Finite Group Databasebeta

← #13517313

Subgroups — #13517313

Order 1792.

2766 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90298C211yesmaximal, characteristic
2C4×C7×#121C211yesmaximal, characteristic, complemented
3#11740078C211yesmaximal, characteristic, complemented
4D4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
5#11739840C212yesmaximal, complemented
6#11739786C211yesmaximal, characteristic, complemented
7#11739774C212yesmaximal, complemented
8C4×#6493C211yesmaximal, characteristic, complemented
9#11739515C211yesmaximal, characteristic, complemented
10#11733878C211yesmaximal, characteristic, complemented
11#11733876C211yesmaximal, characteristic, complemented
12#11733430C211yesmaximal, characteristic, complemented
13#11733424C211yesmaximal, characteristic, complemented
14#11733285C212yesmaximal, complemented
15#11732938C212yesmaximal, complemented
16#11732321C212yesmaximal, complemented
17#11732112C212yesmaximal, complemented
18#11731448C211yesmaximal, characteristic, complemented
19#11731317C211yesmaximal, characteristic, complemented
20#11731219C211yesmaximal, characteristic, complemented
21#11731078C211yesmaximal, characteristic, complemented
22#11731022C212yesmaximal, complemented
23#11730920C212yesmaximal, complemented
24C22×D4×D7C2211yescharacteristic
25C22×#1157C2211yescharacteristic
26C2×C7×#121C2211yescharacteristic
27C2×C4×C7×D4C2211yescharacteristic
28C2×C4×C7×D4C2212yescomplemented
29C22×C42×C7C2211yescharacteristic, complemented
30C2×#6503C2212yes—
31C2×#6501C2211yescharacteristic
32C2×#6500C2212yes—
33C2×D4×Dic7C2211yescharacteristic
34C2×#6493C2211yescharacteristic
35C2×C4×C22⋊D7C2212yescomplemented
36C22×(C2×D7)⋊C4C2212yes—
37C2×#6489C2211yescharacteristic, complemented
38#90298C4116yescomplemented
39C2×#6458C2211yescharacteristic
40C2×#6456C2211yescharacteristic
41C2×#6455C2211yescharacteristic
42C2×#6455C2211yescharacteristic, complemented
43C2×D7×C4⋊C4C2211yescharacteristic, complemented
44C2×#6448C2212yes—
45C2×#6445C2212yes—
46C2×(C22⋊D7)⋊C4C2212yescomplemented
47C2×D7×C22⋊C4C2212yes—
48C2×C4×D28C2211yescharacteristic
49C2×C4×D28C2212yescomplemented
50C7×#390C2211yescharacteristic
51C7×#389C2211yescharacteristic, complemented
52C7×#388C2212yescomplemented
53C7×#386C2212yescomplemented
54C7×#380C2211yescharacteristic, complemented
55C4×C7×C4⋊C4C2211yescharacteristic, complemented
56C4×C7×C22⋊C4C2212yescomplemented
57#89993C2211yescharacteristic
58#89993C2212yescomplemented
59#89992C2212yescomplemented
60#89985C2211yescharacteristic
61#89985C2211yescharacteristic
62#89985C2212yes—
63#89985C2212yescomplemented
64#89985C2211yescharacteristic, complemented
65#89985C2211yescharacteristic, complemented
66#89985C2212yescomplemented
67#89984C2211yescharacteristic, complemented
68C4×C22⋊Dic7C2212yescomplemented
69#89762C2212yes—
70#89762C2212yescomplemented
71#89760C2211yescharacteristic
72#89760C2212yescomplemented
73#89759C2211yescharacteristic
74#89759C2211yescharacteristic
75#89757C2211yescharacteristic, complemented
76#89749C2212yescomplemented
77C4⋊C4×Dic7C2211yescharacteristic, complemented
78C4⋊C4×Dic7C2211yescharacteristic, complemented
79#89745C2211yescharacteristic, complemented
80#89730C2212yes—
81#89729C2212yes—
82#89729C2212yescomplemented
83#89729C2212yescomplemented
84#89728C2212yes—
85#89728C2212yes—
86#89728C2212yescomplemented
87#89728C2212yescomplemented
88#89728C2212yescomplemented
89#89727C2212yes—
90#89727C2212yes—
91#89723C2212yescomplemented
92#89722C2212yescomplemented
93#89718C2212yescomplemented
