Finite Group Databasebeta

← C2×#87211 #11709034

Subgroups — C2×#87211 #11709034

Order 768.

10794 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×2−1+4C211yesmaximal, characteristic, complemented
2C2×#5968C211yesmaximal, characteristic, complemented
3C2×C3×#578C211yesmaximal, characteristic, complemented
4C2×#5838C211yesmaximal, characteristic, complemented
5C2×#5837C211yesmaximal, characteristic, complemented
6#87211C2132yesmaximal, direct product factor
7C2×#5779C213yesmaximal, complemented
8C2×#5778C213yesmaximal, complemented
9C2×#5777C213yesmaximal, complemented
10C2×D3×#137C213yesmaximal, complemented
11C2×#5770C213yesmaximal, complemented
12C2×#5768C213yesmaximal, complemented
13C2×#5766C213yesmaximal, complemented
14C22×#918C213yesmaximal, complemented
15C2×#5751C211yesmaximal, characteristic, complemented
16C2×#5750C211yesmaximal, characteristic, complemented
17C2×#3586—31nomaximal, Sylow
18C2×C3×2−1+4C2211yescharacteristic, complemented
19C2×C3×2−1+4C2211yescharacteristic, complemented
20#5968—28no—
21#5968C22116yescomplemented
22D3×2−1+4—28no—
23D3×2−1+4C22116yescomplemented
24C2×#1010—23no—
25C2×#1010C2213yescomplemented
26C2×#1010C2211yescharacteristic, complemented
27C2×#1009—23no—
28C2×#1009C2213yescomplemented
29C2×#1009C2211yescharacteristic, complemented
30C2×D3×#41—23no—
31C2×D3×#41—23no—
32C2×D3×#41C2213yes—
33C2×D3×#41C2211yescharacteristic
34C2×D3×#41C2213yescomplemented
35C2×#1007—21no—
36C2×#1007—21no—
37C2×#1007C2213yescomplemented
38C2×#1007C2213yescomplemented
39C22×#239—21no—
40C22×#239C2213yes—
41C22×D3×Q8—21no—
42C22×D3×Q8C2213yescomplemented
43C3×#578C22116yescomplemented
44C2×C3×#137C2213yescomplemented
45C2×C3×#137C2213yescomplemented
46C2×C3×#135C2213yescomplemented
47C22×C3×Q16C2213yescomplemented
48C2×C3×#131C2211yescharacteristic, complemented
49#5838C22116yescomplemented
50#5837C22116yescomplemented
51C2×#951C2213yescomplemented
52C2×#950C2213yescomplemented
53C2×#950C2213yescomplemented
54C2×#949C2213yescomplemented
55C2×#948C2211yescharacteristic, complemented
56C22×#216C2213yescomplemented
57C2×#942C2213yescomplemented
58C2×#942C2213yescomplemented
59C22×#215C2213yescomplemented
60#5779C22148yescomplemented
61#5778C22148yescomplemented
62#5777C22148yescomplemented
63D3×#137C22148yescomplemented
64#5770C22148yescomplemented
65#5768C22148yescomplemented
66#5766C22148yescomplemented
67C2×#919C2216yescomplemented
68C2×#918C2213yescomplemented
69C2×#918C2216yescomplemented
70C2×#918C2216yescomplemented
71C2×#918C2216yescomplemented
72C2×#918C2213yescomplemented
73C2×#918C22148yescomplemented
74C2×D3×Q16C2216yescomplemented
75C2×#916C2216yescomplemented
76C2×#915C2213yescomplemented
77C2×#915C2213yescomplemented
78C2×#914C2213yescomplemented
79C2×#914C2213yescomplemented
80C2×D3×SD16C2216yescomplemented
81C2×#911C2211yescharacteristic, complemented
82C2×#911C2213yescomplemented
83#5751C22116yescomplemented
84#5750C22116yescomplemented
85C2×#909C2213yescomplemented
86C2×#908C2213yescomplemented
87C2×#907C2213yescomplemented
88C2×D3×M16C2213yescomplemented
89C2×#904C2213yescomplemented
90C22×#204C2213yescomplemented
91C2×#901C2213yescomplemented
92C22×ΓL(1,𝔽25)C2213yescomplemented
93C2×#585—31no—
94C22×2−1+4—31no—
95#3586—332no—
96C2×#578—31no—
