Finite Group Databasebeta

← #11904777

Subgroups — #11904777

Order 1152.

3179 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2C2×D3×#235C211yesmaximal, characteristic, complemented
3#10596287C211yesmaximal, characteristic, complemented
4C2×C3×#946C211yesmaximal, characteristic, complemented
5#10595427C212yesmaximal, complemented
6#10595424C212yesmaximal, complemented
7D3×#946C212yesmaximal, complemented
8#10595402C212yesmaximal, complemented
9#10595400C212yesmaximal, complemented
10#10595398C212yesmaximal, complemented
11#10595397C212yesmaximal, complemented
12#10595357C212yesmaximal, complemented
13#10595065C214yesmaximal, complemented
14#10595043C211yesmaximal, characteristic, complemented
15#10595022C211yesmaximal, characteristic, complemented
16#10594986C211yesmaximal, characteristic, complemented
17#10594885C214yesmaximal, complemented
18#87295—31nomaximal
19#85985—31nomaximal
20C22×C32×Q8C2211yescharacteristic, complemented
21C2×#3828C2211yescharacteristic
22C3×#1007—28no—
23C2×C3×#239C2212yescomplemented
24C2×C3×#239C2212yescomplemented
25C2×C3×D3×Q8C2212yescomplemented
26C2×C3×D3×Q8C2212yescomplemented
27C2×C3×#235C2211yescharacteristic
28C2×C3×#235C2214yescomplemented
29C2×C3×#235C2211yescharacteristic, complemented
30C22×C3×C4×D3C2211yescharacteristic
31C2×D3×#67C2212yes—
32C2×#3804C2212yes—
33D3×#235—28no—
34C2×D3×D12C2211yescharacteristic
35C2×C4×D32C2212yes—
36C2×#3799C2211yescharacteristic
37C2×#3798C2212yes—
38C2×#3795C2211yescharacteristic
39C2×D3×Dic6C2211yescharacteristic
40#64156C2212yescomplemented
41#64155C2212yescomplemented
42#64155C2212yescomplemented
43#64153C2212yescomplemented
44#64138C2214yescomplemented
45#64135C2211yescharacteristic, complemented
46C3×#946C2212yes—
47C3×#946C2212yes—
48C3×#946C2212yescomplemented
49C3×#946C2212yescomplemented
50C2×C3×(C2×D3)⋊C4C2212yes—
51C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
52C2×C3×Dic3⋊C4C2212yescomplemented
53#63978C2214yescomplemented
54#63976C2212yes—
55Dic3×#67C2214yescomplemented
56#63961C2212yescomplemented
57#63922C2214yes—
58D3×(C2×D3)⋊C4C2214yes—
59#63916C2212yescomplemented
60#63909C2212yescomplemented
61#63908C2211yescharacteristic
62#63908C2211yescharacteristic, complemented
63#63907C2214yescomplemented
64#63906C2214yescomplemented
65#63905C2214yescomplemented
66#63904C2214yescomplemented
67C4×#625C2212yes—
68C4×#625C2212yescomplemented
69#63898C2212yescomplemented
70D3×C4⋊Dic3C2212yescomplemented
71#63888C2214yescomplemented
72#63887C2214yes—
73#63886C2214yescomplemented
74#63885C2214yescomplemented
75#63884C2214yescomplemented
76#63879C2214yes—
77D3×Dic3⋊C4C2214yescomplemented
78#63871C2212yescomplemented
79#63857C2212yescomplemented
80#63856C2211yescharacteristic
81#63856C2211yescharacteristic, complemented
82#63851C2214yescomplemented
83#63850C2214yescomplemented
84#63843C2212yescomplemented
85#63841C2212yescomplemented
86#63839C2214yescomplemented
87C2×C3×2−1+4—31no—
88C2×D3×#41—31no—
89C2×#1007D311yescharacteristic, complemented
90C22×#235—31no—
91C2×C3×C22⋊Q8—31no—
92#5833—32no—
93#5833—31no—
94#5829—32no—
