Finite Group Databasebeta

← #11863891

Subgroups — #11863891

Order 1152.

1604 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×#63947C211yesmaximal, characteristic, complemented
3C2×#63806C211yesmaximal, characteristic, complemented
4#10594626C211yesmaximal, characteristic, complemented
5#10592507C211yesmaximal, characteristic, complemented
6C3×#4806C211yesmaximal, characteristic, complemented
7C3×#4804C211yesmaximal, characteristic, complemented
8#10591595C211yesmaximal, characteristic, complemented
9#10591593C211yesmaximal, characteristic, complemented
10#10590964C211yesmaximal, characteristic, complemented
11#10590946C211yesmaximal, characteristic, complemented
12D3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
13#10590618C211yesmaximal, characteristic, complemented
14#10590610C211yesmaximal, characteristic, complemented
15#10590595C211yesmaximal, characteristic, complemented
16#80038—31nomaximal
17#78833—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21D3×#239—24no—
22D3×#239—24no—
23C2×D3×D12—21no—
24C2×D3×D12C2211yescharacteristic
25C2×C4×D32—21no—
26C2×C4×D32C2211yescharacteristic
27C2×#3799—21no—
28C2×#3799C2211yescharacteristic
29C2×#3796—21no—
30C2×#3796C2211yescharacteristic
31C2×#3795C2211yescharacteristic, complemented
32C2×#3756C2211yescharacteristic, complemented
33C2×#3744C2211yescharacteristic, complemented
34#64106C2211yescharacteristic, complemented
35C2×C3×#215C2211yescharacteristic, complemented
36C2×C3×#204C2211yescharacteristic, complemented
37C2×C3×D3×C8C2211yescharacteristic, complemented
38C3×#895C2211yescharacteristic
39C3×#892C2211yescharacteristic, complemented
40#63947—24no—
41#63922—21no—
42#63916C2211yescharacteristic, complemented
43Dic3×D12—21no—
44#63891—21no—
45#63880—21no—
46#63857C2211yescharacteristic
47C2×#3719C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63806—24no—
53C32×#103C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
65C2×D3×#41—31no—
66C22×#239—31no—
67C2×#950—31no—
68C2×#916—31no—
69C2×#916—31no—
70C2×#904—31no—
71#5606—31no—
72#5524—31no—
73C3×#448—31no—
74C3×#416—31no—
75#5228—31no—
76#5172—31no—
77#5172—31no—
78C2×(C2×D3)⋊C8—31no—
79#5036—31no—
80#5002—31no—
81#4810—31no—
82#4809—31no—
83#4808—31no—
84#4808—31no—
85#4808—31no—
86#4808—61no—
87#4806D311yescharacteristic, complemented
88#4804—31no—
89#4804D311yescharacteristic, complemented
90#4783—31no—
91#4781—31no—
92#4776—31no—
93#4773—31no—
94#4731—31no—
95D3×C22⋊C8—31no—
96C22×D32—21no—
97C22×D32D411yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99#3832—22no—
100#3832—22no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3—21no—
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C3×#239—22no—
107C3×#239D414yescomplemented
108C3×D3×Q8—22no—
109C3×D3×Q8—22no—
110C2×C3×D12—21no—
111C2×C3×D12—21no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6—21no—
119C2×C3×Dic6C2311yescharacteristic
120C2×#626—21no—
121C2×#626—21no—
122C2×#626—21no—
123C2×#626—21no—
124C2×#625—21no—
