Finite Group Databasebeta

← #11904396

Subgroups — #11904396

Order 1152.

3291 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64308C211yesmaximal, characteristic, complemented
2C2×#64306C211yesmaximal, characteristic, complemented
3C2×#64103C211yesmaximal, characteristic, complemented
4C3×#5507C212yesmaximal, complemented
5#10595084C211yesmaximal, characteristic, complemented
6#10595080C211yesmaximal, characteristic, complemented
7#10595079C211yesmaximal, characteristic, complemented
8#10595075C212yesmaximal, complemented
9#10595068C212yesmaximal, complemented
10#10595058C211yesmaximal, characteristic, complemented
11#10594888C212yesmaximal, complemented
12#10594623C212yesmaximal, complemented
13#10594622C212yesmaximal, complemented
14#10594619C212yesmaximal, complemented
15#10594611C212yesmaximal, complemented
16D3×#894C212yesmaximal, complemented
17#10594516C212yesmaximal, complemented
18#10594372C212yesmaximal, complemented
19#10594328C212yesmaximal, complemented
20#86700—32nomaximal
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×C3×#235C2212yescomplemented
24C2×C3×#235C2212yescomplemented
25C2×#3811C2211yescharacteristic
26C2×#3811C2211yescharacteristic
27C2×#3811C2212yescomplemented
28C2×#3811C2211yescharacteristic, complemented
29C2×#3805C2212yescomplemented
30#64308—28no—
31#64306—28no—
32C2×#3802C2211yescharacteristic, complemented
33C2×D3×D12C2212yes—
34C2×D3×D12C2212yescomplemented
35C2×C4×D32C2211yescharacteristic, complemented
36C2×C4×D32C2211yescharacteristic, complemented
37C2×#3799C2212yes—
38C2×#3799C2212yescomplemented
39C2×#3798C2212yescomplemented
40C2×#3797C2211yescharacteristic, complemented
41C2×#3796C2212yescomplemented
42C2×C32×C4⋊C4C2211yescharacteristic, complemented
43C2×#3752C2211yescharacteristic, complemented
44C2×#3752C2211yescharacteristic, complemented
45C2×#3752C2211yescharacteristic, complemented
46C2×#3750C2211yescharacteristic, complemented
47#64103C2212yescomplemented
48#64103C2212yescomplemented
49#64103C2212yescomplemented
50#64103C2212yescomplemented
51C3×#930C2212yescomplemented
52C3×#929C2212yescomplemented
53C3×#929C2212yescomplemented
54C3×C4×#67C2212yescomplemented
55C3×#896C2212yescomplemented
56C3×#896C2212yescomplemented
57C3×#895C2212yescomplemented
58C3×#894C2212yescomplemented
59C3×#894C2212yescomplemented
60C3×#893C2212yescomplemented
61C3×D3×C4⋊C4C2212yescomplemented
62C3×#888C2212yescomplemented
63#63981C2212yescomplemented
64#63980C2212yescomplemented
65#63974C2211yescharacteristic, complemented
66#67⋊Dic3C2212yescomplemented
67#63962C2212yescomplemented
68#63923C2212yescomplemented
69#63922C2212yescomplemented
70#63922C2212yescomplemented
71#63922C2212yescomplemented
72#63922C2212yescomplemented
73#63921C2211yescharacteristic, complemented
74#63921C2211yescharacteristic, complemented
75D3×(C2×D3)⋊C4C2212yescomplemented
76D3×(C2×D3)⋊C4C2212yescomplemented
77D3×(C2×D3)⋊C4C2212yescomplemented
78#63910C2212yescomplemented
79#63910C2212yescomplemented
80#63907C2212yescomplemented
81#63906C2212yescomplemented
82#63906C2212yescomplemented
83#63905C2212yescomplemented
84#63904C2212yescomplemented
85#63904C2212yescomplemented
86#63897C2212yescomplemented
87#63895C2212yescomplemented
88#63890C2212yescomplemented
89#63888C2212yescomplemented
90#63887C2212yescomplemented
91#63886C2212yescomplemented
92#63886C2212yescomplemented
93#63885C2212yescomplemented
94#63884C2212yescomplemented
95#63883C2211yescharacteristic, complemented
96#63883C2211yescharacteristic, complemented
97#63880C2212yescomplemented
98#63880C2212yescomplemented
99#63879C2212yescomplemented
100D3×Dic3⋊C4C2212yescomplemented
101#63854C2212yescomplemented
102#63854C2212yescomplemented