95#5829—34no—
96#5828—31no—
97#5828—32no—
98#5827—31no—
99#5824—32no—
100#5824—34no—
101#5817—32no—
102#5816—31no—
103#5816—31no—
104#5816—32no—
105#5816—61no—
106Q8×#67—32no—
107C2×#946—32no—
108C2×#946D311yescharacteristic, complemented
109#5791—31no—
110#5633—32no—
111#5632—32no—
112#5631—32no—
113#5630—32no—
114#5629—32no—
115#5628—32no—
116#5627—32no—
117D3×C22⋊Q8—32no—
118#5510—31no—
119#5507—34no—
120#5504—31no—
121#5490—34no—
122C23×C3×D3C2311yescharacteristic
123C22×D32C2312yes—
124C2×C32×Q8—24no—
125C2×C32×Q8C2312yes—
126C2×C32×Q8C2312yes—
127C22×C32×C4C2312yes—
128C22×C32×C4C2311yescharacteristic
129C2×#638C2312yes—
130#3828—24no—
131C2×C4⋊(C3⋊D3)C2311yescharacteristic
132C2×C4×C3⋊D3C2312yes—
133C2×#634C2311yescharacteristic
134C2×C3×#67C2312yes—
135C2×C3×#67C2312yes—
136C22×C3×Dic3C2311yescharacteristic
137C22×C3×Dic3C2312yes—
138C3×#239—28no—
139C3×#239—28no—
140C3×D3×Q8—28no—
141C3×D3×Q8—28no—
142C3×#235—24no—
143C3×#235—216no—
144C3×#235D418yescomplemented
145C2×C3×D12C2314yes—
146C2×C3×D12C2311yescharacteristic
147C2×C3×D12C2311yescharacteristic
148C2×C3×C4×D3—24no—
149C2×C3×C4×D3C2311yescharacteristic
150C2×C3×C4×D3C2311yescharacteristic
151C2×C3×C4×D3C2311yescharacteristic
152C2×C3×C4×D3C2311yescharacteristic
153C2×C3×C4×D3C2314yes—
154C2×C3×C4×D3C2314yes—
155C2×C3×C4×D3C2312yes—
156C2×C3×C4×D3C2312yes—
157C2×C3×Dic6C2314yes—
158C2×C3×Dic6C2311yescharacteristic
159C2×C3×Dic6C2311yescharacteristic
160D3×#67—28no—
161C2×#627C2312yes—
162C2×#626C2312yes—
163C2×#626C2312yes—
164C2×#626C2314yes—
165C2×#625C2312yes—
166C2×#625C2312yes—
167C2×#625C2312yes—
168C2×#624C2312yes—
169#3804—28no—
170C2×D3×Dic3C2312yes—
171C2×D3×Dic3C2312yes—
172C2×D3×Dic3C2314yes—
173D3×D12—24no—
174C4×D32—28no—
175#3799—24no—
176#3798—28no—
177#3795—24no—
178D3×Dic6—24no—
179#3757C2312yes—
180#3752C2314yes—
181#3752C2314yes—
182C4⋊(C3⋊Dic3)C2311yescharacteristic
183C4⋊(C3⋊Dic3)C2311yescharacteristic
184#3750C2314yes—
185#3750C2314yes—
186C4×C3⋊Dic3C2312yes—
187C3×(C2×D3)⋊C4C2314yes—
188C3×(C2×D3)⋊C4C2314yes—
189C3×C4⋊Dic3C2312yes—
190C3×C4⋊Dic3C2312yes—
191C3×Dic3⋊C4C2314yes—
192C3×Dic3⋊C4C2314yes—
193#3724C2312yes—
194#3724C2312yes—
195Dic3⋊Dic3C2314yes—
196Dic3⋊Dic3C2314yes—
197#3722C2314yes—
198(C2×D3)⋊Dic3C2314yes—
199(C2×D3)⋊Dic3C2312yes—
200(C2×D3)⋊Dic3C2314yes—
201(C2×D3)⋊Dic3C2312yes—
202(C2×D3)⋊Dic3C2312yes—
203(C2×D3)⋊Dic3C2312yes—
204Dic32C2314yes—
205#3489—91noSylow
206C3×2−1+4—68no—
207C2×C3×#41—32no—
208C2×C3×#41—32no—
209C2×C3×#41—31no—
210C2×C3×#41—34no—
211C2×C3×#41—31no—
212C22×C3×Q8—21no—
213C22×C3×Q8—32no—
214C22×C3×Q8—32no—
215C22×C3×Q8C2×D311yescharacteristic, complemented
216C22×C3×Q8C2×D311yescharacteristic, complemented
217C23×C3×C4—31no—
218C22×#67—32no—
219D3×#41—68no—
220#1007—28no—
221C2×#239—31no—
222C2×#239C2×D312yescomplemented
223C2×#239C2×D312yescomplemented
224C2×D3×Q8—31no—
225C2×D3×Q8C2×D312yescomplemented
226C2×D3×Q8C2×D312yescomplemented
227C2×#237—32no—
228C2×#237—31no—
229C2×D3×D4—32no—
230C2×D3×D4—31no—
231C2×#235—31no—
232C2×#235—31no—
233C2×#235—32no—
234C2×#235—31no—
235C2×#235—32no—
