Finite Group Databasebeta

← #11633039

Subgroups — #11633039

Order 768.

3210 conjugacy classes of subgroups.

The subgroup lattice has 1270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5817C211yesmaximal, characteristic, complemented
2C22×#946C211yesmaximal, characteristic, complemented
3C2×#5726C211yesmaximal, characteristic, complemented
4C2×#5627C211yesmaximal, characteristic, complemented
5C3×#2434C211yesmaximal, characteristic, complemented
6#83259C211yesmaximal, characteristic, complemented
7#83255C211yesmaximal, characteristic, complemented
8#83254C211yesmaximal, characteristic, complemented
9#82815C211yesmaximal, characteristic, complemented
10#77262C212yesmaximal, complemented
11#77259C212yesmaximal, complemented
12#77252C212yesmaximal, complemented
13#77176C212yesmaximal, complemented
14#76624C211yesmaximal, characteristic, complemented
15#76620C211yesmaximal, characteristic, complemented
16#76618C211yesmaximal, characteristic, complemented
17#76491C211yesmaximal, characteristic, complemented
18#74605C212yesmaximal, complemented
19#74603C212yesmaximal, complemented
20#74418C212yesmaximal, complemented
21#74393C212yesmaximal, complemented
22C4×#882C211yesmaximal, characteristic, complemented
23#73467C211yesmaximal, characteristic, complemented
24#59002—31nomaximal, Sylow
25C23×C3×Q8C2211yescharacteristic
26C22×#239C2211yescharacteristic
27C22×#239C2211yescharacteristic, complemented
28C23×C4×D3C2211yescharacteristic
29C2×C3×C4⋊Q8C2211yescharacteristic, complemented
30C2×C3×C4⋊Q8C2211yescharacteristic, complemented
31C2×C3×C22⋊Q8C2211yescharacteristic
32#5817—28no—
33C2×#947C2211yescharacteristic, complemented
34C2×#947C2212yescomplemented
35C2×#946—28no—
36C2×#946C2211yescharacteristic
37C2×#946C2211yescharacteristic
38C2×#946C2211yescharacteristic
39C2×#946C2211yescharacteristic
40C2×#946C2212yes—
41C2×#946C2212yes—
42C2×#946C2211yescharacteristic
43C2×#946C2211yescharacteristic, complemented
44C2×#946C2211yescharacteristic, complemented
45C2×#946C2212yescomplemented
46C2×Q8×Dic3C2211yescharacteristic, complemented
47C2×#930C2212yes—
48C2×#930C2211yescharacteristic
49C2×C4×#67C2211yescharacteristic
50C2×C4×#67C2212yes—
51C22×(C2×D3)⋊C4C2212yes—
52C22×C4⋊Dic3C2211yescharacteristic
53C22×Dic3⋊C4C2212yes—
54#5726—28no—
55#5627—28no—
56C2×#895C2211yescharacteristic
57C2×#895C2212yes—
58C2×#894C2212yes—
59C2×#894C2212yes—
60C2×#894C2212yescomplemented
61C2×#893C2212yes—
62C2×#892C2211yescharacteristic
63C2×D3×C4⋊C4C2212yescomplemented
64C2×#882C2211yescharacteristic
65C2×#882C2212yes—
66C2×#67⋊C4C2212yes—
67C2×#67⋊C4C2212yes—
68C2×C4×D12C2211yescharacteristic
69C2×C4×D12C2211yescharacteristic
70C2×C4×D12C2211yescharacteristic, complemented
71C3×#395C2212yescomplemented
72C3×#395C2212yescomplemented
73C3×#391C2211yescharacteristic, complemented
74C3×#391C2211yescharacteristic, complemented
75C3×#385C2212yes—
76C3×#385C2212yes—
77C3×C4×C22⋊C4C2211yescharacteristic
78#5229C2211yescharacteristic, complemented
79#4994C2212yes—
80#4994C2212yescomplemented
81#4993C2212yes—
82#4993C2212yescomplemented
83#4991C2212yes—
84#4991C2212yes—
85#4990C2212yes—
86#4989C2212yescomplemented
87#4989C2212yescomplemented
88#4988C2212yes—
89#4987C2211yescharacteristic, complemented
90#4982C2212yescomplemented
91#4982C2212yescomplemented
92#4976C2212yescomplemented
93#4975C2212yescomplemented
94#4972C2211yescharacteristic, complemented
95#4958C2211yescharacteristic
96#4958C2212yes—
97#4958C2212yes—
98#4955C2211yescharacteristic
99#4950C2211yescharacteristic