125C2×#624—21no—
126C2×#624D411yescharacteristic
127C2×D3×Dic3—21no—
128C2×D3×Dic3—21no—
129C2×D3×Dic3D411yescharacteristic
130C2×D3×Dic3D411yescharacteristic
131D3×D12—28no—
132D3×D12—22no—
133D3×D12—22no—
134C4×D32—28no—
135C4×D32—22no—
136C4×D32—22no—
137#3799—28no—
138#3799—22no—
139#3799D414yescomplemented
140#3796—28no—
141#3796—22no—
142#3796—22no—
143#3795—22no—
144#3795—22no—
145C2×C32×C8C2311yescharacteristic
146C32×C4⋊C4C2311yescharacteristic
147#3756—22no—
148#3752—21no—
149C4⋊(C3⋊Dic3)—21no—
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151#3744—22no—
152C3×#215—22no—
153C3×(C2×D3)⋊C4—21no—
154C3×(C2×D3)⋊C4—21no—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×C4×Dic3—21no—
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×#204—22no—
160C3×D3×C8—22no—
161Dic3⋊Dic3—21no—
162(C2×D3)⋊Dic3—21no—
163(C2×D3)⋊Dic3—21no—
164#3719—22no—
165#3716—22no—
166#3714—22no—
167#3713—22no—
168D3×C3⋊C8—22no—
169#3002—91noSylow
170C2×C3×#41—31no—
171C22×C3×Q8—31no—
172D3×#41—64no—
173D3×#41—64no—
174C2×#239—31no—
175C2×#239—31no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—61no—
179C2×#239—61no—
180C2×#239—61no—
181C2×#239—64no—
182C2×#239—64no—
183C2×#239C2×D311yescharacteristic
184C2×D3×Q8C2×D311yescharacteristic
185C2×#237—31no—
186C2×#237—31no—
187C2×#237—61no—
188C2×D3×D4—31no—
189C2×D3×D4—61no—
190C2×#235—31no—
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—
199C2×C3×SD16—31no—
200C2×C3×SD16—31no—
201C22×C3×C8—31no—
202C3×#121—31no—
203C3×#117—31no—
204#950—64no—
205C2×#216—31no—
206C2×#216—31no—
207C2×#216—31no—
208C2×#216—61no—
209C2×#215C2×D311yescharacteristic, complemented
210#938—31no—
211#937—61no—
212D4×Dic3—61no—
213C2×#214—31no—
214C2×#213—31no—
215C2×#213—31no—
216C2×#213—31no—
217#924—31no—
218C22×C3⋊C8—31no—
219#916—64no—
220#916—64no—
221C2×Dic12—31no—
222#904—64no—
223C2×D24—31no—
224C2×#204—31no—
225C2×#204—31no—
226C2×#204—31no—
227C2×#204—61no—
228C2×#204C2×D311yescharacteristic, complemented
229C2×D3×C8—31no—
230C2×D3×C8C2×D311yescharacteristic, complemented
231#897—31no—
232#897—31no—
233#897—31no—
234#897—61no—
235#895—31no—
236#895C2×D311yescharacteristic
237#892C2×D311yescharacteristic, complemented
238#886—61no—
239#883—61no—
240#882—61no—
241#67⋊C4—61no—
242C4×D12—61no—
243C4×D12—61no—
244C3×#103—21no—
245C3×#103—31no—
246C3×#103—31no—
247C3×#103C2×D311yescharacteristic, complemented
248C3×#103C2×D311yescharacteristic, complemented
249C3×#102—31no—
250C3×#102—31no—
251C3×C22⋊C8—31no—
252#835—31no—
253#835C2×D311yescharacteristic, complemented
254#830—31no—
255#821—31no—
256#821C2×D311yescharacteristic, complemented
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—61no—
263(C2×D3)⋊C8C2×D311yescharacteristic
264#810—31no—
265#810C2×D311yescharacteristic, complemented
266#809—31no—
267#809—31no—
268#809—31no—
269#809—61no—
270#809C2×D311yescharacteristic, complemented
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—22no—
280C2×D32—41no—
281C2×D32—42no—