97C2×#578—33no—
98C2×#578—33no—
99C2×#578D311yescharacteristic, complemented
100C2×#577—31no—
101C2×#577—33no—
102C2×#577—33no—
103C2×#577—31no—
104C2×#575—33no—
105C2×#575—33no—
106C22×#137—33no—
107C22×#137—33no—
108C2×#568—31no—
109C3×2−1+4—24no—
110C3×2−1+4—24no—
111C3×2−1+4C2318yescomplemented
112C3×2−1+4C2318yescomplemented
113C2×C3×#41—23no—
114C2×C3×#41—23no—
115C2×C3×#41C2313yes—
116C2×C3×#41C2313yes—
117C2×C3×#41C2311yescharacteristic
118C22×C3×Q8—21no—
119C22×C3×Q8—21no—
120C22×C3×Q8C2313yes—
121C22×C3×Q8C2313yes—
122#1010—24no—
123#1010—248no—
124#1010—212no—
125#1010C23124yescomplemented
126#1010C2318yescomplemented
127#1009—24no—
128#1009—248no—
129#1009—212no—
130#1009C23124yescomplemented
131#1009C2318yescomplemented
132D3×#41—248no—
133D3×#41—248no—
134D3×#41—212no—
135D3×#41—212no—
136D3×#41D418yes—
137D3×#41C23124yes—
138D3×#41C2318yes—
139D3×#41C23124yescomplemented
140#1007—216no—
141#1007—216no—
142#1007—212no—
143#1007—212no—
144#1007C23124yescomplemented
145#1007C23124yescomplemented
146C2×#239—21no—
147C2×#239—216no—
148C2×#239—23no—
149C2×#239—23no—
150C2×#239—23no—
151C2×#239—23no—
152C2×#239—212no—
153C2×#239D411yescharacteristic
154C2×#239C2313yes—
155C2×#239C2316yes—
156C2×#239C23124yes—
157C2×#239C2313yes—
158C2×D3×Q8—21no—
159C2×D3×Q8—216no—
160C2×D3×Q8—23no—
161C2×D3×Q8—23no—
162C2×D3×Q8—212no—
163C2×D3×Q8—23no—
164C2×D3×Q8—23no—
165C2×D3×Q8D411yescharacteristic
166C2×D3×Q8C2313yes—
167C2×D3×Q8C2316yes—
168C2×D3×Q8C2313yes—
169C2×D3×Q8C23124yescomplemented
170C2×#237—23no—
171C2×#237—26no—
172C2×#237—23no—
173C2×#237—23no—
174C2×#237D413yes—
175C2×#237C2311yescharacteristic
176C2×#237C2313yes—
177C2×D3×D4—23no—
178C2×D3×D4—23no—
179C2×D3×D4—23no—
180C2×D3×D4—26no—
181C2×D3×D4D413yes—
182C2×D3×D4C2313yes—
183C2×D3×D4C2311yescharacteristic
184C2×#235—26no—
185C2×#235—26no—
186C2×#235—23no—
187C2×#235—23no—
188C2×#235—23no—
189C2×#235—23no—
190C2×#235C2313yes—
191C2×#235C2313yes—
192C2×#235C2313yes—
193C22×D12—23no—
194C22×D12—23no—
195C22×D12C2313yes—
196C22×C4×D3—23no—
197C22×C4×D3—23no—
198C22×C4×D3—23no—
199C22×C4×D3—23no—
200C22×C4×D3C2313yes—
201C22×Dic6—23no—
202C22×Dic6—23no—
203C22×Dic6C2313yes—
204C3×#137C23124yescomplemented
205C3×#137C23124yescomplemented
206C3×#135C23124yescomplemented
207C2×C3×Q16C2313yes—
208C2×C3×Q16C2316yes—
209C2×C3×Q16C23124yescomplemented
210C2×C3×SD16C2313yes—
211C2×C3×SD16C2313yes—
212C2×C3×D8C2311yescharacteristic
213C3×#131C2318yescomplemented
214C2×C3×M16C2313yes—
215C22×C3×C8C2313yes—
216#951C23124yescomplemented
217#950C23124yescomplemented
218#950C23124yescomplemented
219#949C23124yescomplemented
220#948C2318yescomplemented
221C2×#216C2313yes—
222C2×#216C2313yes—
223C2×#216C2316yes—
224C2×#216C23124yescomplemented
225#942C23124yescomplemented
226#942C23124yescomplemented
227C2×#215C2316yes—
228C2×#215C2313yes—
229C2×#215C2313yes—
230C2×#215C23124yescomplemented
231C2×#214C2313yes—
232C2×#214C2311yescharacteristic
233C2×#213C2311yescharacteristic
234C2×#213C2313yes—
235C2×#208C2313yes—
236C22×C3⋊C8C2313yes—
237#919C23148yescomplemented
238#918C23124yescomplemented
239#918C23148yescomplemented
240#918C23148yescomplemented
241#918C23148yescomplemented
242#918C23124yescomplemented
243D3×Q16C23148yescomplemented