103#63853C2212yescomplemented
104#63853C2212yescomplemented
105#63852C2212yescomplemented
106#63851C2212yescomplemented
107#63850C2212yescomplemented
108#63839C2212yescomplemented
109#63836C2212yescomplemented
110C2×#1009—32no—
111C2×D3×#41—32no—
112C3×#547—32no—
113#5829—32no—
114#5824—32no—
115#5726—32no—
116#5724—32no—
117#5655—32no—
118#5655—32no—
119#5654—32no—
120#5654—32no—
121#5653—32no—
122#5653—32no—
123D3×#123—32no—
124D3×#123—32no—
125#5631—32no—
126#5630—32no—
127#5628—32no—
128#5627—32no—
129#5610—32no—
130#5610—32no—
131#5605—32no—
132#5605—32no—
133#5554—32no—
134#5550—32no—
135#5547—32no—
136#5545—32no—
137#5507—32no—
138#5507D312yescomplemented
139C2×#894—32no—
140C2×#894—32no—
141C2×#894—61no—
142C23×C3⋊D3C2311yescharacteristic
143C23×C3⋊D3C2311yescharacteristic
144C22×D32C2311yescharacteristic
145C22×D32C2312yes—
146C22×D32C2311yescharacteristic
147C22×D32C2311yescharacteristic
148C22×C32×C4C2311yescharacteristic
149C22×C32×C4C2311yescharacteristic
150C22×C32×C4C2311yescharacteristic
151C22×C3⋊Dic3C2311yescharacteristic
152C22×C3⋊Dic3C2311yescharacteristic
153C2×C4⋊(C3⋊D3)—24no—
154C2×C4⋊(C3⋊D3)C2312yes—
155C2×C4⋊(C3⋊D3)C2312yes—
156C2×C4×C3⋊D3—24no—
157C2×C4×C3⋊D3C2311yescharacteristic
158C2×C4×C3⋊D3C2311yescharacteristic
159C2×C4×C3⋊D3C2311yescharacteristic
160C2×C4×C3⋊D3C2311yescharacteristic
161C2×C3×#67C2312yes—
162C2×C3×#67C2312yes—
163C2×C3×#67C2312yes—
164C3×#235—28no—
165C3×#235—28no—
166C2×C3×D12C2312yes—
167C2×C3×D12C2312yes—
168C2×C3×D12C2312yes—
169C2×C3×C4×D3C2312yes—
170C2×C3×C4×D3C2312yes—
171C2×C3×C4×D3C2312yes—
172C2×C3×C4×D3C2312yes—
173C2×C3×C4×D3C2312yes—
174C2×C3×Dic6C2312yes—
175C2×C3×Dic6C2312yes—
176#3811—24no—
177#3811—24no—
178#3811—28no—
179#3811D418yescomplemented
180C2×#627C2312yes—
181C2×#626C2312yes—
182C2×#626C2312yes—
183C2×#626C2312yes—
184C2×#626C2312yes—
185C2×#626C2312yes—
186C2×#626C2312yes—
187C2×#626C2312yes—
188C2×#625C2312yes—
189C2×#625C2312yes—
190C2×#624C2311yescharacteristic
191C2×#624C2312yes—
192C2×#624C2311yescharacteristic
193C2×#624C2311yescharacteristic
194C2×#624C2311yescharacteristic
195C2×#624C2311yescharacteristic
196#3805—28no—
197C2×D3×Dic3C2312yes—
198C2×D3×Dic3C2312yes—
199C2×D3×Dic3C2312yes—
200#3802—24no—
201D3×D12—28no—
202D3×D12—28no—
203C4×D32—24no—
204C4×D32—24no—
205#3799—28no—
206#3799—28no—
207#3798—28no—
208#3797—24no—
209#3796—28no—
210C32×C4⋊C4C2312yes—
211C32×C4⋊C4C2312yes—
212#3752C2312yes—
213#3752C2312yes—
214#3752C2312yes—
215#3752C2312yes—
216#3752C2312yes—
217#3752C2312yes—
218#3750C2312yes—
219#3750C2312yes—
220C3×#217C2312yes—
221C3×(C2×D3)⋊C4C2312yes—
222C3×(C2×D3)⋊C4C2312yes—
223C3×(C2×D3)⋊C4C2312yes—
224C3×(C2×D3)⋊C4C2312yes—
225C3×(C2×D3)⋊C4C2312yes—
226C3×(C2×D3)⋊C4C2312yes—
227C3×(C2×D3)⋊C4C2312yes—
228C3×C4⋊Dic3C2312yes—
229C3×Dic3⋊C4C2312yes—
230C3×Dic3⋊C4C2312yes—
231C3×Dic3⋊C4C2312yes—
232C3×Dic3⋊C4C2312yes—
233C3×Dic3⋊C4C2312yes—
234C3×C4×Dic3C2312yes—
235#3724C2312yes—
236Dic3⋊Dic3C2312yes—
237Dic3⋊Dic3C2312yes—
238Dic3⋊Dic3C2312yes—
239#3722C2312yes—
240#3722C2312yes—
241#3722C2312yes—
242(C2×D3)⋊Dic3C2312yes—
243(C2×D3)⋊Dic3C2312yes—
244(C2×D3)⋊Dic3C2312yes—
245(C2×D3)⋊Dic3C2312yes—
246(C2×D3)⋊Dic3C2312yes—
247Dic32C2312yes—
248#3485—91noSylow
249C2×C3×#41—32no—
250C2×C3×#41—32no—
251#1009—616no—
252D3×#41—616no—
253C2×#239—32no—
254C2×#239—32no—
255C2×#239—32no—
256C2×D3×Q8—32no—
257C2×#237—32no—
258C2×#237—32no—
259C2×#237—32no—
260C2×D3×D4—32no—
261C2×D3×D4—32no—
262C2×D3×D4—32no—
263C2×D3×D4—32no—
264C2×D3×D4—32no—
265C2×D3×D4—32no—
266C2×D3×D4—32no—
267C2×D3×D4—32no—
268C2×#235—32no—
269C2×#235—32no—
270C2×#235—32no—
271C2×#235—32no—
272C2×#235C2×D312yescomplemented
273C2×#235C2×D312yescomplemented
274C22×D12—32no—
