Finite Group Databasebeta

← #11001978

Subgroups — #11001978

Order 768.

3038 conjugacy classes of subgroups.

The subgroup lattice has 1272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5560C211yesmaximal, characteristic, complemented
2C22×#895C211yesmaximal, characteristic, complemented
3C3×#2579C211yesmaximal, characteristic, complemented
4#82403C211yesmaximal, characteristic, complemented
5#82198C211yesmaximal, characteristic, complemented
6#77967C212yesmaximal, complemented
7#77847C212yesmaximal, complemented
8#77429C212yesmaximal, complemented
9#77428C212yesmaximal, complemented
10#75389C212yesmaximal, complemented
11#75150C212yesmaximal, complemented
12#74935C211yesmaximal, characteristic, complemented
13#74905C211yesmaximal, characteristic, complemented
14#74887C211yesmaximal, characteristic, complemented
15#74887C211yesmaximal, characteristic, complemented
16#74655C211yesmaximal, characteristic, complemented
17#74630C212yesmaximal, complemented
18#74627C212yesmaximal, complemented
19#74621C211yesmaximal, characteristic, complemented
20#74601C211yesmaximal, characteristic, complemented
21#74601C211yesmaximal, characteristic, complemented
22#74016C211yesmaximal, characteristic, complemented
23#74005C211yesmaximal, characteristic, complemented
24#36706—31nomaximal, Sylow
25C23×D12C2211yescharacteristic
26C23×D12C2211yescharacteristic
27C23×D12C2211yescharacteristic
28C23×C4×D3C2211yescharacteristic
29C2×C3×C4×D4C2211yescharacteristic
30C22×C3×C4⋊C4C2211yescharacteristic
31C2×#939C2211yescharacteristic
32C2×#937C2211yescharacteristic
33C2×#937C2211yescharacteristic
34C2×#937C2211yescharacteristic
35C2×#930C2211yescharacteristic, complemented
36C2×#930C2212yescomplemented
37C2×#929C2211yescharacteristic, complemented
38C2×C4×#67C2211yescharacteristic
39C22×(C2×D3)⋊C4C2211yescharacteristic
40C22×(C2×D3)⋊C4C2211yescharacteristic
41#5560—28no—
42C2×#898C2211yescharacteristic, complemented
43C2×#896C2212yescomplemented
44C2×#895—28no—
45C2×#895C2212yes—
46C2×#895C2212yes—
47C2×#895C2212yes—
48C2×#895C2212yes—
49C2×#895C2212yescomplemented
50C2×#895C2212yescomplemented
51C2×#895C2212yescomplemented
52C2×#894C2211yescharacteristic, complemented
53C2×#885C2211yescharacteristic, complemented
54C2×#884C2211yescharacteristic, complemented
55C2×#884C2212yescomplemented
56C2×#884C2212yescomplemented
57C2×#884C2212yescomplemented
58C2×#882C2211yescharacteristic
59C2×#882C2211yescharacteristic
60C2×#882C2211yescharacteristic
61C2×D3×C22⋊C4C2211yescharacteristic
62C2×D3×C22⋊C4C2211yescharacteristic
63C2×#878C2211yescharacteristic
64C2×#876C2211yescharacteristic, complemented
65C2×#875C2211yescharacteristic, complemented
66C3×#398C2212yescomplemented
67C3×#396C2212yescomplemented
68C3×#387C2212yescomplemented
69C3×#386C2211yescharacteristic
70C3×#386C2211yescharacteristic
71C3×#385C2211yescharacteristic
72C3×#385C2211yescharacteristic
73C3×#385C2212yescomplemented
74C3×#380C2211yescharacteristic
75#5213C2211yescharacteristic
76#5213C2211yescharacteristic
77#5212C2211yescharacteristic
78#5210C2211yescharacteristic
79#5210C2211yescharacteristic
80#4994C2212yescomplemented
81#4994C2212yescomplemented
82#4993C2212yescomplemented
83#4991C2212yescomplemented
84#4991C2212yescomplemented
85#4991C2212yescomplemented
86#4989C2212yescomplemented
87#4989C2212yescomplemented
88#4989C2212yescomplemented
89#4989C2212yescomplemented
90#4988C2212yescomplemented
91#4982C2212yescomplemented
