Finite Group Databasebeta

← #11864093

Subgroups — #11864093

Order 1152.

1592 conjugacy classes of subgroups.

The subgroup lattice has 1013 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C211yesmaximal, characteristic, complemented
2C2×C3×#918C211yesmaximal, characteristic, complemented
3#10595424C211yesmaximal, characteristic, complemented
4C2×#63939C211yesmaximal, characteristic, complemented
5#10592886C211yesmaximal, characteristic, complemented
6C3×#5187C211yesmaximal, characteristic, complemented
7#10591657C211yesmaximal, characteristic, complemented
8#10591656C211yesmaximal, characteristic, complemented
9#10591593C211yesmaximal, characteristic, complemented
10#10591586C211yesmaximal, characteristic, complemented
11#10591557C211yesmaximal, characteristic, complemented
12#10590964C211yesmaximal, characteristic, complemented
13#10590939C211yesmaximal, characteristic, complemented
14#10590936C211yesmaximal, characteristic, complemented
15#10590823C211yesmaximal, characteristic, complemented
16#83980—31nomaximal
17#80227—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21C2×C3×D3×Q8C2211yescharacteristic
22D3×#239—24no—
23D3×#239—24no—
24C2×D3×D12—21no—
25C2×D3×D12C2211yescharacteristic
26C2×C4×D32—21no—
27C2×C4×D32C2211yescharacteristic
28C2×#3799—21no—
29C2×#3799C2211yescharacteristic
30C2×#3796—21no—
31C2×#3796C2211yescharacteristic
32C2×C32×Q16C2211yescharacteristic, complemented
33#64155C2211yescharacteristic, complemented
34C2×#3755C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic, complemented
36C2×C3×#216C2211yescharacteristic, complemented
37C2×C3×#215C2211yescharacteristic, complemented
38C2×C3×#215C2211yescharacteristic, complemented
39C3×#918—24no—
40C2×C3×#204C2211yescharacteristic, complemented
41C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
42#63939—24no—
43#63922—21no—
44#63916C2211yescharacteristic, complemented
45#63908C2211yescharacteristic, complemented
46#63904—21no—
47#63884—21no—
48#63879—21no—
49#63841C2211yescharacteristic
50C2×#3714C2211yescharacteristic, complemented
51C2×#3713C2211yescharacteristic, complemented
52C2×#3711C2211yescharacteristic
53#63662C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55#63647C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#239—31no—
67C2×C3×#137—31no—
68#5828—31no—
69C2×#949—31no—
70C2×#918D311yescharacteristic, complemented
71C2×#914—31no—
72#5627—31no—
73C3×#452—31no—
74#5238—31no—
75#5225—31no—
76#5187—31no—
77#5187—31no—
78#5187—31no—
79#5187—31no—
80#5187—61no—
81#5187D311yescharacteristic, complemented
82#5173—31no—
83#5172—31no—
84#5172—31no—
85#5172—31no—
86#5172—31no—
87#5131—31no—
88#5126—31no—
89#5047—31no—
90#4810—31no—
91#4802—31no—
92#4781—31no—
93#4770—31no—
94#4734—31no—
95#4726—31no—
96C22×D32—21no—
97C22×D32D411yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99C2×C32×Q8C2311yescharacteristic
100#3832—22no—
101#3832—22no—
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3C2311yescharacteristic