94#89716C2212yescomplemented
95#89716C2212yescomplemented
96#89712C2212yes—
97#89712C2212yescomplemented
98#89712C2212yescomplemented
99#89711C2211yescharacteristic
100#89711C2211yescharacteristic
101#89711C2211yescharacteristic
102C4×(C2×D7)⋊C4C2211yescharacteristic
103C4×(C2×D7)⋊C4C2211yescharacteristic
104C4×(C2×D7)⋊C4C2211yescharacteristic, complemented
105C4×(C2×D7)⋊C4C2212yescomplemented
106C4×(C2×D7)⋊C4C2211yescharacteristic, complemented
107C4×C4⋊Dic7C2211yescharacteristic, complemented
108#89704C2212yescomplemented
109#89701C2211yescharacteristic, complemented
110#89701C2211yescharacteristic, complemented
111#89700C2211yescharacteristic, complemented
112#89442C2212yes—
113#89442C2212yescomplemented
114#89441C2212yes—
115#89440C2212yescomplemented
116#89440C2212yescomplemented
117#89438C2212yescomplemented
118#89437C2212yes—
119#89437C2212yescomplemented
120#89437C2212yescomplemented
121#89422C2212yescomplemented
122#89420C2212yescomplemented
123#89418C2212yescomplemented
124#34415—71nomaximal, Sylow
125C24×D7C2312yes—
126C22×C7×D4C2311yescharacteristic
127C22×C7×D4C2312yes—
128C23×C4×C7C2311yescharacteristic
129C23×C4×C7C2312yes—
130C23×C4×C7C2311yescharacteristic
131C23×C4×C7C2311yescharacteristic
132C22×C22⋊D7C2312yes—
133C22×C22⋊D7C2312yes—
134C22×C22⋊D7C2312yes—
135C22×C22⋊D7C2311yescharacteristic
136C22×C22⋊D7C2311yescharacteristic
137C23×Dic7C2312yes—
138C2×D4×D7—42no—
139C2×D4×D7—42no—
140C2×D4×D7C2×C418yescomplemented
141C2×#1157—42no—
142C2×#1157—42no—
143C2×#1157C2×C418yescomplemented
144C22×D28C2311yescharacteristic
145C22×D28C2312yes—
146C22×D28C2311yescharacteristic
147C22×C4×D7C2311yescharacteristic
148C22×C4×D7C2311yescharacteristic
149C22×C4×D7C2312yes—
150C22×C4×D7C2312yes—
151C22×C4×D7C2312yes—
152C22×Dic14C2311yescharacteristic
153C7×#121C2×C418yescomplemented
154C4×C7×D4—42no—
155C4×C7×D4—44no—
156C2×C7×C4⋊C4C2311yescharacteristic
157C2×C7×C4⋊C4C2311yescharacteristic
158C2×C7×C4⋊C4C2312yes—
159C2×C7×C4⋊C4C2311yescharacteristic
160C2×C7×C22⋊C4C2312yes—
161C2×C7×C22⋊C4C2312yes—
162C2×C7×C22⋊C4C2312yes—
163C2×C7×C22⋊C4C2312yes—
164C2×C7×C22⋊C4C2312yes—
165C2×C42×C7—42no—
166C2×C42×C7C2311yescharacteristic
167C2×C42×C7C2312yes—
168C2×C42×C7C2311yescharacteristic
169C2×C42×C7C2311yescharacteristic
170C2×C42×C7C2311yescharacteristic
171C2×C22⋊Dic7C2312yes—
172C2×C22⋊Dic7C2311yescharacteristic
173C2×C22⋊Dic7C2311yescharacteristic
174C2×C22⋊Dic7C2312yes—
175C2×C22⋊Dic7C2312yes—
176C2×C22⋊Dic7C2312yes—
177C2×C22⋊Dic7C2312yes—
178#6503C2×C4116yescomplemented
179#6501C2×C418yescomplemented
180#6500C2×C4116yescomplemented
181D4×Dic7—42no—
182#6493C2×C418yescomplemented
183C4×C22⋊D7—44no—
184C2×(C2×D7)⋊C4—44no—
185C2×(C2×D7)⋊C4C2311yescharacteristic
186C2×(C2×D7)⋊C4C2312yes—
187C2×(C2×D7)⋊C4C2311yescharacteristic
188C2×(C2×D7)⋊C4C2311yescharacteristic
189C2×(C2×D7)⋊C4C2311yescharacteristic
190C2×(C2×D7)⋊C4C2312yes—
191C2×(C2×D7)⋊C4C2312yes—
192C2×(C2×D7)⋊C4C2312yes—
193C2×(C2×D7)⋊C4C2312yes—
194C2×(C2×D7)⋊C4C2312yes—
195C2×(C2×D7)⋊C4C2311yescharacteristic
196C2×(C2×D7)⋊C4C2312yes—
197C2×(C2×D7)⋊C4C2312yes—
198C2×(C2×D7)⋊C4C2312yes—
199C2×(C2×D7)⋊C4C2311yescharacteristic
200C2×(C2×D7)⋊C4C2311yescharacteristic
201C2×(C2×D7)⋊C4C2311yescharacteristic
202C2×(C2×D7)⋊C4C2312yes—
203C2×(C2×D7)⋊C4C2312yes—
204C2×(C2×D7)⋊C4C2312yes—
205#6489—42no—
206C2×C4⋊Dic7C2311yescharacteristic
207C2×C4⋊Dic7C2311yescharacteristic
208C2×C4⋊Dic7C2312yes—
209C2×C4⋊Dic7C2311yescharacteristic
210C2×C4⋊Dic7C2311yescharacteristic
211C2×C4⋊Dic7C2311yescharacteristic
212C2×Dic7⋊C4C2312yes—