282C2×D32—42no—
283C32×Q8—21no—
284C32×Q8C2×D412yes—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4C2411yescharacteristic
288C2×C3⋊Dic3—21no—
289C2×C3⋊Dic3C2×D411yescharacteristic
290C4⋊(C3⋊D3)—24no—
291C4⋊(C3⋊D3)—21no—
292C4⋊(C3⋊D3)C2×D412yes—
293C4×C3⋊D3—24no—
294C4×C3⋊D3—21no—
295C4×C3⋊D3—21no—
296#634—21no—
297#634—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—21no—
310C3×C4×D3—21no—
311C3×C4×D3—24no—
312C3×C4×D3C2×D412yes—
313C3×C4×D3C2×D412yes—
314C3×Dic6—24no—
315C3×Dic6—21no—
316C3×Dic6C2×D412yes—
317#626—24no—
318#626—24no—
319#626—24no—
320#626—42no—
321#625—42no—
322#624—22no—
323#624—24no—
324D3×Dic3—24no—
325D3×Dic3—22no—
326D3×Dic3—22no—
327D3×Dic3—42no—
328C32×C8—21no—
329C3⋊(C3⋊C8)—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C22×#41—91no—
333C2×#135—91no—
334C2×#135—91no—
335#525—91no—
336#452—91no—
337#452—91no—
338#451—91no—
339#450—91no—
340#449—91no—
341#449—91no—
342#448—31no—
343#447—91no—
344#416—31no—
345#416—91no—
346C2×C22⋊C8—91no—
347C23×D3—31no—
348C23×D3—31no—
349C23×D3—61no—
350C23×D3—61no—
351C3×#41—34no—
352C3×#41—62no—
353C2×C3×Q8—21no—
354C2×C3×Q8—31no—
355C2×C3×Q8—61no—
356C2×C3×Q8—62no—
357C2×C3×Q8—62no—
358C2×C3×Q8C22×D311yescharacteristic
359C2×C3×Q8C22×D311yescharacteristic
360C2×C3×D4—31no—
361C2×C3×D4—31no—
362C2×C3×D4—61no—
363C2×C3×D4—61no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—61no—
367C22×C3×C4—61no—
368C2×#67—61no—
369C2×#67—61no—
370C2×#67—61no—
371C2×#67—61no—
372C2×#67—61no—
373C2×#67—61no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378#239—22no—
379#239—34no—
380#239—68no—
381#239—62no—
382#239—68no—
383#239—62no—
384#239—62no—
385#239—62no—
386#239—62no—
387#239—62no—
388#239—62no—
389#239—122no—
390#239—122no—
391#239D1214yescomplemented
392D3×Q8—22no—
393D3×Q8—22no—
394#237—62no—
395#237—68no—
396#237—62no—
397#237—62no—
398#237—62no—
399D3×D4—62no—
400D3×D4—62no—
401D3×D4—68no—
402#235—34no—
403#235—62no—
404#235—68no—
405#235—62no—
406#235—62no—
407C2×D12—21no—
408C2×D12—21no—
409C2×D12—31no—
410C2×D12—31no—
411C2×D12—61no—
412C2×D12—62no—
413C2×D12—68no—
414C2×D12—61no—
415C2×D12—61no—
416C2×D12—61no—
417C2×D12—61no—
418C2×D12—61no—
419C2×D12—62no—
420C2×D12—61no—
421C2×D12—121no—
422C2×D12C22×D311yescharacteristic
423C2×D12C22×D311yescharacteristic
424C2×C4×D3—21no—
425C2×C4×D3—21no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—61no—
433C2×C4×D3—62no—
434C2×C4×D3—62no—
435C2×C4×D3—68no—
436C2×C4×D3—68no—
437C2×C4×D3—61no—
438C2×C4×D3—61no—
439C2×C4×D3—61no—
440C2×C4×D3—61no—
441C2×C4×D3—61no—
442C2×C4×D3—62no—
443C2×C4×D3—62no—
444C2×C4×D3—61no—
445C2×C4×D3—121no—
446C2×C4×D3C22×D311yescharacteristic
447C2×C4×D3C22×D311yescharacteristic
448C2×Dic6—21no—
449C2×Dic6—31no—
450C2×Dic6—31no—
451C2×Dic6—61no—
452C2×Dic6C22×D311yescharacteristic
453C3×SD16—62no—
454C3×SD16—62no—
455C2×C3×C8—21no—
456C2×C3×C8—31no—
457C2×C3×C8—31no—
458C2×C3×C8—62no—
459C2×C3×C8C22×D311yescharacteristic
460C2×C3×C8C22×D311yescharacteristic