106C3×#239—22no—
107C3×#239—22no—
108C3×#239—22no—
109C3×#239—22no—
110C3×D3×Q8—22no—
111C3×D3×Q8D414yescomplemented
112C2×C3×D12—21no—
113C2×C3×D12—21no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×Dic6—21no—
122C2×C3×Dic6C2311yescharacteristic
123C2×#626—21no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#625—21no—
128C2×#624—21no—
129C2×#624D411yescharacteristic
130C2×D3×Dic3—21no—
131C2×D3×Dic3D411yescharacteristic
132C2×D3×Dic3D411yescharacteristic
133D3×D12—28no—
134D3×D12—22no—
135D3×D12D414yescomplemented
136C4×D32—28no—
137C4×D32—22no—
138C4×D32—22no—
139#3799—28no—
140#3799—22no—
141#3799—22no—
142#3796—28no—
143#3796—22no—
144#3796—22no—
145C32×Q16—22no—
146C2×C32×C8C2311yescharacteristic
147#3755—22no—
148#3752—21no—
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150#3750—21no—
151C2×C3⋊(C3⋊C8)C2311yescharacteristic
152C3×#216—22no—
153C3×#215—22no—
154C3×#215—22no—
155C3×(C2×D3)⋊C4—21no—
156C3×C4⋊Dic3C2311yescharacteristic
157C3×Dic3⋊C4—21no—
158C2×C3×C3⋊C8C2311yescharacteristic
159C2×C3×C3⋊C8C2311yescharacteristic
160C3×#204—22no—
161C3×ΓL(1,𝔽25)—22no—
162(C2×D3)⋊Dic3—21no—
163(C2×D3)⋊Dic3—21no—
164(C2×D3)⋊Dic3—21no—
165Dic32—21no—
166#3714—22no—
167#3713—22no—
168#3711—22no—
169#3005—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172C22×C3×Q8—31no—
173D3×#41—64no—
174D3×#41—64no—
175C2×#239—31no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—31no—
179C2×#239—61no—
180C2×#239—61no—
181C2×#239—61no—
182C2×#239—64no—
183C2×#239—64no—
184C2×#239C2×D311yescharacteristic
185C2×#239C2×D311yescharacteristic
186C2×D3×Q8C2×D311yescharacteristic
187C2×#237—31no—
188C2×#237—61no—
189C2×D3×D4—31no—
190C2×D3×D4—61no—
191C2×#235—31no—
192C2×#235—61no—
193C22×D12—31no—
194C22×D12—61no—
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×C4×D3—61no—
198C22×C4×D3—61no—
199C3×#137—64no—
200C2×C3×Q16—21no—
201C2×C3×Q16—31no—
202C2×C3×Q16C2×D311yescharacteristic, complemented
203C2×C3×Q16C2×D311yescharacteristic, complemented
204C2×C3×SD16—31no—
205C2×C3×SD16—31no—
206C2×C3×SD16—31no—
207C2×C3×M16—31no—
208C3×C22⋊Q8—31no—
209#949—64no—
210#946—31no—
211#946—31no—
212#946—61no—
213#946C2×D311yescharacteristic, complemented
214C2×#216C2×D311yescharacteristic, complemented
215C2×#215—31no—
216C2×#215—31no—
217C2×#215—61no—
218C2×#215C2×D311yescharacteristic, complemented
219C2×#215C2×D311yescharacteristic, complemented
220#938—31no—
221#938—31no—
222#937—61no—
223#935—61no—
224C2×#213—31no—
225C2×#213—31no—
226C2×#213—31no—
227#930—31no—
228C4×#67—61no—
229C4×#67—61no—
230#926—31no—
231C2×#208—31no—
232#918—24no—
233#914—64no—
234C2×D24—31no—
235C2×#204C2×D311yescharacteristic, complemented
236C2×ΓL(1,𝔽25)—31no—
237C2×ΓL(1,𝔽25)C2×D311yescharacteristic
238#895—31no—
239#894—61no—
240#893—61no—
241#892—31no—
242#882—61no—
243#67⋊C4—61no—
244C3×#103—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#835—31no—
248#835—31no—
249#835—31no—
250#835—31no—
251#835—61no—