92#4978C2212yescomplemented
93#4960C2212yescomplemented
94#4960C2212yescomplemented
95#4960C2212yescomplemented
96#4960C2212yescomplemented
97#4959C2212yescomplemented
98#4956C2212yescomplemented
99#4955C2211yescharacteristic
100#4955C2211yescharacteristic
101#4955C2211yescharacteristic
102#4955C2211yescharacteristic
103#4942C2211yescharacteristic
104#4942C2211yescharacteristic
105#4939C2212yescomplemented
106#4676C2212yescomplemented
107#4675C2212yescomplemented
108#4673C2212yescomplemented
109#4672C2212yescomplemented
110#4672C2212yescomplemented
111#4672C2212yescomplemented
112#4672C2212yescomplemented
113#4671C2212yescomplemented
114#4671C2212yescomplemented
115#4671C2212yescomplemented
116#4668C2212yescomplemented
117#4668C2212yescomplemented
118#4668C2212yescomplemented
119#4667C2212yescomplemented
120#4667C2212yescomplemented
121#4665C2212yescomplemented
122#4665C2212yescomplemented
123#4665C2212yescomplemented
124#4665C2212yescomplemented
125#4665C2212yescomplemented
126C2×#538—31no—
127C22×#121—31no—
128#2848—31no—
129#2847—31no—
130#2691—32no—
131#2691—32no—
132#2676—32no—
133#2676—32no—
134#2675—32no—
135#2675—32no—
136#2671—32no—
137#2671—32no—
138#2626—31no—
139#2617—31no—
140#2579—31no—
141#2579D311yescharacteristic, complemented
142#2410—31no—
143#2410—31no—
144#2410—31no—
145#2410—31no—
146#2408—31no—
147#2408—31no—
148#2315—31no—
149C24×D3C2311yescharacteristic
150C24×D3C2311yescharacteristic
151C24×D3C2311yescharacteristic
152C22×C3×D4C2311yescharacteristic
153C23×C3×C4C2311yescharacteristic
154C23×C3×C4C2311yescharacteristic
155C23×C3×C4C2311yescharacteristic
156C23×C3×C4C2311yescharacteristic
157C22×#67C2311yescharacteristic
158C22×#67C2312yes—
159C22×#67C2311yescharacteristic
160C22×#67C2311yescharacteristic
161C22×#67C2311yescharacteristic
162C22×#67C2312yes—
163C23×Dic3C2311yescharacteristic
164C22×D12—24no—
165C22×D12—24no—
166C22×D12—24no—
167C22×D12—44no—
168C22×D12—44no—
169C22×D12—44no—
170C22×D12C2312yes—
171C22×D12C2312yes—
172C22×D12C2312yes—
173C22×D12C2312yes—
174C22×D12C2312yes—
175C22×D12C2312yes—
176C22×D12C2312yes—
177C22×D12C2311yescharacteristic
178C22×D12C2311yescharacteristic
179C22×D12C2312yes—
180C22×C4×D3—24no—
181C22×C4×D3—44no—
182C22×C4×D3C2312yes—
183C22×C4×D3C2312yes—
184C22×C4×D3C2311yescharacteristic
185C22×C4×D3C2312yes—
186C22×C4×D3C2312yes—
187C22×Dic6C2311yescharacteristic
188C3×C4×D4—24no—
189C2×C3×C4⋊C4—24no—
190C2×C3×C4⋊C4C2312yes—
191C2×C3×C4⋊C4C2312yes—
192C2×C3×C4⋊C4C2312yes—
193C2×C3×C4⋊C4C2311yescharacteristic
194C2×C3×C4⋊C4C2312yes—
195C2×C3×C4⋊C4C2312yes—
196C2×C3×C22⋊C4C2311yescharacteristic
197C2×C3×C22⋊C4C2311yescharacteristic
198C2×C3×C22⋊C4C2311yescharacteristic
199C2×C3×C22⋊C4C2312yes—
200C2×C3×C22⋊C4C2311yescharacteristic
201C2×C3×C22⋊C4C2312yes—
202C2×C3×C42C2311yescharacteristic
203C2×#217C2311yescharacteristic
204C2×#217C2311yescharacteristic
205C2×#217C2311yescharacteristic
206C2×#217C2311yescharacteristic
207#939—24no—
208#937—24no—
209#937—42no—
210#937—42no—
211#930—24no—
212#930—44no—
213#929—24no—
214C4×#67—24no—
215C2×(C2×D3)⋊C4—24no—
216C2×(C2×D3)⋊C4D418yescomplemented
217C2×(C2×D3)⋊C4C2311yescharacteristic
218C2×(C2×D3)⋊C4C2311yescharacteristic
219C2×(C2×D3)⋊C4C2311yescharacteristic
220C2×(C2×D3)⋊C4C2311yescharacteristic
221C2×(C2×D3)⋊C4C2311yescharacteristic
222C2×(C2×D3)⋊C4C2312yes—
223C2×(C2×D3)⋊C4C2312yes—
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)⋊C4C2312yes—
231C2×(C2×D3)⋊C4C2312yes—