213C2×Dic7⋊C4C2312yes—
214C2×Dic7⋊C4C2312yes—
215C2×C4×Dic7C2312yes—
216C2×C4×Dic7C2311yescharacteristic
217C2×C4×Dic7C2311yescharacteristic
218C2×C4×Dic7C2312yes—
219C2×C4×Dic7C2312yes—
220C2×C4×Dic7C2312yes—
221C2×C4×Dic7C2312yes—
222#6458C2×C418yescomplemented
223#6456—42no—
224#6455—42no—
225#6455C2×C418yescomplemented
226D7×C4⋊C4—42no—
227#6448C2×C4116yescomplemented
228#6445C2×C4116yescomplemented
229(C22⋊D7)⋊C4—44no—
230D7×C22⋊C4—44no—
231C4×D28—42no—
232C4×D28—44no—
233C7×#95C2312yes—
234C7×#95C2312yes—
235C7×#95C2312yes—
236C7⋊#95C2312yes—
237C7⋊#95C2312yes—
238C7⋊#95C2312yes—
239C7⋊#95C2311yescharacteristic
240C7⋊#95C2312yes—
241C7⋊#95C2311yescharacteristic
242C7⋊#95C2312yes—
243C7⋊#95C2311yescharacteristic
244C7⋊#95C2311yescharacteristic
245C7⋊#95C2312yes—
246C7⋊#95C2312yes—
247C7⋊#95C2312yes—
248C7⋊#95C2311yescharacteristic
249C7⋊#95C2311yescharacteristic
250C7⋊#95C2311yescharacteristic
251C7⋊#95C2311yescharacteristic
252C7⋊#95C2312yes—
253C2×#535—71no—
254#2379—72no—
255#2375—72no—
256#2372—72no—
257#2363—71no—
258#2363—71no—
259#2361—71no—
260#2361—71no—
261#2358—72no—
262#2346—71no—
263#2346—71no—
264D4×C22⋊C4—71no—
265D4×C22⋊C4—71no—
266#2328—72no—
267#2328—72no—
268#2324—71no—
269#2324—71no—
270#2321—72no—
271#2321—72no—
272#2311—71no—
273C4×#121—71no—
274C4×#121D711yescharacteristic, complemented
275#2297—71no—
276C24×C7C2412yes—
277C24×C7C2411yescharacteristic
278C23×D7—42no—
279C23×D7—42no—
280C23×D7—42no—
281C23×D7—42no—
282C23×D7—42no—
283C23×D7—42no—
284C23×D7C22×C418yes—
285C23×D7C2411yescharacteristic
286C23×D7C2412yes—
287C23×D7C2411yescharacteristic
288C2×C7×D4—22no—
289C2×C7×D4—22no—
290C2×C7×D4—42no—
291C2×C7×D4—42no—
292C2×C7×D4C22×C414yes—
293C2×C7×D4C22×C418yes—
294C22×C4×C7—22no—
295C22×C4×C7—22no—
296C22×C4×C7—22no—
297C22×C4×C7—22no—
298C22×C4×C7—24no—
299C22×C4×C7—41no—
300C22×C4×C7—41no—
301C22×C4×C7—41no—
302C22×C4×C7—41no—
303C22×C4×C7—42no—
304C22×C4×C7—42no—
305C22×C4×C7C22×C414yes—
306C22×C4×C7C2411yescharacteristic
307C22×C4×C7C2412yes—
308C22×C4×C7C2411yescharacteristic
309C22×C4×C7C2412yes—
310C22×C4×C7C2412yes—
311C22×C4×C7C2411yescharacteristic
312C22×C4×C7C2411yescharacteristic
313C22×C4×C7C2411yescharacteristic
314C22×C4×C7C2411yescharacteristic
315C2×C22⋊D7—42no—
316C2×C22⋊D7—42no—
317C2×C22⋊D7—41no—
318C2×C22⋊D7—41no—
319C2×C22⋊D7—41no—
320C2×C22⋊D7—41no—
321C2×C22⋊D7—42no—
322C2×C22⋊D7—42no—
323C2×C22⋊D7—42no—
324C2×C22⋊D7—42no—
325C2×C22⋊D7C22×C418yes—
326C2×C22⋊D7C22×C418yes—
327C2×C22⋊D7C22×C418yes—
328C2×C22⋊D7C22×C414yes—
329C2×C22⋊D7C22×C414yes—
330C22×Dic7—42no—
331C22×Dic7—42no—
332C22×Dic7—42no—
333C22×Dic7C2411yescharacteristic
334C22×Dic7C2411yescharacteristic
335C22×Dic7C2412yes—
336C22×Dic7C2411yescharacteristic
337C22×Dic7C2412yes—
338C22×Dic7C2411yescharacteristic
339C22×Dic7C2411yescharacteristic
340C22×Dic7C2412yes—
341C22×Dic7C2411yescharacteristic
342D4×D7—416no—
343#1157—416no—
344C2×D28—22no—
345C2×D28—22no—
346C2×D28—42no—
347C2×D28—42no—
348C2×D28—41no—
349C2×D28—41no—
350C2×D28C22×C414yes—
351C2×D28C22×C414yes—
352C2×D28C22×C418yes—
353C2×C4×D7—22no—
354C2×C4×D7—22no—
355C2×C4×D7—22no—
356C2×C4×D7—22no—
357C2×C4×D7—24no—
358C2×C4×D7—42no—
359C2×C4×D7—42no—
360C2×C4×D7—42no—
361C2×C4×D7—42no—
362C2×C4×D7—42no—
363C2×C4×D7—42no—
364C2×C4×D7—42no—
365C2×C4×D7—42no—
366C2×C4×D7C22×C414yes—
367C2×C4×D7C22×C414yes—
368C2×Dic14—41no—
369C2×Dic14—41no—
370C2×Dic14C22×C414yes—
371C7×C4⋊C4—22no—
372C7×C4⋊C4—22no—
373C7×C4⋊C4—42no—
374C7×C4⋊C4C22×C414yes—
375C7×C22⋊C4—24no—
376C7×C22⋊C4—42no—
