Finite Group Databasebeta

← #13517076

Subgroups — #13517076

Order 1792.

2118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90371C211yesmaximal, characteristic
2C7×#2337C211yesmaximal, characteristic, complemented
3#11740399C211yesmaximal, characteristic, complemented
4#11734057C212yesmaximal, complemented
5#11733928C212yesmaximal, complemented
6#11733282C212yesmaximal, complemented
7#11733280C212yesmaximal, complemented
8#11732939C212yesmaximal, complemented
9#11732919C212yesmaximal, complemented
10#11732322C212yesmaximal
11#11732108C212yesmaximal, complemented
12#11731848C212yesmaximal, complemented
13#11731839C212yesmaximal, complemented
14D7×#383C211yesmaximal, characteristic, complemented
15#11731706C211yesmaximal, characteristic, complemented
16#11731198C211yesmaximal, characteristic, complemented
17#11731075C211yesmaximal, characteristic, complemented
18#11731023C212yesmaximal, complemented
19#11730900C212yesmaximal, complemented
20C2×C7×#124C2211yescharacteristic
21C2×#6509C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C2×#6501C2211yescharacteristic
24C2×D4×Dic7C2211yescharacteristic
25C2×C4×C22⋊D7C2212yes—
26#90371C4116yescomplemented
27C2×#6446C2212yes—
28C2×(C22⋊D7)⋊C4C2212yes—
29C2×(C22⋊D7)⋊C4C2212yes—
30C2×#6442C2212yes—
31C2×#6440C2212yes—
32C2×#6435C2211yescharacteristic
33C2×#6435C2211yescharacteristic
34C2×C42×D7C2211yescharacteristic
35C2×#6433C2211yescharacteristic
36C7×#391C2212yes—
37C7×#388C2212yes—
38C7×#388C2212yes—
39C7×#386C2212yes—
40C7×#385C2212yes—
41C7×#383C2211yescharacteristic
42C4×C7×C4⋊C4C2211yescharacteristic
43C4×C7×C22⋊C4C2212yes—
44#90002C2212yes—
45#89992C2212yes—
46#89982C2212yes—
47#89982C2212yes—
48C2×C7⋊#95C2212yes—
49#89761C2212yes—
50#89759C2212yes—
51#89750C2212yes—
52#89748C2212yes—
53C4⋊C4×Dic7C2212yes—
54#89745C2212yes—
55#89744C2212yes—
56#89744C2212yes—
57#89728C2212yes—
58#89728C2212yes—
59#89723C2212yes—
60#89723C2212yes—
61#89722C2212yes—
62#89718C2212yes—
63#89718C2212yes—
64#89717C2212yes—
65#89717C2212yes—
66#89716C2212yes—
67#89716C2212yes—
68#89715C2212yes—
69#89714C2212yes—
70C22⋊C4×Dic7C2212yes—
71C22⋊C4×Dic7C2212yes—
72C4×(C2×D7)⋊C4C2212yes—
73#89709C2211yescharacteristic
74C4×C4⋊Dic7C2211yescharacteristic
75#89705C2212yes—
76#89705C2212yes—
77#89704C2212yes—
78C4×Dic7⋊C4C2212yes—
79C4×Dic7⋊C4C2211yescharacteristic
80C4×Dic7⋊C4C2211yescharacteristic
81#89700C2212yes—
82#89440C2212yes—
83#89439C2212yes—
84#89438C2212yes—
85D7×#95C2211yescharacteristic
86D7×#95C2212yes—
87D7×#95C2212yes—
88D7×#95C2211yescharacteristic