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)⋊C4C2312yes—
240C2×(C2×D3)⋊C4C2312yes—
241C2×(C2×D3)⋊C4C2311yescharacteristic
242C2×(C2×D3)⋊C4C2311yescharacteristic
243C2×(C2×D3)⋊C4C2311yescharacteristic
244C2×(C2×D3)⋊C4C2311yescharacteristic
245C2×C4⋊Dic3C2311yescharacteristic
246C2×C4⋊Dic3C2312yes—
247C2×Dic3⋊C4C2311yescharacteristic
248C2×Dic3⋊C4C2311yescharacteristic
249C2×Dic3⋊C4C2312yes—
250C2×Dic3⋊C4C2311yescharacteristic
251C2×Dic3⋊C4C2311yescharacteristic
252C2×Dic3⋊C4C2312yes—
253C2×Dic3⋊C4C2312yes—
254C2×Dic3⋊C4C2312yes—
255C2×C4×Dic3C2311yescharacteristic
256#898—24no—
257#896—44no—
258#895—28no—
259#895—28no—
260#895—28no—
261#895—28no—
262#895—44no—
263#895—44no—
264#895—44no—
265#894—24no—
266#885—24no—
267#884—24no—
268#884—44no—
269#884—44no—
270#884—44no—
271#882—24no—
272#882—42no—
273#882—42no—
274D3×C22⋊C4—42no—
275D3×C22⋊C4—42no—
276#878—24no—
277#876—24no—
278#875—24no—
279C3×#95C2312yes—
280C3×#95C2312yes—
281C3×#95C2312yes—
282C3×#95C2312yes—
283C3×#95C2312yes—
284C3⋊#95C2312yes—
285C3⋊#95C2312yes—
286C3⋊#95C2312yes—
287C3⋊#95C2312yes—
288C3⋊#95C2312yes—
289C3⋊#95C2312yes—
290C3⋊#95C2312yes—
291C23×D4—31no—
292C23×D4—31no—
293C23×D4—31no—
294C24×C4—31no—
295#538—68no—
296C2×#126—31no—
297C2×#126—31no—
298C2×#124—31no—
299C2×#124—31no—
300C2×#123—31no—
301C2×#123—31no—
302C2×C22⋊Q8—32no—
303C2×C22⋊Q8—31no—
304C2×#121—31no—
305C2×#121—31no—
306C2×#121—32no—
307C2×#121—32no—
308C2×#121—32no—
309C2×#121—32no—
310C2×#121—32no—
311C2×#121—32no—
312C2×#121—32no—
313C2×#121—32no—
314C2×#121—31no—
315C2×#121—32no—
316C2×#121—32no—
317C2×#121—32no—
318C2×#121—68no—
319C2×#120—31no—
320C2×#120—31no—
321C2×#120—31no—
322C2×#120—31no—
323C2×#120—31no—
324C2×#120—31no—
325C2×C4×D4—31no—
326C2×C4×D4C2×D311yescharacteristic
327C22×C4⋊C4C2×D311yescharacteristic
328C22×C22⋊C4—31no—
329C22×C22⋊C4—31no—
330C22×C22⋊C4—31no—
331C22×C22⋊C4—31no—
332#399—32no—
333#398—32no—
334#398C2×D312yescomplemented
335#397—32no—
336#396—32no—
337#396—32no—
338#396—32no—
339#396C2×D312yescomplemented
340#394—32no—
341#394—32no—
342#394—32no—
343#394—32no—
344#394—32no—
345#394—32no—
346#394—32no—
347#394—32no—
348#393—32no—
349#392—32no—
350#392—32no—
351#392—32no—
352#392—32no—
353#392—32no—
354#392—32no—
355#392—32no—
356#390—32no—
357#390—32no—
358#387—32no—
359#387C2×D312yescomplemented
360#386—31no—
361#386—31no—
362#386—32no—
363#386—32no—
364#386—32no—
365#386—32no—
366#386—32no—
367#386—32no—
368#386C2×D311yescharacteristic
369#386C2×D311yescharacteristic
370#385—31no—
371#385—31no—
372#385—32no—
373#385—32no—
374#385—32no—
375#385—32no—
376#385—32no—
377#385—32no—
378#385—32no—
379#385C2×D311yescharacteristic
380#385C2×D311yescharacteristic
381#385C2×D312yescomplemented
382#380—31no—
383#380—31no—
384#380—31no—
385#380—32no—
386#380—32no—
387#380C2×D311yescharacteristic
388#379—31no—
389#379—31no—
390#379—31no—
391#379—31no—
392C24×C3C2411yescharacteristic
393C24×C3C2411yescharacteristic
394C23×D3—22no—
395C23×D3—22no—
396C23×D3—22no—
397C23×D3—24no—
398C23×D3—22no—
399C23×D3—22no—
400C23×D3—22no—
401C23×D3—22no—
402C23×D3—22no—
403C23×D3—42no—
404C23×D3—42no—
405C23×D3—42no—
406C23×D3—42no—
407C23×D3—42no—
408C23×D3C2×D414yes—
409C23×D3C2412yes—
410C23×D3C2411yescharacteristic
411C23×D3C2411yescharacteristic
412C23×D3C2411yescharacteristic
413C23×D3C2412yes—
414C2×C3×D4—22no—
415C2×C3×D4—22no—
416C2×C3×D4—22no—
417C22×C3×C4—22no—
418C22×C3×C4—24no—
419C22×C3×C4—22no—