275C22×D12—32no—
276C22×D12—32no—
277C22×D12—61no—
278C22×C4×D3—32no—
279C22×C4×D3—32no—
280C22×C4×D3—32no—
281C22×C4×D3—61no—
282C3×C4⋊Q8—32no—
283C3×#123—32no—
284C3×#123—32no—
285C3×#123—32no—
286C3×#123—32no—
287C3×C22⋊Q8—32no—
288C3×C22⋊Q8—32no—
289C3×#121—32no—
290C3×#121—32no—
291C3×C4×D4—32no—
292C3×C4×D4—32no—
293C2×C3×C4⋊C4—21no—
294C2×C3×C4⋊C4—32no—
295C2×C3×C4⋊C4C2×D312yescomplemented
296#947—32no—
297#946—32no—
298#946—32no—
299#944—32no—
300#939—32no—
301#939—32no—
302#939—32no—
303#939—32no—
304#939—32no—
305#937—32no—
306#937—32no—
307#937—32no—
308#937—32no—
309#937—32no—
310#935—32no—
311#935—32no—
312D4×Dic3—32no—
313#930—32no—
314#930—32no—
315#930C2×D312yescomplemented
316#929—32no—
317#929—32no—
318#929C2×D312yescomplemented
319#929C2×D312yescomplemented
320C4×#67—32no—
321C4×#67—32no—
322C4×#67—32no—
323C4×#67C2×D312yescomplemented
324C2×(C2×D3)⋊C4—32no—
325C2×(C2×D3)⋊C4—32no—
326C2×(C2×D3)⋊C4—32no—
327C2×(C2×D3)⋊C4—32no—
328C2×(C2×D3)⋊C4—32no—
329C2×(C2×D3)⋊C4—32no—
330C2×(C2×D3)⋊C4—61no—
331C2×(C2×D3)⋊C4—61no—
332C2×(C2×D3)⋊C4—61no—
333#924—32no—
334C2×Dic3⋊C4—32no—
335C2×Dic3⋊C4—32no—
336C2×Dic3⋊C4—61no—
337#897—32no—
338#896—32no—
339#896—32no—
340#896—32no—
341#896C2×D312yescomplemented
342#896C2×D312yescomplemented
343#895—32no—
344#895—32no—
345#895—32no—
346#895—32no—
347#895C2×D312yescomplemented
348#894—32no—
349#894—32no—
350#894—32no—
351#894—32no—
352#894—32no—
353#894—32no—
354#894—32no—
355#894—32no—
356#894—32no—
357#894—32no—
358#894—32no—
359#894—32no—
360#894—32no—
361#894—32no—
362#894—32no—
363#894—32no—
364#894—32no—
365#894—62no—
366#894—62no—
367#894—62no—
368#894—62no—
369#894C2×D312yescomplemented
370#894C2×D312yescomplemented
371#893—32no—
372#893—32no—
373#893C2×D312yescomplemented
374#892—32no—
375D3×C4⋊C4—32no—
376D3×C4⋊C4—32no—
377D3×C4⋊C4—32no—
378D3×C4⋊C4C2×D312yescomplemented
379#888—32no—
380#888C2×D312yescomplemented
381#886—32no—
382#886—32no—
383#885—32no—
384#885—32no—
385#884—32no—
386#884—32no—
387#884—32no—
388#884—32no—
389#884—32no—
390#883—32no—
391#883—32no—
392#883—32no—
393#883—32no—
394#883—32no—
395#882—32no—
396#882—32no—
397#882—32no—
398#882—32no—
399#882—32no—
400#882—32no—
401#882—32no—
402#67⋊C4—32no—
403#67⋊C4—32no—
404#67⋊C4—32no—
405#67⋊C4—32no—
406D3×C22⋊C4—32no—
407D3×C22⋊C4—32no—
408D3×C22⋊C4—32no—
409D3×C22⋊C4—32no—
410D3×C22⋊C4—32no—
411D3×C22⋊C4—32no—
412#878—32no—
413#875—32no—
414C4×D12—32no—
415C4×D12—32no—
416#872—32no—
417C23×C32C2411yescharacteristic
418C22×C3⋊D3—22no—
419C22×C3⋊D3—41no—
420C22×C3⋊D3—41no—
421C22×C3⋊D3—41no—
422C22×C3⋊D3—41no—
423C22×C3⋊D3C2×D414yes—
424C22×C3⋊D3C2412yes—
425C22×C3⋊D3C2411yescharacteristic
426C22×C3⋊D3C2411yescharacteristic
427C22×C3×D3C2412yes—
428C22×C3×D3C2412yes—
429C22×C3×D3C2412yes—
430C2×D32—22no—
431C2×D32—22no—
432C2×D32—24no—
433C2×D32—41no—
434C2×D32—41no—
435C2×D32—41no—
436C2×D32—41no—
437C2×D32—42no—
438C2×D32—42no—
439C2×D32—41no—
440C2×D32—41no—
441C2×D32C2×D414yes—
442C2×C32×C4—22no—
443C2×C32×C4—22no—
444C2×C32×C4—41no—
445C2×C32×C4C2412yes—
446C2×C32×C4C2412yes—
447C2×C32×C4C2411yescharacteristic
448C2×C32×C4C2411yescharacteristic
449C2×C3⋊Dic3—22no—
450C2×C3⋊Dic3—41no—
451C2×C3⋊Dic3C2412yes—
452C2×C3⋊Dic3C2411yescharacteristic
453C2×C3⋊Dic3C2411yescharacteristic
454C4⋊(C3⋊D3)—24no—
455C4⋊(C3⋊D3)—24no—
456C4×C3⋊D3—22no—
457C4×C3⋊D3—22no—
458C4×C3⋊D3—22no—
459C4×C3⋊D3—22no—
460C3×#67—24no—
461C3×#67—24no—
462C3×#67C2×D418yes—
463C2×C3×Dic3C2412yes—
464C2×C3×Dic3C2412yes—
465C2×C3×Dic3C2412yes—
466C2×C3×Dic3C2412yes—
467C2×C3×Dic3C2412yes—
468C3×D12—24no—
469C3×D12—24no—
470C3×D12—42no—
471C3×C4×D3—24no—
472C3×C4×D3—24no—
473C3×C4×D3—24no—
474C3×C4×D3—24no—
475C3×C4×D3—42no—