100#4942C2212yes—
101#4939C2211yescharacteristic, complemented
102C4×(C2×D3)⋊C4C2211yescharacteristic
103C4×(C2×D3)⋊C4C2211yescharacteristic
104C4×C4⋊Dic3C2211yescharacteristic, complemented
105#4928C2211yescharacteristic, complemented
106#4675C2212yes—
107#4675C2212yescomplemented
108#4672C2212yes—
109#4672C2212yes—
110#4672C2212yescomplemented
111#4671C2212yes—
112#4670C2212yes—
113#4670C2212yescomplemented
114#4669C2212yes—
115#4669C2212yescomplemented
116#4668C2211yescharacteristic
117#4668C2211yescharacteristic
118#4668C2212yescomplemented
119#4668C2212yescomplemented
120#4667C2212yescomplemented
121#4665C2212yes—
122#4665C2212yes—
123#4665C2211yescharacteristic
124#4665C2211yescharacteristic
125#4655C2212yescomplemented
126#4649C2212yescomplemented
127#4647C2212yescomplemented
128C2×#548—31no—
129C2×#547—31no—
130C2×#525—31no—
131C22×C22⋊Q8—31no—
132#2680—32no—
133#2672—32no—
134#2542—31no—
135#2461—32no—
136#2449—32no—
137#2443—32no—
138#2434D311yescharacteristic, complemented
139#2432—31no—
140#2429—31no—
141#2427—31no—
142#2424—32no—
143#2418—32no—
144#2417—31no—
145#2415—31no—
146#2407—31no—
147#2362—31no—
148#2361—31no—
149D4×C4⋊C4—32no—
150C4×#120—31no—
151C24×D3C2311yescharacteristic
152C22×C3×Q8—24no—
153C22×C3×Q8—24no—
154C22×C3×Q8—42no—
155C22×C3×Q8C2311yescharacteristic
156C22×C3×Q8C2311yescharacteristic
157C22×C3×Q8C2312yes—
158C22×C3×Q8C2311yescharacteristic
159C23×C3×C4C2312yes—
160C23×C3×C4C2311yescharacteristic
161C22×#67C2311yescharacteristic
162C22×#67C2312yes—
163C23×Dic3C2311yescharacteristic
164C23×Dic3C2312yes—
165C2×#239—24no—
166C2×#239—24no—
167C2×#239—24no—
168C2×#239—24no—
169C2×#239—42no—
170C2×#239—42no—
171C22×D12C2312yes—
172C22×D12C2311yescharacteristic
173C22×D12C2311yescharacteristic
174C22×D12C2312yes—
175C22×D12C2312yes—
176C22×D12C2311yescharacteristic
177C22×C4×D3—24no—
178C22×C4×D3—24no—
179C22×C4×D3—42no—
180C22×C4×D3C2311yescharacteristic
181C22×C4×D3C2311yescharacteristic
182C22×C4×D3C2312yes—
183C22×C4×D3C2311yescharacteristic
184C22×C4×D3C2311yescharacteristic
185C22×C4×D3C2312yes—
186C22×C4×D3C2312yes—
187C22×C4×D3C2311yescharacteristic
188C3×C4⋊Q8—24no—
189C3×C4⋊Q8—42no—
190C3×C22⋊Q8—24no—
191C2×C3×C4⋊C4C2311yescharacteristic
192C2×C3×C4⋊C4C2312yes—
193C2×C3×C4⋊C4C2312yes—
194C2×C3×C4⋊C4C2312yes—
195C2×C3×C4⋊C4C2312yes—
196C2×C3×C4⋊C4C2312yes—
197C2×C3×C22⋊C4C2312yes—
198C2×C3×C22⋊C4C2311yescharacteristic
199C2×C3×C22⋊C4C2311yescharacteristic
200C2×C3×C42C2311yescharacteristic
201C2×C3×C42C2311yescharacteristic
202C2×#217C2311yescharacteristic
203#947—24no—
204#947—28no—
205#946—24no—
206#946—24no—
207#946—28no—
208#946—28no—
209#946—24no—
210#946—24no—
211#946—24no—
212#946—24no—
213#946—28no—
214#946D418yescomplemented
215Q8×Dic3—24no—
216#930—28no—
217#930D418yescomplemented
218C4×#67—24no—
219C4×#67—28no—
220C2×(C2×D3)⋊C4—28no—
221C2×(C2×D3)⋊C4C2311yescharacteristic
222C2×(C2×D3)⋊C4C2311yescharacteristic
223C2×(C2×D3)⋊C4C2311yescharacteristic
224C2×(C2×D3)⋊C4C2312yes—
225C2×(C2×D3)⋊C4C2311yescharacteristic
226C2×(C2×D3)⋊C4C2312yes—
227C2×(C2×D3)⋊C4C2312yes—
228C2×(C2×D3)⋊C4C2312yes—
229C2×(C2×D3)⋊C4C2312yes—
230C2×(C2×D3)⋊C4C2311yescharacteristic
231C2×(C2×D3)⋊C4C2311yescharacteristic
232C2×(C2×D3)⋊C4C2312yes—
233C2×(C2×D3)⋊C4C2312yes—
234C2×(C2×D3)⋊C4C2312yes—
235C2×(C2×D3)⋊C4C2312yes—
236C2×(C2×D3)⋊C4C2312yes—
237C2×(C2×D3)⋊C4C2312yes—
238C2×(C2×D3)⋊C4C2312yes—
239C2×(C2×D3)⋊C4C2311yescharacteristic
240C2×(C2×D3)⋊C4C2312yes—
241C2×(C2×D3)⋊C4C2311yescharacteristic
