Finite Group Databasebeta

← #11863897

Subgroups — #11863897

Order 1152.

1609 conjugacy classes of subgroups.

The subgroup lattice has 1017 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C211yesmaximal, characteristic, complemented
2C2×#63949C211yesmaximal, characteristic, complemented
3C2×#63808C211yesmaximal, characteristic, complemented
4#10594627C211yesmaximal, characteristic, complemented
5#10592509C211yesmaximal, characteristic, complemented
6C3×#4809C211yesmaximal, characteristic, complemented
7C3×#4804C211yesmaximal, characteristic, complemented
8#10591602C211yesmaximal, characteristic, complemented
9#10591584C211yesmaximal, characteristic, complemented
10#10590965C211yesmaximal, characteristic, complemented
11#10590947C211yesmaximal, characteristic, complemented
12D3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
13#10590617C211yesmaximal, characteristic, complemented
14#10590610C211yesmaximal, characteristic, complemented
15#10590596C211yesmaximal, characteristic, complemented
16#80182—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×#3799C2211yescharacteristic, complemented
30C2×#3796—21no—
31C2×#3796C2211yescharacteristic
32C2×#3755C2211yescharacteristic, complemented
33C2×#3745C2211yescharacteristic, complemented
34#64104C2211yescharacteristic, complemented
35C2×C3×#216C2211yescharacteristic, complemented
36C2×C3×Dic12C2211yescharacteristic, complemented
37C2×C3×D3×C8C2211yescharacteristic, complemented
38C3×#897C2211yescharacteristic
39C3×#892C2211yescharacteristic, complemented
40#63949—24no—
41#63923—21no—
42#63909C2211yescharacteristic
43#63894—21no—
44#63890—21no—
45#63880—21no—
46#63871C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63808—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×#919—31no—
69C2×#919—31no—
70C2×#904—31no—
71#5627—31no—
72#5524—31no—
73C3×#451—31no—
74C3×#416—31no—
75#5227—31no—
76#5187—31no—
77#5187—31no—
78C2×(C2×D3)⋊C8—31no—
79#5046—31no—
80#5002—31no—
81#4810—31no—
82#4810—31no—
83#4810—31no—
84#4810—61no—
85#4809D311yescharacteristic, complemented
86#4808—31no—
87#4806—31no—
88#4804—31no—
89#4804D311yescharacteristic, complemented
90#4783—31no—
91#4781—31no—
92#4776—31no—
93#4773—31no—
94#4732—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)—21no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3C2311yescharacteristic
107C3×#239—22no—
108C3×#239D414yescomplemented
109C3×D3×Q8—22no—
110C3×D3×Q8—22no—
111C2×C3×D12—21no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6—21no—
118C2×C3×Dic6C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×#626—21no—
121C2×#626—21no—
122C2×#626—21no—
123C2×#626—21no—
124C2×#626—21no—
125C2×#624—21no—
126C2×#624—21no—
127C2×#624D411yescharacteristic
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#3799—22no—
140#3799—22no—
141#3799D414yescomplemented
142#3796—28no—
143#3796—22no—
144#3796—22no—
145C2×C32×C8C2311yescharacteristic
146C32×C4⋊C4C2311yescharacteristic
147#3755—22no—
148#3752—21no—
149C2×C3⋊(C3⋊C8)C2311yescharacteristic
150#3745—22no—
151C3×#216—22no—
152C3×(C2×D3)⋊C4—21no—
153C3×(C2×D3)⋊C4—21no—
154C3×C4⋊Dic3—21no—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×C4×Dic3—21no—
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×Dic12—22no—
160C3×D3×C8—22no—
161Dic3⋊Dic3—21no—
162#3722—21no—
163#3722—21no—