461C3×C4⋊C4—21no—
462C3×C4⋊C4—31no—
463C3×C4⋊C4C22×D311yescharacteristic
464C3×C4⋊C4C22×D311yescharacteristic
465C3×C22⋊C4—61no—
466C3×C22⋊C4—61no—
467C3×C42—61no—
468#217—61no—
469#217—61no—
470#216—62no—
471#216—62no—
472#216—62no—
473#216—122no—
474#215—22no—
475#214—62no—
476#213—62no—
477#213—62no—
478#213—62no—
479(C2×D3)⋊C4—21no—
480(C2×D3)⋊C4—21no—
481(C2×D3)⋊C4—61no—
482(C2×D3)⋊C4—61no—
483(C2×D3)⋊C4—61no—
484(C2×D3)⋊C4—61no—
485(C2×D3)⋊C4—121no—
486C4⋊Dic3—61no—
487C4⋊Dic3—61no—
488C4⋊Dic3—61no—
489C4⋊Dic3—121no—
490C4⋊Dic3C22×D311yescharacteristic
491Dic3⋊C4—61no—
492C4×Dic3—21no—
493C2×C3⋊C8—31no—
494C2×C3⋊C8—31no—
495C2×C3⋊C8—61no—
496C2×C3⋊C8—62no—
497C2×C3⋊C8C22×D311yescharacteristic
498C2×C3⋊C8C22×D311yescharacteristic
499Dic12—62no—
500D24—62no—
501#204—22no—
502#204—62no—
503#204—62no—
504#204—62no—
505#204—122no—
506D3×C8—22no—
507D3×C8—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—21no—
519C2×C3×D3—22no—
520C2×C3×D3—41no—
521C2×C3×D3—41no—
522C2×C3×D3—41no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3#12012yes—
526C2×C3×D3#13512yescomplemented
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—91no—
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#135—184no—
554#135—184no—
555C2×Q16—91no—
556C2×Q16—91no—
557C2×SD16—31no—
558C2×SD16—31no—
559C2×SD16—91no—
560C2×SD16—91no—
561C2×D8—91no—
562C2×D8—91no—
563C22×C8—31no—
564C22×C8—91no—
565#123—181no—
566C22⋊Q8—91no—
567C22⋊Q8—91no—
568#121—31no—
569#121—91no—
570#120—181no—
571C4×D4—181no—
572C4×D4—181no—
573#117—31no—
574#103—31no—
575#103—31no—
576#103—91no—
577#103D3211yescharacteristic, complemented
578#102—31no—
579#102—31no—
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—62no—
596C22×D3—62no—
597C22×D3—64no—
598C22×D3—64no—
599C22×D3—61no—
600C22×D3—61no—
601C22×D3—62no—
602C22×D3—62no—
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—22no—
615C3×Q8—32no—
616C3×Q8—41no—
617C3×Q8—64no—
618C3×Q8—61no—
619C3×Q8C2×D1212yes—
620C3×Q8D3×D412yes—
621C3×D4—32no—
622C3×D4—64no—
623C3×D4—61no—
624C3×D4—61no—
625C3×D4—61no—
626C3×D4—122no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—31no—
633C2×C3×C4—32no—
634C2×C3×C4—32no—
635C2×C3×C4—31no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—64no—
639C2×C3×C4—64no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4C23×D311yescharacteristic
645C2×C3×C4C23×D311yescharacteristic
646#67—64no—
647#67—64no—
648#67—64no—
649#67—122no—
650#67—122no—
651#67—122no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—31no—
655C2×Dic3—31no—
656C2×Dic3—61no—
657C2×Dic3—62no—
658C2×Dic3—64no—
659C2×Dic3—62no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—121no—
663C2×Dic3—122no—
664C2×Dic3D3×D411yescharacteristic
665C2×Dic3D3×D411yescharacteristic
666D12—24no—
667D12—21no—
668D12—21no—
669D12—21no—
670D12—32no—
671D12—32no—
672D12—42no—
673D12—62no—
674D12—64no—
675D12—64no—
676D12—64no—
677D12—64no—
678D12—64no—
679D12—61no—
680D12—61no—
681D12—121no—
682D12—124no—