236C2×#235—32no—
237C2×#235—31no—
238C2×#235—61no—
239C2×#235—68no—
240C2×#235C2×D311yescharacteristic
241C2×#235C2×D314yescomplemented
242C2×#235C2×D311yescharacteristic, complemented
243C22×D12—31no—
244C22×C4×D3—32no—
245C22×C4×D3—32no—
246C22×C4×D3C2×D311yescharacteristic
247C22×Dic6—31no—
248C3×C22⋊Q8—32no—
249C3×C22⋊Q8—32no—
250C3×C22⋊Q8—32no—
251C3×C22⋊Q8—32no—
252C2×C3×C4⋊C4—32no—
253C2×C3×C4⋊C4—31no—
254C2×C3×C22⋊C4—32no—
255#953—32no—
256#947—32no—
257#947—32no—
258#947—34no—
259#947—62no—
260#946—32no—
261#946—32no—
262#946—32no—
263#946—32no—
264#946—31no—
265#946—31no—
266#946—34no—
267#946—32no—
268#946—34no—
269#946—62no—
270#946—62no—
271#946C2×D312yes—
272#946C2×D312yes—
273#946C2×D312yescomplemented
274#946C2×D312yescomplemented
275Q8×Dic3—32no—
276#944—32no—
277#944—32no—
278#944—34no—
279#944—62no—
280#939—34no—
281#939—34no—
282#939—34no—
283#938—31no—
284#938—31no—
285#938—32no—
286#937—32no—
287#937—34no—
288#935—32no—
289#935—34no—
290D4×Dic3—34no—
291D4×Dic3—32no—
292#930—34no—
293#930—31no—
294#930—31no—
295#930—34no—
296#930—32no—
297#929—34no—
298#929—34no—
299#929—32no—
300#929—34no—
301#929—34no—
302#929—64no—
303C4×#67—34no—
304C4×#67—32no—
305C4×#67—32no—
306C4×#67—32no—
307C4×#67—32no—
308C4×#67—34no—
309C4×#67—34no—
310C2×(C2×D3)⋊C4—34no—
311C2×(C2×D3)⋊C4C2×D312yes—
312#926—31no—
313#926—31no—
314#926—32no—
315#926—61no—
316C2×C4⋊Dic3—32no—
317C2×C4⋊Dic3C2×D311yescharacteristic, complemented
318#924—31no—
319#924—31no—
320#924—32no—
321#924—34no—
322C2×Dic3⋊C4—34no—
323C2×Dic3⋊C4C2×D312yescomplemented
324#897—32no—
325#897—32no—
326#896—34no—
327#896—34no—
328#895—34no—
329#895—32no—
330#895—32no—
331#894—34no—
332#894—34no—
333#893—32no—
334#893—34no—
335#892—32no—
336D3×C4⋊C4—32no—
337D3×C4⋊C4—34no—
338#888—34no—
339#887—32no—
340#885—34no—
341#884—34no—
342#884—34no—
343#883—34no—
344#882—34no—
345#67⋊C4—34no—
346D3×C22⋊C4—34no—
347#878—34no—
348C23×C32C2411yescharacteristic
349C22×C3⋊D3C2412yes—
350C22×C3×D3—22no—
351C22×C3×D3—22no—
352C22×C3×D3—41no—
353C22×C3×D3C2411yescharacteristic
354C22×C3×D3C2412yes—
355C22×C3×D3C2412yes—
356C22×C3×D3C2411yescharacteristic
357C2×D32—24no—
358C2×D32—24no—
359C2×D32—42no—
360C32×Q8—24no—
361C32×Q8—24no—
362C2×C32×C4—24no—
363C2×C32×C4C2×D414yes—
364C2×C32×C4C2414yes—
365C2×C32×C4C2411yescharacteristic
366C2×C32×C4C2411yescharacteristic
367#638—24no—
368C2×C3⋊Dic3C2412yes—
369C2×C3⋊Dic3C2412yes—
370C2×C3⋊Dic3C2412yes—
371C4⋊(C3⋊D3)—22no—
372C4×C3⋊D3—24no—
373#634—22no—
374C3×#67—24no—
375C3×#67C2×D418yes—
376C2×C3×Dic3—22no—
377C2×C3×Dic3—42no—
378C2×C3×Dic3C2414yes—
379C2×C3×Dic3C2412yes—
380C2×C3×Dic3C2411yescharacteristic
381C2×C3×Dic3C2411yescharacteristic
382C2×C3×Dic3C2412yes—
383C3×D12—28no—
384C3×D12—22no—
385C3×D12C2×D414yes—
386C3×C4×D3—28no—
387C3×C4×D3—22no—
388C3×C4×D3—22no—
389C3×C4×D3—22no—
390C3×C4×D3—22no—
391C3×C4×D3—24no—
392C3×C4×D3—28no—
393C3×C4×D3C2×D418yes—
394C3×Dic6—22no—
395C3×Dic6—28no—
396C3×Dic6C2×D414yes—
397#627—24no—
398#626—24no—
399#626—24no—
400#626—44no—
401#625—24no—
402#625—24no—
403#625—42no—
404#624—24no—