89#89427C2212yes—
90#89426C2212yes—
91#89426C2212yes—
92#89426C2212yes—
93#89425C2212yes—
94#89425C2212yes—
95#89425C2212yes—
96#89424C2212yes—
97#89424C2212yes—
98#89423C2211yescharacteristic
99#89423C2212yes—
100#89423C2212yes—
101#89423C2211yescharacteristic
102#89423C2212yes—
103#89422C2212yes—
104#89422C2212yes—
105#89421C2212yes—
106#89419C2212yes—
107#89419C2212yes—
108#34401—71nomaximal, Sylow
109C22×C7×Q8C2311yescharacteristic
110C22×C7×D4C2311yescharacteristic
111C23×C4×C7C2312yes—
112C22×C22⋊D7C2312yes—
113C23×Dic7C2312yes—
114C23×Dic7C2312yes—
115C22×C4×D7C2311yescharacteristic
116C22×C4×D7C2312yes—
117C22×C4×D7C2312yes—
118C22×C4×D7C2311yescharacteristic
119C22×C4×D7C2311yescharacteristic
120C7×#124C2×C418yescomplemented
121C2×C7×C4⋊C4C2312yes—
122C2×C7×C4⋊C4C2312yes—
123C2×C7×C22⋊C4C2312yes—
124C2×C7×C22⋊C4C2312yes—
125C2×C7×C22⋊C4C2312yes—
126C2×C7×C22⋊C4C2312yes—
127C2×C7×C22⋊C4C2312yes—
128C2×C42×C7C2311yescharacteristic
129C2×C42×C7C2311yescharacteristic
130C2×C42×C7C2312yes—
131C2×C42×C7C2311yescharacteristic
132C2×C22⋊Dic7C2312yes—
133C2×C22⋊Dic7C2312yes—
134C2×C22⋊Dic7C2312yes—
135C2×C22⋊Dic7C2312yes—
136C2×C22⋊Dic7C2312yes—
137#6509C2×C418yescomplemented
138Q8×Dic7C2×C418yescomplemented
139#6501C2×C418yes—
140D4×Dic7C2×C418yescomplemented
141C4×C22⋊D7—44no—
142C2×(C2×D7)⋊C4C2312yes—
143C2×(C2×D7)⋊C4C2312yes—
144C2×(C2×D7)⋊C4C2312yes—
145C2×C4⋊Dic7C2312yes—
146C2×C4⋊Dic7C2312yes—
147C2×C4⋊Dic7C2311yescharacteristic
148C2×C4⋊Dic7C2311yescharacteristic
149C2×C4⋊Dic7C2312yes—
150C2×Dic7⋊C4C2312yes—
151C2×Dic7⋊C4C2312yes—
152C2×Dic7⋊C4C2312yes—
153C2×Dic7⋊C4C2312yes—
154C2×Dic7⋊C4C2312yes—
155C2×Dic7⋊C4C2312yes—
156C2×Dic7⋊C4C2312yes—
157C2×Dic7⋊C4C2312yes—
158C2×Dic7⋊C4C2312yes—
159C2×Dic7⋊C4C2312yes—
160C2×Dic7⋊C4C2312yes—
161C2×C4×Dic7C2311yescharacteristic
162C2×C4×Dic7C2311yescharacteristic
163C2×C4×Dic7C2312yes—
164C2×C4×Dic7C2312yes—
165C2×C4×Dic7C2312yes—
166C2×C4×Dic7C2312yes—
167C2×C4×Dic7C2312yes—
168C2×C4×Dic7C2311yescharacteristic
169C2×C4×Dic7C2311yescharacteristic
170C2×C4×Dic7C2311yescharacteristic
171C2×C4×Dic7C2312yes—
172#6446C2×C4116yescomplemented
173(C22⋊D7)⋊C4—44no—
174(C22⋊D7)⋊C4C2×C4116yescomplemented
175#6442C2×C4116yescomplemented
176#6440C2×C4116yescomplemented
177#6435—42no—
178#6435—42no—
179C42×D7C2×C418yescomplemented
180#6433C2×C418yescomplemented
181C7×#95C2311yescharacteristic
182C7×#95C2312yes—
183C7×#95C2312yes—
184C7×#95C2312yes—
185C7×#95C2312yes—
186C7×#95C2312yes—
187C7×#95C2311yescharacteristic
188C7⋊#95C2312yes—