377C7×C22⋊C4—42no—
378C7×C22⋊C4—42no—
379C7×C22⋊C4C22×C418yes—
380C42×C7—22no—
381C42×C7—24no—
382C42×C7—22no—
383C42×C7—41no—
384C42×C7—41no—
385C22⋊Dic7—42no—
386C22⋊Dic7—41no—
387C22⋊Dic7—41no—
388C22⋊Dic7—42no—
389C22⋊Dic7—42no—
390C22⋊Dic7—42no—
391C22⋊Dic7C22×C418yes—
392(C2×D7)⋊C4—22no—
393(C2×D7)⋊C4—24no—
394(C2×D7)⋊C4—22no—
395(C2×D7)⋊C4—22no—
396(C2×D7)⋊C4—22no—
397(C2×D7)⋊C4—42no—
398(C2×D7)⋊C4—42no—
399(C2×D7)⋊C4—42no—
400(C2×D7)⋊C4—42no—
401(C2×D7)⋊C4—42no—
402(C2×D7)⋊C4—42no—
403(C2×D7)⋊C4—41no—
404(C2×D7)⋊C4—41no—
405(C2×D7)⋊C4—42no—
406(C2×D7)⋊C4—41no—
407(C2×D7)⋊C4—41no—
408(C2×D7)⋊C4—42no—
409(C2×D7)⋊C4C22×C418yes—
410(C2×D7)⋊C4C22×C418yes—
411(C2×D7)⋊C4C22×C418yes—
412C4⋊Dic7—22no—
413C4⋊Dic7—22no—
414C4⋊Dic7—42no—
415C4⋊Dic7—41no—
416C4⋊Dic7—41no—
417C4⋊Dic7C22×C414yes—
418Dic7⋊C4—42no—
419Dic7⋊C4—42no—
420Dic7⋊C4—42no—
421C4×Dic7—24no—
422C4×Dic7—22no—
423C4×Dic7—22no—
424C4×Dic7—42no—
425C4×Dic7—42no—
426C4×Dic7—42no—
427C4×Dic7C22×C418yes—
428C22×#41—71no—
429C23×D4—71no—
430#535—716no—
431C2×#127—72no—
432C2×#124—72no—
433C2×#121—71no—
434C2×#121—71no—
435C2×#121—71no—
436C2×#121C2×D711yescharacteristic
437C2×#120—72no—
438C2×#120—72no—
439C2×C4×D4—71no—
440C2×C4×D4—72no—
441C2×C4×D4—71no—
442C2×C4×D4—72no—
443C2×C4×D4—72no—
444C2×C4×D4—71no—
445C2×C4×D4C2×D711yescharacteristic
446C2×C4×D4C2×D712yescomplemented
447C2×#117—71no—
448C2×#117—71no—
449C2×#117—71no—
450C22×C4⋊C4—71no—
451C22×C22⋊C4—72no—
452C22×C22⋊C4—72no—
453C22×C42C2×D711yescharacteristic, complemented
454#391—71no—
455#391—71no—
456#391—72no—
457#390—72no—
458#390—71no—
459#390—71no—
460#390—72no—
461#390—72no—
462#390—72no—
463#390—72no—
464#390—71no—
465#390—71no—
466#390—71no—
467#390C2×D711yescharacteristic
468#389—71no—
469#389—71no—
470#389—71no—
471#389C2×D711yescharacteristic, complemented
472#388—72no—
473#388—72no—
474#388—72no—
475#388—72no—
476#388—72no—
477#388—72no—
478#388—72no—
479#388—72no—
480#388—72no—
481#388—72no—
482#388—72no—
483#388C2×D712yescomplemented
484#386—72no—
485#386—71no—
486#386—71no—
487#386—72no—
488#386—71no—
489#386—71no—
490#386—72no—
491#386—72no—
492#386—72no—
493#386—72no—
494#386—72no—
495#386—72no—
496#386—72no—
497#386—72no—
498#386—72no—
499#386—72no—
500#386—72no—
501#386C2×D712yescomplemented
502#385—72no—
503#385—72no—
504#385—72no—
505#385—72no—
506#382—72no—
507#382—72no—
508#380—71no—
509#380—71no—
510#380—71no—
511#380C2×D711yescharacteristic, complemented
512#379—72no—
513#379—72no—
514C4×C4⋊C4—71no—
515C4×C4⋊C4—71no—
516C4×C4⋊C4—71no—
517C4×C4⋊C4C2×D711yescharacteristic, complemented
518C4×C22⋊C4—72no—
519C4×C22⋊C4—71no—
520C4×C22⋊C4—71no—
521C4×C22⋊C4—72no—
522C4×C22⋊C4—71no—
523C4×C22⋊C4—71no—
524C4×C22⋊C4—72no—
525C4×C22⋊C4C2×D712yescomplemented
526#376—72no—
527#376—72no—
528C23×C7—21no—
529C23×C7—21no—
530C23×C7—22no—
531C23×C7—22no—
532C23×C7—21no—
533C23×C7—22no—
534C23×C7—22no—
535C23×C7—21no—
536C23×C7—22no—
537C23×C7—21no—
538C23×C7—22no—
539C23×C7—21no—
540C23×C7C23×C414yes—
541C23×C7C23×C412yes—
542C23×C7C2511yescharacteristic
543C22×D7—21no—
544C22×D7—21no—
545C22×D7—22no—
546C22×D7—21no—
547C22×D7—21no—
548C22×D7—21no—
549C22×D7—22no—
550C22×D7—22no—
551C22×D7—22no—
552C22×D7—21no—
553C22×D7—21no—
554C22×D7—21no—
555C22×D7—21no—
556C22×D7—21no—
557C22×D7—22no—
558C22×D7—21no—
559C22×D7—21no—
560C22×D7—22no—
561C22×D7—48no—
562C22×D7—48no—
563C22×D7—48no—
564C22×D7—84no—
565C22×D7—84no—
566C22×D7—84no—
567C22×D7—84no—
568C22×D7C23×C412yes—
569C22×D7C23×C414yes—
570C22×D7C23×C412yes—
571C7×D4—28no—
572C7×D4—48no—
