—188no—
906#41—188no—
907#41—188no—
908#41—188no—
909#41—182no—
910#41—182no—
911#41—188no—
912#41—188no—
913C2×Q8—34no—
914C2×Q8—31no—
915C2×Q8—31no—
916C2×Q8—31no—
917C2×Q8—61no—
918C2×Q8—62no—
919C2×Q8—91no—
920C2×Q8—94no—
921C2×Q8—94no—
922C2×Q8—94no—
923C2×Q8—94no—
924C2×Q8—94no—
925C2×Q8—91no—
926C2×Q8—91no—
927C2×Q8—181no—
928C2×Q8—181no—
929C2×Q8—181no—
930C2×Q8—181no—
931C2×Q8—182no—
932C2×Q8—182no—
933C2×Q8—182no—
934C2×Q8—181no—
935C2×Q8—188no—
936C2×Q8—188no—
937C2×Q8—182no—
938C2×Q8—182no—
939C2×Q8C2×D3211yescharacteristic
940C2×D4—31no—
941C2×D4—61no—
942C2×D4—61no—
943C2×D4—61no—
944C2×D4—91no—
945C2×D4—91no—
946C2×D4—91no—
947C2×D4—181no—
948C2×D4—181no—
949C2×D4—181no—
950C2×D4C2×D3211yescharacteristic
951C22×C4—31no—
952C22×C4—31no—
953C22×C4—61no—
954C22×C4—61no—
955C22×C4—61no—
956C22×C4—61no—
957C22×C4—91no—
958C22×C4—181no—
959C22×C4—181no—
960C22×C4—181no—
961C22×C4—181no—
962C22×C4—181no—
963C22×C4—181no—
964C22×C4—181no—
965C22×C4—181no—
966Q16—34no—
967Q16—34no—
968Q16—34no—
969Q16—94no—
970Q16—94no—
971Q16—94no—
972Q16—94no—
973Q16—94no—
974Q16—94no—
975SD16—34no—
976SD16—34no—
977SD16—94no—
978SD16—94no—
979SD16—94no—
980SD16C2×D3214yes—
981D8—34no—
982M16—34no—
983M16—94no—
984M16—94no—
985C2×C8—31no—
986C2×C8—31no—
987C2×C8—34no—
988C2×C8—94no—
989C2×C8—94no—
990C2×C8—91no—
991C2×C8C2×D3211yescharacteristic
992C22×C3—22no—
993C22×C3—22no—
994C22×C3—21no—
995C22×C3—32no—
996C22×C3—32no—
997C22×C3—42no—
998C22×C3—42no—
999C22×C3—42no—
1000C22×C3—62no—
1001C22×C3—62no—
1002C22×C3—62no—
1003C22×C3—82no—
1004C22×C3—122no—
1005C22×C3C2×D3×D411yescharacteristic
1006C22×C3C2×D3×D411yescharacteristic
1007C2×D3—22no—
1008C2×D3—22no—
1009C2×D3—22no—
1010C2×D3—32no—
1011C2×D3—32no—
1012C2×D3—42no—
1013C2×D3—62no—
1014C2×D3—62no—
1015C2×D3—62no—
1016C2×D3—122no—
1017C2×D3C2×D3×D412yes—
1018C2×D3C2×D3×D412yes—
1019C3×C4—22no—
1020C3×C4—22no—
1021C3×C4—21no—
1022C3×C4—21no—
1023C3×C4—32no—
1024C3×C4—32no—
1025C3×C4—42no—
1026C3×C4—62no—
1027C3×C4—62no—
1028C3×C4—62no—
1029C3×C4C2×D3×D411yescharacteristic
1030C3×C4C2×D3×D411yescharacteristic
1031C3×C4C24×D311yescharacteristic
1032C3×C4C24×D311yescharacteristic
1033Dic3—22no—
1034Dic3—22no—
1035Dic3—22no—
1036Dic3—32no—
1037Dic3—32no—
1038Dic3—62no—
1039Dic3—62no—
1040Dic3—62no—
1041Dic3—62no—
1042Dic3—62no—
1043Dic3—122no—
1044Dic3—122no—
1045Dic3C2×D3×D412yes—
1046Dic3C2×D3×D412yes—
1047C32C2×#57811yescharacteristic, complemented, Sylow
1048C23—21no—
1049C23—31no—
1050C23—31no—
1051C23—61no—
1052C23—91no—
1053Q8—21no—
1054Q8—32no—
1055Q8—32no—
1056Q8—32no—
1057Q8—64no—
1058Q8—61no—
1059Q8—61no—
1060Q8—61no—
1061Q8—94no—
1062Q8—92no—
1063Q8—92no—
1064Q8—184no—
1065Q8—184no—
1066Q8—184no—
1067Q8—184no—
1068Q8—184no—
1069Q8—181no—
1070Q8—181no—
1071Q8C22×D3212yes—
1072D4—21no—
1073D4—32no—
1074D4—64no—
1075D4—64no—
1076D4—64no—
1077D4—61no—
1078D4—94no—
1079D4—94no—
1080D4—94no—
1081D4—184no—
1082D4—184no—