242C2×(C2×D3)⋊C4C2311yescharacteristic
243C2×(C2×D3)⋊C4C2312yes—
244C2×(C2×D3)⋊C4C2312yes—
245C2×(C2×D3)⋊C4C2312yes—
246C2×C4⋊Dic3—24no—
247C2×C4⋊Dic3C2311yescharacteristic
248C2×C4⋊Dic3C2312yes—
249C2×C4⋊Dic3C2312yes—
250C2×C4⋊Dic3C2311yescharacteristic
251C2×C4⋊Dic3C2311yescharacteristic
252C2×C4⋊Dic3C2311yescharacteristic
253C2×C4⋊Dic3C2311yescharacteristic
254C2×Dic3⋊C4—28no—
255C2×Dic3⋊C4C2312yes—
256C2×Dic3⋊C4C2312yes—
257C2×Dic3⋊C4C2312yes—
258C2×Dic3⋊C4C2312yes—
259C2×Dic3⋊C4C2311yescharacteristic
260C2×Dic3⋊C4C2312yes—
261C2×Dic3⋊C4C2312yes—
262C2×Dic3⋊C4C2312yes—
263C2×Dic3⋊C4C2312yes—
264C2×Dic3⋊C4C2312yes—
265C2×C4×Dic3C2312yes—
266C2×C4×Dic3C2312yes—
267C2×C4×Dic3C2312yes—
268C2×C4×Dic3C2311yescharacteristic
269#895—24no—
270#895—28no—
271#894—28no—
272#894—28no—
273#894—28no—
274#893—28no—
275#892—24no—
276D3×C4⋊C4—28no—
277#882—28no—
278#882—24no—
279#67⋊C4—28no—
280#67⋊C4—28no—
281C4×D12—24no—
282C4×D12—24no—
283C4×D12—42no—
284C3×#95C2312yes—
285C3×#95C2312yes—
286C3×#95C2312yes—
287C3×#95C2311yescharacteristic
288C3×#95C2311yescharacteristic
289C3×#95C2312yes—
290C3⋊#95C2312yes—
291C3⋊#95C2311yescharacteristic
292C3⋊#95C2311yescharacteristic
293C3⋊#95C2312yes—
294C3⋊#95C2312yes—
295C3⋊#95C2311yescharacteristic
296C3⋊#95C2311yescharacteristic
297C3⋊#95C2312yes—
298C3⋊#95C2312yes—
299C3⋊#95C2312yes—
300C22×#41—31no—
301C22×#41—31no—
302C23×Q8C2×D311yescharacteristic
303C24×C4—31no—
304#548—68no—
305#547—68no—
306C2×C4⋊Q8C2×D311yescharacteristic, complemented
307C2×C4⋊Q8C2×D311yescharacteristic, complemented
308C2×#124—32no—
309C2×#124—31no—
310#525—68no—
311C2×#123—32no—
312C2×#123—32no—
313C2×#123—32no—
314C2×C22⋊Q8—31no—
315C2×C22⋊Q8—31no—
316C2×C22⋊Q8—31no—
317C2×C22⋊Q8—32no—
318C2×C22⋊Q8—31no—
319C2×C22⋊Q8—32no—
320C2×C22⋊Q8—31no—
321C2×C22⋊Q8—31no—
322C2×C22⋊Q8—31no—
323C2×C22⋊Q8—32no—
324C2×C22⋊Q8—68no—
325C2×C22⋊Q8C2×D311yescharacteristic
326C2×#121—31no—
327C2×#121—32no—
328C2×#121—31no—
329C2×#121—32no—
330C2×#120—32no—
331C2×#120—31no—
332C2×C4×Q8—31no—
333C2×C4×D4—32no—
334C2×C4×D4—31no—
335C2×C4×D4—32no—
336C2×C4×D4—32no—
337C2×C4×D4—32no—
338C2×C4×D4—31no—
339C2×C4×D4—31no—
340C2×C4×D4—31no—
341C2×#117—31no—
342C22×C4⋊C4—32no—
343C22×C4⋊C4—31no—
344C22×C4⋊C4—32no—
345C22×C22⋊C4—32no—
346#399—32no—
347#399—32no—
348#398—32no—
349#398—32no—
350#397—32no—
351#397—32no—
352#396—32no—
353#396—32no—
354#395C2×D312yescomplemented
355#395C2×D312yescomplemented
356#394—32no—
357#394—32no—
358#394—32no—
359#394—32no—
360#394—32no—
361#392—32no—
362#391—31no—
363#391C2×D311yescharacteristic, complemented
364#391C2×D311yescharacteristic, complemented
365#390—32no—
366#390—31no—
367#389—32no—
368#389—31no—
369#389—31no—
370#389—32no—
371#388—32no—
372#388—32no—
373#388—32no—
374#388—32no—
375#388—32no—
376#387—32no—
377#386—32no—
378#386—32no—
379#386—31no—
380#386—32no—
381#386—31no—
382#386—32no—
383#386—31no—
384#385—32no—
385#385—32no—
386#385—31no—
387#385—32no—
388#385—32no—
389#385—31no—
390#385—31no—
391#385C2×D312yes—
392#385C2×D312yes—
393#384—32no—
394#380—31no—
395#380—32no—
396#380—32no—
397#379—31no—
398C4×C4⋊C4—31no—
399C4×C4⋊C4—32no—
400C4×C22⋊C4—31no—
401C4×C22⋊C4—31no—
402C4×C22⋊C4C2×D311yescharacteristic
403C24×C3C2411yescharacteristic
404C23×D3—22no—
405C23×D3—22no—
406C23×D3—22no—
407C23×D3—22no—
408C23×D3—22no—
409C23×D3—41no—
410C23×D3—41no—
411C23×D3C2411yescharacteristic
412C23×D3C2411yescharacteristic
413C23×D3C2412yes—
414C23×D3C2411yescharacteristic
415C2×C3×Q8—22no—
416C2×C3×Q8—24no—
417C2×C3×Q8—22no—