189C7⋊#95C2312yes—
190C7⋊#95C2312yes—
191C7⋊#95C2312yes—
192C7⋊#95C2312yes—
193C7⋊#95C2312yes—
194C7⋊#95C2312yes—
195C7⋊#95C2312yes—
196C7⋊#95C2312yes—
197C7⋊#95C2312yes—
198C7⋊#95C2312yes—
199C7⋊#95C2312yes—
200C7⋊#95C2312yes—
201C7⋊#95C2312yes—
202C7⋊#95C2312yes—
203C7⋊#95C2312yes—
204C7⋊#95C2311yescharacteristic
205C7⋊#95C2311yescharacteristic
206C7⋊#95C2312yes—
207C7⋊#95C2312yes—
208C7⋊#95C2312yes—
209C7⋊#95C2312yes—
210C7⋊#95C2312yes—
211C2×#529—71no—
212#2383—72no—
213#2383—72no—
214#2359—72no—
215#2359—72no—
216#2353—72no—
217#2349—72no—
218#2347—72no—
219#2343—72no—
220#2337—71no—
221#2337D711yescharacteristic, complemented
222#2336—71no—
223#2336—71no—
224#2329—72no—
225#2325—72no—
226#2320—72no—
227#2318—72no—
228#2285—71no—
229C2×#383—71no—
230C24×C7C2412yes—
231C23×D7C2411yescharacteristic
232C2×C7×Q8—42no—
233C2×C7×Q8C22×C414yes—
234C2×C7×D4—42no—
235C2×C7×D4C22×C414yes—
236C22×C4×C7—42no—
237C22×C4×C7—42no—
238C22×C4×C7—42no—
239C22×C4×C7C2412yes—
240C22×C4×C7C2412yes—
241C22×C4×C7C2412yes—
242C22×C4×C7C2412yes—
243C22×C4×C7C2411yescharacteristic
244C22×C4×C7C2411yescharacteristic
245C22×C4×C7C2412yes—
246C22×C4×C7C2411yescharacteristic
247C2×C22⋊D7—24no—
248C2×C22⋊D7—24no—
249C2×C22⋊D7C22×C418yes—
250C22×Dic7—42no—
251C22×Dic7—42no—
252C22×Dic7—42no—
253C22×Dic7—42no—
254C22×Dic7—42no—
255C22×Dic7C22×C418yes—
256C22×Dic7C2412yes—
257C22×Dic7C2412yes—
258C22×Dic7C2412yes—
259C22×Dic7C2412yes—
260C22×Dic7C2411yescharacteristic
261C22×Dic7C2412yes—
262C22×Dic7C2411yescharacteristic
263C22×Dic7C2412yes—
264C22×Dic7C2411yescharacteristic
265C2×C4×D7—22no—
266C2×C4×D7—22no—
267C2×C4×D7—24no—
268C2×C4×D7—24no—
269C2×C4×D7—42no—
270C2×C4×D7—42no—
271C2×C4×D7—42no—
272C2×C4×D7—42no—
273C2×C4×D7—42no—
274C2×C4×D7—42no—
275C2×C4×D7C22×C414yes—
276C2×C4×D7C22×C414yes—
277C2×C4×D7C22×C414yes—
278C7×C4⋊C4—42no—
279C7×C4⋊C4—42no—
280C7×C22⋊C4—42no—
281C7×C22⋊C4—42no—
282C7×C22⋊C4—42no—
283C7×C22⋊C4C22×C418yes—
284C7×C22⋊C4C22×C418yes—
285C42×C7—41no—
286C42×C7—41no—
287C42×C7—42no—
288C42×C7C22×C414yes—
289C22⋊Dic7—42no—
290C22⋊Dic7—42no—
291C22⋊Dic7—42no—
292C22⋊Dic7C22×C418yes—
293C22⋊Dic7C22×C418yes—
294(C2×D7)⋊C4—24no—
295(C2×D7)⋊C4—24no—
296(C2×D7)⋊C4C22×C418yes—
297C4⋊Dic7—42no—
298C4⋊Dic7—42no—
299C4⋊Dic7C22×C414yes—
300C4⋊Dic7C22×C414yes—
301C4⋊Dic7C22×C418yes—
302Dic7⋊C4—42no—
303Dic7⋊C4—42no—
304Dic7⋊C4—42no—
305Dic7⋊C4—42no—
306Dic7⋊C4—42no—
307Dic7⋊C4—42no—
308Dic7⋊C4—42no—
309Dic7⋊C4—42no—
310Dic7⋊C4C22×C418yes—
311Dic7⋊C4C22×C418yes—
312Dic7⋊C4C22×C418yes—
313C4×Dic7—41no—