252#835C2×D311yescharacteristic, complemented
253#832—31no—
254#830—31no—
255#821—31no—
256#821—31no—
257#821—31no—
258#821—31no—
259#821—61no—
260#821C2×D311yescharacteristic, complemented
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8—31no—
265(C2×D3)⋊C8—31no—
266(C2×D3)⋊C8—61no—
267(C2×D3)⋊C8C2×D311yescharacteristic, complemented
268#816—31no—
269#810—31no—
270#809—31no—
271C22×C3⋊D3—21no—
272C22×C3⋊D3C2×D411yescharacteristic
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3C2×D411yescharacteristic
276C22×C3×D3C2×D411yescharacteristic
277C2×D32—24no—
278C2×D32—22no—
279C2×D32—41no—
280C2×D32—41no—
281C2×D32—42no—
282C2×D32—42no—
283C32×Q8—21no—
284C32×Q8—21no—
285C32×Q8—21no—
286C32×Q8C2×D412yes—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4C2411yescharacteristic
290C2×C3⋊Dic3—21no—
291C2×C3⋊Dic3C2×D411yescharacteristic
292C4⋊(C3⋊D3)—24no—
293C4⋊(C3⋊D3)—21no—
294C4⋊(C3⋊D3)C2×D412yes—
295C4×C3⋊D3—24no—
296C4×C3⋊D3—21no—
297C4×C3⋊D3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3C2×D411yescharacteristic
301C2×C3×Dic3C2×D411yescharacteristic
302C3×D12—24no—
303C3×D12—21no—
304C3×D12—21no—
305C3×D12—21no—
306C3×D12—42no—
307C3×D12C2×D412yes—
308C3×C4×D3—24no—
309C3×C4×D3—24no—
310C3×C4×D3—21no—
311C3×C4×D3—21no—
312C3×C4×D3—42no—
313C3×C4×D3C2×D412yes—
314C3×C4×D3C2×D412yes—
315C3×Dic6—21no—
316C3×Dic6—24no—
317C3×Dic6C2×D412yes—
318#626—24no—
319#626—24no—
320#626—24no—
321#626—42no—
322#625—42no—
323#624—24no—
324#624—22no—
325D3×Dic3—24no—
326D3×Dic3—22no—
327D3×Dic3—22no—
328C32×C8—21no—
329C3⋊(C3⋊C8)—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C22×#41—91no—
333C2×#137—31no—
334C2×AGL(1,ℤ/8)—91no—
335#525—91no—
336#452—31no—
337#452—91no—
338#452—91no—
339#452—91no—
340#449—91no—
341#449—91no—
342#449—91no—
343#449—91no—
344#419—91no—
345#418—91no—
346#407—91no—
347C23×D3—31no—
348C23×D3—31no—
349C23×D3—61no—
350C23×D3—61no—
351C3×#41—62no—
352C3×#41—62no—
353C3×#41—62no—
354C3×#41—62no—
355C2×C3×Q8—21no—
356C2×C3×Q8—21no—
357C2×C3×Q8—34no—
358C2×C3×Q8—31no—
359C2×C3×Q8—61no—
360C2×C3×Q8—62no—
361C2×C3×Q8C22×D311yescharacteristic
362C2×C3×Q8C22×D311yescharacteristic
363C2×C3×Q8C22×D311yescharacteristic
364C2×C3×Q8C22×D311yescharacteristic
365C2×C3×D4—31no—
366C2×C3×D4—31no—
367C2×C3×D4—61no—
368C2×C3×D4—61no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—61no—
372C22×C3×C4—61no—
373C22×C3×C4—61no—
374C2×#67—61no—
375C2×#67—61no—
376C2×#67—61no—
377C2×#67—61no—
378C2×#67—61no—
379C2×#67—61no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—61no—
383#239—22no—
384#239—22no—
385#239—22no—
386#239—22no—
387#239—62no—
388#239—62no—
389#239—68no—
390#239—62no—
391#239—68no—
392#239—62no—
393#239—62no—
394#239—62no—
395#239—62no—
396#239—62no—
397#239—122no—
398#239—122no—
399D3×Q8—22no—
400D3×Q8#6714yescomplemented
401#237—62no—
402#237—68no—
403#237—62no—
404D3×D4—34no—
405D3×D4—68no—
406D3×D4—62no—
407#235—62no—
408#235—68no—
409#235—62no—
410C2×D12—21no—
411C2×D12—21no—