418C2×C3×Q8—24no—
419C2×C3×Q8—22no—
420C2×C3×Q8—22no—
421C2×C3×Q8—22no—
422C2×C3×Q8—22no—
423C2×C3×Q8—22no—
424C2×C3×Q8—22no—
425C2×C3×Q8—42no—
426C2×C3×Q8—416no—
427C2×C3×Q8C2×D414yes—
428C22×C3×C4—22no—
429C22×C3×C4—22no—
430C22×C3×C4—24no—
431C22×C3×C4—24no—
432C22×C3×C4—42no—
433C22×C3×C4C2×D414yes—
434C22×C3×C4C2411yescharacteristic
435C22×C3×C4C2411yescharacteristic
436C22×C3×C4C2412yes—
437C22×C3×C4C2412yes—
438C22×C3×C4C2412yes—
439C22×C3×C4C2412yes—
440C22×C3×C4C2411yescharacteristic
441C22×C3×C4C2411yescharacteristic
442C22×C3×C4C2411yescharacteristic
443C22×C3×C4C2411yescharacteristic
444C2×#67—24no—
445C2×#67—24no—
446C2×#67—22no—
447C2×#67—22no—
448C2×#67—22no—
449C2×#67C2×D418yes—
450C22×Dic3—22no—
451C22×Dic3—24no—
452C22×Dic3—22no—
453C22×Dic3—24no—
454C22×Dic3—41no—
455C22×Dic3—42no—
456C22×Dic3C2411yescharacteristic
457C22×Dic3C2411yescharacteristic
458C22×Dic3C2412yes—
459C22×Dic3C2411yescharacteristic
460C22×Dic3C2411yescharacteristic
461C22×Dic3C2412yes—
462C22×Dic3C2411yescharacteristic
463C22×Dic3C2412yes—
464#239—416no—
465#239—416no—
466C2×D12—22no—
467C2×D12—22no—
468C2×D12—22no—
469C2×D12—24no—
470C2×D12—24no—
471C2×D12—24no—
472C2×D12—24no—
473C2×D12—22no—
474C2×D12—24no—
475C2×D12—24no—
476C2×D12—22no—
477C2×D12—22no—
478C2×D12—41no—
479C2×D12—41no—
480C2×D12—42no—
481C2×D12—42no—
482C2×D12—42no—
483C2×D12C2×D414yes—
484C2×C4×D3—22no—
485C2×C4×D3—22no—
486C2×C4×D3—24no—
487C2×C4×D3—24no—
488C2×C4×D3—22no—
489C2×C4×D3—22no—
490C2×C4×D3—24no—
491C2×C4×D3—22no—
492C2×C4×D3—22no—
493C2×C4×D3—22no—
494C2×C4×D3—22no—
495C2×C4×D3—22no—
496C2×C4×D3—24no—
497C2×C4×D3—22no—
498C2×C4×D3—22no—
499C2×C4×D3—24no—
500C2×C4×D3—24no—
501C2×C4×D3—22no—
502C2×C4×D3—416no—
503C2×C4×D3—41no—
504C2×C4×D3—41no—
505C2×C4×D3—42no—
506C2×C4×D3—42no—
507C2×C4×D3—42no—
508C2×C4×D3C2×D414yes—
509C3×C4⋊C4—24no—
510C3×C4⋊C4—22no—
511C3×C4⋊C4—24no—
512C3×C4⋊C4—24no—
513C3×C4⋊C4—42no—
514C3×C4⋊C4—42no—
515C3×C22⋊C4—24no—
516C3×C22⋊C4—22no—
517C3×C22⋊C4#4114yescomplemented
518C3×C42—22no—
519C3×C42—22no—
520#217—22no—
521(C2×D3)⋊C4—22no—
522(C2×D3)⋊C4—24no—
523(C2×D3)⋊C4—24no—
524(C2×D3)⋊C4—24no—
525(C2×D3)⋊C4—24no—
526(C2×D3)⋊C4—22no—
527(C2×D3)⋊C4—24no—
528(C2×D3)⋊C4—22no—
529(C2×D3)⋊C4—24no—
530(C2×D3)⋊C4—22no—
531(C2×D3)⋊C4—22no—
532(C2×D3)⋊C4—22no—
533(C2×D3)⋊C4—24no—
534(C2×D3)⋊C4—24no—
535(C2×D3)⋊C4—24no—
536(C2×D3)⋊C4—24no—
537(C2×D3)⋊C4—24no—
538(C2×D3)⋊C4—24no—
539(C2×D3)⋊C4—41no—
540(C2×D3)⋊C4—41no—
541(C2×D3)⋊C4—41no—
542(C2×D3)⋊C4—42no—
543(C2×D3)⋊C4—42no—
544(C2×D3)⋊C4C2×D418yes—
545(C2×D3)⋊C4C2×D418yes—
546C4⋊Dic3—22no—
547C4⋊Dic3—22no—
548C4⋊Dic3—24no—
549C4⋊Dic3—24no—
550C4⋊Dic3—41no—
551C4⋊Dic3C2×D414yes—
552C4⋊Dic3C2×D414yes—
553Dic3⋊C4—24no—
554Dic3⋊C4—22no—
555Dic3⋊C4—24no—
556Dic3⋊C4—24no—
557Dic3⋊C4—24no—
558Dic3⋊C4—24no—
559Dic3⋊C4—24no—
560Dic3⋊C4—24no—
561Dic3⋊C4—42no—
562Dic3⋊C4C2×D418yes—
563C4×Dic3—22no—
564C4×Dic3—24no—
565C4×Dic3—24no—
566C4×Dic3—24no—
567C25—31no—
568C2×#41—64no—
569C2×#41—64no—
570C2×#41—64no—
571C2×#41—64no—
572C2×#41—122no—
573C2×#41—122no—
574C22×Q8—24no—
575C22×Q8—24no—
576C22×Q8—42no—
577C22×Q8C22×D311yescharacteristic
578C22×Q8C22×D311yescharacteristic
579C22×Q8C22×D312yes—
580C22×Q8C22×D311yescharacteristic
581C22×D4—32no—
582C22×D4—31no—
583C22×D4—31no—
584C22×D4—31no—
585C22×D4—32no—
586C22×D4—31no—
587C22×D4—32no—
588C22×D4—32no—
589C23×C4—31no—
590C23×C4—32no—
591C23×C4—31no—
592C23×C4—31no—
593C23×C4—31no—
594C23×C4—32no—
595C23×C4—32no—
596C23×C4—32no—
597C23×C4—31no—
598C23×C4—31no—
599C23×C4—64no—