314C4×Dic7—41no—
315C4×Dic7—42no—
316C4×Dic7—42no—
317C4×Dic7—42no—
318C4×Dic7—42no—
319C4×Dic7—42no—
320C4×Dic7C22×C414yes—
321C4×Dic7C22×C414yes—
322C4×Dic7C22×C414yes—
323C4×Dic7C22×C418yes—
324#529—716no—
325C2×#126—72no—
326C2×#125—71no—
327C2×#124C2×D711yescharacteristic
328C2×#123—72no—
329C2×C22⋊Q8—71no—
330C2×#121—71no—
331C2×C4×Q8—71no—
332C2×C4×D4—71no—
333C2×C4×D4—72no—
334C2×C4×D4—72no—
335C2×C4×D4—72no—
336C2×#117—72no—
337C2×#117—71no—
338C2×#117—71no—
339C22×C42—71no—
340#391—72no—
341#391C2×D712yes—
342#389—72no—
343#389—72no—
344#389—72no—
345#389—72no—
346#389—72no—
347#389—72no—
348#388—72no—
349#388—72no—
350#388—72no—
351#388—72no—
352#388—72no—
353#388—72no—
354#388C2×D712yes—
355#388C2×D712yes—
356#387—72no—
357#387—72no—
358#387—72no—
359#387—72no—
360#387—72no—
361#387—72no—
362#387—72no—
363#387—72no—
364#387—72no—
365#387—72no—
366#387—72no—
367#387—72no—
368#386—72no—
369#386—72no—
370#386—72no—
371#386C2×D712yes—
372#385—72no—
373#385—72no—
374#385—72no—
375#385—72no—
376#385—72no—
377#385—72no—
378#385—72no—
379#385C2×D712yes—
380#384—72no—
381#383—71no—
382#383—72no—
383#383—72no—
384#383—72no—
385#383—71no—
386#383—71no—
387#383C2×D711yescharacteristic
388#382—72no—
389#382—72no—
390#381—72no—
391#380—72no—
392#380—72no—
393#380—72no—
394C4×C4⋊C4—72no—
395C4×C4⋊C4—71no—
396C4×C4⋊C4—72no—
397C4×C4⋊C4—71no—
398C4×C4⋊C4—71no—
399C4×C4⋊C4—72no—
400C4×C4⋊C4C2×D711yescharacteristic
401C4×C22⋊C4—72no—
402C4×C22⋊C4—72no—
403C4×C22⋊C4—72no—
404C4×C22⋊C4—72no—
405C4×C22⋊C4C2×D712yes—
406#376—72no—
407C2×#95—72no—
408C2×#95—72no—
409C2×#95—71no—
410C2×#95—71no—
411C2×#95—72no—
412C23×C7—22no—
413C23×C7—22no—
414C23×C7—22no—
415C23×C7—22no—
416C23×C7—22no—
417C23×C7—22no—
418C23×C7C23×C414yes—
419C23×C7C2511yescharacteristic
420C22×D7—22no—
421C22×D7—22no—
422C22×D7C23×C412yes—
423C22×D7H(5,𝔽2)12yes—
424C22×D72−1+412yes—
425C7×Q8—44no—
426C7×D4—44no—
427C2×C4×C7—21no—
428C2×C4×C7—21no—
429C2×C4×C7—22no—
430C2×C4×C7—22no—
431C2×C4×C7—22no—
432C2×C4×C7—22no—
433C2×C4×C7—22no—
434C2×C4×C7—22no—
435C2×C4×C7—22no—
436C2×C4×C7—22no—
437C2×C4×C7—22no—
438C2×C4×C7—22no—
439C2×C4×C7—22no—
440C2×C4×C7—22no—
441C2×C4×C7—22no—
442C2×C4×C7—22no—
443C2×C4×C7—22no—
444C2×C4×C7—22no—
445C2×C4×C7—84no—
446C2×C4×C7C23×C412yes—
447C2×C4×C7C23×C412yes—
448C2×C4×C7C23×C414yes—
449C2×C4×C7C23×C412yes—
450C22⋊D7—216no—
451C2×Dic7—22no—
452C2×Dic7—21no—
453C2×Dic7—21no—
454C2×Dic7—22no—
455C2×Dic7—22no—
456C2×Dic7—22no—
457C2×Dic7—22no—
458C2×Dic7—22no—
459C2×Dic7—22no—
460C2×Dic7—22no—