420C22×C3×C4—22no—
421C22×C3×C4—42no—
422C22×C3×C4—42no—
423C22×C3×C4—42no—
424C22×C3×C4C2×D414yes—
425C22×C3×C4C2412yes—
426C22×C3×C4C2412yes—
427C22×C3×C4C2412yes—
428C22×C3×C4C2411yescharacteristic
429C22×C3×C4C2411yescharacteristic
430C22×C3×C4C2411yescharacteristic
431C22×C3×C4C2411yescharacteristic
432C22×C3×C4C2411yescharacteristic
433C22×C3×C4C2412yes—
434C2×#67—22no—
435C2×#67—22no—
436C2×#67—22no—
437C2×#67—22no—
438C2×#67—22no—
439C2×#67—24no—
440C2×#67—22no—
441C2×#67—42no—
442C2×#67—42no—
443C2×#67—42no—
444C2×#67—42no—
445C2×#67—42no—
446C2×#67—42no—
447C2×#67—42no—
448C2×#67—42no—
449C22×Dic3—42no—
450C22×Dic3C2×D414yes—
451C22×Dic3C2411yescharacteristic
452C22×Dic3C2412yes—
453C22×Dic3C2412yes—
454C22×Dic3C2411yescharacteristic
455C22×Dic3C2411yescharacteristic
456C22×Dic3C2411yescharacteristic
457C22×Dic3C2411yescharacteristic
458C2×D12—24no—
459C2×D12—24no—
460C2×D12—24no—
461C2×D12—24no—
462C2×D12—24no—
463C2×D12—24no—
464C2×D12—24no—
465C2×D12—24no—
466C2×D12—24no—
467C2×D12—24no—
468C2×D12—24no—
469C2×D12—24no—
470C2×D12—22no—
471C2×D12—22no—
472C2×D12—24no—
473C2×D12—42no—
474C2×D12—42no—
475C2×D12—42no—
476C2×D12—42no—
477C2×D12—42no—
478C2×D12—42no—
479C2×D12—416no—
480C2×D12—416no—
481C2×D12—416no—
482C2×D12—42no—
483C2×D12—42no—
484C2×D12—42no—
485C2×D12—42no—
486C2×D12—42no—
487C2×D12—42no—
488C2×D12—42no—
489C2×C4×D3—24no—
490C2×C4×D3—24no—
491C2×C4×D3—24no—
492C2×C4×D3—24no—
493C2×C4×D3—22no—
494C2×C4×D3—42no—
495C2×C4×D3—42no—
496C2×C4×D3—416no—
497C2×C4×D3—42no—
498C2×C4×D3—42no—
499C2×C4×D3—42no—
500C2×C4×D3—42no—
501C2×C4×D3—42no—
502C2×C4×D3—42no—
503C2×C4×D3—42no—
504C2×Dic6—22no—
505C2×Dic6—42no—
506C3×C4⋊C4—22no—
507C3×C4⋊C4—24no—
508C3×C4⋊C4—24no—
509C3×C4⋊C4—24no—
510C3×C4⋊C4—42no—
511C3×C4⋊C4—42no—
512C3×C22⋊C4—22no—
513C3×C22⋊C4—22no—
514C3×C22⋊C4—22no—
515C3×C22⋊C4—22no—
516C3×C22⋊C4—24no—
517C3×C22⋊C4—42no—
518C3×C42—22no—
519#217—22no—
520#217—22no—
521#217—22no—
522#217—22no—
523(C2×D3)⋊C4—22no—
524(C2×D3)⋊C4—22no—
525(C2×D3)⋊C4—22no—
526(C2×D3)⋊C4—22no—
527(C2×D3)⋊C4—24no—
528(C2×D3)⋊C4—24no—
529(C2×D3)⋊C4—22no—
530(C2×D3)⋊C4—24no—
531(C2×D3)⋊C4—22no—
532(C2×D3)⋊C4—24no—
533(C2×D3)⋊C4—24no—
534(C2×D3)⋊C4—42no—
535(C2×D3)⋊C4—42no—
536(C2×D3)⋊C4—42no—
537(C2×D3)⋊C4—42no—
538(C2×D3)⋊C4—42no—
539(C2×D3)⋊C4—42no—
540(C2×D3)⋊C4—42no—
541(C2×D3)⋊C4—42no—
542(C2×D3)⋊C4—42no—
543(C2×D3)⋊C4—42no—
544(C2×D3)⋊C4—42no—
545(C2×D3)⋊C4—42no—
546(C2×D3)⋊C4—42no—
547(C2×D3)⋊C4C2×D414yes—
548(C2×D3)⋊C4C2×D414yes—
549(C2×D3)⋊C4C2×D414yes—
550(C2×D3)⋊C4C2×D414yes—
551C4⋊Dic3—22no—
552C4⋊Dic3—42no—
553Dic3⋊C4—22no—
554Dic3⋊C4—24no—
555Dic3⋊C4—22no—
556Dic3⋊C4—22no—
557Dic3⋊C4—22no—
558Dic3⋊C4—42no—
559Dic3⋊C4—42no—
560Dic3⋊C4—42no—
561C4×Dic3—22no—
562C25—31no—
563C25—31no—
564C25—31no—
565C22×Q8—31no—
566C22×D4—31no—
567C22×D4—31no—
568C22×D4—31no—
569C22×D4—32no—
570C22×D4—31no—
571C22×D4—32no—
572C22×D4—32no—
573C22×D4—32no—
574C22×D4—32no—
575C22×D4—32no—
576C22×D4—32no—
577C22×D4—32no—
578C22×D4—31no—
579C22×D4—31no—
580C22×D4—32no—
581C22×D4—32no—
582C22×D4—64no—
583C22×D4—64no—
584C22×D4—64no—
585C22×D4—124no—
586C22×D4—124no—
587C22×D4—124no—
588C22×D4C22×D311yescharacteristic
589C23×C4—31no—
590C23×C4—32no—
591C23×C4—32no—
592C23×C4—31no—
593C23×C4—32no—
594C23×C4—32no—
595C23×C4—64no—
596C23×C4—124no—
597C23×C4C22×D311yescharacteristic
598C23×C4C22×D311yescharacteristic
599C23×C4C22×D311yescharacteristic
600C23×C4C22×D311yescharacteristic
601#126—64no—