600C23×C4—64no—
601C23×C4—122no—
602C23×C4C22×D312yes—
603C23×C4C22×D311yescharacteristic
604C4⋊Q8—24no—
605C4⋊Q8—42no—
606#124—68no—
607#124—64no—
608#123—68no—
609#123—68no—
610#123—68no—
611C22⋊Q8—24no—
612C22⋊Q8—38no—
613C22⋊Q8—68no—
614C22⋊Q8—68no—
615C22⋊Q8—64no—
616C22⋊Q8—68no—
617C22⋊Q8—64no—
618C22⋊Q8—64no—
619C22⋊Q8—64no—
620C22⋊Q8—64no—
621C22⋊Q8—64no—
622#121—38no—
623#121—68no—
624#121—64no—
625#121—68no—
626#120—68no—
627#120—64no—
628C4×Q8—64no—
629C4×D4—64no—
630C4×D4—64no—
631C4×D4—68no—
632C4×D4—68no—
633C4×D4—68no—
634C4×D4—64no—
635C4×D4—68no—
636C4×D4—122no—
637#117—64no—
638C2×C4⋊C4—32no—
639C2×C4⋊C4—31no—
640C2×C4⋊C4—31no—
641C2×C4⋊C4—31no—
642C2×C4⋊C4—32no—
643C2×C4⋊C4—31no—
644C2×C4⋊C4—32no—
645C2×C4⋊C4—32no—
646C2×C4⋊C4—32no—
647C2×C4⋊C4—32no—
648C2×C4⋊C4—32no—
649C2×C4⋊C4—31no—
650C2×C4⋊C4—32no—
651C2×C4⋊C4—32no—
652C2×C4⋊C4—32no—
653C2×C4⋊C4—31no—
654C2×C4⋊C4—32no—
655C2×C4⋊C4—68no—
656C2×C4⋊C4—68no—
657C2×C4⋊C4—64no—
658C2×C4⋊C4C22×D312yes—
659C2×C4⋊C4C22×D311yescharacteristic
660C2×C4⋊C4C22×D312yes—
661C2×C4⋊C4C22×D312yes—
662C2×C4⋊C4C22×D312yes—
663C2×C4⋊C4C22×D312yes—
664C2×C22⋊C4—32no—
665C2×C22⋊C4—32no—
666C2×C22⋊C4—31no—
667C2×C22⋊C4—32no—
668C2×C22⋊C4—32no—
669C2×C22⋊C4—32no—
670C2×C22⋊C4—32no—
671C2×C22⋊C4—32no—
672C2×C22⋊C4—32no—
673C2×C22⋊C4—31no—
674C2×C22⋊C4—31no—
675C2×C22⋊C4—32no—
676C2×C22⋊C4—32no—
677C2×C22⋊C4—31no—
678C2×C22⋊C4—32no—
679C2×C22⋊C4—31no—
680C2×C22⋊C4—31no—
681C2×C22⋊C4—32no—
682C2×C22⋊C4—32no—
683C2×C22⋊C4—32no—
684C2×C22⋊C4—31no—
685C2×C22⋊C4—31no—
686C2×C22⋊C4—31no—
687C2×C22⋊C4—31no—
688C2×C22⋊C4—32no—
689C2×C22⋊C4—32no—
690C2×C22⋊C4—68no—
691C2×C22⋊C4C22×D312yes—
692C2×C22⋊C4C22×D311yescharacteristic
693C2×C22⋊C4C22×D311yescharacteristic
694C2×C42—32no—
695C2×C42—31no—
696C2×C42—32no—
697C2×C42—32no—
698C2×C42C22×D311yescharacteristic
699C2×C42C22×D311yescharacteristic
700#95—31no—
701#95—31no—
702#95—31no—
703#95—31no—
704#95—32no—
705#95—32no—
706#95—32no—
707#95—32no—
708#95—32no—
709#95—32no—
710#95C22×D311yescharacteristic
711#95C22×D311yescharacteristic
712#95C22×D312yes—
713#95C22×D312yes—
714#95C22×D312yes—
715#95C22×D312yes—
716C23×C3—21no—
717C23×C3—21no—
718C23×C3—21no—
719C23×C3—21no—
720C23×C3C22×D412yes—
721C23×C3C2×#4112yes—
722C23×C32−1+412yes—
723C23×C3C2511yescharacteristic
724C22×D3—28no—
725C22×D3—21no—
726C22×D3—21no—
727C22×D3—21no—
728C22×D3—22no—
729C22×D3—22no—
730C22×D3—21no—
731C22×D3—21no—
732C22×D3—21no—
733C22×D3—21no—
734C22×D3—22no—
735C22×D3—22no—
736C22×D3—22no—
737C22×D3—21no—
738C22×D3—21no—
739C22×D3—21no—
740C22×D3—22no—
741C22×D3—21no—
742C22×D3—21no—
743C22×D3—21no—
744C22×D3—21no—
745C22×D3—21no—
746C22×D3—21no—
747C22×D3—21no—
748C22×D3—21no—
749C22×D3—21no—
750C22×D3—44no—
751C22×D3—44no—
752C22×D3—44no—
753C22×D3—44no—
754C22×D3—44no—
755C22×D3—44no—
756C22×D3C22×D412yes—
757C22×D3C22×D414yes—
758C22×D32−1+412yes—
759C3×Q8—28no—
760C3×Q8—48no—
761C3×Q8—44no—
762C3×Q8—44no—
763C2×C3×C4—22no—
764C2×C3×C4—21no—
765C2×C3×C4—21no—
766C2×C3×C4—21no—
767C2×C3×C4—21no—
768C2×C3×C4—22no—
769C2×C3×C4—21no—
770C2×C3×C4—21no—
771C2×C3×C4—28no—
772C2×C3×C4—22no—
773C2×C3×C4—22no—
774C2×C3×C4—22no—
775C2×C3×C4—22no—
776C2×C3×C4—22no—
777C2×C3×C4—21no—
778C2×C3×C4—21no—
779C2×C3×C4—22no—
780C2×C3×C4—22no—
781C2×C3×C4—21no—
782C2×C3×C4—21no—
783C2×C3×C4—21no—
784C2×C3×C4—22no—
785C2×C3×C4—22no—
786C2×C3×C4—21no—
787C2×C3×C4—48no—
788C2×C3×C4C22×D414yes—
789C2×C3×C4C22×D412yes—
790C2×C3×C4C22×D412yes—
791C2×C3×C4C22×D412yes—
792C2×C3×C4C2×#4112yes—