164#3717—22no—
165#3717—22no—
166#3715—22no—
167#3714—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—31no—
179C2×#239—61no—
180C2×#239—61no—
181C2×#239—61no—
182C2×#239—64no—
183C2×#239—64no—
184C2×#239C2×D311yescharacteristic
185C2×D3×Q8C2×D311yescharacteristic
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×Q16—31no—
200C2×C3×Q16—31no—
201C22×C3×C8—31no—
202C3×C22⋊Q8—31no—
203C3×#117—31no—
204#950—64no—
205#946—31no—
206C2×#216C2×D311yescharacteristic, complemented
207C2×#215—31no—
208C2×#215—31no—
209C2×#215—31no—
210C2×#215—31no—
211C2×#215—31no—
212C2×#215—61no—
213C2×#214—31no—
214C2×#213—31no—
215#930—31no—
216C22×C3⋊C8—31no—
217#919—64no—
218#919—64no—
219C2×Dic12C2×D311yescharacteristic, complemented
220#904—64no—
221C2×D24—31no—
222C2×D24—31no—
223C2×D24—31no—
224C2×D24—61no—
225C2×#204—31no—
226C2×#204—31no—
227C2×D3×C8—31no—
228C2×D3×C8C2×D311yescharacteristic, complemented
229#897—31no—
230#897C2×D311yescharacteristic
231#895—31no—
232#895—31no—
233#895—31no—
234#895—61no—
235#894—61no—
236#893—61no—
237#892C2×D311yescharacteristic, complemented
238#886—61no—
239#882—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⋊D3—21no—
273C22×C3⋊D3C2×D411yescharacteristic
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⋊Dic3C2×D411yescharacteristic
289C4⋊(C3⋊D3)—24no—
290C4⋊(C3⋊D3)—21no—
291C4⋊(C3⋊D3)—21no—
292C4⋊(C3⋊D3)—21no—
293C4⋊(C3⋊D3)—42no—
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×Dic3—21no—
301C2×C3×Dic3C2×D411yescharacteristic
302C2×C3×Dic3C2×D411yescharacteristic
303C3×D12—24no—
304C3×D12—21no—
305C3×D12C2×D412yes—
306C3×C4×D3—24no—
307C3×C4×D3—21no—
308C3×C4×D3—21no—
309C3×C4×D3—24no—
310C3×C4×D3C2×D412yes—
311C3×C4×D3C2×D412yes—
312C3×Dic6—24no—
313C3×Dic6—21no—
314C3×Dic6—21no—
315C3×Dic6—21no—
316C3×Dic6C2×D412yes—
317#626—24no—
318#626—24no—
319#626—24no—
320#626—42no—
321#626—42no—
322#624—22no—
323#624—24no—
324#624—42no—
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×#135—91no—
334C2×#135—91no—
335#525—91no—
336#452—91no—
337#452—91no—
338#451—31no—
339#450—91no—
340#449—91no—
341#449—91no—
342#448—91no—
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—31no—
356C2×C3×Q8—61no—
357C2×C3×Q8—62no—
358C2×C3×Q8—62no—
359C2×C3×Q8C22×D311yescharacteristic
360C2×C3×Q8C22×D311yescharacteristic
361C2×C3×D4—31no—
362C2×C3×D4—61no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—61no—
366C22×C3×C4—61no—
367C2×#67—61no—
368C2×#67—61no—
369C2×#67—61no—
370C2×#67—61no—
371C2×#67—61no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—61no—
375#239—22no—
376#239—34no—
377#239—68no—
378#239—62no—
379#239—68no—
380#239—62no—
381#239—62no—
382#239—62no—
383#239—62no—
384#239—62no—
385#239—62no—
386#239—62no—
387#239—62no—
388#239—122no—
389#239—122no—
390#239D1214yescomplemented
391D3×Q8—22no—
392D3×Q8—22no—
393#237—62no—
394#237—68no—
395#237—62no—
396D3×D4—62no—
397D3×D4—62no—
398D3×D4—68no—
399#235—34no—
400#235—62no—
401#235—68no—
402#235—62no—
403#235—62no—
404C2×D12—21no—
405C2×D12—31no—
406C2×D12—31no—
407C2×D12—31no—
408C2×D12—31no—
409C2×D12—61no—
410C2×D12—61no—
411C2×D12—62no—
412C2×D12—68no—
413C2×D12—61no—
414C2×D12—61no—
415C2×D12—61no—
416C2×D12—61no—
417C2×D12—61no—
418C2×D12—62no—
419C2×D12—61no—
420C2×D12—61no—
421C2×D12—61no—
422C2×D12—61no—
423C2×D12—121no—
424C2×D12—121no—
