Finite Group Databasebeta

← #13561774

Subgroups — #13561774

Order 1792.

1646 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#387C211yesmaximal, characteristic, complemented
2#11739644C211yesmaximal, characteristic
3#11739628C211yesmaximal, characteristic, complemented
4#11739620C212yesmaximal, complemented
5#11739522C211yesmaximal, characteristic
6#11739521C211yesmaximal, characteristic, complemented
7#11732883C212yesmaximal, complemented
8#11732870C212yesmaximal, complemented
9#11732849C212yesmaximal, complemented
10#11732715C212yesmaximal, complemented
11#11732664C212yesmaximal, complemented
12#11732651C212yesmaximal, complemented
13#11732609C212yesmaximal, complemented
14#11732606C212yesmaximal, complemented
15#11730820C212yesmaximal, complemented
16#11730797C212yesmaximal, complemented
17#11730796C212yesmaximal, complemented
18#11730779C211yesmaximal, characteristic, complemented
19#11730778C211yesmaximal, characteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C42×C7C2211yescharacteristic
23C2×#6493C2211yescharacteristic
24C2×#6492C2212yes—
25C2×C4×C22⋊D7C2212yes—
26C2×#6487C2211yescharacteristic
27C2×#6487C2212yes—
28C2×#6461C2212yes—
29C2×#6438C2211yescharacteristic
30C2×#6432C2211yescharacteristic
31C7×#387C2212yes—
32C7×#387C2212yes—
33C7×#387C2212yes—
34C7×#387C2212yes—
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2211yescharacteristic
39#89985C2212yes—
40#89985C2212yes—
41#89985C2212yes—
42#89985C2212yes—
43#89984C2211yescharacteristic
44#89984C2211yescharacteristic
45#89984C2212yes—
46#89983C2212yes—
47#89982C2212yes—
48#89982C2212yes—
49C4×C22⋊Dic7C2212yes—
50#89766C2212yes—
51#89766C2212yes—
52#89766C2212yes—
53#89765C2212yes—
54#89763C2212yes—
55#89762C2212yes—
56#89758C2212yes—
57#89758C2212yes—
58#89756C2212yes—
59#89756C2212yes—
60#89755C2212yes—
61#89754C2212yes—
62#89753C2212yes—
63#89751C2212yes—
64#89750C2212yes—
65#89712C2212yes—
66#89712C2212yes—
67#89711C2211yescharacteristic
68#89708C2211yescharacteristic
69#89707C2211yescharacteristic
70#89701C2212yes—
71#89701C2211yescharacteristic
72#89700C2211yescharacteristic
73#89700C2212yes—
74#89700C2211yescharacteristic
75#89448C2212yes—
76#89447C2212yes—
77#89447C2212yes—
78#89446C2212yes—
79#89445C2212yes—
80#89445C2212yes—
81#89442C2212yes—
82#89442C2212yes—
83#89441C2212yes—
84#89440C2212yes—
85#89440C2212yes—
86#89440C2212yes—
87#89439C2212yes—