602#126—64no—
603#124—64no—
604#124—64no—
605#123—64no—
606#123—64no—
607C22⋊Q8—64no—
608C22⋊Q8—124no—
609#121—64no—
610#121—68no—
611#121—68no—
612#121—68no—
613#121—68no—
614#121—64no—
615#121—64no—
616#121—124no—
617#121—124no—
618#121—124no—
619#121—124no—
620#121—124no—
621#121—124no—
622#121—124no—
623#120—64no—
624#120—64no—
625#120—122no—
626#120—122no—
627#120—122no—
628#120—122no—
629C4×D4—24no—
630C4×D4—64no—
631C2×C4⋊C4—24no—
632C2×C4⋊C4—31no—
633C2×C4⋊C4—31no—
634C2×C4⋊C4—31no—
635C2×C4⋊C4—32no—
636C2×C4⋊C4—31no—
637C2×C4⋊C4—31no—
638C2×C4⋊C4—32no—
639C2×C4⋊C4—32no—
640C2×C4⋊C4—32no—
641C2×C4⋊C4—32no—
642C2×C4⋊C4C22×D312yes—
643C2×C4⋊C4C22×D312yes—
644C2×C4⋊C4C22×D311yescharacteristic
645C2×C4⋊C4C22×D312yes—
646C2×C4⋊C4C22×D312yes—
647C2×C4⋊C4C22×D312yes—
648C2×C22⋊C4—38no—
649C2×C22⋊C4—31no—
650C2×C22⋊C4—31no—
651C2×C22⋊C4—31no—
652C2×C22⋊C4—31no—
653C2×C22⋊C4—31no—
654C2×C22⋊C4—31no—
655C2×C22⋊C4—31no—
656C2×C22⋊C4—31no—
657C2×C22⋊C4—32no—
658C2×C22⋊C4—32no—
659C2×C22⋊C4—31no—
660C2×C22⋊C4—31no—
661C2×C22⋊C4—31no—
662C2×C22⋊C4—31no—
663C2×C22⋊C4—31no—
664C2×C22⋊C4—32no—
665C2×C22⋊C4—32no—
666C2×C22⋊C4—32no—
667C2×C22⋊C4—31no—
668C2×C22⋊C4—32no—
669C2×C22⋊C4—32no—
670C2×C22⋊C4—32no—
671C2×C22⋊C4—32no—
672C2×C22⋊C4—32no—
673C2×C22⋊C4—32no—
674C2×C22⋊C4—32no—
675C2×C22⋊C4—32no—
676C2×C22⋊C4—32no—
677C2×C22⋊C4—32no—
678C2×C22⋊C4—32no—
679C2×C22⋊C4—32no—
680C2×C22⋊C4—32no—
681C2×C22⋊C4—64no—
682C2×C22⋊C4—122no—
683C2×C22⋊C4—122no—
684C2×C22⋊C4C22×D311yescharacteristic
685C2×C22⋊C4C22×D311yescharacteristic
686C2×C22⋊C4C22×D311yescharacteristic
687C2×C22⋊C4C22×D311yescharacteristic
688C2×C22⋊C4C22×D312yes—
689C2×C22⋊C4C22×D312yes—
690C2×C42—31no—
691C2×C42C22×D311yescharacteristic
692#95—32no—
693#95—32no—
694#95—32no—
695#95—32no—
696#95—32no—
697#95—32no—
698#95—32no—
699#95C22×D312yes—
700#95C22×D312yes—
701#95C22×D312yes—
702#95C22×D312yes—
703#95C22×D312yes—
704C23×C3—22no—
705C23×C3—22no—
706C23×C3—21no—
707C23×C3—22no—
708C23×C3—22no—
709C23×C3—21no—
710C23×C3—21no—
711C23×C3C22×D412yes—
712C23×C3H(5,𝔽2)12yes—
713C23×C32−1+412yes—
714C23×C3C2511yescharacteristic
715C22×D3—28no—
716C22×D3—22no—
717C22×D3—22no—
718C22×D3—21no—
719C22×D3—21no—
720C22×D3—22no—
721C22×D3—22no—
722C22×D3—22no—
723C22×D3—22no—
724C22×D3—22no—
725C22×D3—22no—
726C22×D3—22no—
727C22×D3—21no—
728C22×D3—21no—
729C22×D3—22no—
730C22×D3—28no—
731C22×D3—21no—
732C22×D3—22no—
733C22×D3—22no—
734C22×D3—22no—
735C22×D3—22no—
736C22×D3—22no—
737C22×D3—22no—
738C22×D3—22no—
739C22×D3—22no—
740C22×D3—21no—
741C22×D3—21no—
742C22×D3—22no—
743C22×D3—44no—
744C22×D3—44no—
745C22×D3—48no—
746C22×D3—48no—
747C22×D3—44no—
748C22×D3—44no—
749C22×D3—44no—
750C22×D3—44no—
751C22×D3—44no—
752C22×D3—84no—
753C22×D3—84no—
754C22×D3—84no—
755C22×D3—84no—
756C22×D3C22×D412yes—
757C22×D3C22×D412yes—
758C22×D3H(5,𝔽2)14yes—
759C3×D4—44no—
760C2×C3×C4—28no—
761C2×C3×C4—22no—
762C2×C3×C4—22no—
763C2×C3×C4—22no—
764C2×C3×C4—22no—
765C2×C3×C4—21no—
766C2×C3×C4—21no—
767C2×C3×C4—21no—
768C2×C3×C4—22no—
769C2×C3×C4—22no—
770C2×C3×C4—22no—
771C2×C3×C4—22no—
772C2×C3×C4—22no—
773C2×C3×C4—22no—
774C2×C3×C4—21no—
775C2×C3×C4—22no—
776C2×C3×C4—22no—
777C2×C3×C4—22no—
778C2×C3×C4—22no—
779C2×C3×C4—22no—
780C2×C3×C4—21no—
781C2×C3×C4—44no—
782C2×C3×C4—44no—
783C2×C3×C4—82no—
784C2×C3×C4C22×D412yes—
785C2×C3×C4C22×D412yes—
786C2×C3×C4H(5,𝔽2)14yes—
787#67—44no—
788#67—82no—
789#67—82no—
790#67—82no—
791#67—84no—
792#67—84no—