793C2×C3×C4C2×#4112yes—
794C2×C3×C4H(5,𝔽2)12yes—
795#67—216no—
796#67—44no—
797C2×Dic3—21no—
798C2×Dic3—22no—
799C2×Dic3—22no—
800C2×Dic3—21no—
801C2×Dic3—22no—
802C2×Dic3—22no—
803C2×Dic3—21no—
804C2×Dic3—21no—
805C2×Dic3—21no—
806C2×Dic3—21no—
807C2×Dic3—22no—
808C2×Dic3—21no—
809C2×Dic3—21no—
810C2×Dic3—22no—
811C2×Dic3—21no—
812C2×Dic3—21no—
813C2×Dic3—21no—
814C2×Dic3—21no—
815C2×Dic3—21no—
816C2×Dic3—21no—
817C2×Dic3—22no—
818C2×Dic3—44no—
819C2×Dic3—48no—
820C2×Dic3C22×D414yes—
821C2×Dic3C22×D412yes—
822C2×Dic3C22×D414yes—
823D12—28no—
824D12—44no—
825D12—44no—
826D12—48no—
827D12—48no—
828D12—48no—
829C4×D3—28no—
830C4×D3—48no—
831C4×D3—44no—
832C4×D3—48no—
833C4×D3—44no—
834C4×D3—48no—
835C4×D3—44no—
836C4×D3—44no—
837C24—31no—
838C24—31no—
839C24—32no—
840C24—31no—
841C24—62no—
842C24—62no—
843C24—62no—
844C24—62no—
845C24—62no—
846C24—121no—
847C24—121no—
848C24C23×D311yescharacteristic
849#41—1216no—
850#41—1216no—
851C2×Q8—22no—
852C2×Q8—22no—
853C2×Q8—24no—
854C2×Q8—22no—
855C2×Q8—24no—
856C2×Q8—22no—
857C2×Q8—22no—
858C2×Q8—22no—
859C2×Q8—22no—
860C2×Q8—22no—
861C2×Q8—42no—
862C2×Q8—416no—
863C2×Q8D3×D414yes—
864C2×D4—38no—
865C2×D4—34no—
866C2×D4—64no—
867C2×D4—62no—
868C2×D4—64no—
869C2×D4—64no—
870C2×D4—64no—
871C2×D4—62no—
872C2×D4—64no—
873C2×D4—64no—
874C2×D4—64no—
875C2×D4—62no—
876C2×D4—62no—
877C2×D4—62no—
878C2×D4—62no—
879C2×D4—64no—
880C2×D4—62no—
881C2×D4—62no—
882C2×D4—62no—
883C2×D4—121no—
884C2×D4—122no—
885C2×D4—122no—
886C2×D4—121no—
887C2×D4—122no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—24no—
891C22×C4—24no—
892C22×C4—32no—
893C22×C4—31no—
894C22×C4—32no—
895C22×C4—34no—
896C22×C4—31no—
897C22×C4—31no—
898C22×C4—32no—
899C22×C4—31no—
900C22×C4—31no—
901C22×C4—42no—
902C22×C4—64no—
903C22×C4—64no—
904C22×C4—62no—
905C22×C4—64no—
906C22×C4—64no—
907C22×C4—62no—
908C22×C4—64no—
909C22×C4—62no—
910C22×C4—62no—
911C22×C4—62no—
912C22×C4—62no—
913C22×C4—64no—
914C22×C4—64no—
915C22×C4—62no—
916C22×C4—62no—
917C22×C4—62no—
918C22×C4—62no—
919C22×C4—62no—
920C22×C4—62no—
921C22×C4—62no—
922C22×C4—62no—
923C22×C4—64no—
924C22×C4—121no—
925C22×C4—121no—
926C22×C4—122no—
927C22×C4—122no—
928C22×C4—122no—
929C22×C4—1216no—
930C22×C4—121no—
931C22×C4—122no—
932C22×C4D3×D414yes—
933C22×C4C23×D311yescharacteristic
934C22×C4C23×D311yescharacteristic
935C22×C4C23×D312yes—
936C22×C4C23×D312yes—
937C22×C4C23×D312yes—
938C22×C4C23×D312yes—
939C22×C4C23×D311yescharacteristic
940C22×C4C23×D311yescharacteristic
941C22×C4C23×D311yescharacteristic
942C22×C4C23×D311yescharacteristic
943C4⋊C4—24no—
944C4⋊C4—22no—
945C4⋊C4—24no—
946C4⋊C4—24no—
947C4⋊C4—38no—
948C4⋊C4—34no—
949C4⋊C4—34no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—62no—
953C4⋊C4—64no—
954C4⋊C4—64no—
955C4⋊C4—64no—
956C4⋊C4—64no—
957C4⋊C4—64no—
958C4⋊C4—64no—
959C4⋊C4—64no—
960C4⋊C4—64no—
961C4⋊C4—62no—
962C4⋊C4—62no—
963C4⋊C4—64no—
964C4⋊C4—121no—
965C4⋊C4—122no—
966C22⋊C4—24no—
967C22⋊C4—22no—
968C22⋊C4—38no—
969C22⋊C4—38no—
970C22⋊C4—64no—
971C22⋊C4—64no—
972C22⋊C4—64no—
973C22⋊C4—64no—
974C22⋊C4—62no—
975C22⋊C4—64no—
976C22⋊C4—64no—
977C22⋊C4—64no—
978C22⋊C4—64no—
979C22⋊C4—62no—
980C22⋊C4—64no—
981C22⋊C4—64no—
982C22⋊C4—62no—
983C22⋊C4—62no—
984C22⋊C4—64no—
985C22⋊C4—62no—
986C22⋊C4—64no—
987C22⋊C4—62no—
988C22⋊C4—62no—
989C22⋊C4—121no—
990C22⋊C4—121no—
991C22⋊C4—122no—
992C22⋊C4—121no—
993C22⋊C4—122no—
994C22⋊C4#23914yescomplemented
995C42—22no—
996C42—22no—
997C42—64no—
998C42—64no—
999C42—62no—
1000C42—64no—
1001C22×C3—22no—
1002C22×C3—22no—