88#89437C2212yes—
89#89436C2212yes—
90#89432C2212yes—
91#89430C2212yes—
92#89430C2212yes—
93#89430C2212yes—
94#89429C2212yes—
95#89429C2212yes—
96#89427C2212yes—
97#89426C2212yes—
98#89426C2212yes—
99#89425C2212yes—
100#89424C2212yes—
101#89424C2212yes—
102#89422C2212yes—
103#89419C2212yes—
104#89418C2212yes—
105#89418C2212yes—
106#89418C2212yes—
107#36763—71nomaximal, Sylow
108C23×C4×C7C2311yescharacteristic
109C23×C4×C7C2311yescharacteristic
110C23×C4×C7C2311yescharacteristic
111C23×C4×C7C2311yescharacteristic
112C23×C4×C7C2311yescharacteristic
113C23×C4×C7C2311yescharacteristic
114C23×C4×C7C2311yescharacteristic
115C22×C22⋊D7C2312yes—
116C22×D28C2311yescharacteristic
117C22×C4×D7C2312yes—
118C22×Dic14C2312yes—
119C22×Dic14C2311yescharacteristic
120C2×C7×C4⋊C4—24no—
121C2×C7×C4⋊C4—42no—
122C2×C7×C4⋊C4C2312yes—
123C2×C7×C4⋊C4C2312yes—
124C2×C7×C4⋊C4C2312yes—
125C2×C7×C4⋊C4C2312yes—
126C2×C42×C7—42no—
127C2×C42×C7C2311yescharacteristic
128C2×C42×C7C2311yescharacteristic
129C2×C42×C7C2311yescharacteristic
130C2×C42×C7C2311yescharacteristic
131C2×C22⋊Dic7C2312yes—
132C2×C22⋊Dic7C2312yes—
133C2×C22⋊Dic7C2312yes—
134#6493—24no—
135#6492—44no—
136C4×C22⋊D7—44no—
137C2×(C2×D7)⋊C4C2312yes—
138C2×(C2×D7)⋊C4C2312yes—
139C2×(C2×D7)⋊C4C2312yes—
140C2×(C2×D7)⋊C4C2312yes—
141C2×(C2×D7)⋊C4C2312yes—
142C2×(C2×D7)⋊C4C2312yes—
143C2×(C2×D7)⋊C4C2312yes—
144C2×(C2×D7)⋊C4C2312yes—
145C2×(C2×D7)⋊C4C2312yes—
146C2×(C2×D7)⋊C4C2312yes—
147C2×(C2×D7)⋊C4C2312yes—
148C2×(C2×D7)⋊C4C2312yes—
149C2×C4⋊Dic7C2312yes—
150C2×C4⋊Dic7C2311yescharacteristic
151C2×C4⋊Dic7C2311yescharacteristic
152C2×C4⋊Dic7C2311yescharacteristic
153C2×C4⋊Dic7C2311yescharacteristic
154C2×C4⋊Dic7C2311yescharacteristic
155C2×C4⋊Dic7C2312yes—
156C2×C4⋊Dic7C2312yes—
157C2×C4⋊Dic7C2311yescharacteristic
158#6487—24no—
159#6487—44no—
160C2×Dic7⋊C4C2312yes—
161C2×Dic7⋊C4C2312yes—
162C2×Dic7⋊C4C2312yes—
163C2×Dic7⋊C4C2312yes—
164C2×Dic7⋊C4C2312yes—
165C2×Dic7⋊C4C2312yes—
166C2×Dic7⋊C4C2312yes—
167C2×Dic7⋊C4C2312yes—
168C2×Dic7⋊C4C2312yes—
169C2×Dic7⋊C4C2312yes—
170C2×C4×Dic7C2312yes—
171C2×C4×Dic7C2312yes—
172C2×C4×Dic7C2312yes—
173#6461—44no—
174#6438—42no—
175#6432—42no—
176C7×#95C2312yes—
177C7×#95C2312yes—
178C7×#95C2312yes—
179C7×#95C2312yes—
180C7×#95C2312yes—
181C7×#95C2312yes—
182C7×#95C2312yes—
183C7×#95C2312yes—
184C7⋊#95C2312yes—
185C7⋊#95C2312yes—
186C7⋊#95C2312yes—
187C7⋊#95C2312yes—