244#916C23148yescomplemented
245#915C23124yescomplemented
246#915C23124yescomplemented
247#914C23124yescomplemented
248#914C23124yescomplemented
249D3×SD16C23148yescomplemented
250#911C2318yescomplemented
251#911C23124yescomplemented
252#909C23124yescomplemented
253#908C23124yescomplemented
254#907C23124yescomplemented
255D3×M16C23124yescomplemented
256C2×Dic12C2313yes—
257#904C23124yescomplemented
258C2×D24C2313yes—
259C2×#204C2313yes—
260C2×#204C2316yes—
261C2×#204C2311yescharacteristic
262C2×#204C23124yescomplemented
263#901C23124yescomplemented
264C2×ΓL(1,𝔽25)C2311yescharacteristic
265C2×ΓL(1,𝔽25)C2313yes—
266C2×ΓL(1,𝔽25)C2313yes—
267C2×ΓL(1,𝔽25)C2313yes—
268C2×ΓL(1,𝔽25)C23124yescomplemented
269C2×D3×C8C2316yes—
270#585—316no—
271#585—68no—
272C2×2−1+4—316no—
273C2×2−1+4—33no—
274C2×2−1+4—31no—
275C2×2−1+4—33no—
276C2×2−1+4—33no—
277C2×2−1+4—61no—
278C2×2−1+4—61no—
279C2×2−1+4—63no—
280C2×2−1+4—68no—
281C2×2−1+4C2×D311yescharacteristic, complemented
282C2×2−1+4C2×D311yescharacteristic, complemented
283C2×H(5,𝔽2)—33no—
284C2×H(5,𝔽2)—31no—
285C2×H(5,𝔽2)—63no—
286C22×#41—31no—
287C22×#41—33no—
288C22×#41—33no—
289C22×#41—33no—
290C22×#41—63no—
291C22×#41—61no—
292C22×#41—63no—
293C23×Q8—33no—
294C23×Q8—61no—
295#578—316no—
296#578—348no—
297#578—348no—
298#578C2×D3116yescomplemented
299#577—316no—
300#577—348no—
301#577—348no—
302#577—316no—
303#575—348no—
304#575—348no—
305C2×#137—33no—
306C2×#137—33no—
307C2×#137—33no—
308C2×#137—348no—
309C2×#137—36no—
310C2×#137—33no—
311C2×#137—36no—
312C2×#137—36no—
313C2×#137—33no—
314C2×#137—348no—
315C2×#137—33no—
316C2×#137—33no—
317C2×#137—33no—
318C2×#137C2×D313yescomplemented
319C2×#137C2×D313yescomplemented
320C2×AGL(1,ℤ/8)—33no—
321C2×AGL(1,ℤ/8)—33no—
322C2×AGL(1,ℤ/8)—33no—
323C2×AGL(1,ℤ/8)—31no—
324C2×AGL(1,ℤ/8)—33no—
325C2×AGL(1,ℤ/8)—33no—
326C2×#135—33no—
327C2×#135—33no—
328C2×#135—36no—
329C2×#135—36no—
330C2×#135—33no—
331C2×#135C2×D313yescomplemented
332C22×Q16—33no—
333C22×Q16—36no—
334C22×Q16C2×D313yescomplemented
335C22×SD16—33no—
336C22×SD16—36no—
337C22×SD16—33no—
338#568—316no—
339C2×#131—31no—
340C2×#131—33no—
341C2×#131—33no—
342C2×#131C2×D311yescharacteristic, complemented
343C22×M16—33no—
344C22×M16—33no—
345C23×D3—23no—
346C23×D3—21no—
347C23×D3—23no—
348C23×D3C2×D413yes—
349C3×#41—224no—
350C3×#41—224no—
351C3×#41—26no—
352C3×#41—26no—
353C3×#41C2×D414yes—
354C3×#41C24112yes—
355C3×#41C24112yes—
356C3×#41C2414yes—
357C2×C3×Q8—28no—
358C2×C3×Q8—28no—
359C2×C3×Q8—23no—
360C2×C3×Q8—26no—
361C2×C3×Q8—23no—
362C2×C3×Q8—26no—
363C2×C3×Q8C2×D411yescharacteristic
364C2×C3×Q8C2413yes—
365C2×C3×Q8C2413yes—
366C2×C3×Q8C24112yes—
367C2×C3×Q8C24112yes—
368C2×C3×D4—23no—
369C2×C3×D4—23no—
370C2×C3×D4C2×D413yes—
371C2×C3×D4C2411yescharacteristic
372C2×C3×D4C2411yescharacteristic
373C22×C3×C4—23no—
374C22×C3×C4—23no—
375C22×C3×C4—23no—
376C22×C3×C4—23no—
377C22×C3×C4C2413yes—
378C2×#67—23no—
379C2×#67—23no—
380C2×#67—21no—
381C2×#67—23no—
382C2×#67—23no—
383C2×#67—21no—
384C2×#67C2×D416yes—
385C22×Dic3—23no—
386C22×Dic3—23no—
387C22×Dic3—21no—
388C22×Dic3C2×D413yes—
389#239—28no—
390#239—224no—
391#239—224no—
392#239—224no—
393#239—26no—
394#239—224no—
395#239—212no—
396#239—26no—
397#239C2×D418yes—
398#239C24112yes—
399#239C24112yes—