683D12—122no—
684D12C2×D1212yes—
685C4×D3—24no—
686C4×D3—21no—
687C4×D3—21no—
688C4×D3—24no—
689C4×D3—62no—
690C4×D3—64no—
691C4×D3—64no—
692C4×D3—64no—
693C4×D3—62no—
694C4×D3—64no—
695C4×D3—62no—
696C4×D3—61no—
697C4×D3—61no—
698C4×D3—61no—
699C4×D3—61no—
700C4×D3—62no—
701C4×D3—64no—
702C4×D3—121no—
703C4×D3—121no—
704C4×D3—124no—
705C4×D3—122no—
706C4×D3C2×D1212yes—
707C4×D3D3×D412yes—
708Dic6—24no—
709Dic6—21no—
710Dic6—61no—
711Dic6—61no—
712Dic6—61no—
713Dic6—61no—
714Dic6—121no—
715Dic6—121no—
716Dic6D3×D412yes—
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×C32C2×#13511yescharacteristic
729C2×C32#57511yescharacteristic
730C3⋊D3—41no—
731C3⋊D3—42no—
732C3×D3—22no—
733C3×D3—22no—
734C3×D3—42no—
735C3×D3—81no—
736C24—91no—
737C24—181no—
738#41—34no—
739#41—62no—
740#41—94no—
741#41—182no—
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—31no—
751C2×Q8—61no—
752C2×Q8—62no—
753C2×Q8—62no—
754C2×Q8—91no—
755C2×Q8C2×D3211yescharacteristic
756C2×D4—31no—
757C2×D4—31no—
758C2×D4—61no—
759C2×D4—61no—
760C2×D4—91no—
761C2×D4—181no—
762C2×D4—181no—
763C2×D4—182no—
764C2×D4—182no—
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—91no—
775C22×C4—91no—
776C22×C4—91no—
777C22×C4—91no—
778C22×C4—181no—
779C22×C4—182no—
780C22×C4—182no—
781C22×C4—181no—
782C22×C4—181no—
783C22×C4—188no—
784C22×C4—181no—
785Q16—182no—
786Q16—182no—
787SD16—62no—
788SD16—62no—
789SD16—182no—
790SD16—182no—
791D8—182no—
792D8—182no—
793C2×C8—31no—
794C2×C8—31no—
795C2×C8—62no—
796C2×C8—91no—
797C2×C8—182no—
798C2×C8C2×D3211yescharacteristic
799C4⋊C4—31no—
800C4⋊C4—181no—
801C4⋊C4—181no—
802C4⋊C4C2×D3211yescharacteristic
803C22⋊C4—61no—
804C22⋊C4—61no—
805C22⋊C4—181no—
806C22⋊C4—181no—
807C22⋊C4—181no—
808C42—61no—
809C22×C3—21no—
810C22×C3—32no—
811C22×C3—32no—
812C22×C3—61no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—61no—
816C22×C3—62no—
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—22no—
829C2×D3—41no—
830C2×D3—41no—
831C2×D3—41no—
832C2×D3—41no—
833C2×D3—41no—
834C2×D3—62no—
835C2×D3—61no—
836C2×D3—61no—
837C2×D3—61no—
838C2×D3—61no—
839C2×D3—61no—
840C2×D3—62no—
841C2×D3—61no—
842C2×D3—122no—
843C2×D3—121no—
844C2×D3—121no—
845C2×D3—121no—
846C2×D3—124no—
847C2×D3—124no—
848C2×D3—128no—
849C2×D3—128no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—241no—
855C2×D3—241no—
856C2×D3#88212yes—
857C2×D3#91612yescomplemented
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×C4C22×D1211yescharacteristic
871C3×C4C2×D3×D411yescharacteristic
872C3×C4C2×D3×D411yescharacteristic
873C3×C4C2×D3×D411yescharacteristic
874Dic3—21no—
875Dic3—22no—
876Dic3—41no—
877Dic3—61no—
878Dic3—61no—
879Dic3—121no—
880Dic3—121no—
881Dic3—121no—
882Dic3—241no—
883Dic3#88212yes—
884C32#300211yescharacteristic, complemented, Sylow
885C23—31no—
886C23—31no—
887C23—61no—
888C23—61no—
889C23—91no—
890C23—182no—
891C23—182no—
892C23—184no—
893C23—181no—
894C23—362no—
895C23—361no—
896C23—362no—
897Q8—21no—
898Q8—32no—
899Q8—64no—
900Q8—61no—