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⋊#95C2312yes—
205C7⋊#95C2312yes—
206#2857—71no—
207#2850—71no—
208#2799—72no—
209#2790—72no—
210#2772—72no—
211#2767—72no—
212#2751—72no—
213#2739—72no—
214#2716—72no—
215#2715—72no—
216#2627—71no—
217#2618—71no—
218#2488—72no—
219#2481—72no—
220#2450—72no—
221#2419—72no—
222#2329—71no—
223#2325—71no—
224C2×#387D711yescharacteristic, complemented
225C24×C7C2411yescharacteristic
226C23×D7C2412yes—
227C22×C4×C7—22no—
228C22×C4×C7—22no—
229C22×C4×C7—22no—
230C22×C4×C7—22no—
231C22×C4×C7—22no—
232C22×C4×C7—22no—
233C22×C4×C7—22no—
234C22×C4×C7—22no—
235C22×C4×C7—22no—
236C22×C4×C7—22no—
237C22×C4×C7—41no—
238C22×C4×C7—41no—
239C22×C4×C7—41no—
240C22×C4×C7—41no—
241C22×C4×C7—41no—
242C22×C4×C7—41no—
243C22×C4×C7—41no—
244C22×C4×C7—41no—
245C22×C4×C7—41no—
246C22×C4×C7—41no—
247C22×C4×C7#4114yes—
248C22×C4×C7C2411yescharacteristic
249C22×C4×C7C2412yes—
250C22×C4×C7C2412yes—
251C22×C4×C7C2412yes—
252C22×C4×C7C2412yes—
253C22×C4×C7C2411yescharacteristic
254C22×C4×C7C2411yescharacteristic
255C22×C4×C7C2411yescharacteristic
256C22×C4×C7C2411yescharacteristic
257C22×C4×C7C2411yescharacteristic
258C2×C22⋊D7—24no—
259C2×C22⋊D7—24no—
260C2×C22⋊D7—24no—
261C22×Dic7C2412yes—
262C22×Dic7C2412yes—
263C22×Dic7C2412yes—
264C22×Dic7C2412yes—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C2×D28—22no—
269C2×D28—41no—
270C2×D28—41no—
271C2×C4×D7—42no—
272C2×C4×D7—42no—
273C2×C4×D7—42no—
274C2×Dic14—22no—
275C2×Dic14—24no—
276C2×Dic14—42no—
277C2×Dic14—41no—
278C2×Dic14—42no—
279C2×Dic14—41no—
280C7×C4⋊C4—24no—
281C7×C4⋊C4—24no—
282C7×C4⋊C4—24no—
283C7×C4⋊C4—42no—
284C42×C7—22no—
285C42×C7—22no—
286C42×C7—41no—
287C42×C7—41no—
288C22⋊Dic7—24no—
289C22⋊Dic7—24no—
290C22⋊Dic7—24no—
291(C2×D7)⋊C4—24no—
292(C2×D7)⋊C4—24no—
293(C2×D7)⋊C4—24no—
294(C2×D7)⋊C4—42no—
295(C2×D7)⋊C4—42no—
296(C2×D7)⋊C4—42no—
297(C2×D7)⋊C4—42no—
298(C2×D7)⋊C4—42no—
299(C2×D7)⋊C4—42no—
300(C2×D7)⋊C4—42no—
301(C2×D7)⋊C4—42no—
302(C2×D7)⋊C4—42no—
303C4⋊Dic7—22no—
304C4⋊Dic7—22no—
305C4⋊Dic7—24no—
306C4⋊Dic7—41no—
307C4⋊Dic7—41no—
308C4⋊Dic7—42no—
309C4⋊Dic7—42no—
310C4⋊Dic7—41no—
311C4⋊Dic7—41no—
312Dic7⋊C4—24no—
313Dic7⋊C4—42no—
314Dic7⋊C4—42no—
315Dic7⋊C4—42no—
316Dic7⋊C4—42no—
317Dic7⋊C4—42no—
318Dic7⋊C4—42no—
319Dic7⋊C4—42no—
320Dic7⋊C4—42no—
321Dic7⋊C4—42no—
322C4×Dic7—42no—
323C4×Dic7—42no—
324C4×Dic7—42no—
325C2×C4⋊Q8—71no—
326C2×#126—72no—
327C2×#124—71no—