1083D4—184no—
1084D4C22×D3212yes—
1085C2×C4—21no—
1086C2×C4—31no—
1087C2×C4—31no—
1088C2×C4—32no—
1089C2×C4—32no—
1090C2×C4—32no—
1091C2×C4—32no—
1092C2×C4—64no—
1093C2×C4—64no—
1094C2×C4—64no—
1095C2×C4—64no—
1096C2×C4—61no—
1097C2×C4—61no—
1098C2×C4—61no—
1099C2×C4—91no—
1100C2×C4—92no—
1101C2×C4—92no—
1102C2×C4—184no—
1103C2×C4—184no—
1104C2×C4—184no—
1105C2×C4—184no—
1106C2×C4—184no—
1107C2×C4—184no—
1108C2×C4—184no—
1109C2×C4—184no—
1110C2×C4—181no—
1111C2×C4—181no—
1112C2×C4C22×D3211yescharacteristic
1113C8—32no—
1114C8—32no—
1115C8—92no—
1116C8C22×D3212yes—
1117C2×C3—21no—
1118C2×C3—22no—
1119C2×C3—42no—
1120C2×C3—42no—
1121C2×C3—62no—
1122C2×C3—62no—
1123C2×C3—82no—
1124C2×C3—122no—
1125C2×C3#577112yescomplemented
1126C2×C3#577912yescomplemented
1127C2×C3C22×D3×D411yescharacteristic
1128C2×C3C22×D3×D411yescharacteristic
1129D3—22no—
1130D3—22no—
1131D3—42no—
1132D3—62no—
1133D3—62no—
1134D3—122no—
1135C22—22no—
1136C22—32no—
1137C22—32no—
1138C22—42no—
1139C22—62no—
1140C22—62no—
1141C22—62no—
1142C22—92no—
1143C22—122no—
1144C22—182no—
1145C22D32×D411yescharacteristic
1146C4—22no—
1147C4—32no—
1148C4—32no—
1149C4—62no—
1150C4—62no—
1151C4—62no—
1152C4—92no—
1153C4—182no—
1154C4—182no—
1155C4D32×D411yescharacteristic
1156C4C23×D3211yescharacteristic
1157C3—21no—
1158C3C2×#577111yescharacteristic, complemented
1159C3C2×#577911yescharacteristic, complemented
1160C2—42no—
1161C2—62no—
1162C2—62no—
1163C2—122no—
1164C2—182no—
1165C2#1059475612yesdirect product factor
1166C2C2×D32×D411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32C2×#578
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×#64315C2semidirect
2. C2×#64309C2semidirect
3. C2×#64124C2semidirect
4. C2×C3×#916C2semidirect
5. C2×C3×#915C2semidirect
6. C2×#63944C2semidirect
7. C2×#63943C2semidirect
8. C2×D3×#216C2semidirect
9. C2×#63936C2semidirect
10. C2×#63933C2semidirect
11. C2×#63929C2semidirect
12. #10594756C2direct (N × H)
13. C2×#63811C2semidirect
14. C2×#63804C2semidirect
15. C2×#63800C2semidirect
16. C2×D3×Dic12C2semidirect
30. #64315C22semidirect
32. #64309C22semidirect
47. #64124C22semidirect
54. C3×#916C22semidirect
55. C3×#915C22semidirect
60. #63944C22semidirect
61. #63943C22semidirect
62. D3×#216C22semidirect
63. #63936C22semidirect
64. #63933C22semidirect
65. #63929C22semidirect
75. #63811C22semidirect
76. #63804C22semidirect
77. #63800C22semidirect
78. D3×Dic12C22semidirect
98. C2×#916D3semidirect
105. C2×#915D3semidirect
308. #916C2×D3semidirect
315. #915C2×D3semidirect
887. C2×C32#578semidirect
1047. C32C2×#578semidirect
1125. C2×C3#5771semidirect
1126. C2×C3#5779semidirect
1158. C3C2×#5771semidirect
1159. C3C2×#5779semidirect
1165. C2#10594756direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643152
C2×#643092
C2×#641242
C2×C3×#9162
C2×C3×#9152
C2×#639442
C2×#639432
C2×D3×#2162
C2×#639362
C2×#639332
C2×#639292
#105947562
C2×#638112
C2×#638042
C2×#638002
C2×D3×Dic122
C2×#57793
C2×#57713