425C2×D12C22×D311yescharacteristic
426C2×C4×D3—21no—
427C2×C4×D3—21no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—61no—
435C2×C4×D3—62no—
436C2×C4×D3—62no—
437C2×C4×D3—68no—
438C2×C4×D3—68no—
439C2×C4×D3—61no—
440C2×C4×D3—61no—
441C2×C4×D3—61no—
442C2×C4×D3—61no—
443C2×C4×D3—61no—
444C2×C4×D3—62no—
445C2×C4×D3—62no—
446C2×C4×D3—61no—
447C2×C4×D3—61no—
448C2×C4×D3—121no—
449C2×C4×D3C22×D311yescharacteristic
450C2×C4×D3C22×D311yescharacteristic
451C2×Dic6—21no—
452C2×Dic6C22×D311yescharacteristic
453C2×Dic6C22×D311yescharacteristic
454C3×Q16—62no—
455C3×Q16—62no—
456C2×C3×C8—21no—
457C2×C3×C8—31no—
458C2×C3×C8—31no—
459C2×C3×C8—62no—
460C2×C3×C8C22×D311yescharacteristic
461C2×C3×C8C22×D311yescharacteristic
462C3×C4⋊C4—21no—
463C3×C4⋊C4—31no—
464C3×C4⋊C4—61no—
465C3×C4⋊C4C22×D311yescharacteristic
466C3×C4⋊C4C22×D311yescharacteristic
467C3×C22⋊C4—61no—
468C3×C22⋊C4—61no—
469C3×C42—61no—
470#216—22no—
471#215—62no—
472#215—62no—
473#215—62no—
474#215—62no—
475#215—62no—
476#215—122no—
477#214—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—61no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—121no—
488C4⋊Dic3—21no—
489C4⋊Dic3—61no—
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—22no—
500D24—62no—
501D24—62no—
502D24—62no—
503D24—122no—
504#204—62no—
505#204—62no—
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—41no—
516C2×C3⋊D3—41no—
517C2×C3⋊D3—41no—
518C2×C3×D3—21no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—21no—
522C2×C3×D3—22no—
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—21no—
535C3×Dic3—22no—
536C3×Dic3—41no—
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—31no—
556C2×Q16—31no—
557C2×SD16—91no—
558C2×SD16—91no—
559C2×SD16—91no—
560C2×SD16—91no—
561C2×D8—91no—
562C2×D8—91no—
563C22×C8—31no—
564C22×C8—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—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—
589C22×D3—21no—
590C22×D3—31no—
591C22×D3—31no—
592C22×D3—61no—
593C22×D3—62no—
594C22×D3—62no—
595C22×D3—64no—
596C22×D3—64no—
597C22×D3—61no—
598C22×D3—61no—
599C22×D3—62no—
600C22×D3—62no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—121no—
604C22×D3—121no—
605C22×D3—121no—
606C22×D3—121no—
607C22×D3—122no—
608C22×D3—122no—
609C22×D3—122no—
610C22×D3—122no—
611C22×D3D3×D411yescharacteristic
612C22×D3D3×D411yescharacteristic
613C3×Q8—21no—
614C3×Q8—21no—
615C3×Q8—22no—
616C3×Q8—32no—
617C3×Q8—41no—
618C3×Q8—64no—
619C3×Q8—61no—
620C3×Q8—61no—
621C3×Q8—61no—
622C3×Q8C2×D1212yes—
623C3×Q8D3×D412yes—
624C3×D4—32no—
625C3×D4—64no—
626C3×D4—61no—
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×C4—61no—
645C2×C3×C4C23×D311yescharacteristic
646C2×C3×C4C23×D311yescharacteristic
647#67—64no—
648#67—64no—
649#67—64no—
650#67—122no—
651#67—122no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—31no—
656C2×Dic3—31no—
657C2×Dic3—61no—
658C2×Dic3—62no—
659C2×Dic3—64no—
660C2×Dic3—62no—
661C2×Dic3D3×D411yescharacteristic
662C2×Dic3D3×D411yescharacteristic
663D12—24no—
664D12—21no—
665D12—32no—
666D12—32no—
667D12—62no—
668D12—64no—
669D12—64no—
670D12—64no—
671D12—64no—
672D12—64no—
673D12—61no—
674D12—61no—
675D12—61no—
676D12—61no—
677D12—61no—
678D12—61no—
679D12—121no—
680D12—121no—
681D12—121no—
682D12—124no—
683D12—122no—
684D12—122no—
685D12—122no—
686D12—122no—
687D12—242no—
688D12C2×D1212yes—