1003C22×C3—22no—
1004C22×C3—22no—
1005C22×C3—22no—
1006C22×C3—22no—
1007C22×C3#54714yescomplemented
1008C22×C3C23×D411yescharacteristic
1009C22×C3C23×D411yescharacteristic
1010C22×C3C22×#4111yescharacteristic
1011C22×C3C2×H(5,𝔽2)11yescharacteristic
1012C22×C3C2×2−1+411yescharacteristic
1013C22×C3C2×2−1+411yescharacteristic
1014C22×C3#58511yescharacteristic
1015C2×D3—22no—
1016C2×D3—24no—
1017C2×D3—24no—
1018C2×D3—22no—
1019C2×D3—22no—
1020C2×D3—22no—
1021C2×D3—22no—
1022C2×D3—24no—
1023C2×D3—22no—
1024C2×D3—416no—
1025C2×D3—41no—
1026C2×D3—41no—
1027C2×D3—41no—
1028C2×D3—42no—
1029C2×D3—41no—
1030C2×D3—42no—
1031C2×D3—41no—
1032C2×D3—42no—
1033C2×D3—41no—
1034C2×D3—42no—
1035C2×D3—41no—
1036C2×D3—41no—
1037C2×D3—41no—
1038C2×D3—41no—
1039C2×D3—41no—
1040C2×D3—41no—
1041C2×D3—41no—
1042C2×D3—41no—
1043C2×D3—41no—
1044C3×C4—22no—
1045C3×C4—24no—
1046C3×C4—22no—
1047C3×C4—22no—
1048C3×C4—42no—
1049C3×C4—42no—
1050C3×C4—41no—
1051C3×C4—42no—
1052C3×C4—41no—
1053C3×C4D4214yes—
1054Dic3—22no—
1055Dic3—24no—
1056Dic3—24no—
1057Dic3—41no—
1058Dic3—41no—
1059Dic3—41no—
1060Dic3—42no—
1061Dic3—41no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—32no—
1067C23—34no—
1068C23—32no—
1069C23—68no—
1070C23—61no—
1071C23—61no—
1072C23—61no—
1073C23—62no—
1074C23—61no—
1075C23—61no—
1076C23—62no—
1077C23—62no—
1078C23—61no—
1079C23—61no—
1080C23—62no—
1081C23—61no—
1082C23—61no—
1083C23—62no—
1084C23—61no—
1085C23—62no—
1086C23—61no—
1087C23—61no—
1088C23—61no—
1089C23—61no—
1090C23—61no—
1091C23—61no—
1092C23—61no—
1093C23—61no—
1094C23—61no—
1095C23—124no—
1096C23—124no—
1097C23—124no—
1098C23—124no—
1099C23—124no—
1100C23—124no—
1101C23C2×D3×D412yes—
1102C23C2×#23912yes—
1103C23#100712yes—
1104C23C24×D311yescharacteristic
1105Q8—28no—
1106Q8—48no—
1107Q8—44no—
1108Q8—44no—
1109D4—616no—
1110D4—68no—
1111D4—128no—
1112D4—124no—
1113D4—124no—
1114D4—128no—
1115D4—128no—
1116D4—124no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—22no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—28no—
1126C2×C4—21no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—21no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—22no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—34no—
1142C2×C4—34no—
1143C2×C4—32no—
1144C2×C4—48no—
1145C2×C4—61no—
1146C2×C4—61no—
1147C2×C4—62no—
1148C2×C4—62no—
1149C2×C4—62no—
1150C2×C4—62no—
1151C2×C4—68no—
1152C2×C4—61no—
1153C2×C4—61no—
1154C2×C4—62no—
1155C2×C4—61no—
1156C2×C4—61no—
1157C2×C4—61no—
1158C2×C4—61no—
1159C2×C4—61no—
1160C2×C4—61no—
1161C2×C4—61no—
1162C2×C4—62no—
1163C2×C4—61no—
1164C2×C4—61no—
1165C2×C4—62no—
1166C2×C4—61no—
1167C2×C4—124no—
1168C2×C4—128no—
1169C2×C4—124no—
1170C2×C4—128no—
1171C2×C4—128no—
1172C2×C4—124no—
1173C2×C4—128no—
1174C2×C4—124no—
1175C2×C4—124no—
1176C2×C4C2×D3×D412yes—
1177C2×C4C2×D3×D414yes—
1178C2×C4C2×D3×D412yes—
1179C2×C4C2×D3×D412yes—
1180C2×C4#100412yes—
1181C2×C4C2×#23912yes—
1182C2×C4C2×#23912yes—
1183C2×C3—24no—
1184C2×C3C2×D4211yescharacteristic
1185C2×C3C2×#54711yescharacteristic
1186C2×C3D4×#4111yescharacteristic
1187C2×C3#348611yescharacteristic
1188C2×C3#348911yescharacteristic
1189C2×C3#352011yescharacteristic
1190C2×C3#354111yescharacteristic
1191D3—44no—
1192D3—42no—
1193D3—42no—
1194D3—81no—
1195C22—22no—
1196C22—22no—
1197C22—22no—
1198C22—22no—
1199C22—22no—
1200C22—22no—
1201C22—62no—
1202C22—64no—
1203C22—62no—
1204C22—64no—
1205C22—64no—
1206C22—62no—
1207C22—62no—
1208C22—62no—
1209C22—62no—
1210C22—1216no—
1211C22—121no—
1212C22—121no—