405D3×Dic3—24no—
406D3×Dic3—24no—
407D3×Dic3—44no—
408C2×2−1+4—31no—
409C22×#41—91no—
410D4×Q8—92no—
411#548—92no—
412#547—94no—
413#547—92no—
414#546—94no—
415#546—92no—
416#537—91no—
417#537—92no—
418#536—92no—
419#536—91no—
420#525—92no—
421#525—91no—
422C2×C22⋊Q8—31no—
423C2×C22⋊Q8—92no—
424#520—91no—
425C24×C3—31no—
426C23×D3—32no—
427C23×D3—32no—
428C23×D3C22×D311yescharacteristic
429C3×#41—38no—
430C3×#41—616no—
431C3×#41—68no—
432C3×#41—68no—
433C3×#41—64no—
434C2×C3×Q8—24no—
435C2×C3×Q8—24no—
436C2×C3×Q8—22no—
437C2×C3×Q8—22no—
438C2×C3×Q8—31no—
439C2×C3×Q8—34no—
440C2×C3×Q8—31no—
441C2×C3×Q8—44no—
442C2×C3×Q8—68no—
443C2×C3×Q8—68no—
444C2×C3×Q8C22×D312yes—
445C2×C3×Q8C22×D312yes—
446C2×C3×Q8C22×D312yes—
447C2×C3×Q8C22×D312yes—
448C2×C3×D4—32no—
449C2×C3×D4—32no—
450C2×C3×D4—31no—
451C2×C3×D4—34no—
452C2×C3×D4—31no—
453C22×C3×C4—21no—
454C22×C3×C4—22no—
455C22×C3×C4—32no—
456C22×C3×C4—31no—
457C22×C3×C4—32no—
458C22×C3×C4—34no—
459C22×C3×C4—34no—
460C22×C3×C4—32no—
461C22×C3×C4—31no—
462C22×C3×C4—31no—
463C22×C3×C4—31no—
464C22×C3×C4—31no—
465C22×C3×C4—64no—
466C22×C3×C4C22×D312yes—
467C22×C3×C4C22×D312yes—
468C22×C3×C4C22×D311yescharacteristic
469C22×C3×C4C22×D311yescharacteristic
470C2×#67—32no—
471C2×#67—32no—
472C2×#67—32no—
473C2×#67—32no—
474C2×#67—32no—
475C2×#67—32no—
476C2×#67—32no—
477C2×#67—32no—
478C2×#67—32no—
479C2×#67—32no—
480C2×#67—34no—
481C2×#67—62no—
482C2×#67—68no—
483C2×#67C22×D312yes—
484C2×#67C22×D312yes—
485C22×Dic3—32no—
486C22×Dic3—32no—
487C22×Dic3—34no—
488C22×Dic3C22×D311yescharacteristic
489C22×Dic3C22×D312yes—
490#239—28no—
491#239—28no—
492#239—64no—
493D3×Q8—28no—
494D3×Q8—28no—
495D3×Q8—64no—
496#237—64no—
497#237—68no—
498D3×D4—64no—
499D3×D4—68no—
500#235—24no—
501#235—216no—
502#235—68no—
503#235—64no—
504#235—64no—
505#235—68no—
506#235—64no—
507#235—68no—
508#235—64no—
509#235—124no—
510#235#6718yescomplemented
511C2×D12—32no—
512C2×D12—32no—
513C2×D12—31no—
514C2×D12—31no—
515C2×D12—34no—
516C2×D12—61no—
517C2×D12—64no—
518C2×D12C22×D314yes—
519C2×D12C22×D311yescharacteristic
520C2×D12C22×D311yescharacteristic
521C2×C4×D3—24no—
522C2×C4×D3—32no—
523C2×C4×D3—32no—
524C2×C4×D3—32no—
525C2×C4×D3—32no—
526C2×C4×D3—32no—
527C2×C4×D3—32no—
528C2×C4×D3—34no—
529C2×C4×D3—62no—
530C2×C4×D3—68no—
531C2×C4×D3—68no—
532C2×C4×D3C22×D314yes—
533C2×C4×D3C22×D314yes—
534C2×C4×D3C22×D312yes—
535C2×C4×D3C22×D311yescharacteristic
536C2×C4×D3C22×D311yescharacteristic
537C2×C4×D3C22×D311yescharacteristic
538C2×C4×D3C22×D311yescharacteristic
539C2×C4×D3C22×D312yes—
540C2×Dic6—31no—
541C2×Dic6—31no—
542C2×Dic6—32no—
543C2×Dic6—32no—
544C2×Dic6—61no—
545C2×Dic6—64no—
546C2×Dic6C22×D314yes—
547C2×Dic6C22×D311yescharacteristic
548C2×Dic6C22×D311yescharacteristic
549C3×C4⋊C4—32no—
550C3×C4⋊C4—34no—
551C3×C4⋊C4—32no—
552C3×C4⋊C4—34no—
553C3×C22⋊C4—34no—
554C3×C22⋊C4—34no—
555#217—32no—
556#217—32no—
557#217—32no—
558#217—32no—
559#217—32no—
560#217—34no—
561#217—34no—
562#217—32no—
563#217—62no—
564(C2×D3)⋊C4—34no—
565(C2×D3)⋊C4—34no—
566(C2×D3)⋊C4—32no—
567(C2×D3)⋊C4—32no—
568(C2×D3)⋊C4—32no—