400#239C24124yes—
401D3×Q8—28no—
402D3×Q8—26no—
403D3×Q8—224no—
404D3×Q8—212no—
405D3×Q8—224no—
406D3×Q8—26no—
407D3×Q8—224no—
408D3×Q8—224no—
409D3×Q8C2×D418yes—
410D3×Q8C24124yes—
411D3×Q8C24112yes—
412D3×Q8C24112yes—
413#237—224no—
414#237—248no—
415#237—224no—
416#237—224no—
417#237—22no—
418#237—26no—
419#237C2×D4124yes—
420#237C2414yes—
421#237C24112yes—
422D3×D4—224no—
423D3×D4—224no—
424D3×D4—224no—
425D3×D4—248no—
426D3×D4—22no—
427D3×D4—26no—
428D3×D4C2×D4124yes—
429D3×D4C24112yes—
430D3×D4C2414yes—
431#235—26no—
432#235—26no—
433#235—248no—
434#235—248no—
435#235—224no—
436#235—224no—
437#235—224no—
438#235—224no—
439#235C2×D4112yes—
440#235C24112yes—
441#235C24112yes—
442#235C24112yes—
443C2×D12—23no—
444C2×D12—26no—
445C2×D12—224no—
446C2×D12—23no—
447C2×D12—23no—
448C2×D12—26no—
449C2×D12—224no—
450C2×D12C2×D413yes—
451C2×D12C2413yes—
452C2×D12C2411yescharacteristic
453C2×D12C24112yes—
454C2×C4×D3—23no—
455C2×C4×D3—23no—
456C2×C4×D3—26no—
457C2×C4×D3—224no—
458C2×C4×D3—23no—
459C2×C4×D3—23no—
460C2×C4×D3—23no—
461C2×C4×D3—26no—
462C2×C4×D3—23no—
463C2×C4×D3—224no—
464C2×C4×D3—224no—
465C2×C4×D3—224no—
466C2×C4×D3C2×D413yes—
467C2×C4×D3C2×D413yes—
468C2×C4×D3C2×D4112yes—
469C2×C4×D3C2413yes—
470C2×C4×D3C2411yescharacteristic
471C2×C4×D3C24112yes—
472C2×Dic6—23no—
473C2×Dic6—26no—
474C2×Dic6—26no—
475C2×Dic6—23no—
476C2×Dic6—224no—
477C2×Dic6—23no—
478C2×Dic6—224no—
479C2×Dic6C2×D413yes—
480C2×Dic6C2413yes—
481C2×Dic6C2411yescharacteristic
482C2×Dic6C24112yes—
483C3×Q16C24124yes—
484C3×Q16C24112yes—
485C3×SD16C24112yes—
486C3×SD16C24112yes—
487C3×D8C2414yes—
488C3×M16C24112yes—
489C2×C3×C8C2413yes—
490C2×C3×C8C2411yescharacteristic
491C2×C3×C8C24112yes—
492#216C24112yes—
493#216C24112yes—
494#216C24124yes—
495#215C24124yes—
496#215C24112yes—
497#215C24112yes—
498#214C24112yes—
499#214C2414yes—
500#213C2414yes—
501#213C24112yes—
502#208C24112yes—
503C2×C3⋊C8C2413yes—
504C2×C3⋊C8C2411yescharacteristic
505C2×C3⋊C8C24112yes—
506Dic12C24112yes—
507D24C24112yes—
508#204C24112yes—
509#204C24124yes—
510#204C2414yes—
511ΓL(1,𝔽25)C2414yes—
512ΓL(1,𝔽25)C24112yes—
513ΓL(1,𝔽25)C24112yes—
514ΓL(1,𝔽25)C24112yes—
515D3×C8C24124yes—
5162−1+4—24no—
5172−1+4—24no—
5182−1+4—324no—
5192−1+4—38no—
5202−1+4—324no—
5212−1+4—324no—
5222−1+4—616no—
5232−1+4—616no—
5242−1+4—612no—
5252−1+4—612no—
5262−1+4—648no—
5272−1+4—612no—
5282−1+4—64no—
5292−1+4C22×D318yescomplemented
5302−1+4C22×D318yescomplemented
531H(5,𝔽2)—324no—
532H(5,𝔽2)—38no—
533H(5,𝔽2)—648no—
534H(5,𝔽2)—612no—
535H(5,𝔽2)—64no—
536C2×#41—23no—
537C2×#41—23no—
538C2×#41—38no—
539C2×#41—38no—
540C2×#41—31no—
541C2×#41—33no—
542C2×#41—33no—
543C2×#41—324no—
544C2×#41—324no—
545C2×#41—33no—
546C2×#41—36no—
547C2×#41—33no—
548C2×#41—324no—
549C2×#41—33no—
550C2×#41—31no—
551C2×#41—33no—
552C2×#41—33no—
553C2×#41—63no—
554C2×#41—63no—
555C2×#41—66no—
556C2×#41—66no—
557C2×#41—63no—
558C2×#41—63no—
559C2×#41—63no—
560C2×#41—63no—
561C2×#41—63no—
562C2×#41—63no—
563C2×#41—612no—
564C2×#41—612no—
565C2×#41—612no—
566C2×#41—66no—
567C2×#41—63no—
568C2×#41—63no—
569C2×#41—648no—
570C2×#41—616no—
571C2×#41—648no—
572C2×#41—61no—
573C2×#41—63no—
574C2×#41C22×D313yes—
575C2×#41C22×D313yes—
576C2×#41C22×D311yescharacteristic
577C22×Q8—21no—