461C2×Dic7—22no—
462C2×Dic7—22no—
463C2×Dic7—22no—
464C2×Dic7—22no—
465C2×Dic7—22no—
466C2×Dic7—22no—
467C2×Dic7—22no—
468C2×Dic7—22no—
469C2×Dic7—22no—
470C2×Dic7—22no—
471C2×Dic7—48no—
472C2×Dic7—84no—
473C2×Dic7C23×C412yes—
474C2×Dic7C23×C412yes—
475C2×Dic7C23×C412yes—
476C2×Dic7C23×C414yes—
477C2×Dic7C23×C414yes—
478C4×D7—28no—
479C4×D7—44no—
480C4×D7—44no—
481C4×D7—84no—
482C4×D7—84no—
483C22×Q8C22×D711yescharacteristic
484C22×D4—72no—
485C22×D4C22×D711yescharacteristic
486C23×C4—72no—
487C23×C4—71no—
488C23×C4—71no—
489C23×C4—71no—
490C23×C4—72no—
491C23×C4—72no—
492C23×C4—72no—
493C23×C4C22×D712yes—
494#126—716no—
495#125—78no—
496#124C4×D718yescomplemented
497#123—716no—
498C22⋊Q8—78no—
499#121—78no—
500C4×Q8—78no—
501C4×D4—78no—
502C4×D4—716no—
503C4×D4—284no—
504C4×D4—284no—
505#117—716no—
506#117—282no—
507#117—282no—
508C2×C4⋊C4—72no—
509C2×C4⋊C4—72no—
510C2×C4⋊C4—71no—
511C2×C4⋊C4—72no—
512C2×C4⋊C4—71no—
513C2×C4⋊C4—72no—
514C2×C4⋊C4—72no—
515C2×C4⋊C4—72no—
516C2×C4⋊C4—72no—
517C2×C4⋊C4—72no—
518C2×C4⋊C4—72no—
519C2×C4⋊C4—72no—
520C2×C4⋊C4—72no—
521C2×C4⋊C4—72no—
522C2×C4⋊C4—72no—
523C2×C4⋊C4—72no—
524C2×C4⋊C4C22×D712yes—
525C2×C4⋊C4C22×D712yes—
526C2×C22⋊C4—72no—
527C2×C22⋊C4—72no—
528C2×C22⋊C4—72no—
529C2×C22⋊C4—72no—
530C2×C22⋊C4—72no—
531C2×C22⋊C4—72no—
532C2×C22⋊C4—72no—
533C2×C22⋊C4—72no—
534C2×C22⋊C4C22×D712yes—
535C2×C22⋊C4C22×D712yes—
536C2×C22⋊C4C22×D712yes—
537C2×C22⋊C4C22×D712yes—
538C2×C22⋊C4C22×D712yes—
539C2×C42—71no—
540C2×C42—72no—
541C2×C42—71no—
542C2×C42—71no—
543C2×C42—78no—
544C2×C42—71no—
545C2×C42—71no—
546C2×C42—72no—
547C2×C42—72no—
548C2×C42—72no—
549C2×C42—72no—
550C2×C42—72no—
551C2×C42C22×D711yescharacteristic
552C2×C42C22×D711yescharacteristic
553C2×C42C22×D712yes—
554C2×C42C22×D711yescharacteristic
555#95—72no—
556#95—72no—
557#95—72no—
558#95—72no—
559#95—71no—
560#95—72no—
561#95—72no—
562#95—72no—
563#95—72no—
564#95—72no—
565#95—71no—
566#95—72no—
567#95—72no—
568#95—72no—
569#95—72no—
570#95—72no—
571#95—72no—
572#95—72no—
573#95—72no—
574#95—72no—
575#95—72no—
576#95—72no—
577#95—72no—
578#95C22×D712yes—
579#95C22×D711yescharacteristic
580#95C22×D712yes—
581#95C22×D711yescharacteristic
582#95C22×D712yes—
583#95C22×D712yes—
584#95C22×D712yes—
585C22×C7—24no—
586C22×C7—24no—
587C22×C7—24no—
588C22×C7—42no—
589C22×C7—42no—
590C22×C7—42no—
591C22×C7—42no—
592C22×C7C24×C411yescharacteristic
593C22×C7C2×H(5,𝔽2)11yescharacteristic
594C22×C7C2×2−1+411yescharacteristic
595C22×C7#58512yes—
596C22×C7#58512yes—
597C2×D7—22no—
598C2×D7—22no—