569(C2×D3)⋊C4—32no—
570(C2×D3)⋊C4—34no—
571(C2×D3)⋊C4—34no—
572(C2×D3)⋊C4—34no—
573(C2×D3)⋊C4—34no—
574(C2×D3)⋊C4—34no—
575(C2×D3)⋊C4—34no—
576(C2×D3)⋊C4—64no—
577(C2×D3)⋊C4—64no—
578(C2×D3)⋊C4C22×D314yes—
579(C2×D3)⋊C4C22×D314yes—
580C4⋊Dic3—31no—
581C4⋊Dic3—31no—
582C4⋊Dic3—31no—
583C4⋊Dic3—31no—
584C4⋊Dic3—34no—
585C4⋊Dic3—34no—
586C4⋊Dic3—61no—
587C4⋊Dic3—61no—
588C4⋊Dic3C22×D312yes—
589C4⋊Dic3C22×D312yes—
590Dic3⋊C4—34no—
591Dic3⋊C4—34no—
592Dic3⋊C4—34no—
593Dic3⋊C4—34no—
594Dic3⋊C4—34no—
595Dic3⋊C4—32no—
596Dic3⋊C4—32no—
597Dic3⋊C4—34no—
598Dic3⋊C4—32no—
599Dic3⋊C4—32no—
600Dic3⋊C4—64no—
601Dic3⋊C4—64no—
602Dic3⋊C4C22×D314yes—
603Dic3⋊C4C22×D314yes—
604C4×Dic3—32no—
605C4×Dic3—32no—
606C4×Dic3—34no—
607C4×Dic3—34no—
608C4×Dic3—62no—
609C22×C32—21no—
610C22×C32—21no—
611C22×C32C22×D412yes—
612C22×C32C2511yescharacteristic
613C2×C3⋊D3—22no—
614C2×C3⋊D3—22no—
615C2×C3⋊D3—22no—
616C2×C3×D3—21no—
617C2×C3×D3—22no—
618C2×C3×D3—22no—
619C2×C3×D3—21no—
620C2×C3×D3—21no—
621C2×C3×D3—22no—
622C2×C3×D3—22no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—22no—
626C2×C3×D3—44no—
627C2×C3×D3C22×D414yes—
628C2×C3×D32−1+412yescomplemented
629D32—48no—
630C32×C4—24no—
631C32×C4C22×D412yes—
632C32×C4C22×D412yes—
633C3⋊Dic3—22no—
634C3⋊Dic3—22no—
635C3⋊Dic3—22no—
636C3×Dic3—21no—
637C3×Dic3—21no—
638C3×Dic3—22no—
639C3×Dic3—24no—
640C3×Dic3C22×D414yes—
6412−1+4—68no—
642C2×#41—32no—
643C2×#41—32no—
644C2×#41—31no—
645C2×#41—31no—
646C2×#41—34no—
647C2×#41—92no—
648C2×#41—92no—
649C2×#41—91no—
650C2×#41—91no—
651C2×#41—91no—
652C2×#41—188no—
653C22×Q8—32no—
654C22×Q8—32no—
655C22×Q8—91no—
656C22×Q8D3211yescharacteristic, complemented
657C22×D4—91no—
658C22×D4—92no—
659C23×C4—31no—
660C23×C4—92no—
661C4⋊Q8—94no—
662C4⋊Q8—92no—
663#124—94no—
664#124—92no—
665#123—94no—
666#123—94no—
667#123—94no—
668#123—92no—
669#123—94no—
670C22⋊Q8—32no—
671C22⋊Q8—32no—
672C22⋊Q8—32no—
673C22⋊Q8—32no—
674C22⋊Q8—94no—
675C22⋊Q8—94no—
676C22⋊Q8—92no—
677C22⋊Q8—92no—
678C22⋊Q8—94no—
679C22⋊Q8—91no—
680C22⋊Q8—91no—
681C22⋊Q8—92no—
682C22⋊Q8—92no—
683#121—94no—
684#121—94no—
685#121—92no—
686#121—92no—
687#121—94no—
688#121—91no—
689#121—91no—
690#121—94no—
691#120—94no—
692#120—92no—
693C4×Q8—92no—
694C4×D4—94no—
695C4×D4—94no—
696C4×D4—92no—
697C4×D4—92no—
698C4×D4—92no—
699C4×D4—94no—
700#117—92no—
701#117—91no—
702C2×C4⋊C4—31no—
703C2×C4⋊C4—32no—
704C2×C4⋊C4—92no—
705C2×C4⋊C4—94no—
706C2×C22⋊C4—32no—
707C2×C22⋊C4—94no—
708C23×C3—21no—
709C23×C3—31no—
710C23×C3—32no—
711C23×C3—32no—
712C23×C3—31no—
713C23×C3—62no—
714C23×C3—62no—
715C23×C3—121no—
716C23×C3C23×D311yescharacteristic
717C23×C3C23×D311yescharacteristic
718C22×D3—22no—
719C22×D3—22no—
720C22×D3—32no—
721C22×D3—32no—
722C22×D3—41no—
723C22×D3—62no—
724C22×D3—64no—
725C22×D3—64no—
726C22×D3—64no—
727C22×D3—64no—
728C22×D3—122no—
729C22×D3—122no—
730C22×D3C23×D312yes—
731C22×D3C23×D311yescharacteristic
732C22×D3C23×D311yescharacteristic
733C22×D3C23×D312yes—
734C3×Q8—24no—
735C3×Q8—24no—
736C3×Q8—24no—
737C3×Q8—24no—
738C3×Q8—34no—
739C3×Q8—44no—
740C3×Q8—44no—
741C3×Q8—68no—
742C3×Q8—62no—