476C3×Dic6—24no—
477C3×Dic6—24no—
478#627—24no—
479#626—24no—
480#626—24no—
481#626—24no—
482#626—24no—
483#626—42no—
484#626—42no—
485#626C2×D418yes—
486#625—24no—
487#625—42no—
488#624—22no—
489#624—22no—
490#624—24no—
491#624—41no—
492#624—41no—
493#624C2×D414yes—
494D3×Dic3—24no—
495D3×Dic3—24no—
496D3×Dic3—42no—
497C2×H(5,𝔽2)—91no—
498C22×#41—91no—
499#547—32no—
500#547—92no—
501#547—92no—
502#547—92no—
503#546—92no—
504#546—92no—
505#546—92no—
506#546—92no—
507#536—92no—
508#534—91no—
509#534—92no—
510#534—91no—
511#525—92no—
512C2×#123—92no—
513C2×#123—91no—
514C2×#123—91no—
515#518—91no—
516C23×D3—32no—
517C23×D3—32no—
518C23×D3—32no—
519C23×D3—32no—
520C23×D3—32no—
521C23×D3—32no—
522C23×D3—32no—
523C23×D3—61no—
524C23×D3—61no—
525C3×#41—68no—
526C3×#41—68no—
527C2×C3×Q8—32no—
528C2×C3×Q8—32no—
529C2×C3×D4—32no—
530C2×C3×D4—32no—
531C2×C3×D4—32no—
532C2×C3×D4—32no—
533C2×C3×D4—32no—
534C2×C3×D4—32no—
535C22×C3×C4—21no—
536C22×C3×C4—21no—
537C22×C3×C4—21no—
538C22×C3×C4—32no—
539C22×C3×C4—32no—
540C22×C3×C4—32no—
541C22×C3×C4—32no—
542C22×C3×C4—32no—
543C22×C3×C4C22×D312yes—
544C22×C3×C4C22×D312yes—
545C22×C3×C4C22×D312yes—
546C2×#67—32no—
547C2×#67—32no—
548C2×#67—32no—
549C2×#67—32no—
550C2×#67—32no—
551C2×#67—32no—
552C2×#67—32no—
553C2×#67—32no—
554C2×#67—32no—
555C2×#67—32no—
556C2×#67—32no—
557C2×#67C22×D312yes—
558C2×#67C22×D312yes—
559C2×#67C22×D312yes—
560C22×Dic3—32no—
561C22×Dic3—32no—
562C22×Dic3—32no—
563C22×Dic3—32no—
564C22×Dic3—32no—
565C22×Dic3—61no—
566C22×Dic3—61no—
567#239—68no—
568#239—68no—
569#239—68no—
570D3×Q8—68no—
571#237—68no—
572#237—68no—
573#237—68no—
574D3×D4—316no—
575D3×D4—68no—
576D3×D4—68no—
577D3×D4—68no—
578D3×D4—68no—
579D3×D4—68no—
580D3×D4—68no—
581D3×D4—68no—
582#235—28no—
583#235—28no—
584#235—68no—
585#235—68no—
586#235—68no—
587#235—68no—
588C2×D12—32no—
589C2×D12—32no—
590C2×D12—32no—
591C2×D12—32no—
592C2×D12—32no—
593C2×D12—32no—
594C2×D12—32no—
595C2×D12—32no—
596C2×D12—32no—
597C2×D12—32no—
598C2×D12—32no—
599C2×D12—62no—
600C2×D12—62no—
601C2×D12—68no—
602C2×D12—68no—
603C2×D12—68no—
604C2×D12—124no—
605C2×D12C22×D312yes—
606C2×D12C22×D312yes—
607C2×D12C22×D312yes—
608C2×C4×D3—32no—
609C2×C4×D3—32no—
610C2×C4×D3—32no—
611C2×C4×D3—32no—
612C2×C4×D3—32no—
613C2×C4×D3—32no—
614C2×C4×D3—32no—
615C2×C4×D3—32no—
616C2×C4×D3—32no—
617C2×C4×D3—32no—
618C2×C4×D3—32no—
619C2×C4×D3—32no—
620C2×C4×D3—32no—
621C2×C4×D3—32no—
622C2×C4×D3—61no—
623C2×C4×D3—61no—
624C2×C4×D3—61no—
625C2×C4×D3—61no—
626C2×C4×D3—68no—
627C2×C4×D3—68no—
628C2×C4×D3—68no—
629C2×C4×D3—124no—
630C2×C4×D3C22×D312yes—
631C2×C4×D3C22×D312yes—
632C2×C4×D3C22×D312yes—
633C2×C4×D3C22×D312yes—
634C2×C4×D3C22×D312yes—
635C2×Dic6—32no—
636C2×Dic6—32no—
637C2×Dic6C22×D312yes—
638C2×Dic6C22×D312yes—
639C3×C4⋊C4—22no—
640C3×C4⋊C4—22no—
641C3×C4⋊C4—32no—
642C3×C4⋊C4—32no—
643C3×C4⋊C4—32no—
644C3×C4⋊C4—32no—
645C3×C4⋊C4—32no—
646C3×C4⋊C4—32no—
647C3×C4⋊C4C22×D312yes—
648C3×C4⋊C4C22×D312yes—
649C3×C4⋊C4C22×D312yes—
650C3×C4⋊C4C22×D312yes—
651C3×C22⋊C4—32no—
652C3×C22⋊C4—32no—
653C3×C22⋊C4—32no—
654C3×C22⋊C4—32no—
655C3×C22⋊C4—32no—
656C3×C22⋊C4—32no—
657C3×C22⋊C4—32no—
658C3×C22⋊C4—32no—
659C3×C42—32no—
660#217—32no—
661#217—32no—
662#217—32no—
663#217—32no—
664#217—32no—
665#217C22×D312yes—
666(C2×D3)⋊C4—32no—
667(C2×D3)⋊C4—32no—
668(C2×D3)⋊C4—32no—
669(C2×D3)⋊C4—32no—
670(C2×D3)⋊C4—32no—
671(C2×D3)⋊C4—32no—
672(C2×D3)⋊C4—32no—
673(C2×D3)⋊C4—32no—
674(C2×D3)⋊C4—32no—
675(C2×D3)⋊C4—32no—
676(C2×D3)⋊C4—32no—
677(C2×D3)⋊C4—32no—
678(C2×D3)⋊C4—32no—
679(C2×D3)⋊C4—32no—
680(C2×D3)⋊C4—32no—
681(C2×D3)⋊C4—32no—
682(C2×D3)⋊C4—32no—
683(C2×D3)⋊C4—32no—
684(C2×D3)⋊C4—32no—
685(C2×D3)⋊C4—32no—
686(C2×D3)⋊C4—32no—