599C2×D7—24no—
600C2×D7—24no—
601C2×D7#52014yes—
602C4×C7—22no—
603C4×C7—22no—
604C4×C7—22no—
605C4×C7—24no—
606C4×C7—42no—
607C4×C7—42no—
608C4×C7—42no—
609C4×C7—42no—
610Dic7—22no—
611Dic7—24no—
612Dic7—22no—
613Dic7—22no—
614Dic7—24no—
615Dic7—42no—
616Dic7—42no—
617Dic7—42no—
618Dic7—42no—
619C24—71no—
620C24C23×D712yes—
621C2×Q8—42no—
622C2×Q8C2×C4×D714yes—
623C2×D4—42no—
624C2×D4—78no—
625C2×D4—144no—
626C2×D4—144no—
627C2×D4C2×C4×D714yes—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—71no—
632C22×C4—72no—
633C22×C4—71no—
634C22×C4—71no—
635C22×C4—72no—
636C22×C4—78no—
637C22×C4—74no—
638C22×C4—74no—
639C22×C4—74no—
640C22×C4—72no—
641C22×C4—72no—
642C22×C4—72no—
643C22×C4—72no—
644C22×C4—142no—
645C22×C4—142no—
646C22×C4—144no—
647C22×C4—144no—
648C22×C4—282no—
649C22×C4—282no—
650C22×C4—282no—
651C22×C4—282no—
652C22×C4—282no—
653C22×C4—282no—
654C22×C4—282no—
655C22×C4—282no—
656C22×C4—282no—
657C22×C4—282no—
658C22×C4—282no—
659C22×C4C23×D712yes—
660C22×C4C23×D712yes—
661C22×C4C23×D712yes—
662C22×C4C23×D712yes—
663C22×C4C23×D711yescharacteristic
664C22×C4C23×D711yescharacteristic
665C22×C4C23×D712yes—
666C22×C4C23×D711yescharacteristic
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—78no—
670C4⋊C4—78no—
671C4⋊C4—78no—
672C4⋊C4—74no—
673C4⋊C4—74no—
674C4⋊C4—78no—
675C4⋊C4—282no—
676C4⋊C4—282no—
677C4⋊C4—282no—
678C4⋊C4—282no—
679C4⋊C4—282no—
680C4⋊C4—282no—
681C4⋊C4—282no—
682C4⋊C4—282no—
683C4⋊C4—282no—
684C4⋊C4—282no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—78no—
689C22⋊C4—78no—
690C22⋊C4—78no—
691C22⋊C4—144no—
692C22⋊C4—144no—
693C22⋊C4—282no—
694C22⋊C4—282no—
695C22⋊C4—282no—
696C22⋊C4C2×C4×D718yes—
697C22⋊C4C2×C4×D718yes—
698C42—41no—
699C42—41no—
700C42—42no—
701C42—74no—
702C42—74no—
703C42—74no—
704C42—78no—
705C42—282no—
706C42—282no—
707C42—282no—
708C42—281no—
709C42—281no—
710C42—282no—
711C42—282no—
712C42C2×C4×D714yes—
713C2×C7—44no—
714C2×C7C2×#52011yescharacteristic
715C2×C7#342811yescharacteristic
716C2×C7#342811yescharacteristic
717C2×C7#356012yes—
718C2×C7#356412yes—
719D7—24no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—72no—
727C23—72no—
728C23—72no—
729C23—142no—
730C23—142no—
731C23C22×C4×D714yes—
732C23C24×D711yescharacteristic
733Q8—44no—
734D4—44no—
735D4—1416no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—72no—
755C2×C4—72no—
756C2×C4—72no—
757C2×C4—74no—
758C2×C4—74no—
759C2×C4—84no—
760C2×C4—148no—
761C2×C4—142no—
762C2×C4—142no—
763C2×C4—142no—
764C2×C4—142no—
765C2×C4—141no—
766C2×C4—142no—
767C2×C4—141no—