578C22×Q8—21no—
579C22×Q8—31no—
580C22×Q8—36no—
581C22×Q8—33no—
582C22×Q8—33no—
583C22×Q8—324no—
584C22×Q8—33no—
585C22×Q8—63no—
586C22×Q8—63no—
587C22×Q8—63no—
588C22×Q8—63no—
589C22×Q8—612no—
590C22×Q8—616no—
591C22×Q8—63no—
592C22×Q8—63no—
593C22×Q8—61no—
594C22×Q8C22×D313yes—
595C22×Q8C22×D313yes—
596C22×D4—33no—
597C22×D4—33no—
598C22×D4—31no—
599C22×D4—33no—
600C22×D4—63no—
601C22×D4—63no—
602C22×D4—66no—
603C22×D4—63no—
604C22×D4—63no—
605C22×D4—63no—
606C23×C4—33no—
607C23×C4—63no—
608C23×C4—63no—
609C23×C4—63no—
610C23×C4—63no—
611#137—324no—
612#137—324no—
613#137—324no—
614#137—348no—
615#137—324no—
616#137—348no—
617#137—348no—
618#137—324no—
619#137—324no—
620#137—324no—
621#137—324no—
622#137C22×D3124yescomplemented
623#137C22×D3124yescomplemented
624AGL(1,ℤ/8)—324no—
625AGL(1,ℤ/8)—324no—
626AGL(1,ℤ/8)—324no—
627AGL(1,ℤ/8)—38no—
628AGL(1,ℤ/8)—324no—
629AGL(1,ℤ/8)—324no—
630#135—324no—
631#135—324no—
632#135—348no—
633#135—348no—
634#135—324no—
635#135C22×D3124yescomplemented
636C2×Q16—33no—
637C2×Q16—36no—
638C2×Q16—33no—
639C2×Q16—324no—
640C2×Q16—348no—
641C2×Q16—33no—
642C2×Q16C22×D316yes—
643C2×Q16C22×D313yes—
644C2×Q16C22×D3124yescomplemented
645C2×SD16—33no—
646C2×SD16—36no—
647C2×SD16—324no—
648C2×SD16—33no—
649C2×SD16—33no—
650C2×SD16—31no—
651C2×SD16—348no—
652C2×SD16—36no—
653C2×SD16—33no—
654C2×SD16—324no—
655C2×SD16—31no—
656C2×SD16C22×D313yes—
657C2×SD16C22×D313yes—
658C2×D8—31no—
659C2×D8—33no—
660C2×D8—33no—
661C2×D8C22×D311yescharacteristic
662#131—38no—
663#131—324no—
664#131—324no—
665#131C22×D318yescomplemented
666C2×M16—33no—
667C2×M16—324no—
668C2×M16—33no—
669C2×M16—31no—
670C2×M16—33no—
671C2×M16—33no—
672C2×M16—324no—
673C2×M16C22×D313yes—
674C22×C8—33no—
675C22×C8—36no—
676C22×C8C22×D313yes—
677C23×C3—21no—
678C23×C3—21no—
679C23×C3C22×D413yes—
680C22×D3—21no—
681C22×D3—23no—
682C22×D3—212no—
683C22×D3—24no—
684C22×D3—212no—
685C22×D3—46no—
686C22×D3—44no—
687C22×D3—86no—
688C22×D3—86no—
689C22×D3C22×D411yescharacteristic
690C22×D3C22×D413yes—
691C22×D3C22×D4112yes—
692C3×Q8—23no—
693C3×Q8—212no—
694C3×Q8—23no—
695C3×Q8—212no—
696C3×Q8C22×D414yes—
697C3×Q8C2516yes—
698C3×Q8C2516yes—
699C3×D4—212no—
700C3×D4—212no—
701C3×D4—21no—
702C3×D4—21no—
703C3×D4C22×D4112yes—
704C3×D4C2512yes—
705C3×D4C2512yes—
706C2×C3×C4—23no—
707C2×C3×C4—212no—
708C2×C3×C4—23no—
709C2×C3×C4—212no—
710C2×C3×C4—212no—
711C2×C3×C4—212no—
712C2×C3×C4C22×D413yes—
713C2×C3×C4C22×D416yes—
714C2×C3×C4C2511yescharacteristic
715C2×C3×C4C2516yes—
716#67—212no—
717#67—212no—
718#67—24no—
719#67—212no—
720#67—212no—
721#67—24no—
722#67C22×D4124yes—
723C2×Dic3—23no—
724C2×Dic3—21no—
725C2×Dic3—212no—
726C2×Dic3—212no—
727C2×Dic3—24no—
728C2×Dic3C22×D413yes—
729C2×Dic3C22×D411yescharacteristic
730C2×Dic3C22×D4112yes—
731D12—212no—
732D12—224no—
733D12—212no—
734D12—23no—
735D12—212no—
736D12—21no—
737D12C22×D4112yes—
738D12C2516yes—
739D12C2512yes—
740C4×D3—212no—
741C4×D3—212no—
742C4×D3—224no—
743C4×D3—212no—
744C4×D3—212no—
745C4×D3—212no—
746C4×D3—224no—
747C4×D3—212no—
748C4×D3C22×D4112yes—
749C4×D3C22×D4112yes—
750C4×D3C22×D412yes—
751C4×D3C22×D416yes—
752C4×D3C2516yes—
753C4×D3C2512yes—
754Dic6—23no—
755Dic6—212no—
756Dic6—21no—
757Dic6—224no—
758Dic6—212no—
759Dic6—212no—
760Dic6C22×D4112yes—