687(C2×D3)⋊C4—32no—
688(C2×D3)⋊C4—32no—
689(C2×D3)⋊C4—62no—
690(C2×D3)⋊C4—62no—
691(C2×D3)⋊C4—62no—
692(C2×D3)⋊C4—62no—
693(C2×D3)⋊C4—62no—
694(C2×D3)⋊C4—62no—
695(C2×D3)⋊C4C22×D312yes—
696(C2×D3)⋊C4C22×D312yes—
697(C2×D3)⋊C4C22×D312yes—
698(C2×D3)⋊C4C22×D312yes—
699(C2×D3)⋊C4C22×D312yes—
700(C2×D3)⋊C4C22×D312yes—
701(C2×D3)⋊C4C22×D312yes—
702C4⋊Dic3—32no—
703C4⋊Dic3—32no—
704C4⋊Dic3—32no—
705C4⋊Dic3C22×D312yes—
706Dic3⋊C4—32no—
707Dic3⋊C4—32no—
708Dic3⋊C4—32no—
709Dic3⋊C4—32no—
710Dic3⋊C4—32no—
711Dic3⋊C4—32no—
712Dic3⋊C4—32no—
713Dic3⋊C4—32no—
714Dic3⋊C4—32no—
715Dic3⋊C4—62no—
716Dic3⋊C4—62no—
717Dic3⋊C4C22×D312yes—
718Dic3⋊C4C22×D312yes—
719Dic3⋊C4C22×D312yes—
720Dic3⋊C4C22×D312yes—
721Dic3⋊C4C22×D312yes—
722C4×Dic3—32no—
723C4×Dic3—32no—
724C4×Dic3C22×D312yes—
725C22×C32—21no—
726C22×C32—21no—
727C22×C32C22×D412yes—
728C22×C32C2511yescharacteristic
729C2×C3⋊D3—21no—
730C2×C3⋊D3—21no—
731C2×C3⋊D3—21no—
732C2×C3⋊D3—21no—
733C2×C3⋊D3—22no—
734C2×C3⋊D3—22no—
735C2×C3⋊D3—22no—
736C2×C3⋊D3—44no—
737C2×C3⋊D3—82no—
738C2×C3⋊D3C22×D412yes—
739C2×C3⋊D3C22×D412yes—
740C2×C3×D3—22no—
741C2×C3×D3—22no—
742C2×C3×D3—22no—
743C2×C3×D3—22no—
744C2×C3×D3—22no—
745C2×C3×D3—22no—
746C2×C3×D3—22no—
747C2×C3×D3—22no—
748C2×C3×D3C22×D414yes—
749D32—44no—
750D32—44no—
751D32—84no—
752D32—82no—
753C32×C4—21no—
754C32×C4—22no—
755C32×C4—21no—
756C32×C4—22no—
757C3⋊Dic3—21no—
758C3⋊Dic3—21no—
759C3⋊Dic3—22no—
760C3×Dic3—22no—
761C3×Dic3—22no—
762C3×Dic3—22no—
763C3×Dic3—22no—
764C3×Dic3C22×D414yes—
765H(5,𝔽2)—188no—
766C2×#41—32no—
767C2×#41—32no—
768C2×#41—92no—
769C2×#41—92no—
770C2×#41—92no—
771C2×#41—92no—
772C2×#41—92no—
773C2×#41—188no—
774C22×Q8—91no—
775C22×D4—92no—
776C22×D4—92no—
777C22×D4—91no—
778C22×D4—91no—
779C22×D4—91no—
780C22×D4—91no—
781C22×D4—92no—
782C22×D4—91no—
783C23×C4—91no—
784C23×C4—91no—
785C23×C4—91no—
786C4⋊Q8—32no—
787C4⋊Q8—92no—
788#124—92no—
789#124—92no—
790#123—32no—
791#123—32no—
792#123—32no—
793#123—32no—
794#123—92no—
795#123—92no—
796#123—92no—
797#123—92no—
798#123—92no—
799#123—92no—
800#123—92no—
801#123—92no—
802#123—92no—
803#123—92no—
804#123—92no—
805#123—92no—
806#123—92no—
807#123—92no—
808C22⋊Q8—32no—
809C22⋊Q8—32no—
810C22⋊Q8—92no—
811C22⋊Q8—92no—
812C22⋊Q8—92no—
813C22⋊Q8—92no—
814#121—32no—
815#121—32no—
816#121—92no—
817#121—92no—
818#121—92no—
819#121—92no—
820#121—92no—
821#121—92no—
822#121—92no—
823#121—92no—
824#120—92no—
825#120—92no—
826#120—92no—
827#120—92no—
828#120—92no—
829#120—92no—
830C4×D4—32no—
831C4×D4—32no—
832C4×D4—92no—
833C4×D4—92no—
834C4×D4—92no—
835C4×D4—92no—
836C4×D4—92no—
837C4×D4—92no—
838#117—92no—
839C2×C4⋊C4—32no—
840C2×C4⋊C4—91no—
841C2×C4⋊C4—91no—
842C2×C4⋊C4—92no—
843C2×C4⋊C4—91no—
844C2×C4⋊C4D3211yescharacteristic, complemented
845C2×C22⋊C4—91no—
846C2×C22⋊C4—91no—
847C2×C22⋊C4—91no—
848C2×C22⋊C4—92no—
849C2×C22⋊C4—92no—
850C2×C22⋊C4—92no—
851C2×C22⋊C4—91no—
852C2×C22⋊C4—91no—
853C2×C22⋊C4—91no—
854C23×C3—21no—
855C23×C3—32no—
856C23×C3—32no—
857C23×C3—32no—
858C23×C3C23×D312yes—
859C22×D3—32no—
860C22×D3—32no—
861C22×D3—38no—
862C22×D3—38no—
863C22×D3—32no—
864C22×D3—32no—
865C22×D3—64no—
866C22×D3—61no—
867C22×D3—61no—
868C22×D3—62no—
869C22×D3—64no—
870C22×D3—64no—
871C22×D3—64no—
872C22×D3—64no—
873C22×D3—64no—
874C22×D3—122no—
875C22×D3—122no—
876C22×D3—122no—
877C22×D3—122no—
878C22×D3—122no—
879C22×D3—122no—
880C22×D3—122no—
881C22×D3—122no—
882C22×D3—122no—
883C22×D3—122no—
884C22×D3—122no—
885C22×D3—122no—
886C22×D3—122no—
887C22×D3—122no—
888C22×D3—122no—
889C22×D3—122no—
890C22×D3—122no—
891C22×D3—122no—
892C22×D3—122no—
893C22×D3C23×D312yes—
894C22×D3C23×D312yes—
895C22×D3C23×D312yes—
896C3×Q8—64no—
897C3×Q8—64no—
898C3×D4—38no—
899C3×D4—64no—