412C2×D12—31no—
413C2×D12—31no—
414C2×D12—34no—
415C2×D12—61no—
416C2×D12—62no—
417C2×D12—68no—
418C2×D12—61no—
419C2×D12—61no—
420C2×D12—61no—
421C2×D12—61no—
422C2×D12—61no—
423C2×D12—61no—
424C2×D12—121no—
425C2×D12C22×D311yescharacteristic
426C2×D12C22×D311yescharacteristic
427C2×C4×D3—21no—
428C2×C4×D3—21no—
429C2×C4×D3—21no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—31no—
435C2×C4×D3—31no—
436C2×C4×D3—61no—
437C2×C4×D3—62no—
438C2×C4×D3—62no—
439C2×C4×D3—68no—
440C2×C4×D3—68no—
441C2×C4×D3—61no—
442C2×C4×D3—61no—
443C2×C4×D3—61no—
444C2×C4×D3—61no—
445C2×C4×D3—61no—
446C2×C4×D3—62no—
447C2×C4×D3—62no—
448C2×C4×D3—121no—
449C2×C4×D3C22×D311yescharacteristic
450C2×C4×D3C22×D311yescharacteristic
451C2×Dic6—21no—
452C2×Dic6C22×D311yescharacteristic
453C3×Q16—22no—
454C3×Q16—22no—
455C3×Q16—42no—
456C3×Q16—62no—
457C3×SD16—62no—
458C3×SD16—62no—
459C3×SD16—62no—
460C3×M16—62no—
461C2×C3×C8—21no—
462C2×C3×C8—31no—
463C2×C3×C8—31no—
464C2×C3×C8C22×D311yescharacteristic
465C2×C3×C8C22×D311yescharacteristic
466C3×C4⋊C4—31no—
467C3×C4⋊C4—61no—
468C3×C22⋊C4—61no—
469#217—61no—
470#217—61no—
471#217—61no—
472#216—22no—
473#215—22no—
474#215—22no—
475#215—62no—
476#215—62no—
477#215—122no—
478#213—62no—
479#213—62no—
480#213—62no—
481(C2×D3)⋊C4—21no—
482(C2×D3)⋊C4—61no—
483(C2×D3)⋊C4—61no—
484(C2×D3)⋊C4—61no—
485(C2×D3)⋊C4—61no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—121no—
488C4⋊Dic3—31no—
489C4⋊Dic3—31no—
490C4⋊Dic3—61no—
491C4⋊Dic3C22×D311yescharacteristic
492Dic3⋊C4—21no—
493Dic3⋊C4—61no—
494Dic3⋊C4—61no—
495Dic3⋊C4—121no—
496C4×Dic3—61no—
497C4×Dic3—61no—
498#208—62no—
499C2×C3⋊C8—31no—
500C2×C3⋊C8—31no—
501C2×C3⋊C8—61no—
502C2×C3⋊C8C22×D311yescharacteristic
503C2×C3⋊C8C22×D311yescharacteristic
504D24—62no—
505#204—22no—
506ΓL(1,𝔽25)—22no—
507ΓL(1,𝔽25)—62no—
508C22×C32C22×D411yescharacteristic
509C2×C3⋊D3—21no—
510C2×C3⋊D3—22no—
511C2×C3⋊D3—21no—
512C2×C3⋊D3—21no—
513C2×C3⋊D3—41no—
514C2×C3⋊D3—41no—
515C2×C3×D3—21no—
516C2×C3×D3—21no—
517C2×C3×D3—21no—
518C2×C3×D3—22no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—41no—
522C2×C3×D3—41no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3#12012yes—
527D32—44no—
528D32—48no—
529C32×C4—22no—
530C32×C4—41no—
531C32×C4C22×D411yescharacteristic
532C32×C4C22×D411yescharacteristic
533C3⋊Dic3—21no—
534C3⋊Dic3—41no—
535C3×Dic3—21no—
536C3×Dic3—22no—
537C3×Dic3—41no—
538C3×Dic3#12012yes—
539C2×#41—31no—
540C2×#41—31no—
541C2×#41—91no—
542C2×#41—91no—
543C2×#41—91no—
544C2×#41—181no—
545C2×#41—181no—
546C2×#41—184no—
547C2×#41—184no—
548C22×Q8—31no—
549C22×D4—91no—
550C22×D4—181no—
551C23×C4—91no—
552C23×C4—181no—
553#137—64no—
554AGL(1,ℤ/8)—184no—
555C2×Q16—31no—
556C2×Q16D3211yescharacteristic, complemented
557C2×SD16—31no—
558C2×SD16—31no—
559C2×SD16—31no—
560C2×SD16—91no—
561C2×D8—91no—
562C2×D8—91no—
563C2×M16—31no—
564C2×M16—91no—
565#123—181no—
566C22⋊Q8—31no—
567C22⋊Q8—91no—
568#121—91no—
569#121—91no—
570#120—181no—
571C4×D4—181no—
572C4×D4—181no—