761Dic6C2516yes—
762Dic6C2512yes—
763C3×C8C2516yes—
764C3×C8C2512yes—
765C3⋊C8C2516yes—
766C3⋊C8C2512yes—
767C24—33no—
768C24—61no—
769C24—63no—
770C24—63no—
771#41—224no—
772#41—224no—
773#41—26no—
774#41—26no—
775#41—38no—
776#41—324no—
777#41—312no—
778#41—312no—
779#41—312no—
780#41—324no—
781#41—312no—
782#41—312no—
783#41—34no—
784#41—312no—
785#41—312no—
786#41—624no—
787#41—624no—
788#41—648no—
789#41—648no—
790#41—624no—
791#41—624no—
792#41—624no—
793#41—62no—
794#41—624no—
795#41—66no—
796#41—66no—
797#41—624no—
798#41—624no—
799#41—612no—
800#41—66no—
801#41—648no—
802#41—624no—
803#41—624no—
804#41—68no—
805#41—624no—
806#41—66no—
807#41—66no—
808#41D3×D414yes—
809#41C23×D3112yes—
810#41C23×D3112yes—
811#41C23×D314yes—
812C2×Q8—28no—
813C2×Q8—28no—
814C2×Q8—23no—
815C2×Q8—23no—
816C2×Q8—26no—
817C2×Q8—26no—
818C2×Q8—38no—
819C2×Q8—33no—
820C2×Q8—324no—
821C2×Q8—312no—
822C2×Q8—312no—
823C2×Q8—33no—
824C2×Q8—31no—
825C2×Q8—312no—
826C2×Q8—63no—
827C2×Q8—66no—
828C2×Q8—63no—
829C2×Q8—624no—
830C2×Q8—624no—
831C2×Q8—66no—
832C2×Q8—624no—
833C2×Q8—624no—
834C2×Q8—612no—
835C2×Q8—66no—
836C2×Q8—624no—
837C2×Q8—624no—
838C2×Q8—68no—
839C2×Q8—63no—
840C2×Q8—66no—
841C2×Q8D3×D411yescharacteristic
842C2×Q8C23×D313yes—
843C2×Q8C23×D3112yes—
844C2×Q8C23×D313yes—
845C2×Q8C23×D3112yes—
846C2×D4—23no—
847C2×D4—23no—
848C2×D4—36no—
849C2×D4—324no—
850C2×D4—312no—
851C2×D4—34no—
852C2×D4—33no—
853C2×D4—31no—
854C2×D4—33no—
855C2×D4—312no—
856C2×D4—624no—
857C2×D4—63no—
858C2×D4—66no—
859C2×D4—63no—
860C2×D4—624no—
861C2×D4—62no—
862C2×D4—66no—
863C2×D4—63no—
864C2×D4—61no—
865C2×D4—648no—
866C2×D4—624no—
867C2×D4—624no—
868C2×D4—61no—
869C2×D4—63no—
870C2×D4—63no—
871C2×D4—63no—
872C2×D4—624no—
873C2×D4—63no—
874C2×D4—66no—
875C2×D4D3×D413yes—
876C2×D4C23×D311yescharacteristic
877C2×D4C23×D311yescharacteristic
878C22×C4—23no—
879C22×C4—23no—
880C22×C4—23no—
881C22×C4—23no—
882C22×C4—33no—
883C22×C4—33no—
884C22×C4—33no—
885C22×C4—312no—
886C22×C4—33no—
887C22×C4—31no—
888C22×C4—312no—
889C22×C4—63no—
890C22×C4—66no—
891C22×C4—63no—
892C22×C4—624no—
893C22×C4—624no—
894C22×C4—624no—
895C22×C4—63no—
896C22×C4—63no—
897C22×C4—624no—
898C22×C4—66no—
899C22×C4—61no—
900C22×C4—63no—
901C22×C4—63no—
902C22×C4—63no—
903C22×C4—63no—
904C22×C4C23×D313yes—
905Q16—312no—
906Q16—324no—
907Q16—312no—
908Q16—312no—
909Q16C23×D3124yes—
910Q16C23×D3112yes—
911SD16—312no—
912SD16—324no—
913SD16—312no—
914SD16—312no—
915SD16—34no—
916SD16—324no—
917SD16—312no—
918SD16—34no—
919SD16C23×D3112yes—
920SD16C23×D3112yes—
921D8—34no—
922D8—312no—
923D8—312no—
924D8C23×D314yes—
925M16—312no—
926M16—312no—
927M16—34no—
928M16—312no—
929M16—312no—
930M16C23×D3112yes—
931C2×C8—31no—
932C2×C8—33no—
933C2×C8—312no—
934C2×C8—324no—
935C2×C8C23×D313yes—
936C2×C8C23×D311yescharacteristic
937C2×C8C23×D3112yes—
938C22×C3—26no—
939C22×C3—22no—
940C22×C3—22no—
941C22×C3—42no—
942C22×C3—42no—
943C22×C3C23×D416yes—
944C22×C3C23×D411yescharacteristic
945C2×D3—22no—
946C2×D3—26no—
947C2×D3—22no—
948C2×D3—26no—
949C2×D3—412no—
950C2×D3—48no—
951C2×D3—42no—
952C2×D3—46no—
953C2×D3—812no—
954C2×D3—812no—
955C2×D3C23×D412yes—
956C2×D3C23×D416yes—
957C3×C4—26no—
958C3×C4—26no—
959C3×C4C23×D411yescharacteristic
960C3×C4C23×D416yes—