328C2×#123—72no—
329C2×C22⋊Q8—71no—
330C2×C22⋊Q8—72no—
331C2×#121—71no—
332C2×C4×D4—72no—
333C22×C4⋊C4C2×D711yescharacteristic
334C22×C4⋊C4C2×D711yescharacteristic
335C22×C42C2×D711yescharacteristic
336#400—72no—
337#400—72no—
338#400—72no—
339#400—72no—
340#400—72no—
341#400—72no—
342#400—72no—
343#398—72no—
344#398—72no—
345#398—72no—
346#398—72no—
347#398—72no—
348#397—72no—
349#397—72no—
350#397—72no—
351#397—72no—
352#396—72no—
353#396—72no—
354#396—72no—
355#396—72no—
356#395—72no—
357#394—72no—
358#393—72no—
359#393—72no—
360#391—71no—
361#391—72no—
362#391—72no—
363#391—72no—
364#391—72no—
365#390—71no—
366#389—72no—
367#389—71no—
368#389—71no—
369#389—72no—
370#388—72no—
371#388—72no—
372#388—72no—
373#388—72no—
374#388—72no—
375#388—72no—
376#387—72no—
377#387—72no—
378#387—72no—
379#387—72no—
380#387—72no—
381#387—72no—
382#387—72no—
383#387—72no—
384#387C2×D712yes—
385#387C2×D712yes—
386#387C2×D712yes—
387#387C2×D712yes—
388#386—72no—
389#386—72no—
390#386—72no—
391#386—72no—
392#386—72no—
393#385—72no—
394#385—72no—
395#385—72no—
396#385—72no—
397#385—72no—
398#384—71no—
399#382—71no—
400#382—72no—
401#381—72no—
402#381—72no—
403#380—71no—
404#380—71no—
405#380—72no—
406#380—72no—
407C4×C22⋊C4—72no—
408C2×#95C2×D711yescharacteristic
409C2×#95C2×D711yescharacteristic
410C2×#95C2×D711yescharacteristic
411C2×#95C2×D711yescharacteristic
412C23×C7—21no—
413C23×C7—21no—
414C23×C7—21no—
415C23×C7—21no—
416C23×C7C2×#4112yes—
417C23×C7H(5,𝔽2)12yes—
418C23×C72−1+412yes—
419C23×C7C2511yescharacteristic
420C22×D7—22no—
421C22×D7—22no—
422C22×D7—22no—
423C22×D7—22no—
424C22×D7—22no—
425C22×D7—22no—
426C22×D7—22no—
427C2×C4×C7—21no—
428C2×C4×C7—21no—
429C2×C4×C7—21no—
430C2×C4×C7—21no—
431C2×C4×C7—21no—
432C2×C4×C7—21no—
433C2×C4×C7—21no—
434C2×C4×C7—21no—
435C2×C4×C7—22no—
436C2×C4×C7—22no—
437C2×C4×C7—22no—
438C2×C4×C7—22no—
439C2×C4×C7—21no—
440C2×C4×C7—22no—
441C2×C4×C7—22no—
442C2×C4×C7—21no—
443C2×C4×C7—21no—
444C2×C4×C7—21no—
445C2×C4×C7—22no—
446C2×C4×C7—21no—
447C2×C4×C7—22no—
448C2×C4×C7—22no—
449C2×C4×C7—22no—
450C2×C4×C7—22no—
451C2×C4×C7—22no—
452C2×C4×C7—21no—
453C2×C4×C7—44no—
454C2×C4×C7—44no—
455C2×C4×C7—44no—
456C2×C4×C7—44no—
457C2×C4×C7—44no—
458C2×C4×C7—82no—
459C2×C4×C7—82no—
460C2×C4×C7C2×#4112yes—
461C2×C4×C7C2×#4112yes—
462C2×C4×C7H(5,𝔽2)12yes—
463C2×C4×C72−1+412yes—
464C22⋊D7—48no—
465C2×Dic7—22no—
466C2×Dic7—22no—