743C3×D4—38no—
744C3×D4—34no—
745C3×D4—68no—
746C3×D4—64no—
747C3×D4—62no—
748C2×C3×C4—24no—
749C2×C3×C4—24no—
750C2×C3×C4—21no—
751C2×C3×C4—21no—
752C2×C3×C4—24no—
753C2×C3×C4—24no—
754C2×C3×C4—32no—
755C2×C3×C4—38no—
756C2×C3×C4—34no—
757C2×C3×C4—32no—
758C2×C3×C4—31no—
759C2×C3×C4—31no—
760C2×C3×C4—44no—
761C2×C3×C4—68no—
762C2×C3×C4—68no—
763C2×C3×C4—62no—
764C2×C3×C4—64no—
765C2×C3×C4—62no—
766C2×C3×C4—62no—
767C2×C3×C4—62no—
768C2×C3×C4—62no—
769C2×C3×C4—122no—
770C2×C3×C4D3×D414yes—
771C2×C3×C4C2×#6714yes—
772C2×C3×C4C23×D314yes—
773C2×C3×C4C23×D314yes—
774C2×C3×C4C23×D311yescharacteristic
775C2×C3×C4C23×D311yescharacteristic
776C2×C3×C4C23×D311yescharacteristic
777C2×C3×C4C23×D311yescharacteristic
778#67—24no—
779#67—64no—
780#67—64no—
781#67—64no—
782#67—64no—
783#67—64no—
784#67—64no—
785#67—64no—
786#67—64no—
787#67—124no—
788#67—124no—
789#67—122no—
790#67—122no—
791#67C2×#6718yes—
792C2×Dic3—22no—
793C2×Dic3—32no—
794C2×Dic3—32no—
795C2×Dic3—32no—
796C2×Dic3—32no—
797C2×Dic3—32no—
798C2×Dic3—32no—
799C2×Dic3—42no—
800C2×Dic3—62no—
801C2×Dic3—62no—
802C2×Dic3—62no—
803C2×Dic3—64no—
804C2×Dic3—64no—
805C2×Dic3—124no—
806C2×Dic3C23×D314yes—
807C2×Dic3C23×D311yescharacteristic
808C2×Dic3C23×D311yescharacteristic
809C2×Dic3C23×D312yes—
810C2×Dic3C23×D312yes—
811D12—28no—
812D12—22no—
813D12—64no—
814D12—64no—
815D12—62no—
816D12—62no—
817D12—122no—
818D12—124no—
819D12C2×#6714yes—
820C4×D3—28no—
821C4×D3—22no—
822C4×D3—22no—
823C4×D3—22no—
824C4×D3—22no—
825C4×D3—24no—
826C4×D3—28no—
827C4×D3—64no—
828C4×D3—64no—
829C4×D3—64no—
830C4×D3—64no—
831C4×D3—64no—
832C4×D3—64no—
833C4×D3—124no—
834C4×D3—124no—
835C4×D3C2×#6718yes—
836Dic6—22no—
837Dic6—28no—
838Dic6—64no—
839Dic6—62no—
840Dic6—62no—
841Dic6—64no—
842Dic6—122no—
843Dic6C2×#6714yes—
844C2×C32—22no—
845C2×C32C23×D411yescharacteristic
846C2×C32C2×2−1+411yescharacteristic
847C2×C32#58511yescharacteristic
848C3⋊D3—42no—
849C3×D3—22no—
850C3×D3—24no—
851C3×D3—42no—
852C3×D3—41no—
853C24—31no—
854C24—92no—
855#41—38no—
856#41—616no—
857#41—68no—
858#41—68no—
859#41—64no—
860#41—188no—
861#41—188no—
862#41—184no—
863#41—184no—
864#41—184no—
865C2×Q8—24no—
866C2×Q8—31no—
867C2×Q8—31no—
868C2×Q8—34no—
869C2×Q8—68no—
870C2×Q8—68no—
871C2×Q8—92no—
872C2×Q8—91no—
873C2×Q8—184no—
874C2×Q8C2×D3212yes—
875C2×Q8C2×D3212yes—
876C2×D4—32no—
877C2×D4—32no—
878C2×D4—31no—
879C2×D4—34no—
880C2×D4—31no—
881C2×D4—92no—
882C2×D4—92no—
883C2×D4—94no—
884C2×D4—92no—
885C2×D4—92no—
886C2×D4—92no—
887C2×D4—92no—
888C2×D4—91no—
889C2×D4—184no—
890C2×D4—188no—
891C22×C4—32no—
892C22×C4—31no—
893C22×C4—32no—
894C22×C4—34no—
895C22×C4—34no—
896C22×C4—32no—
897C22×C4—31no—
898C22×C4—31no—
899C22×C4—31no—
900C22×C4—31no—
901C22×C4—64no—
902C22×C4—92no—
903C22×C4—92no—
904C22×C4—92no—
905C22×C4—94no—
906C22×C4—92no—
907C22×C4—188no—
908C22×C4C2×D3212yes—
909C22×C4C2×D3211yescharacteristic
910C4⋊C4—32no—
911C4⋊C4—34no—
912C4⋊C4—32no—
913C4⋊C4—34no—
914C4⋊C4—92no—
915C4⋊C4—94no—
916C4⋊C4—94no—
917C4⋊C4—92no—
918C4⋊C4—91no—
919C4⋊C4—94no—
920C4⋊C4—91no—
921C4⋊C4—94no—
922C22⋊C4—34no—