573C2×C4×C7—21no—
574C2×C4×C7—22no—
575C2×C4×C7—21no—
576C2×C4×C7—21no—
577C2×C4×C7—21no—
578C2×C4×C7—22no—
579C2×C4×C7—21no—
580C2×C4×C7—21no—
581C2×C4×C7—28no—
582C2×C4×C7—22no—
583C2×C4×C7—21no—
584C2×C4×C7—22no—
585C2×C4×C7—22no—
586C2×C4×C7—21no—
587C2×C4×C7—22no—
588C2×C4×C7—21no—
589C2×C4×C7—22no—
590C2×C4×C7—21no—
591C2×C4×C7—22no—
592C2×C4×C7—21no—
593C2×C4×C7—21no—
594C2×C4×C7—44no—
595C2×C4×C7—44no—
596C2×C4×C7—84no—
597C2×C4×C7C23×C414yes—
598C2×C4×C7C23×C412yes—
599C2×C4×C7C23×C412yes—
600C2×C4×C7H(5,𝔽2)12yes—
601C2×C4×C7H(5,𝔽2)12yes—
602C2×C4×C7H(5,𝔽2)12yes—
603C2×C4×C7H(5,𝔽2)12yes—
604C22⋊D7—44no—
605C22⋊D7—44no—
606C22⋊D7—48no—
607C22⋊D7—48no—
608C22⋊D7—48no—
609C2×Dic7—22no—
610C2×Dic7—21no—
611C2×Dic7—21no—
612C2×Dic7—21no—
613C2×Dic7—21no—
614C2×Dic7—22no—
615C2×Dic7—21no—
616C2×Dic7—21no—
617C2×Dic7—21no—
618C2×Dic7—21no—
619C2×Dic7—22no—
620C2×Dic7—22no—
621C2×Dic7—21no—
622C2×Dic7—22no—
623C2×Dic7—22no—
624C2×Dic7—21no—
625C2×Dic7—22no—
626C2×Dic7—21no—
627C2×Dic7—21no—
628C2×Dic7—21no—
629C2×Dic7—21no—
630C2×Dic7—22no—
631C2×Dic7—21no—
632C2×Dic7—21no—
633C2×Dic7—84no—
634C2×Dic7C23×C412yes—
635C2×Dic7C23×C414yes—
636C2×Dic7C23×C412yes—
637D28—28no—
638D28—48no—
639D28—44no—
640C4×D7—28no—
641C4×D7—28no—
642C4×D7—84no—
643C4×D7—84no—
644C4×D7—84no—
645Dic14—44no—
646C25—72no—
647C2×#41—78no—
648C2×#41—282no—
649C2×#41—282no—
650C22×Q8—71no—
651C22×D4—72no—
652C22×D4—72no—
653C22×D4—71no—
654C22×D4—72no—
655C22×D4—71no—
656C22×D4—78no—
657C22×D4—71no—
658C22×D4—72no—
659C22×D4—71no—
660C22×D4—282no—
661C22×D4—282no—
662C22×D4C22×D711yescharacteristic
663C22×D4C22×D712yes—
664C23×C4—71no—
665C23×C4—71no—
666C23×C4—72no—
667C23×C4—72no—
668C23×C4—72no—
669C23×C4—72no—
670C23×C4C22×D711yescharacteristic
671C23×C4C22×D712yes—
672C23×C4C22×D711yescharacteristic
673C23×C4C22×D711yescharacteristic
674#127—716no—
675#124—716no—
676#121—78no—
677#121—78no—
678#121—78no—
679#121C4×D718yescomplemented
680#120—716no—
681#120—716no—
682C4×D4—42no—
683C4×D4—44no—
684C4×D4—284no—
685C4×D4—282no—
686C4×D4—284no—
687C4×D4—282no—
688C4×D4—282no—
689C4×D4—284no—
690#117—78no—
691#117—282no—
692#117—282no—
693C2×C4⋊C4—71no—
694C2×C4⋊C4—71no—
695C2×C4⋊C4—71no—
696C2×C4⋊C4—72no—
697C2×C4⋊C4—71no—
698C2×C4⋊C4—71no—
699C2×C4⋊C4—72no—
700C2×C4⋊C4—72no—
701C2×C4⋊C4—72no—
702C2×C4⋊C4—282no—
703C2×C4⋊C4C22×D711yescharacteristic
704C2×C4⋊C4C22×D711yescharacteristic
705C2×C4⋊C4C22×D712yes—
706C2×C4⋊C4C22×D711yescharacteristic
707C2×C22⋊C4—72no—
708C2×C22⋊C4—72no—
709C2×C22⋊C4—72no—
710C2×C22⋊C4—72no—
711C2×C22⋊C4—71no—
712C2×C22⋊C4—71no—
713C2×C22⋊C4—72no—
714C2×C22⋊C4—71no—
715C2×C22⋊C4—71no—
716C2×C22⋊C4—72no—
717C2×C22⋊C4—71no—
718C2×C22⋊C4—71no—
719C2×C22⋊C4—72no—
720C2×C22⋊C4—72no—
721C2×C22⋊C4—72no—
722C2×C22⋊C4—72no—
723C2×C22⋊C4—72no—
724C2×C22⋊C4—72no—
725C2×C22⋊C4—72no—
726C2×C22⋊C4—72no—
727C2×C22⋊C4—72no—
728C2×C22⋊C4—72no—
729C2×C22⋊C4—71no—
730C2×C22⋊C4—71no—
731C2×C22⋊C4—72no—
732C2×C22⋊C4—71no—
733C2×C22⋊C4—71no—
734C2×C22⋊C4—284no—
735C2×C22⋊C4—284no—
736C2×C22⋊C4C22×D712yes—
737C2×C22⋊C4C22×D712yes—
738C2×C22⋊C4C22×D712yes—
739C2×C22⋊C4C22×D712yes—
740C2×C22⋊C4C22×D712yes—
741C2×C42—42no—
742C2×C42—72no—
743C2×C42—71no—
744C2×C42—71no—
745C2×C42—72no—
746C2×C42—72no—
747C2×C42—72no—
748C2×C42—72no—
749C2×C42C22×D712yes—
750C2×C42C22×D711yescharacteristic
751C2×C42C22×D711yescharacteristic
752C2×C42C22×D711yescharacteristic
753C2×C42C22×D711yescharacteristic
754#95—71no—
755#95—71no—
756#95—72no—
757#95—72no—
758#95—72no—
759#95—72no—
760#95—72no—