901Q8—181no—
902Q8—181no—
903Q8D3×D1212yes—
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—184no—
932C2×C4—182no—
933C2×C4—184no—
934C2×C4—182no—
935C2×C4—182no—
936C2×C4—184no—
937C2×C4—181no—
938C2×C4—181no—
939C2×C4—181no—
940C2×C4—362no—
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—62no—
951C2×C3—122no—
952C2×C3—241no—
953C2×C3C2×#88211yescharacteristic
954C2×C3D3×#12011yescharacteristic
955C2×C3C2×#91611yescharacteristic
956C2×C3D3×#13511yescharacteristic
957C2×C3#576811yescharacteristic
958C2×C3#577711yescharacteristic
959D3—22no—
960D3—22no—
961D3—42no—
962D3—81no—
963D3—121no—
964D3—122no—
965D3—121no—
966D3—122no—
967D3—241no—
968D3—242no—
969C22—32no—
970C22—32no—
971C22—61no—
972C22—61no—
973C22—61no—
974C22—61no—
975C22—62no—
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—
998C4C2×D3×D1211yescharacteristic
999C4D32×D411yescharacteristic
1000C3—21no—
1001C3#7883311yescharacteristic, complemented
1002C3#8003811yescharacteristic, complemented
1003C2—62no—
1004C2—62no—
1005C2—122no—
1006C2—241no—
1007C2—361no—
1008C2—362no—
1009C2D3×#88211yescharacteristic
1010C2D3×#91611yescharacteristic
1011C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3002
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. C2×D3×#239C2semidirect
2. C2×#63947C2semidirect
3. C2×#63806C2semidirect
4. #10594626C2semidirect
5. #10592507C2semidirect
6. C3×#4806C2semidirect
7. C3×#4804C2semidirect
8. #10591595C2semidirect
9. #10591593C2semidirect
10. #10590964C2semidirect
11. #10590946C2semidirect
12. D3×(C2×D3)⋊C8C2semidirect
13. #10590618C2semidirect
14. #10590610C2semidirect
15. #10590595C2semidirect
31. C2×#3795C22semidirect
32. C2×#3756C22semidirect
33. C2×#3744C22semidirect
34. #64106C22semidirect
35. C2×C3×#215C22semidirect
36. C2×C3×#204C22semidirect
37. C2×C3×D3×C8C22semidirect
39. C3×#892C22semidirect
42. #63916C22semidirect
47. C2×#3719C22semidirect
48. C2×#3716C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×D3×C3⋊C8C22semidirect
53. C32×#103C22semidirect
54. #63647C22semidirect
55. #63636C22semidirect
56. C3×#835C22semidirect
57. C3×#821C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. #63565C22semidirect
62. #63564C22semidirect
63. #63557C22semidirect
87. #4806D3semidirect
89. #4804D3semidirect
107. C3×#239D4semidirect
139. #3799D4semidirect
209. C2×#215C2×D3semidirect
228. C2×#204C2×D3semidirect
230. C2×D3×C8C2×D3semidirect
237. #892C2×D3semidirect
247. C3×#103C2×D3semidirect
248. C3×#103C2×D3semidirect
253. #835C2×D3semidirect
256. #821C2×D3semidirect
265. #810C2×D3semidirect
270. #809C2×D3semidirect
391. #239D12semidirect
526. C2×C3×D3#135semidirect
577. #103D32semidirect
857. C2×D3#916semidirect
884. C32#3002semidirect
1001. C3#78833semidirect
1002. C3#80038semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C2×#639472
C2×#638062
#105946262
#105925072
C3×#48062
C3×#48042
#105915952
#105915932
#105909642
#105909462
D3×(C2×D3)⋊C82
#105906182
#105906102
#105905952
#800383
#788333