923C22⋊C4—34no—
924C22⋊C4—94no—
925C22⋊C4—92no—
926C22⋊C4—94no—
927C22⋊C4—92no—
928C22⋊C4—92no—
929C22⋊C4—94no—
930C22⋊C4—92no—
931C22⋊C4—92no—
932C22⋊C4—94no—
933C22⋊C4—94no—
934C42—94no—
935C42—92no—
936C22×C3—21no—
937C22×C3—21no—
938C22×C3—21no—
939C22×C3—21no—
940C22×C3—22no—
941C22×C3—21no—
942C22×C3—34no—
943C22×C3—32no—
944C22×C3—41no—
945C22×C3—41no—
946C22×C3—62no—
947C22×C3—62no—
948C22×C3—61no—
949C22×C3—61no—
950C22×C3—62no—
951C22×C3—62no—
952C22×C3—62no—
953C22×C3—61no—
954C22×C3—61no—
955C22×C3—61no—
956C22×C3—124no—
957C22×C3C2×D3×D412yes—
958C22×C3C22×#6712yes—
959C22×C3C24×D311yescharacteristic
960C22×C3C24×D311yescharacteristic
961C2×D3—21no—
962C2×D3—21no—
963C2×D3—22no—
964C2×D3—22no—
965C2×D3—21no—
966C2×D3—21no—
967C2×D3—21no—
968C2×D3—22no—
969C2×D3—22no—
970C2×D3—22no—
971C2×D3—44no—
972C2×D3—62no—
973C2×D3—62no—
974C2×D3—62no—
975C2×D3—62no—
976C2×D3—62no—
977C2×D3—62no—
978C2×D3—122no—
979C2×D3—122no—
980C2×D3—122no—
981C2×D3—128no—
982C2×D3—128no—
983C2×D3#100712yescomplemented
984C2×D3C22×#6714yes—
985C3×C4—24no—
986C3×C4—24no—
987C3×C4—22no—
988C3×C4—22no—
989C3×C4—34no—
990C3×C4—44no—
991C3×C4—62no—
992C3×C4—64no—
993C3×C4—61no—
994C3×C4—61no—
995C3×C4C2×D3×D412yes—
996C3×C4C2×D3×D412yes—
997C3×C4C22×#6712yes—
998C3×C4C22×#6712yes—
999Dic3—21no—
1000Dic3—21no—
1001Dic3—24no—
1002Dic3—22no—
1003Dic3—62no—
1004Dic3—62no—
1005Dic3—62no—
1006Dic3—62no—
1007Dic3—62no—
1008Dic3—62no—
1009Dic3—122no—
1010Dic3—122no—
1011Dic3—122no—
1012Dic3C22×#6714yes—
1013C32#348911yescharacteristic, complemented, Sylow
1014C23—31no—
1015C23—32no—
1016C23—31no—
1017C23—32no—
1018C23—62no—
1019C23—62no—
1020C23—92no—
1021C23—121no—
1022C23—184no—
1023C23—184no—
1024C23—362no—
1025C23C22×D3211yescharacteristic
1026Q8—24no—
1027Q8—24no—
1028Q8—34no—
1029Q8—68no—
1030Q8—62no—
1031Q8—184no—
1032Q8—182no—
1033D4—38no—
1034D4—34no—
1035D4—68no—
1036D4—64no—
1037D4—62no—
1038D4—184no—
1039D4—184no—
1040D4—184no—
1041D4—184no—
1042D4—184no—
1043D4—182no—
1044D4—364no—
1045D4—362no—
1046C2×C4—24no—
1047C2×C4—32no—
1048C2×C4—38no—
1049C2×C4—34no—
1050C2×C4—32no—
1051C2×C4—31no—
1052C2×C4—31no—
1053C2×C4—68no—
1054C2×C4—68no—
1055C2×C4—62no—
1056C2×C4—62no—
1057C2×C4—62no—
1058C2×C4—62no—
1059C2×C4—62no—
1060C2×C4—64no—
1061C2×C4—92no—
1062C2×C4—92no—
1063C2×C4—92no—
1064C2×C4—122no—
1065C2×C4—184no—
1066C2×C4—184no—
1067C2×C4—184no—
1068C2×C4—184no—
1069C2×C4—364no—
1070C2×C4D3×#6714yes—
1071C2×C4C22×D3214yes—
1072C2×C4C22×D3211yescharacteristic
1073C2×C4C22×D3211yescharacteristic
1074C2×C3—22no—
1075C2×C3—22no—
1076C2×C3—21no—
1077C2×C3—21no—
1078C2×C3—21no—
1079C2×C3—42no—
1080C2×C3—64no—
1081C2×C3—62no—
1082C2×C3—122no—
1083C2×C3—121no—
1084C2×C3C22×D3×D411yescharacteristic
1085C2×C3C2×#100711yescharacteristic
1086C2×C3#596411yescharacteristic
1087C2×C3D3×2−1+411yescharacteristic
1088C2×C3#596811yescharacteristic
1089C2×C3C23×#6711yescharacteristic
1090D3—22no—
1091D3—24no—
1092D3—41no—
1093D3—42no—
1094D3—122no—
1095D3—122no—
1096D3—242no—
1097C22—21no—
1098C22—21no—
1099C22—32no—
1100C22—34no—
1101C22—62no—