961C3×C4C2611yescharacteristic
962Dic3—26no—
963Dic3—22no—
964Dic3C23×D416yes—
965Dic3C23×D412yes—
966C23—21no—
967C23—21no—
968C23—31no—
969C23—33no—
970C23—312no—
971C23—64no—
972C23—612no—
973C23—61no—
974C23—63no—
975C23—612no—
976C23—126no—
977C23—124no—
978C23—246no—
979C23—246no—
980C23C2×D3×D413yes—
981Q8—212no—
982Q8—23no—
983Q8—212no—
984Q8—23no—
985Q8—312no—
986Q8—36no—
987Q8—32no—
988Q8—612no—
989Q8—624no—
990Q8—612no—
991Q8—612no—
992Q8—63no—
993Q8—61no—
994Q8C2×D3×D414yes—
995Q8C24×D316yes—
996Q8C24×D316yes—
997D4—212no—
998D4—212no—
999D4—21no—
1000D4—21no—
1001D4—324no—
1002D4—312no—
1003D4—32no—
1004D4—36no—
1005D4—612no—
1006D4—624no—
1007D4—612no—
1008D4—612no—
1009D4—64no—
1010D4—64no—
1011D4—612no—
1012D4—612no—
1013D4—612no—
1014D4—612no—
1015D4—63no—
1016D4—61no—
1017D4C2×D3×D4112yes—
1018D4C24×D312yes—
1019D4C24×D312yes—
1020C2×C4—212no—
1021C2×C4—212no—
1022C2×C4—23no—
1023C2×C4—23no—
1024C2×C4—212no—
1025C2×C4—212no—
1026C2×C4—312no—
1027C2×C4—31no—
1028C2×C4—33no—
1029C2×C4—32no—
1030C2×C4—312no—
1031C2×C4—312no—
1032C2×C4—36no—
1033C2×C4—36no—
1034C2×C4—32no—
1035C2×C4—612no—
1036C2×C4—624no—
1037C2×C4—612no—
1038C2×C4—612no—
1039C2×C4—612no—
1040C2×C4—624no—
1041C2×C4—64no—
1042C2×C4—612no—
1043C2×C4—612no—
1044C2×C4—61no—
1045C2×C4—63no—
1046C2×C4—612no—
1047C2×C4—612no—
1048C2×C4C2×D3×D416yes—
1049C2×C4C2×D3×D413yes—
1050C2×C4C24×D316yes—
1051C2×C4C24×D311yescharacteristic
1052C8—32no—
1053C8—36no—
1054C8C24×D316yes—
1055C8C24×D312yes—
1056C2×C3—26no—
1057C2×C3—42no—
1058C2×C3—42no—
1059C2×C3#358612yescomplemented
1060C2×C3C24×D411yescharacteristic
1061D3—22no—
1062D3—26no—
1063D3—42no—
1064D3—46no—
1065C22—26no—
1066C22—22no—
1067C22—22no—
1068C22—32no—
1069C22—36no—
1070C22—42no—
1071C22—42no—
1072C22—62no—
1073C22—66no—
1074C22—62no—
1075C22—66no—
1076C22—1212no—
1077C22—128no—
1078C22—122no—
1079C22—126no—
1080C22—2412no—
1081C22—2412no—
1082C22C22×D3×D416yes—
1083C22C22×D3×D411yescharacteristic
1084C4—26no—
1085C4—26no—
1086C4—32no—
1087C4—36no—
1088C4—62no—
1089C4—66no—
1090C4C22×D3×D416yes—
1091C4C22×D3×D411yescharacteristic
1092C4C25×D311yescharacteristic
1093C3C2×#358611yescharacteristic, complemented, Sylow
1094C2—26no—
1095C2—42no—
1096C2—42no—
1097C2—62no—
1098C2—66no—
1099C2—122no—
1100C2—126no—
1101C2#8721112yesdirect product factor
1102C2C23×D3×D411yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC3×C4C26
FrattiniC4C25×D3
FittingC2×C3×#578C2
socleC22×C3C23×D4
hypercenterC2×#578D3
hypocenterC3C2×#3586
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#578

Complements

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

NH ≅ G/Ntype
1. C2×D3×2−1+4C2semidirect
2. C2×#5968C2semidirect
3. C2×C3×#578C2semidirect
4. C2×#5838C2semidirect
5. C2×#5837C2semidirect
6. #87211C2direct (N × H)
7. C2×#5779C2semidirect
8. C2×#5778C2semidirect
9. C2×#5777C2semidirect
10. C2×D3×#137C2semidirect
11. C2×#5770C2semidirect
12. C2×#5768C2semidirect
13. C2×#5766C2semidirect
14. C22×#918C2semidirect
15. C2×#5751C2semidirect
16. C2×#5750C2semidirect
18. C2×C3×2−1+4C22semidirect
19. C2×C3×2−1+4C22semidirect
21. #5968C22semidirect
23. D3×2−1+4C22semidirect
25. C2×#1010C22semidirect
26. C2×#1010C22semidirect
28. C2×#1009C22semidirect
29. C2×#1009C22semidirect