1213C22—121no—
1214C22—121no—
1215C22—122no—
1216C22—121no—
1217C22—121no—
1218C22—122no—
1219C22—121no—
1220C22—121no—
1221C22—122no—
1222C22—122no—
1223C22—121no—
1224C22—121no—
1225C22—121no—
1226C22—121no—
1227C22—121no—
1228C22—121no—
1229C22—121no—
1230C22#572614yescomplemented
1231C22C22×D3×D411yescharacteristic
1232C22C22×D3×D411yescharacteristic
1233C22C2×#100411yescharacteristic
1234C22C22×#23911yescharacteristic
1235C22C2×#100711yescharacteristic
1236C22D3×2−1+411yescharacteristic
1237C22#596811yescharacteristic
1238C4—22no—
1239C4—24no—
1240C4—22no—
1241C4—22no—
1242C4—42no—
1243C4—42no—
1244C4—42no—
1245C4—41no—
1246C4—41no—
1247C4—62no—
1248C4—64no—
1249C4—64no—
1250C4—121no—
1251C4—121no—
1252C4—121no—
1253C4—121no—
1254C4—122no—
1255C4#559014yes—
1256C3#5900211yescharacteristic, complemented, Sylow
1257C2—24no—
1258C2—122no—
1259C2—122no—
1260C2—124no—
1261C2—241no—
1262C2C2×#559011yescharacteristic
1263C2C2×#572611yescharacteristic
1264C2#8635611yescharacteristic
1265C2D4×#23911yescharacteristic
1266C2#8675111yescharacteristic
1267C2#8675411yescharacteristic
1268C2#8675911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2434C2
hypercenter#2434D3
hypocenterC3#59002
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2434

Complements

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

NH ≅ G/Ntype
1. C2×#5817C2semidirect
2. C22×#946C2semidirect
3. C2×#5726C2semidirect
4. C2×#5627C2semidirect
5. C3×#2434C2semidirect
6. #83259C2semidirect
7. #83255C2semidirect
8. #83254C2semidirect
9. #82815C2semidirect
10. #77262C2semidirect
11. #77259C2semidirect
12. #77252C2semidirect
13. #77176C2semidirect
14. #76624C2semidirect
15. #76620C2semidirect
16. #76618C2semidirect
17. #76491C2semidirect
18. #74605C2semidirect
19. #74603C2semidirect
20. #74418C2semidirect
21. #74393C2semidirect
22. C4×#882C2semidirect
23. #73467C2semidirect
27. C22×#239C22semidirect
29. C2×C3×C4⋊Q8C22semidirect
30. C2×C3×C4⋊Q8C22semidirect
33. C2×#947C22semidirect
34. C2×#947C22semidirect
43. C2×#946C22semidirect
44. C2×#946C22semidirect
45. C2×#946C22semidirect
46. C2×Q8×Dic3C22semidirect
60. C2×#894C22semidirect
63. C2×D3×C4⋊C4C22semidirect
70. C2×C4×D12C22semidirect
71. C3×#395C22semidirect
72. C3×#395C22semidirect
73. C3×#391C22semidirect
74. C3×#391C22semidirect
78. #5229C22semidirect
80. #4994C22semidirect
82. #4993C22semidirect
86. #4989C22semidirect
87. #4989C22semidirect
89. #4987C22semidirect
90. #4982C22semidirect
91. #4982C22semidirect
92. #4976C22semidirect
93. #4975C22semidirect
94. #4972C22semidirect
101. #4939C22semidirect
104. C4×C4⋊Dic3C22semidirect
105. #4928C22semidirect
107. #4675C22semidirect
110. #4672C22semidirect
113. #4670C22semidirect
115. #4669C22semidirect
118. #4668C22semidirect
119. #4668C22semidirect
120. #4667C22semidirect
125. #4655C22semidirect
126. #4649C22semidirect
127. #4647C22semidirect
138. #2434D3semidirect
214. #946D4semidirect
217. #930D4semidirect
306. C2×C4⋊Q8C2×D3semidirect
307. C2×C4⋊Q8C2×D3semidirect
354. #395C2×D3semidirect
355. #395C2×D3semidirect
363. #391C2×D3semidirect
364. #391C2×D3semidirect
517. C3×C22⋊C4#41semidirect
994. C22⋊C4#239semidirect
1007. C22×C3#547semidirect
1230. C22#5726semidirect
1256. C3#59002semidirect

Maximal subgroups

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

subgroupindex
C2×#58172
C22×#9462
C2×#57262
C2×#56272
C3×#24342
#832592
#832552
#832542
#828152
#772622
#772592
#772522
#771762
#766242
#766202
#766182
#764912
#746052
#746032
#744182
#743932
C4×#8822
#734672
#590023