1102C22—62no—
1103C22—61no—
1104C22—61no—
1105C22—62no—
1106C22—61no—
1107C22—62no—
1108C22—61no—
1109C22—62no—
1110C22—61no—
1111C22—124no—
1112C22—182no—
1113C22—182no—
1114C22—182no—
1115C22—368no—
1116C22C2×D3×#6712yes—
1117C22C23×D3211yescharacteristic
1118C4—24no—
1119C4—34no—
1120C4—64no—
1121C4—61no—
1122C4—62no—
1123C4—61no—
1124C4—182no—
1125C4—182no—
1126C4—182no—
1127C4C2×D3×#6712yes—
1128C4C2×D3×#6712yes—
1129C3—21no—
1130C3#8598511yescharacteristic, complemented
1131C3#8729511yescharacteristic, complemented
1132C2—22no—
1133C2—62no—
1134C2—64no—
1135C2—121no—
1136C2—122no—
1137C2—362no—
1138C2D3×#100711yescharacteristic
1139C2#1059668811yescharacteristic
1140C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1007C2semidirect
2. C2×D3×#235C2semidirect
3. #10596287C2semidirect
4. C2×C3×#946C2semidirect
5. #10595427C2semidirect
6. #10595424C2semidirect
7. D3×#946C2semidirect
8. #10595402C2semidirect
9. #10595400C2semidirect
10. #10595398C2semidirect
11. #10595397C2semidirect
12. #10595357C2semidirect
13. #10595065C2semidirect
14. #10595043C2semidirect
15. #10595022C2semidirect
16. #10594986C2semidirect
17. #10594885C2semidirect
20. C22×C32×Q8C22semidirect
23. C2×C3×#239C22semidirect
24. C2×C3×#239C22semidirect
25. C2×C3×D3×Q8C22semidirect
26. C2×C3×D3×Q8C22semidirect
28. C2×C3×#235C22semidirect
29. C2×C3×#235C22semidirect
40. #64156C22semidirect
41. #64155C22semidirect
42. #64155C22semidirect
43. #64153C22semidirect
44. #64138C22semidirect
45. #64135C22semidirect
48. C3×#946C22semidirect
49. C3×#946C22semidirect
51. C2×C3×C4⋊Dic3C22semidirect
52. C2×C3×Dic3⋊C4C22semidirect
53. #63978C22semidirect
55. Dic3×#67C22semidirect
56. #63961C22semidirect
59. #63916C22semidirect
60. #63909C22semidirect
62. #63908C22semidirect
63. #63907C22semidirect
64. #63906C22semidirect
65. #63905C22semidirect
66. #63904C22semidirect
68. C4×#625C22semidirect
69. #63898C22semidirect
70. D3×C4⋊Dic3C22semidirect
71. #63888C22semidirect
73. #63886C22semidirect
74. #63885C22semidirect
75. #63884C22semidirect
77. D3×Dic3⋊C4C22semidirect
78. #63871C22semidirect
79. #63857C22semidirect
81. #63856C22semidirect
82. #63851C22semidirect
83. #63850C22semidirect
84. #63843C22semidirect
85. #63841C22semidirect
86. #63839C22semidirect
89. C2×#1007D3semidirect
108. C2×#946D3semidirect
144. C3×#235D4semidirect
215. C22×C3×Q8C2×D3semidirect
216. C22×C3×Q8C2×D3semidirect
222. C2×#239C2×D3semidirect
223. C2×#239C2×D3semidirect
225. C2×D3×Q8C2×D3semidirect
226. C2×D3×Q8C2×D3semidirect
241. C2×#235C2×D3semidirect
242. C2×#235C2×D3semidirect
273. #946C2×D3semidirect
274. #946C2×D3semidirect
317. C2×C4⋊Dic3C2×D3semidirect
323. C2×Dic3⋊C4C2×D3semidirect
510. #235#67semidirect
628. C2×C3×D32−1+4semidirect
656. C22×Q8D32semidirect
983. C2×D3#1007semidirect
1013. C32#3489semidirect
1130. C3#85985semidirect
1131. C3#87295semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C2×D3×#2352
#105962872
C2×C3×#9462
#105954272
#105954242
D3×#9462
#105954022
#105954002
#105953982
#105953972
#105953572
#105950652
#105950432
#105950222
#105949862
#105948852
#872953
#859853