761#95—71no—
762#95—71no—
763#95—72no—
764#95—71no—
765#95—71no—
766#95—71no—
767#95—71no—
768#95—72no—
769#95—72no—
770#95—72no—
771#95C22×D712yes—
772#95C22×D712yes—
773#95C22×D712yes—
774C22×C7—22no—
775C22×C7—24no—
776C22×C7—22no—
777C22×C7—24no—
778C22×C7—22no—
779C22×C7—24no—
780C22×C7—41no—
781C22×C7—41no—
782C22×C7—42no—
783C22×C7—42no—
784C22×C7—42no—
785C22×C7—41no—
786C22×C7—42no—
787C22×C7—41no—
788C22×C7C24×C411yescharacteristic
789C22×C7C2×H(5,𝔽2)11yescharacteristic
790C22×C7C2×H(5,𝔽2)11yescharacteristic
791C22×C7C2×H(5,𝔽2)11yescharacteristic
792C22×C7C2×H(5,𝔽2)11yescharacteristic
793C22×C7#58511yescharacteristic
794C22×C7#58511yescharacteristic
795C2×D7—22no—
796C2×D7—22no—
797C2×D7—24no—
798C2×D7—22no—
799C2×D7—24no—
800C2×D7—22no—
801C2×D7—24no—
802C2×D7—22no—
803C2×D7—22no—
804C2×D7—42no—
805C2×D7—41no—
806C2×D7—41no—
807C2×D7—42no—
808C2×D7—41no—
809C2×D7—41no—
810C2×D7—41no—
811C2×D7—42no—
812C2×D7—41no—
813C2×D7—41no—
814C2×D7—42no—
815C2×D7—41no—
816C2×D7—816no—
817C4×C7—22no—
818C4×C7—24no—
819C4×C7—22no—
820C4×C7—22no—
821C4×C7—41no—
822C4×C7—41no—
823C4×C7—42no—
824C4×C7—42no—
825C4×C7#51814yes—
826Dic7—22no—
827Dic7—22no—
828Dic7—24no—
829Dic7—42no—
830Dic7—41no—
831Dic7—42no—
832Dic7—41no—
833Dic7—41no—
834Dic7—41no—
835C24—71no—
836C24—72no—
837C24—71no—
838C24—78no—
839C24—282no—
840C24—282no—
841C24—282no—
842C24—282no—
843C24—282no—
844C24—282no—
845C24C23×D712yes—
846C24C23×D711yescharacteristic
847#41—2816no—
848C2×Q8—74no—
849C2×Q8—281no—
850C2×Q8—281no—
851C2×D4—22no—
852C2×D4—22no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—74no—
856C2×D4—78no—
857C2×D4—78no—
858C2×D4—78no—
859C2×D4—74no—
860C2×D4—74no—
861C2×D4—74no—
862C2×D4—78no—
863C2×D4—142no—
864C2×D4—142no—
865C2×D4—282no—
866C2×D4—282no—
867C2×D4—281no—
868C2×D4—281no—
869C2×D4—2816no—
870C2×D4—282no—
871C2×D4—282no—
872C2×D4—282no—
873C2×D4—282no—
874C2×D4—282no—
875C2×D4—282no—
876C2×D4—281no—
877C2×D4—281no—
878C2×D4—281no—
879C2×D4—281no—
880C2×D4C2×C4×D714yes—
881C2×D4C2×C4×D718yes—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—24no—
887C22×C4—41no—
888C22×C4—41no—
889C22×C4—41no—
890C22×C4—41no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—71no—
894C22×C4—72no—
895C22×C4—71no—
896C22×C4—74no—
897C22×C4—74no—
898C22×C4—71no—
899C22×C4—71no—
900C22×C4—72no—
901C22×C4—71no—
902C22×C4—72no—
903C22×C4—71no—
904C22×C4—142no—
905C22×C4—142no—
906C22×C4—142no—
907C22×C4—142no—
908C22×C4—144no—
909C22×C4—282no—
910C22×C4—282no—
911C22×C4—282no—
912C22×C4—282no—
913C22×C4—282no—
914C22×C4—282no—
915C22×C4—282no—
916C22×C4—282no—
917C22×C4—282no—
918C22×C4—282no—
919C22×C4—282no—
920C22×C4C2×C4×D714yes—
921C22×C4C23×D711yescharacteristic
922C22×C4C23×D712yes—
923C22×C4C23×D711yescharacteristic
924C22×C4C23×D712yes—
925C22×C4C23×D712yes—
926C22×C4C23×D711yescharacteristic
927C22×C4C23×D711yescharacteristic
928C22×C4C23×D711yescharacteristic
929C22×C4C23×D711yescharacteristic
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—42no—
933C4⋊C4—74no—
934C4⋊C4—142no—
935C4⋊C4—142no—
936C4⋊C4—282no—
937C4⋊C4—282no—
938C4⋊C4—282no—
939C4⋊C4—281no—
940C4⋊C4—281no—
941C4⋊C4—282no—
942C4⋊C4C2×C4×D714yes—
943C22⋊C4—24no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—78no—
948C22⋊C4—78no—
949C22⋊C4—78no—
950C22⋊C4—78no—
951C22⋊C4—142no—
952C22⋊C4—144no—
953C22⋊C4—142no—
954C22⋊C4—142no—
955C22⋊C4—142no—
956C22⋊C4—282no—
957C22⋊C4—282no—
958C22⋊C4—282no—
959C22⋊C4—282no—
960C22⋊C4—281no—
961C22⋊C4—281no—
962C22⋊C4—281no—
963C22⋊C4—281no—
964C22⋊C4—282no—
965C22⋊C4—282no—