573#117—91no—
574#103—31no—
575#103—91no—
576#103—91no—
577#103—91no—
578#102—31no—
579#102—91no—
580#102—91no—
581#102—91no—
582C22⋊C8—31no—
583C22⋊C8—91no—
584C22⋊C8—91no—
585C22⋊C8—91no—
586C23×C3—31no—
587C23×C3—31no—
588C23×C3—61no—
589C23×C3—61no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—31no—
593C22×D3—31no—
594C22×D3—61no—
595C22×D3—64no—
596C22×D3—62no—
597C22×D3—61no—
598C22×D3—61no—
599C22×D3—64no—
600C22×D3—62no—
601C22×D3—121no—
602C22×D3—121no—
603C22×D3—121no—
604C22×D3—121no—
605C22×D3—121no—
606C22×D3—122no—
607C22×D3—122no—
608C22×D3—122no—
609C22×D3—122no—
610C22×D3D3×D411yescharacteristic
611C22×D3D3×D411yescharacteristic
612C3×Q8—21no—
613C3×Q8—21no—
614C3×Q8—21no—
615C3×Q8—21no—
616C3×Q8—21no—
617C3×Q8—21no—
618C3×Q8—22no—
619C3×Q8—32no—
620C3×Q8—41no—
621C3×Q8—41no—
622C3×Q8—41no—
623C3×Q8—64no—
624C3×Q8—61no—
625C3×Q8D3×D412yes—
626C3×Q8C2×#6712yes—
627C3×D4—32no—
628C3×D4—64no—
629C3×D4—61no—
630C3×D4—61no—
631C3×D4—61no—
632C3×D4—122no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—31no—
639C2×C3×C4—32no—
640C2×C3×C4—32no—
641C2×C3×C4—31no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—64no—
645C2×C3×C4—64no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—122no—
651C2×C3×C4C23×D311yescharacteristic
652C2×C3×C4C23×D311yescharacteristic
653#67—64no—
654#67—64no—
655#67—64no—
656#67—122no—
657#67—122no—
658#67—122no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—31no—
662C2×Dic3—31no—
663C2×Dic3—61no—
664C2×Dic3—62no—
665C2×Dic3—64no—
666C2×Dic3—62no—
667C2×Dic3—61no—
668C2×Dic3—61no—
669C2×Dic3—121no—
670C2×Dic3D3×D411yescharacteristic
671C2×Dic3D3×D411yescharacteristic
672D12—24no—
673D12—21no—
674D12—21no—
675D12—21no—
676D12—32no—
677D12—32no—
678D12—42no—
679D12—62no—
680D12—64no—
681D12—64no—
682D12—64no—
683D12—64no—
684D12—64no—
685D12—61no—
686D12—61no—
687D12—121no—
688D12—124no—
689D12—122no—
690D12D3×D412yes—
691C4×D3—24no—
692C4×D3—24no—
693C4×D3—21no—
694C4×D3—21no—
695C4×D3—42no—
696C4×D3—62no—
697C4×D3—64no—
698C4×D3—64no—
699C4×D3—64no—
700C4×D3—64no—
701C4×D3—62no—
702C4×D3—64no—
703C4×D3—62no—
704C4×D3—61no—
705C4×D3—61no—
706C4×D3—61no—
707C4×D3—61no—
708C4×D3—62no—
709C4×D3—121no—
710C4×D3—121no—
711C4×D3—124no—
712C4×D3D3×D412yes—
713C4×D3C2×#6712yes—
714Dic6—21no—
715Dic6—24no—
716Dic6C2×#6712yes—
717C3×C8—21no—
718C3×C8—21no—
719C3×C8—41no—
720C3×C8—61no—
721C3×C8—61no—
722C3⋊C8—21no—
723C3⋊C8—21no—
724C3⋊C8—61no—
725C3⋊C8—61no—
726C3⋊C8—121no—
727C2×C32C2×#12011yescharacteristic
728C2×C32#57511yescharacteristic
729C2×C32#57511yescharacteristic
730C3⋊D3—41no—
731C3⋊D3—42no—
732C3×D3—22no—
733C3×D3—41no—
734C3×D3—42no—
735C3×D3—81no—
736C24—91no—
737C24—181no—
738#41—62no—
739#41—62no—
740#41—62no—
741#41—62no—
742#41—182no—
743#41—182no—
744#41—188no—
745#41—182no—
746#41—182no—
747#41—188no—
748#41—182no—
749#41—182no—
750C2×Q8—34no—
751C2×Q8—31no—
752C2×Q8—61no—
753C2×Q8—62no—
754C2×Q8C2×D3211yescharacteristic