689C4×D3—24no—
690C4×D3—21no—
691C4×D3—21no—
692C4×D3—24no—
693C4×D3—62no—
694C4×D3—64no—
695C4×D3—64no—
696C4×D3—64no—
697C4×D3—62no—
698C4×D3—64no—
699C4×D3—62no—
700C4×D3—61no—
701C4×D3—61no—
702C4×D3—61no—
703C4×D3—61no—
704C4×D3—62no—
705C4×D3—64no—
706C4×D3—121no—
707C4×D3—121no—
708C4×D3—124no—
709C4×D3—122no—
710C4×D3—122no—
711C4×D3C2×D1212yes—
712C4×D3D3×D412yes—
713Dic6—24no—
714Dic6—21no—
715Dic6—21no—
716Dic6—21no—
717Dic6D3×D412yes—
718C3×C8—21no—
719C3×C8—21no—
720C3×C8—41no—
721C3×C8—61no—
722C3×C8—61no—
723C3⋊C8—21no—
724C3⋊C8—21no—
725C3⋊C8—61no—
726C3⋊C8—61no—
727C3⋊C8—121no—
728C2×C32C2×#12011yescharacteristic
729C2×C32C2×#13511yescharacteristic
730C2×C32#57511yescharacteristic
731C3⋊D3—41no—
732C3⋊D3—42no—
733C3⋊D3—81no—
734C3×D3—22no—
735C3×D3—22no—
736C3×D3—42no—
737C24—91no—
738C24—181no—
739#41—34no—
740#41—62no—
741#41—94no—
742#41—182no—
743#41—182no—
744#41—182no—
745#41—188no—
746#41—182no—
747#41—182no—
748#41—188no—
749#41—182no—
750#41—182no—
751C2×Q8—31no—
752C2×Q8—31no—
753C2×Q8—61no—
754C2×Q8—62no—
755C2×Q8—62no—
756C2×Q8C2×D3211yescharacteristic
757C2×D4—31no—
758C2×D4—61no—
759C2×D4—91no—
760C2×D4—91no—
761C2×D4—181no—
762C2×D4—181no—
763C2×D4—181no—
764C2×D4—182no—
765C2×D4—182no—
766C2×D4—188no—
767C2×D4—181no—
768C2×D4—181no—
769C2×D4—181no—
770C2×D4—181no—
771C22×C4—31no—
772C22×C4—31no—
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—181no—
784C22×C4—188no—
785C22×C4—181no—
786Q16—62no—
787Q16—62no—
788SD16—182no—
789SD16—182no—
790SD16—182no—
791SD16—182no—
792D8—182no—
793D8—182no—
794C2×C8—31no—
795C2×C8—31no—
796C2×C8—62no—
797C2×C8—91no—
798C2×C8—182no—
799C2×C8C2×D3211yescharacteristic
800C4⋊C4—31no—
801C4⋊C4—61no—
802C4⋊C4—181no—
803C4⋊C4C2×D3211yescharacteristic
804C22⋊C4—61no—
805C22⋊C4—61no—
806C22⋊C4—181no—
807C22⋊C4—181no—
808C22⋊C4—181no—
809C42—61no—
810C22×C3—21no—
811C22×C3—32no—
812C22×C3—32no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—62no—
818C22×C3—121no—
819C22×C3—121no—
820C22×C3C2×D3×D411yescharacteristic
821C22×C3C2×D3×D411yescharacteristic
822C2×D3—21no—
823C2×D3—21no—
824C2×D3—21no—
825C2×D3—21no—
826C2×D3—22no—
827C2×D3—41no—
828C2×D3—41no—
829C2×D3—62no—
830C2×D3—61no—
831C2×D3—61no—
832C2×D3—61no—
833C2×D3—61no—
834C2×D3—61no—
835C2×D3—62no—
836C2×D3—61no—
837C2×D3—122no—
838C2×D3—121no—
839C2×D3—121no—
840C2×D3—121no—
841C2×D3—124no—
842C2×D3—124no—
843C2×D3—128no—
844C2×D3—128no—
845C2×D3—121no—
846C2×D3—121no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—121no—
855C2×D3—241no—
856C2×D3—241no—
857C2×D3—241no—
858C2×D3—241no—
859C2×D3—241no—
860C2×D3#88212yes—
861C2×D3#91912yescomplemented
862C3×C4—22no—
863C3×C4—22no—
864C3×C4—21no—
865C3×C4—21no—
866C3×C4—32no—
867C3×C4—42no—
868C3×C4—41no—
869C3×C4—41no—
870C3×C4—61no—
871C3×C4—62no—
872C3×C4—81no—
873C3×C4—121no—
874C3×C4—121no—
875C3×C4C22×D1211yescharacteristic
876C3×C4C2×D3×D411yescharacteristic
877C3×C4C2×D3×D411yescharacteristic
878C3×C4C2×D3×D411yescharacteristic
879Dic3—21no—
880Dic3—22no—
881Dic3—41no—
882Dic3—41no—
883Dic3—61no—
884Dic3—61no—
885Dic3—121no—
886Dic3#88212yes—
887C32#300211yescharacteristic, complemented, Sylow
888C23—31no—
889C23—31no—
890C23—61no—
891C23—91no—
892C23—182no—
893C23—182no—
894C23—184no—
895C23—181no—
896C23—181no—
897C23—362no—
898C23—361no—
899C23—362no—
900Q8—21no—