900C3×D4—64no—
901C3×D4—64no—
902C3×D4—64no—
903C3×D4—122no—
904C2×C3×C4—24no—
905C2×C3×C4—24no—
906C2×C3×C4—22no—
907C2×C3×C4—22no—
908C2×C3×C4—21no—
909C2×C3×C4—21no—
910C2×C3×C4—32no—
911C2×C3×C4—32no—
912C2×C3×C4—32no—
913C2×C3×C4—32no—
914C2×C3×C4—32no—
915C2×C3×C4—42no—
916C2×C3×C4—42no—
917C2×C3×C4—42no—
918C2×C3×C4—42no—
919C2×C3×C4—64no—
920C2×C3×C4—64no—
921C2×C3×C4—64no—
922C2×C3×C4—64no—
923C2×C3×C4—122no—
924C2×C3×C4C23×D312yes—
925C2×C3×C4C23×D312yes—
926C2×C3×C4C23×D312yes—
927C2×C3×C4C23×D312yes—
928C2×C3×C4C23×D312yes—
929C2×C3×C4C23×D312yes—
930#67—24no—
931#67—24no—
932#67—38no—
933#67—64no—
934#67—64no—
935#67—64no—
936#67—64no—
937#67—64no—
938#67—64no—
939#67—122no—
940#67—122no—
941#67—122no—
942#67—122no—
943#67D3×D418yes—
944C2×Dic3—32no—
945C2×Dic3—32no—
946C2×Dic3—32no—
947C2×Dic3—32no—
948C2×Dic3—62no—
949C2×Dic3—61no—
950C2×Dic3—61no—
951C2×Dic3—64no—
952C2×Dic3—64no—
953C2×Dic3—64no—
954C2×Dic3—122no—
955C2×Dic3—122no—
956C2×Dic3—122no—
957C2×Dic3—122no—
958C2×Dic3C23×D312yes—
959C2×Dic3C23×D312yes—
960C2×Dic3C23×D312yes—
961C2×Dic3C23×D312yes—
962C2×Dic3C23×D312yes—
963D12—24no—
964D12—24no—
965D12—38no—
966D12—42no—
967D12—64no—
968D12—64no—
969D12—64no—
970D12—64no—
971D12—64no—
972D12—64no—
973D12—64no—
974D12—64no—
975D12—124no—
976D12—124no—
977D12—122no—
978D12—122no—
979C4×D3—24no—
980C4×D3—24no—
981C4×D3—24no—
982C4×D3—24no—
983C4×D3—38no—
984C4×D3—42no—
985C4×D3—64no—
986C4×D3—64no—
987C4×D3—64no—
988C4×D3—64no—
989C4×D3—64no—
990C4×D3—64no—
991C4×D3—64no—
992C4×D3—64no—
993C4×D3—64no—
994C4×D3—64no—
995C4×D3—122no—
996C4×D3—122no—
997C4×D3—122no—
998C4×D3—122no—
999C4×D3—122no—
1000C4×D3—122no—
1001C4×D3—122no—
1002Dic6—24no—
1003Dic6—24no—
1004Dic6—64no—
1005Dic6—64no—
1006C2×C32—22no—
1007C2×C32C23×D411yescharacteristic
1008C2×C32#58511yescharacteristic
1009C2×C32#58511yescharacteristic
1010C3⋊D3—22no—
1011C3⋊D3—22no—
1012C3⋊D3—42no—
1013C3×D3—24no—
1014C3×D3—42no—
1015C3×D3—42no—
1016C24—91no—
1017C24—92no—
1018C24—91no—
1019C24—91no—
1020C24—91no—
1021C24—91no—
1022#41—68no—
1023#41—68no—
1024#41—188no—
1025#41—188no—
1026#41—188no—
1027#41—188no—
1028#41—188no—
1029C2×Q8—32no—
1030C2×Q8—32no—
1031C2×Q8—92no—
1032C2×Q8—184no—
1033C2×D4—32no—
1034C2×D4—32no—
1035C2×D4—32no—
1036C2×D4—32no—
1037C2×D4—32no—
1038C2×D4—32no—
1039C2×D4—92no—
1040C2×D4—92no—
1041C2×D4—92no—
1042C2×D4—92no—
1043C2×D4—92no—
1044C2×D4—92no—
1045C2×D4—92no—
1046C2×D4—98no—
1047C2×D4—92no—
1048C2×D4—92no—
1049C2×D4—92no—
1050C2×D4—92no—
1051C2×D4—184no—
1052C2×D4—188no—
1053C2×D4—188no—
1054C2×D4—188no—
1055C2×D4—184no—
1056C2×D4—184no—
1057C2×D4—184no—
1058C22×C4—32no—
1059C22×C4—32no—
1060C22×C4—32no—
1061C22×C4—32no—
1062C22×C4—32no—
1063C22×C4—91no—
1064C22×C4—91no—
1065C22×C4—92no—
1066C22×C4—91no—
1067C22×C4—91no—
1068C22×C4—91no—
1069C22×C4—92no—
1070C22×C4—92no—
1071C22×C4—92no—
1072C22×C4—91no—
1073C22×C4—91no—
1074C22×C4—91no—
1075C22×C4—91no—
1076C22×C4—91no—
1077C22×C4—91no—
1078C22×C4—184no—
1079C22×C4—184no—
1080C22×C4—184no—
1081C22×C4C2×D3211yescharacteristic
1082C22×C4C2×D3211yescharacteristic
1083C22×C4C2×D3211yescharacteristic
1084C4⋊C4—32no—
1085C4⋊C4—32no—
1086C4⋊C4—32no—
1087C4⋊C4—32no—
1088C4⋊C4—32no—
1089C4⋊C4—32no—
1090C4⋊C4—92no—
1091C4⋊C4—92no—
1092C4⋊C4—92no—
1093C4⋊C4—92no—
1094C4⋊C4—92no—
1095C4⋊C4—92no—
1096C4⋊C4C2×D3212yes—
1097C4⋊C4C2×D3212yes—
1098C22⋊C4—32no—
1099C22⋊C4—32no—
1100C22⋊C4—32no—
1101C22⋊C4—32no—
1102C22⋊C4—32no—
1103C22⋊C4—32no—
1104C22⋊C4—32no—
1105C22⋊C4—32no—
1106C22⋊C4—92no—
1107C22⋊C4—92no—
1108C22⋊C4—92no—
1109C22⋊C4—92no—
1110C22⋊C4—92no—
1111C22⋊C4—92no—
1112C22⋊C4—92no—
1113C22⋊C4—92no—
1114C22⋊C4—92no—
1115C22⋊C4—92no—
1116C22⋊C4—92no—
1117C22⋊C4—92no—