966C22⋊C4—282no—
967C22⋊C4—282no—
968C22⋊C4—282no—
969C22⋊C4—281no—
970C22⋊C4—281no—
971C22⋊C4—282no—
972C22⋊C4—282no—
973C22⋊C4—282no—
974C22⋊C4C2×C4×D718yes—
975C42—22no—
976C42—22no—
977C42—24no—
978C42—41no—
979C42—41no—
980C42—78no—
981C42—142no—
982C42—142no—
983C42—144no—
984C42—282no—
985C42—282no—
986C42—282no—
987C2×C7—44no—
988C2×C7—42no—
989C2×C7C2×#51811yescharacteristic
990C2×C7C4×H(5,𝔽2)11yescharacteristic
991C2×C7C4×H(5,𝔽2)11yescharacteristic
992C2×C7#354211yescharacteristic
993C2×C7#354211yescharacteristic
994C2×C7#354911yescharacteristic
995C2×C7#355111yescharacteristic
996D7—42no—
997D7—44no—
998D7—42no—
999C23—21no—
1000C23—22no—
1001C23—22no—
1002C23—21no—
1003C23—22no—
1004C23—21no—
1005C23—21no—
1006C23—22no—
1007C23—22no—
1008C23—21no—
1009C23—21no—
1010C23—22no—
1011C23—72no—
1012C23—74no—
1013C23—72no—
1014C23—141no—
1015C23—142no—
1016C23—141no—
1017C23—141no—
1018C23—142no—
1019C23—141no—
1020C23—141no—
1021C23—141no—
1022C23—142no—
1023C23—142no—
1024C23—141no—
1025C23—141no—
1026C23—141no—
1027C23—141no—
1028C23—142no—
1029C23—141no—
1030C23—141no—
1031C23—142no—
1032C23—288no—
1033C23—288no—
1034C23—288no—
1035C23—564no—
1036C23—564no—
1037C23—564no—
1038C23—564no—
1039C23C22×C4×D714yes—
1040C23C22×C4×D712yes—
1041C23C24×D711yescharacteristic
1042Q8—284no—
1043D4—28no—
1044D4—48no—
1045D4—148no—
1046D4—288no—
1047D4—284no—
1048D4—288no—
1049D4—288no—
1050D4—288no—
1051D4—284no—
1052D4—284no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—28no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—21no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—21no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—44no—
1075C2×C4—44no—
1076C2×C4—72no—
1077C2×C4—74no—
1078C2×C4—72no—
1079C2×C4—84no—
1080C2×C4—141no—
1081C2×C4—141no—
1082C2×C4—142no—
1083C2×C4—141no—
1084C2×C4—141no—
1085C2×C4—142no—
1086C2×C4—148no—
1087C2×C4—148no—
1088C2×C4—142no—
1089C2×C4—141no—
1090C2×C4—142no—
1091C2×C4—141no—
1092C2×C4—141no—
1093C2×C4—141no—
1094C2×C4—142no—
1095C2×C4—141no—
1096C2×C4—141no—
1097C2×C4—141no—
1098C2×C4—141no—
1099C2×C4—142no—
1100C2×C4—142no—
1101C2×C4—141no—
1102C2×C4—141no—
1103C2×C4—142no—
1104C2×C4—141no—
1105C2×C4—141no—
1106C2×C4—564no—
1107C2×C4—564no—
1108C2×C4—564no—
1109C2×C4—564no—
1110C2×C4C22×C4×D714yes—
1111C2×C4C22×C4×D712yes—
1112C2×C4C22×C4×D712yes—
1113C2×C4#654812yes—
1114C2×C4#654812yes—
1115C2×C4#655312yes—
1116C2×C4#655312yes—
1117C7#3441511yescharacteristic, complemented, Sylow
1118C22—22no—
1119C22—24no—
1120C22—22no—
1121C22—24no—
1122C22—22no—
1123C22—24no—
1124C22—42no—
1125C22—41no—
1126C22—41no—
1127C22—42no—
1128C22—42no—
1129C22—41no—
1130C22—41no—
1131C22—42no—
1132C22—142no—
1133C22—144no—
1134C22—142no—
1135C22—142no—
1136C22—142no—
1137C22—144no—
1138C22—142no—
1139C22—144no—
1140C22—142no—
1141C22—281no—
1142C22—282no—
1143C22—281no—
1144C22—281no—
1145C22—282no—
1146C22—281no—
1147C22—281no—
1148C22—282no—
1149C22—281no—
1150C22—282no—
1151C22—281no—
1152C22—281no—
1153C22—5616no—
1154C22C23×C4×D711yescharacteristic
1155C22C2×#654811yescharacteristic
1156C22C2×#654811yescharacteristic
1157C22C2×#655311yescharacteristic
1158C22C2×#655311yescharacteristic
1159C22#9061611yescharacteristic
1160C22#9061611yescharacteristic
1161C4—22no—
1162C4—24no—
1163C4—22no—
1164C4—22no—
1165C4—41no—
1166C4—42no—
1167C4—42no—
1168C4—41no—
1169C4—142no—
1170C4—142no—
1171C4—144no—
1172C4—281no—
1173C4—281no—
1174C4—281no—
1175C4—282no—
1176C4—281no—
1177C4—282no—
1178C4#9023614yes—
1179C2—44no—
1180C2—42no—