901Q8—32no—
902Q8—64no—
903Q8—61no—
904Q8—61no—
905Q8—61no—
906Q8D3×D1212yes—
907D4—32no—
908D4—64no—
909D4—61no—
910D4—92no—
911D4—184no—
912D4—184no—
913D4—184no—
914D4—184no—
915D4—181no—
916D4—181no—
917D4—181no—
918D4—362no—
919D4—362no—
920D4—362no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—31no—
924C2×C4—32no—
925C2×C4—32no—
926C2×C4—31no—
927C2×C4—64no—
928C2×C4—64no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—61no—
933C2×C4—61no—
934C2×C4—91no—
935C2×C4—184no—
936C2×C4—182no—
937C2×C4—184no—
938C2×C4—182no—
939C2×C4—182no—
940C2×C4—184no—
941C2×C4—181no—
942C2×C4—181no—
943C2×C4—362no—
944C2×C4C22×D3211yescharacteristic
945C8—21no—
946C8—61no—
947C8—61no—
948C8—181no—
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—62no—
953C2×C3—62no—
954C2×C3—122no—
955C2×C3C2×#88211yescharacteristic
956C2×C3D3×#12011yescharacteristic
957C2×C3C2×#91911yescharacteristic
958C2×C3D3×#13511yescharacteristic
959C2×C3#576811yescharacteristic
960C2×C3#577711yescharacteristic
961D3—22no—
962D3—22no—
963D3—42no—
964D3—121no—
965D3—122no—
966D3—121no—
967D3—122no—
968D3—241no—
969D3—242no—
970D3—241no—
971D3—241no—
972D3—481no—
973C22—32no—
974C22—32no—
975C22—61no—
976C22—61no—
977C22—61no—
978C22—61no—
979C22—62no—
980C22—121no—
981C22—121no—
982C22—181no—
983C22—181no—
984C22—182no—
985C22—181no—
986C22—364no—
987C22—368no—
988C22—361no—
989C22—361no—
990C22—361no—
991C22—361no—
992C22—361no—
993C22D32×D411yescharacteristic
994C4—22no—
995C4—32no—
996C4—41no—
997C4—61no—
998C4—62no—
999C4—121no—
1000C4—121no—
1001C4—181no—
1002C4C2×D3×D1211yescharacteristic
1003C4D32×D411yescharacteristic
1004C3—21no—
1005C3#7883311yescharacteristic, complemented
1006C3#8018211yescharacteristic, complemented
1007C2—62no—
1008C2—62no—
1009C2—122no—
1010C2—361no—
1011C2—362no—
1012C2—721no—
1013C2D3×#88211yescharacteristic
1014C2#1059474611yescharacteristic
1015C2D3×#91911yescharacteristic
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×#63949C2semidirect
3. C2×#63808C2semidirect
4. #10594627C2semidirect
5. #10592509C2semidirect
6. C3×#4809C2semidirect
7. C3×#4804C2semidirect
8. #10591602C2semidirect
9. #10591584C2semidirect
10. #10590965C2semidirect
11. #10590947C2semidirect
12. D3×(C2×D3)⋊C8C2semidirect
13. #10590617C2semidirect
14. #10590610C2semidirect
15. #10590596C2semidirect
29. C2×#3799C22semidirect
32. C2×#3755C22semidirect
33. C2×#3745C22semidirect
34. #64104C22semidirect
35. C2×C3×#216C22semidirect
36. C2×C3×Dic12C22semidirect
37. C2×C3×D3×C8C22semidirect
39. C3×#892C22semidirect
46. #63871C22semidirect
47. C2×#3717C22semidirect
48. C2×#3717C22semidirect
49. C2×#3715C22semidirect
50. C2×#3714C22semidirect
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
85. #4809D3semidirect
89. #4804D3semidirect
108. C3×#239D4semidirect
141. #3799D4semidirect
206. C2×#216C2×D3semidirect
219. C2×Dic12C2×D3semidirect
228. 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
390. #239D12semidirect
526. C2×C3×D3#135semidirect
577. #103D32semidirect
861. C2×D3#919semidirect
887. C32#3002semidirect
1005. C3#78833semidirect
1006. C3#80182semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C2×#639492
C2×#638082
#105946272
#105925092
C3×#48092
C3×#48042
#105916022
#105915842
#105909652
#105909472
D3×(C2×D3)⋊C82
#105906172
#105906102
#105905962
#801823
#788333