755C2×Q8C2×D3211yescharacteristic
756C2×D4—31no—
757C2×D4—31no—
758C2×D4—61no—
759C2×D4—61no—
760C2×D4—94no—
761C2×D4—91no—
762C2×D4—181no—
763C2×D4—182no—
764C2×D4—181no—
765C2×D4—188no—
766C2×D4—181no—
767C2×D4—181no—
768C2×D4—181no—
769C2×D4—181no—
770C22×C4—31no—
771C22×C4—31no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—91no—
776C22×C4—91no—
777C22×C4—91no—
778C22×C4—91no—
779C22×C4—181no—
780C22×C4—182no—
781C22×C4—182no—
782C22×C4—181no—
783C22×C4—188no—
784C22×C4—181no—
785Q16—22no—
786Q16—62no—
787SD16—62no—
788SD16—62no—
789SD16—62no—
790SD16—182no—
791D8—182no—
792D8—182no—
793M16—62no—
794M16—182no—
795C2×C8—31no—
796C2×C8—31no—
797C2×C8—91no—
798C2×C8C2×D3211yescharacteristic
799C4⋊C4—31no—
800C4⋊C4—61no—
801C4⋊C4—91no—
802C4⋊C4—181no—
803C22⋊C4—61no—
804C22⋊C4—181no—
805C22⋊C4—181no—
806C22⋊C4—181no—
807C22⋊C4—181no—
808C42—181no—
809C22×C3—21no—
810C22×C3—32no—
811C22×C3—61no—
812C22×C3—61no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—62no—
816C22×C3—61no—
817C22×C3—121no—
818C22×C3—121no—
819C22×C3—121no—
820C22×C3—121no—
821C22×C3—121no—
822C22×C3C2×D3×D411yescharacteristic
823C22×C3C2×D3×D411yescharacteristic
824C2×D3—21no—
825C2×D3—21no—
826C2×D3—21no—
827C2×D3—21no—
828C2×D3—21no—
829C2×D3—22no—
830C2×D3—41no—
831C2×D3—41no—
832C2×D3—41no—
833C2×D3—41no—
834C2×D3—41no—
835C2×D3—61no—
836C2×D3—61no—
837C2×D3—61no—
838C2×D3—61no—
839C2×D3—62no—
840C2×D3—61no—
841C2×D3—62no—
842C2×D3—61no—
843C2×D3—122no—
844C2×D3—121no—
845C2×D3—121no—
846C2×D3—121no—
847C2×D3—124no—
848C2×D3—128no—
849C2×D3—124no—
850C2×D3—128no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—121no—
855C2×D3—241no—
856C2×D3—241no—
857C2×D3#93712yes—
858C3×C4—22no—
859C3×C4—22no—
860C3×C4—21no—
861C3×C4—21no—
862C3×C4—32no—
863C3×C4—42no—
864C3×C4—41no—
865C3×C4—41no—
866C3×C4—61no—
867C3×C4—62no—
868C3×C4—81no—
869C3×C4—121no—
870C3×C4C2×D3×D411yescharacteristic
871C3×C4C2×D3×D411yescharacteristic
872C3×C4C2×D3×D411yescharacteristic
873C3×C4C22×#6711yescharacteristic
874Dic3—22no—
875Dic3—21no—
876Dic3—41no—
877Dic3—61no—
878Dic3—61no—
879Dic3—121no—
880Dic3—121no—
881Dic3—121no—
882Dic3—241no—
883Dic3#93712yes—
884C32#300511yescharacteristic, complemented, Sylow
885C23—31no—
886C23—31no—
887C23—61no—
888C23—61no—
889C23—91no—
890C23—184no—
891C23—182no—
892C23—181no—
893C23—361no—
894C23—361no—
895C23—362no—
896C23—362no—
897Q8—21no—
898Q8—21no—
899Q8—21no—
900Q8—32no—
901Q8—64no—
902Q8—61no—
903Q8D3×#6712yes—
904D4—32no—
905D4—64no—
906D4—61no—
907D4—61no—
908D4—61no—
909D4—92no—
910D4—122no—
911D4—184no—
912D4—184no—
913D4—184no—
914D4—184no—
915D4—181no—
916D4—362no—
917D4—362no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—31no—
921C2×C4—32no—
922C2×C4—32no—
923C2×C4—31no—
924C2×C4—64no—
925C2×C4—64no—
926C2×C4—61no—
927C2×C4—61no—
928C2×C4—61no—
929C2×C4—61no—
930C2×C4—91no—
931C2×C4—122no—
932C2×C4—184no—
933C2×C4—182no—
934C2×C4—182no—
935C2×C4—184no—
936C2×C4—182no—
937C2×C4—184no—
938C2×C4—181no—