768C2×C4—142no—
769C2×C4—142no—
770C2×C4—142no—
771C2×C4—142no—
772C2×C4—142no—
773C2×C4—142no—
774C2×C4—142no—
775C2×C4—142no—
776C2×C4—142no—
777C2×C4—142no—
778C2×C4—142no—
779C2×C4—142no—
780C2×C4—142no—
781C2×C4—284no—
782C2×C4—284no—
783C2×C4—288no—
784C2×C4—564no—
785C2×C4—564no—
786C2×C4—564no—
787C2×C4C22×C4×D712yes—
788C2×C4C22×C4×D712yes—
789C2×C4C22×C4×D712yes—
790C2×C4C22×C4×D714yes—
791C7#3440111yescharacteristic, complemented, Sylow
792C22—24no—
793C22—24no—
794C22—24no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—74no—
800C22—144no—
801C22—144no—
802C22—142no—
803C22—142no—
804C22C23×C4×D711yescharacteristic
805C22#9061612yes—
806C22D7×H(5,𝔽2)11yescharacteristic
807C22#9061812yes—
808C22D7×2−1+411yescharacteristic
809C4—22no—
810C4—22no—
811C4—24no—
812C4—22no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—142no—
818C4—144no—
819C4—142no—
820C4—142no—
821C4—144no—
822C4—282no—
823C4—282no—
824C4—282no—
825C4—282no—
826C2—44no—
827C2—144no—
828C2#1174290211yescharacteristic
829C2#1174292411yescharacteristic
830C2D7×#52011yescharacteristic
831C2#1174349312yes—
832C2#1174363812yes—
subgroupG/H
center, FrattiniC23C24×D7
commutatorC22×C7C24×C4
FittingC7×#2337C2
socle, cosocleC23×C7C25
prime radicalC2×#6501C22
hypercenter#2337D7
hypocenterC7#34401
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2337

Complements

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

NH ≅ G/Ntype
2. C7×#2337C2semidirect
3. #11740399C2semidirect
4. #11734057C2semidirect
5. #11733928C2semidirect
6. #11733282C2semidirect
7. #11733280C2semidirect
8. #11732939C2semidirect
9. #11732919C2semidirect
11. #11732108C2semidirect
12. #11731848C2semidirect
13. #11731839C2semidirect
14. D7×#383C2semidirect
15. #11731706C2semidirect
16. #11731198C2semidirect
17. #11731075C2semidirect
18. #11731023C2semidirect
19. #11730900C2semidirect
26. #90371C4semidirect
120. C7×#124C2×C4semidirect
137. #6509C2×C4semidirect
138. Q8×Dic7C2×C4semidirect
140. D4×Dic7C2×C4semidirect
172. #6446C2×C4semidirect
174. (C22⋊D7)⋊C4C2×C4semidirect
175. #6442C2×C4semidirect
176. #6440C2×C4semidirect
179. C42×D7C2×C4semidirect
180. #6433C2×C4semidirect
221. #2337D7semidirect
496. #124C4×D7semidirect
791. C7#34401semidirect

Maximal subgroups

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

subgroupindex
C2×#903712
C7×#23372
#117403992
#117340572
#117339282
#117332822
#117332802
#117329392
#117329192
#117323222
#117321082
#117318482
#117318392
D7×#3832
#117317062
#117311982
#117310752
#117310232
#117309002
#344017