34. C2×D3×#41C22semidirect
37. C2×#1007C22semidirect
38. C2×#1007C22semidirect
42. C22×D3×Q8C22semidirect
43. C3×#578C22semidirect
44. C2×C3×#137C22semidirect
45. C2×C3×#137C22semidirect
46. C2×C3×#135C22semidirect
47. C22×C3×Q16C22semidirect
48. C2×C3×#131C22semidirect
49. #5838C22semidirect
50. #5837C22semidirect
51. C2×#951C22semidirect
52. C2×#950C22semidirect
53. C2×#950C22semidirect
54. C2×#949C22semidirect
55. C2×#948C22semidirect
56. C22×#216C22semidirect
57. C2×#942C22semidirect
58. C2×#942C22semidirect
59. C22×#215C22semidirect
60. #5779C22semidirect
61. #5778C22semidirect
62. #5777C22semidirect
63. D3×#137C22semidirect
64. #5770C22semidirect
65. #5768C22semidirect
66. #5766C22semidirect
67. C2×#919C22semidirect
68. C2×#918C22semidirect
69. C2×#918C22semidirect
70. C2×#918C22semidirect
71. C2×#918C22semidirect
72. C2×#918C22semidirect
73. C2×#918C22semidirect
74. C2×D3×Q16C22semidirect
75. C2×#916C22semidirect
76. C2×#915C22semidirect
77. C2×#915C22semidirect
78. C2×#914C22semidirect
79. C2×#914C22semidirect
80. C2×D3×SD16C22semidirect
81. C2×#911C22semidirect
82. C2×#911C22semidirect
83. #5751C22semidirect
84. #5750C22semidirect
85. C2×#909C22semidirect
86. C2×#908C22semidirect
87. C2×#907C22semidirect
88. C2×D3×M16C22semidirect
89. C2×#904C22semidirect
90. C22×#204C22semidirect
91. C2×#901C22semidirect
92. C22×ΓL(1,𝔽25)C22semidirect
99. C2×#578D3semidirect
111. C3×2−1+4C23semidirect
112. C3×2−1+4C23semidirect
125. #1010C23semidirect
126. #1010C23semidirect
130. #1009C23semidirect
131. #1009C23semidirect
139. D3×#41C23semidirect
144. #1007C23semidirect
145. #1007C23semidirect
169. C2×D3×Q8C23semidirect
204. C3×#137C23semidirect
205. C3×#137C23semidirect
206. C3×#135C23semidirect
209. C2×C3×Q16C23semidirect
213. C3×#131C23semidirect
216. #951C23semidirect
217. #950C23semidirect
218. #950C23semidirect
219. #949C23semidirect
220. #948C23semidirect
224. C2×#216C23semidirect
225. #942C23semidirect
226. #942C23semidirect
230. C2×#215C23semidirect
237. #919C23semidirect
238. #918C23semidirect
239. #918C23semidirect
240. #918C23semidirect
241. #918C23semidirect
242. #918C23semidirect
243. D3×Q16C23semidirect
244. #916C23semidirect
245. #915C23semidirect
246. #915C23semidirect
247. #914C23semidirect
248. #914C23semidirect
249. D3×SD16C23semidirect
250. #911C23semidirect
251. #911C23semidirect
252. #909C23semidirect
253. #908C23semidirect
254. #907C23semidirect
255. D3×M16C23semidirect
257. #904C23semidirect
262. C2×#204C23semidirect
263. #901C23semidirect
268. C2×ΓL(1,𝔽25)C23semidirect
281. C2×2−1+4C2×D3semidirect
282. C2×2−1+4C2×D3semidirect
298. #578C2×D3semidirect
318. C2×#137C2×D3semidirect
319. C2×#137C2×D3semidirect
331. C2×#135C2×D3semidirect
334. C22×Q16C2×D3semidirect
342. C2×#131C2×D3semidirect
529. 2−1+4C22×D3semidirect
530. 2−1+4C22×D3semidirect
622. #137C22×D3semidirect
623. #137C22×D3semidirect
635. #135C22×D3semidirect
644. C2×Q16C22×D3semidirect
665. #131C22×D3semidirect
1059. C2×C3#3586semidirect
1093. C3C2×#3586semidirect
1101. C2#87211direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×2−1+42
C2×#59682
C2×C3×#5782
C2×#58382
C2×#58372
#872112
C2×#57792
C2×#57782
C2×#57772
C2×D3×#1372
C2×#57702
C2×#57682
C2×#57662
C22×#9182
C2×#57512
C2×#57502
C2×#35863