939C2×C4—181no—
940C2×C4—181no—
941C2×C4C22×D3211yescharacteristic
942C8—21no—
943C8—61no—
944C8—61no—
945C8—181no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—62no—
950C2×C3—121no—
951C2×C3—122no—
952C2×C3—241no—
953C2×C3D3×#12011yescharacteristic
954C2×C3#576811yescharacteristic
955C2×C3#577711yescharacteristic
956C2×C3#577711yescharacteristic
957C2×C3#577711yescharacteristic
958C2×C3C2×#93711yescharacteristic
959D3—22no—
960D3—41no—
961D3—42no—
962D3—81no—
963D3—121no—
964D3—122no—
965D3—121no—
966D3—122no—
967D3—241no—
968D3—242no—
969C22—32no—
970C22—61no—
971C22—61no—
972C22—61no—
973C22—61no—
974C22—62no—
975C22—61no—
976C22—121no—
977C22—121no—
978C22—121no—
979C22—121no—
980C22—121no—
981C22—181no—
982C22—181no—
983C22—182no—
984C22—181no—
985C22—364no—
986C22—368no—
987C22—361no—
988C22—361no—
989C22D32×D411yescharacteristic
990C4—22no—
991C4—32no—
992C4—41no—
993C4—61no—
994C4—62no—
995C4—121no—
996C4—181no—
997C4—361no—
998C4D32×D411yescharacteristic
999C4C2×D3×#6711yescharacteristic
1000C3—21no—
1001C3#8022711yescharacteristic, complemented
1002C3#8398011yescharacteristic, complemented
1003C2—62no—
1004C2—121no—
1005C2—122no—
1006C2—241no—
1007C2—361no—
1008C2—362no—
1009C2#1059476211yescharacteristic
1010C2#1059476311yescharacteristic
1011C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
hypercenterC2×Q16D32
hypocenterC32#3005
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×D3×#239C2semidirect
2. C2×C3×#918C2semidirect
3. #10595424C2semidirect
4. C2×#63939C2semidirect
5. #10592886C2semidirect
6. C3×#5187C2semidirect
7. #10591657C2semidirect
8. #10591656C2semidirect
9. #10591593C2semidirect
10. #10591586C2semidirect
11. #10591557C2semidirect
12. #10590964C2semidirect
13. #10590939C2semidirect
14. #10590936C2semidirect
15. #10590823C2semidirect
32. C2×C32×Q16C22semidirect
33. #64155C22semidirect
34. C2×#3755C22semidirect
35. C3×#946C22semidirect
36. C2×C3×#216C22semidirect
37. C2×C3×#215C22semidirect
38. C2×C3×#215C22semidirect
40. C2×C3×#204C22semidirect
44. #63916C22semidirect
45. #63908C22semidirect
50. C2×#3714C22semidirect
51. C2×#3713C22semidirect
53. #63662C22semidirect
54. #63648C22semidirect
55. #63647C22semidirect
56. C3×#835C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
70. C2×#918D3semidirect
81. #5187D3semidirect
111. C3×D3×Q8D4semidirect
135. D3×D12D4semidirect
202. C2×C3×Q16C2×D3semidirect
203. C2×C3×Q16C2×D3semidirect
213. #946C2×D3semidirect
214. C2×#216C2×D3semidirect
218. C2×#215C2×D3semidirect
219. C2×#215C2×D3semidirect
235. C2×#204C2×D3semidirect
252. #835C2×D3semidirect
260. #821C2×D3semidirect
267. (C2×D3)⋊C8C2×D3semidirect
400. D3×Q8#67semidirect
556. C2×Q16D32semidirect
884. C32#3005semidirect
1001. C3#80227semidirect
1002. C3#83980semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C2×C3×#9182
#105954242
C2×#639392
#105928862
C3×#51872
#105916572
#105916562
#105915932
#105915862
#105915572
#105909642
#105909392
#105909362
#105908232
#839803
#802273