1118C22⋊C4—92no—
1119C22⋊C4—92no—
1120C42—32no—
1121C42—92no—
1122C22×C3—22no—
1123C22×C3—22no—
1124C22×C3—22no—
1125C22×C3—22no—
1126C22×C3—22no—
1127C22×C3—21no—
1128C22×C3—34no—
1129C22×C3—62no—
1130C22×C3—62no—
1131C22×C3—62no—
1132C22×C3—62no—
1133C22×C3—62no—
1134C22×C3—62no—
1135C22×C3—62no—
1136C22×C3—62no—
1137C22×C3C2×D3×D414yes—
1138C22×C3C24×D312yes—
1139C2×D3—22no—
1140C2×D3—22no—
1141C2×D3—22no—
1142C2×D3—22no—
1143C2×D3—22no—
1144C2×D3—22no—
1145C2×D3—22no—
1146C2×D3—22no—
1147C2×D3—34no—
1148C2×D3—34no—
1149C2×D3—62no—
1150C2×D3—62no—
1151C2×D3—62no—
1152C2×D3—62no—
1153C2×D3—62no—
1154C2×D3—62no—
1155C2×D3—62no—
1156C2×D3—62no—
1157C2×D3—62no—
1158C2×D3—62no—
1159C2×D3—62no—
1160C2×D3—62no—
1161C2×D3—121no—
1162C2×D3—121no—
1163C2×D3—121no—
1164C2×D3—121no—
1165C2×D3—122no—
1166C2×D3—122no—
1167C2×D3—122no—
1168C2×D3—128no—
1169C2×D3—128no—
1170C2×D3—128no—
1171C2×D3—128no—
1172C2×D3—244no—
1173C2×D3—244no—
1174C2×D3—244no—
1175C2×D3—244no—
1176C2×D3—244no—
1177C2×D3C2×D3×D414yes—
1178C3×C4—22no—
1179C3×C4—22no—
1180C3×C4—22no—
1181C3×C4—22no—
1182C3×C4—22no—
1183C3×C4—22no—
1184C3×C4—34no—
1185C3×C4—41no—
1186C3×C4—41no—
1187C3×C4—42no—
1188C3×C4—42no—
1189C3×C4—62no—
1190C3×C4—62no—
1191C3×C4—62no—
1192C3×C4—62no—
1193Dic3—22no—
1194Dic3—22no—
1195Dic3—22no—
1196Dic3—22no—
1197Dic3—62no—
1198Dic3—62no—
1199Dic3—62no—
1200Dic3—62no—
1201Dic3—121no—
1202Dic3—121no—
1203Dic3—122no—
1204Dic3C2×D3×D414yes—
1205C32#348511yescharacteristic, complemented, Sylow
1206C23—32no—
1207C23—32no—
1208C23—32no—
1209C23—94no—
1210C23—91no—
1211C23—91no—
1212C23—94no—
1213C23—92no—
1214C23—184no—
1215C23—182no—
1216C23—182no—
1217C23—182no—
1218C23—361no—
1219C23—361no—
1220C23—361no—
1221C23—361no—
1222C23—361no—
1223C23—361no—
1224C23—361no—
1225C23—361no—
1226C23—362no—
1227C23—362no—
1228C23—361no—
1229C23—361no—
1230C23C22×D3211yescharacteristic
1231Q8—64no—
1232Q8—64no—
1233Q8—184no—
1234D4—38no—
1235D4—64no—
1236D4—64no—
1237D4—64no—
1238D4—64no—
1239D4—98no—
1240D4—122no—
1241D4—184no—
1242D4—184no—
1243D4—184no—
1244D4—184no—
1245D4—184no—
1246D4—184no—
1247D4—184no—
1248D4—362no—
1249D4—362no—
1250D4—362no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—32no—
1254C2×C4—32no—
1255C2×C4—32no—
1256C2×C4—32no—
1257C2×C4—32no—
1258C2×C4—41no—
1259C2×C4—64no—
1260C2×C4—64no—
1261C2×C4—64no—
1262C2×C4—64no—
1263C2×C4—94no—
1264C2×C4—92no—
1265C2×C4—91no—
1266C2×C4—91no—
1267C2×C4—122no—
1268C2×C4—182no—
1269C2×C4—182no—
1270C2×C4—182no—
1271C2×C4—182no—
1272C2×C4—184no—
1273C2×C4—184no—
1274C2×C4—182no—
1275C2×C4—182no—
1276C2×C4—184no—
1277C2×C4—182no—
1278C2×C4—361no—
1279C2×C4—361no—
1280C2×C4—362no—
1281C2×C4—361no—
1282C2×C4C22×D3212yes—
1283C2×C4C22×D3211yescharacteristic
1284C2×C4C22×D3211yescharacteristic
1285C2×C4C22×D3212yes—
1286C2×C3—24no—
1287C2×C3—24no—
1288C2×C3—21no—
1289C2×C3—21no—
1290C2×C3—21no—
1291C2×C3—64no—
1292C2×C3—122no—
1293C2×C3—122no—
1294C2×C3C22×D3×D412yes—
1295C2×C3#596412yes—
1296C2×C3#596812yes—
1297D3—24no—
1298D3—42no—
1299D3—42no—
1300D3—64no—
1301D3—64no—
1302D3—122no—
1303D3—122no—
1304D3—122no—
1305D3—122no—
1306D3—242no—
1307C22—21no—
1308C22—21no—
1309C22—34no—
1310C22—62no—
1311C22—62no—
1312C22—62no—
1313C22—62no—
1314C22—62no—
1315C22—62no—
1316C22—62no—
1317C22—62no—
1318C22—92no—
1319C22—92no—
1320C22—181no—
1321C22—181no—
1322C22—181no—
1323C22—181no—
1324C22—182no—
1325C22—182no—
1326C22—182no—
1327C22—364no—
1328C22—364no—
1329C22—364no—
1330C22—722no—
1331C22—724no—
1332C22—722no—
1333C22D32×D412yes—
1334C22C23×D3211yescharacteristic
1335C4—22no—
1336C4—21no—
1337C4—22no—
1338C4—21no—
1339C4—34no—
1340C4—62no—
1341C4—62no—
1342C4—62no—
1343C4—62no—