793C2×Dic3—22no—
794C2×Dic3—22no—
795C2×Dic3—21no—
796C2×Dic3—21no—
797C2×Dic3—21no—
798C2×Dic3—22no—
799C2×Dic3—22no—
800C2×Dic3—22no—
801C2×Dic3—22no—
802C2×Dic3—22no—
803C2×Dic3—22no—
804C2×Dic3—21no—
805C2×Dic3—22no—
806C2×Dic3—22no—
807C2×Dic3—21no—
808C2×Dic3—44no—
809C2×Dic3C22×D412yes—
810C2×Dic3C22×D412yes—
811D12—48no—
812D12—48no—
813D12—48no—
814D12—48no—
815D12—48no—
816D12—48no—
817D12—82no—
818D12—82no—
819D12—84no—
820D12—84no—
821C4×D3—48no—
822C4×D3—48no—
823C4×D3—82no—
824C4×D3—84no—
825C4×D3—84no—
826Dic6—82no—
827C24—31no—
828C24—31no—
829C24—32no—
830C24—34no—
831C24—32no—
832C24—31no—
833C24—64no—
834C24—62no—
835C24—62no—
836C24—62no—
837C24—62no—
838C24—62no—
839C24—62no—
840C24—62no—
841C24—62no—
842C24—122no—
843C24—122no—
844C24—122no—
845C24—122no—
846C24—122no—
847C24C23×D311yescharacteristic
848C24C23×D311yescharacteristic
849C2×Q8—62no—
850C2×Q8—122no—
851C2×D4—22no—
852C2×D4—22no—
853C2×D4—22no—
854C2×D4—64no—
855C2×D4—64no—
856C2×D4—64no—
857C2×D4—64no—
858C2×D4—64no—
859C2×D4—64no—
860C2×D4—64no—
861C2×D4—64no—
862C2×D4—62no—
863C2×D4—62no—
864C2×D4—64no—
865C2×D4—62no—
866C2×D4—62no—
867C2×D4—62no—
868C2×D4—62no—
869C2×D4—62no—
870C2×D4—62no—
871C2×D4—64no—
872C2×D4—64no—
873C2×D4—64no—
874C2×D4—64no—
875C2×D4—64no—
876C2×D4—122no—
877C2×D4—122no—
878C2×D4—122no—
879C2×D4—122no—
880C2×D4—122no—
881C2×D4—122no—
882C2×D4—1216no—
883C2×D4—122no—
884C2×D4—122no—
885C2×D4—122no—
886C2×D4—122no—
887C2×D4—122no—
888C2×D4—122no—
889C2×D4—122no—
890C2×D4—1216no—
891C2×D4—1216no—
892C2×D4—122no—
893C2×D4—122no—
894C2×D4—122no—
895C2×D4—122no—
896C2×D4—122no—
897C2×D4—122no—
898C2×D4—122no—
899C2×D4—122no—
900C22×C4—22no—
901C22×C4—24no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—31no—
905C22×C4—31no—
906C22×C4—34no—
907C22×C4—31no—
908C22×C4—32no—
909C22×C4—32no—
910C22×C4—31no—
911C22×C4—31no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—64no—
916C22×C4—64no—
917C22×C4—64no—
918C22×C4—64no—
919C22×C4—62no—
920C22×C4—122no—
921C22×C4—122no—
922C22×C4—122no—
923C22×C4—122no—
924C22×C4—122no—
925C22×C4—122no—
926C22×C4—122no—
927C22×C4—122no—
928C22×C4—122no—
929C22×C4—1216no—
930C22×C4—122no—
931C22×C4D3×D414yes—
932C22×C4C23×D312yes—
933C22×C4C23×D312yes—
934C22×C4C23×D312yes—
935C22×C4C23×D311yescharacteristic
936C22×C4C23×D311yescharacteristic
937C22×C4C23×D311yescharacteristic
938C22×C4C23×D311yescharacteristic
939C22×C4C23×D311yescharacteristic
940C22×C4C23×D312yes—
941C4⋊C4—24no—
942C4⋊C4—24no—
943C4⋊C4—22no—
944C4⋊C4—24no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—62no—
948C4⋊C4—62no—
949C4⋊C4—62no—
950C4⋊C4—62no—
951C4⋊C4—62no—
952C4⋊C4—64no—
953C4⋊C4—122no—
954C4⋊C4—122no—
955C4⋊C4—122no—
956C4⋊C4—122no—
957C22⋊C4—22no—
958C22⋊C4—22no—
959C22⋊C4—22no—
960C22⋊C4—22no—
961C22⋊C4—24no—
962C22⋊C4—34no—
963C22⋊C4—34no—
964C22⋊C4—34no—
965C22⋊C4—34no—
966C22⋊C4—42no—
967C22⋊C4—64no—
968C22⋊C4—64no—
969C22⋊C4—62no—
970C22⋊C4—62no—
971C22⋊C4—62no—
972C22⋊C4—62no—
973C22⋊C4—62no—
974C22⋊C4—64no—
975C22⋊C4—64no—
976C22⋊C4—62no—
977C22⋊C4—62no—
978C22⋊C4—62no—
979C22⋊C4—62no—
980C22⋊C4—62no—
981C22⋊C4—64no—
982C22⋊C4—122no—
983C22⋊C4—122no—
984C22⋊C4—122no—
985C22⋊C4—122no—
986C22⋊C4—122no—
987C22⋊C4—122no—
988C22⋊C4—122no—
989C22⋊C4—122no—
990C22⋊C4—122no—
991C22⋊C4—122no—
992C22⋊C4—122no—
993C22⋊C4—122no—
994C22⋊C4—122no—
995C42—22no—
996C42—62no—
997C22×C3—22no—
998C22×C3—22no—
999C22×C3—24no—
1000C22×C3—24no—
1001C22×C3—41no—