1181C2—282no—
1182C2—284no—
1183C2—282no—
1184C2C4×#654811yescharacteristic
1185C2C2×#9023611yescharacteristic
1186C2C4×#655311yescharacteristic
1187C2#1174302411yescharacteristic
1188C2#1174312611yescharacteristic
1189C2#1174324411yescharacteristic
1190C2#1174332011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutatorC22×C7C24×C4
FittingC4×C7×#121C2
socle, cosocleC23×C7C25
prime radicalC2×#90298C2
hypercenterC4×#121D7
hypocenterC7#34415
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. C4×C7×#121C2semidirect
3. #11740078C2semidirect
4. D4×(C2×D7)⋊C4C2semidirect
5. #11739840C2semidirect
6. #11739786C2semidirect
7. #11739774C2semidirect
8. C4×#6493C2semidirect
9. #11739515C2semidirect
10. #11733878C2semidirect
11. #11733876C2semidirect
12. #11733430C2semidirect
13. #11733424C2semidirect
14. #11733285C2semidirect
15. #11732938C2semidirect
16. #11732321C2semidirect
17. #11732112C2semidirect
18. #11731448C2semidirect
19. #11731317C2semidirect
20. #11731219C2semidirect
21. #11731078C2semidirect
22. #11731022C2semidirect
23. #11730920C2semidirect
28. C2×C4×C7×D4C22semidirect
29. C22×C42×C7C22semidirect
35. C2×C4×C22⋊D7C22semidirect
37. C2×#6489C22semidirect
38. #90298C4semidirect
42. C2×#6455C22semidirect
43. C2×D7×C4⋊C4C22semidirect
46. C2×(C22⋊D7)⋊C4C22semidirect
49. C2×C4×D28C22semidirect
51. C7×#389C22semidirect
52. C7×#388C22semidirect
53. C7×#386C22semidirect
54. C7×#380C22semidirect
55. C4×C7×C4⋊C4C22semidirect
56. C4×C7×C22⋊C4C22semidirect
58. #89993C22semidirect
59. #89992C22semidirect
63. #89985C22semidirect
64. #89985C22semidirect
65. #89985C22semidirect
66. #89985C22semidirect
67. #89984C22semidirect
68. C4×C22⋊Dic7C22semidirect
70. #89762C22semidirect
72. #89760C22semidirect
75. #89757C22semidirect
76. #89749C22semidirect
77. C4⋊C4×Dic7C22semidirect
78. C4⋊C4×Dic7C22semidirect
79. #89745C22semidirect
82. #89729C22semidirect
83. #89729C22semidirect
86. #89728C22semidirect
87. #89728C22semidirect
88. #89728C22semidirect
91. #89723C22semidirect
92. #89722C22semidirect
93. #89718C22semidirect
94. #89716C22semidirect
95. #89716C22semidirect
97. #89712C22semidirect
98. #89712C22semidirect
104. C4×(C2×D7)⋊C4C22semidirect
105. C4×(C2×D7)⋊C4C22semidirect
106. C4×(C2×D7)⋊C4C22semidirect
107. C4×C4⋊Dic7C22semidirect
108. #89704C22semidirect
109. #89701C22semidirect
110. #89701C22semidirect
111. #89700C22semidirect
113. #89442C22semidirect
115. #89440C22semidirect
116. #89440C22semidirect
117. #89438C22semidirect
119. #89437C22semidirect
120. #89437C22semidirect
121. #89422C22semidirect
122. #89420C22semidirect
123. #89418C22semidirect
140. C2×D4×D7C2×C4semidirect
143. C2×#1157C2×C4semidirect
153. C7×#121C2×C4semidirect
178. #6503C2×C4semidirect
179. #6501C2×C4semidirect
180. #6500C2×C4semidirect
182. #6493C2×C4semidirect
222. #6458C2×C4semidirect
225. #6455C2×C4semidirect
227. #6448C2×C4semidirect
228. #6445C2×C4semidirect
274. C4×#121D7semidirect
446. C2×C4×D4C2×D7semidirect
453. C22×C42C2×D7semidirect
471. #389C2×D7semidirect
483. #388C2×D7semidirect
501. #386C2×D7semidirect
511. #380C2×D7semidirect
517. C4×C4⋊C4C2×D7semidirect
525. C4×C22⋊C4C2×D7semidirect
679. #121C4×D7semidirect
1117. C7#34415semidirect

Maximal subgroups

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

subgroupindex
C2×#902982
C4×C7×#1212
#117400782
D4×(C2×D7)⋊C42
#117398402
#117397862
#117397742
C4×#64932
#117395152
#117338782
#117338762
#117334302
#117334242
#117332852
#117329382
#117323212
#117321122
#117314482
#117313172
#117312192
#117310782
#117310222
#117309202
#344157