1344C4—181no—
1345C4—181no—
1346C4—182no—
1347C3—21no—
1348C3#8670012yescomplemented
1349C2—22no—
1350C2—64no—
1351C2—122no—
1352C2—122no—
1353C2—182no—
1354C2—182no—
1355C2—362no—
1356C2#1059666911yescharacteristic
1357C2C2×D32×D411yescharacteristic
1358C2#1059668911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64308C2semidirect
2. C2×#64306C2semidirect
3. C2×#64103C2semidirect
4. C3×#5507C2semidirect
5. #10595084C2semidirect
6. #10595080C2semidirect
7. #10595079C2semidirect
8. #10595075C2semidirect
9. #10595068C2semidirect
10. #10595058C2semidirect
11. #10594888C2semidirect
12. #10594623C2semidirect
13. #10594622C2semidirect
14. #10594619C2semidirect
15. #10594611C2semidirect
16. D3×#894C2semidirect
17. #10594516C2semidirect
18. #10594372C2semidirect
19. #10594328C2semidirect
22. C22×C4×C3⋊D3C22semidirect
23. C2×C3×#235C22semidirect
24. C2×C3×#235C22semidirect
27. C2×#3811C22semidirect
28. C2×#3811C22semidirect
29. C2×#3805C22semidirect
32. C2×#3802C22semidirect
34. C2×D3×D12C22semidirect
35. C2×C4×D32C22semidirect
36. C2×C4×D32C22semidirect
38. C2×#3799C22semidirect
39. C2×#3798C22semidirect
40. C2×#3797C22semidirect
41. C2×#3796C22semidirect
42. C2×C32×C4⋊C4C22semidirect
43. C2×#3752C22semidirect
44. C2×#3752C22semidirect
45. C2×#3752C22semidirect
46. C2×#3750C22semidirect
47. #64103C22semidirect
48. #64103C22semidirect
49. #64103C22semidirect
50. #64103C22semidirect
51. C3×#930C22semidirect
52. C3×#929C22semidirect
53. C3×#929C22semidirect
54. C3×C4×#67C22semidirect
55. C3×#896C22semidirect
56. C3×#896C22semidirect
57. C3×#895C22semidirect
58. C3×#894C22semidirect
59. C3×#894C22semidirect
60. C3×#893C22semidirect
61. C3×D3×C4⋊C4C22semidirect
62. C3×#888C22semidirect
63. #63981C22semidirect
64. #63980C22semidirect
65. #63974C22semidirect
66. #67⋊Dic3C22semidirect
67. #63962C22semidirect
68. #63923C22semidirect
69. #63922C22semidirect
70. #63922C22semidirect
71. #63922C22semidirect
72. #63922C22semidirect
73. #63921C22semidirect
74. #63921C22semidirect
75. D3×(C2×D3)⋊C4C22semidirect
76. D3×(C2×D3)⋊C4C22semidirect
77. D3×(C2×D3)⋊C4C22semidirect
78. #63910C22semidirect
79. #63910C22semidirect
80. #63907C22semidirect
81. #63906C22semidirect
82. #63906C22semidirect
83. #63905C22semidirect
84. #63904C22semidirect
85. #63904C22semidirect
86. #63897C22semidirect
87. #63895C22semidirect
88. #63890C22semidirect
89. #63888C22semidirect
90. #63887C22semidirect
91. #63886C22semidirect
92. #63886C22semidirect
93. #63885C22semidirect
94. #63884C22semidirect
95. #63883C22semidirect
96. #63883C22semidirect
97. #63880C22semidirect
98. #63880C22semidirect
99. #63879C22semidirect
100. D3×Dic3⋊C4C22semidirect
101. #63854C22semidirect
102. #63854C22semidirect
103. #63853C22semidirect
104. #63853C22semidirect
105. #63852C22semidirect
106. #63851C22semidirect
107. #63850C22semidirect
108. #63839C22semidirect
109. #63836C22semidirect
138. #5507D3semidirect
179. #3811D4semidirect
272. C2×#235C2×D3semidirect
273. C2×#235C2×D3semidirect
295. C2×C3×C4⋊C4C2×D3semidirect
315. #930C2×D3semidirect
318. #929C2×D3semidirect
319. #929C2×D3semidirect
323. C4×#67C2×D3semidirect
341. #896C2×D3semidirect
342. #896C2×D3semidirect
347. #895C2×D3semidirect
369. #894C2×D3semidirect
370. #894C2×D3semidirect
373. #893C2×D3semidirect
378. D3×C4⋊C4C2×D3semidirect
380. #888C2×D3semidirect
844. C2×C4⋊C4D32semidirect
1205. C32#3485semidirect
1348. C3#86700semidirect

Maximal subgroups

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

subgroupindex
C2×#643082
C2×#643062
C2×#641032
C3×#55072
#105950842
#105950802
#105950792
#105950752
#105950682
#105950582
#105948882
#105946232
#105946222
#105946192
#105946112
D3×#8942
#105945162
#105943722
#105943282
#867003