1002C22×C3—41no—
1003C22×C3—41no—
1004C22×C3—42no—
1005C22×C3—42no—
1006C22×C3#53714yes—
1007C22×C3C23×D411yescharacteristic
1008C22×C3C2×H(5,𝔽2)11yescharacteristic
1009C22×C3C2×H(5,𝔽2)12yes—
1010C22×C3C2×H(5,𝔽2)12yes—
1011C22×C3C2×2−1+411yescharacteristic
1012C2×D3—22no—
1013C2×D3—22no—
1014C2×D3—24no—
1015C2×D3—22no—
1016C2×D3—22no—
1017C2×D3—22no—
1018C2×D3—22no—
1019C2×D3—24no—
1020C2×D3—24no—
1021C2×D3—416no—
1022C2×D3—42no—
1023C2×D3—42no—
1024C2×D3—42no—
1025C2×D3—42no—
1026C2×D3—42no—
1027C2×D3—42no—
1028C2×D3—42no—
1029C2×D3—42no—
1030C2×D3—41no—
1031C2×D3—42no—
1032C2×D3—41no—
1033C2×D3—42no—
1034C2×D3—42no—
1035C2×D3—41no—
1036C2×D3—42no—
1037C2×D3—42no—
1038C2×D3—42no—
1039C2×D3—42no—
1040C2×D3—42no—
1041C2×D3—42no—
1042C2×D3—88no—
1043C2×D3—88no—
1044C3×C4—24no—
1045C3×C4—22no—
1046C3×C4—22no—
1047C3×C4—41no—
1048C3×C4—41no—
1049C3×C4—42no—
1050C3×C4—41no—
1051C3×C4—42no—
1052C3×C4—42no—
1053Dic3—22no—
1054Dic3—22no—
1055Dic3—41no—
1056Dic3—41no—
1057Dic3—41no—
1058Dic3—42no—
1059Dic3—42no—
1060C23—22no—
1061C23—22no—
1062C23—21no—
1063C23—21no—
1064C23—22no—
1065C23—21no—
1066C23—22no—
1067C23—32no—
1068C23—32no—
1069C23—34no—
1070C23—68no—
1071C23—62no—
1072C23—62no—
1073C23—61no—
1074C23—61no—
1075C23—62no—
1076C23—61no—
1077C23—61no—
1078C23—62no—
1079C23—62no—
1080C23—62no—
1081C23—62no—
1082C23—62no—
1083C23—62no—
1084C23—62no—
1085C23—68no—
1086C23—61no—
1087C23—62no—
1088C23—61no—
1089C23—62no—
1090C23—62no—
1091C23—62no—
1092C23—62no—
1093C23—62no—
1094C23—61no—
1095C23—62no—
1096C23—62no—
1097C23—62no—
1098C23—124no—
1099C23—124no—
1100C23—128no—
1101C23—128no—
1102C23—124no—
1103C23—124no—
1104C23—124no—
1105C23—124no—
1106C23—124no—
1107C23—244no—
1108C23—244no—
1109C23—244no—
1110C23—244no—
1111C23C2×D3×D412yes—
1112C23#100712yes—
1113C23#100912yes—
1114C23C24×D311yescharacteristic
1115Q8—242no—
1116D4—44no—
1117D4—128no—
1118D4—128no—
1119D4—128no—
1120D4—128no—
1121D4—128no—
1122D4—128no—
1123D4—124no—
1124D4—242no—
1125D4—242no—
1126D4—244no—
1127D4—244no—
1128D4—242no—
1129D4—242no—
1130D4—242no—
1131D4—244no—
1132D4—244no—
1133C2×C4—28no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—22no—
1142C2×C4—21no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—32no—
1155C2×C4—32no—
1156C2×C4—44no—
1157C2×C4—44no—
1158C2×C4—62no—
1159C2×C4—62no—
1160C2×C4—61no—
1161C2×C4—61no—
1162C2×C4—61no—
1163C2×C4—61no—
1164C2×C4—62no—
1165C2×C4—62no—
1166C2×C4—62no—
1167C2×C4—61no—
1168C2×C4—62no—
1169C2×C4—62no—
1170C2×C4—62no—
1171C2×C4—62no—
1172C2×C4—62no—
1173C2×C4—82no—
1174C2×C4—128no—
1175C2×C4—128no—
1176C2×C4—124no—
1177C2×C4—242no—
1178C2×C4—244no—
1179C2×C4—244no—
1180C2×C4C2×D3×D412yes—
1181C2×C4C2×D3×D412yes—
1182C2×C4#100914yes—
1183C2×C3—24no—
1184C2×C3—81no—
1185C2×C3C2×#53711yescharacteristic
1186C2×C3#348411yescharacteristic
1187C2×C3#348411yescharacteristic
1188C2×C3#353612yes—
1189C2×C3#353712yes—
1190D3—44no—
1191D3—42no—
1192D3—42no—
1193D3—81no—
1194D3—82no—
1195C22—22no—
1196C22—22no—
1197C22—24no—
1198C22—24no—
1199C22—41no—
1200C22—41no—
1201C22—42no—
1202C22—42no—
1203C22—41no—
1204C22—62no—
1205C22—62no—
1206C22—64no—
1207C22—62no—
1208C22—62no—
1209C22—64no—
1210C22—64no—
1211C22—62no—
1212C22—62no—
1213C22—1216no—
1214C22—122no—
1215C22—122no—
1216C22—122no—
1217C22—122no—
1218C22—122no—
1219C22—122no—
1220C22—122no—
1221C22—122no—
1222C22—122no—
1223C22—121no—
1224C22—121no—
1225C22—122no—
1226C22—122no—
1227C22—122no—
1228C22—122no—
1229C22—122no—
1230C22—122no—
1231C22—122no—
1232C22—121no—
1233C22—122no—
1234C22—248no—
1235C22—248no—
1236C22#562914yes—
1237C22C22×D3×D411yescharacteristic
1238C22C2×#100711yescharacteristic
1239C22C2×#100912yes—
1240C22C2×#100911yescharacteristic
1241C22D3×H(5,𝔽2)12yes—
1242C4—24no—
1243C4—22no—
1244C4—22no—
1245C4—41no—
1246C4—42no—
1247C4—41no—
1248C4—42no—
1249C4—42no—
1250C4—41no—
1251C4—62no—
1252C4—62no—
1253C4—121no—
1254C4—121no—
1255C4—122no—
1256C4—122no—
1257C4—121no—
1258C3#3670611yescharacteristic, complemented, Sylow
1259C2—24no—
1260C2—81no—
1261C2—124no—
1262C2—122no—
1263C2—122no—
1264C2—242no—
1265C2—241no—
1266C2C2×#562911yescharacteristic
1267C2#8603911yescharacteristic
1268C2#8630811yescharacteristic
1269C2#8691612yes—
1270C2#8695212yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2579C2
hypercenter#2579D3
hypocenterC3#36706
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2579

Complements

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

NH ≅ G/Ntype
1. C2×#5560C2semidirect
2. C22×#895C2semidirect
3. C3×#2579C2semidirect
4. #82403C2semidirect
5. #82198C2semidirect
6. #77967C2semidirect
7. #77847C2semidirect
8. #77429C2semidirect
9. #77428C2semidirect
10. #75389C2semidirect
11. #75150C2semidirect
12. #74935C2semidirect
13. #74905C2semidirect
14. #74887C2semidirect
15. #74887C2semidirect
16. #74655C2semidirect
17. #74630C2semidirect
18. #74627C2semidirect
19. #74621C2semidirect
20. #74601C2semidirect
21. #74601C2semidirect
22. #74016C2semidirect
23. #74005C2semidirect
35. C2×#930C22semidirect
36. C2×#930C22semidirect
37. C2×#929C22semidirect
42. C2×#898C22semidirect
43. C2×#896C22semidirect
49. C2×#895C22semidirect
50. C2×#895C22semidirect
51. C2×#895C22semidirect
52. C2×#894C22semidirect
53. C2×#885C22semidirect
54. C2×#884C22semidirect
55. C2×#884C22semidirect
56. C2×#884C22semidirect
57. C2×#884C22semidirect
64. C2×#876C22semidirect
65. C2×#875C22semidirect
66. C3×#398C22semidirect
67. C3×#396C22semidirect
68. C3×#387C22semidirect
73. C3×#385C22semidirect
80. #4994C22semidirect
81. #4994C22semidirect
82. #4993C22semidirect
83. #4991C22semidirect
84. #4991C22semidirect
85. #4991C22semidirect
86. #4989C22semidirect
87. #4989C22semidirect
88. #4989C22semidirect
89. #4989C22semidirect
90. #4988C22semidirect
91. #4982C22semidirect
92. #4978C22semidirect
93. #4960C22semidirect
94. #4960C22semidirect
95. #4960C22semidirect
96. #4960C22semidirect
97. #4959C22semidirect
98. #4956C22semidirect
105. #4939C22semidirect
106. #4676C22semidirect
107. #4675C22semidirect
108. #4673C22semidirect
109. #4672C22semidirect
110. #4672C22semidirect
111. #4672C22semidirect
112. #4672C22semidirect
113. #4671C22semidirect
114. #4671C22semidirect
115. #4671C22semidirect
116. #4668C22semidirect
117. #4668C22semidirect
118. #4668C22semidirect
119. #4667C22semidirect
120. #4667C22semidirect
121. #4665C22semidirect
122. #4665C22semidirect
123. #4665C22semidirect
124. #4665C22semidirect
125. #4665C22semidirect
141. #2579D3semidirect
216. C2×(C2×D3)⋊C4D4semidirect
334. #398C2×D3semidirect
339. #396C2×D3semidirect
359. #387C2×D3semidirect
381. #385C2×D3semidirect
1258. C3#36706semidirect

Maximal subgroups

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

subgroupindex
C2×#55602
C22×#8952
C3×#25792
#824032
#821982
#779672
#778472
#774292
#774282
#753892
#751502
#749352
#749052
#748872
#746552
#746302
#746272
#746212
#746012
#740162
#740052
#367063