467C2×Dic7—22no—
468C2×Dic7—22no—
469C2×Dic7—22no—
470C2×Dic7—22no—
471C2×Dic7—22no—
472C2×Dic7—22no—
473C2×Dic7—22no—
474C2×Dic7—22no—
475C2×Dic7—22no—
476C2×Dic7—22no—
477C2×Dic7—22no—
478C2×Dic7—22no—
479C2×Dic7—22no—
480C2×Dic7—22no—
481C2×Dic7—22no—
482C2×Dic7—22no—
483C2×Dic7—22no—
484C2×Dic7—22no—
485C2×Dic7—22no—
486D28—82no—
487C4×D7—84no—
488Dic14—82no—
489Dic14—84no—
490C22×Q8—71no—
491C22×Q8—72no—
492C22×D4—72no—
493C22×D4—71no—
494C23×C4—72no—
495C23×C4C22×D711yescharacteristic
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D711yescharacteristic
498C23×C4C22×D711yescharacteristic
499C23×C4C22×D711yescharacteristic
500C23×C4C22×D711yescharacteristic
501C23×C4C22×D711yescharacteristic
502C4⋊Q8—282no—
503#126—284no—
504#124—282no—
505#123—284no—
506C22⋊Q8—144no—
507C22⋊Q8—284no—
508#121—144no—
509C4×D4—284no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—42no—
512C2×C4⋊C4—71no—
513C2×C4⋊C4—72no—
514C2×C4⋊C4—71no—
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—71no—
524C2×C4⋊C4—71no—
525C2×C4⋊C4—72no—
526C2×C4⋊C4—72no—
527C2×C4⋊C4—72no—
528C2×C4⋊C4—71no—
529C2×C4⋊C4—72no—
530C2×C4⋊C4—71no—
531C2×C4⋊C4C22×D712yes—
532C2×C4⋊C4C22×D712yes—
533C2×C4⋊C4C22×D712yes—
534C2×C4⋊C4C22×D712yes—
535C2×C22⋊C4—72no—
536C2×C22⋊C4—72no—
537C2×C22⋊C4—72no—
538C2×C22⋊C4—72no—
539C2×C22⋊C4—72no—
540C2×C22⋊C4—72no—
541C2×C22⋊C4—72no—
542C2×C22⋊C4—72no—
543C2×C22⋊C4—72no—
544C2×C22⋊C4—72no—
545C2×C22⋊C4—72no—
546C2×C22⋊C4—72no—
547C2×C22⋊C4—72no—
548C2×C22⋊C4—72no—
549C2×C22⋊C4—72no—
550C2×C42—42no—
551C2×C42—72no—
552C2×C42—72no—
553C2×C42—72no—
554C2×C42C22×D711yescharacteristic
555C2×C42C22×D711yescharacteristic
556C2×C42C22×D711yescharacteristic
557C2×C42C22×D711yescharacteristic
558#95—72no—
559#95—72no—
560#95—72no—
561#95—72no—
562#95—72no—
563#95—72no—
564#95—72no—
565#95—72no—
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#95—72no—
579#95—72no—
580#95C22×D712yes—
581#95C22×D712yes—
582#95C22×D712yes—
583#95C22×D712yes—
584#95C22×D712yes—
585#95C22×D712yes—
586#95C22×D712yes—
587#95C22×D712yes—
588C22×C7—22no—
589C22×C7—22no—
590C22×C7—22no—
591C22×C7—22no—
592C22×C7—22no—
593C22×C7—22no—
594C22×C7#54214yes—
595C22×C7C22×#4111yescharacteristic
596C22×C7C2×H(5,𝔽2)11yescharacteristic
597C22×C7C2×H(5,𝔽2)11yescharacteristic
598C22×C7C2×2−1+411yescharacteristic
599C22×C7C2×2−1+411yescharacteristic
600C22×C7#58511yescharacteristic
601C22×C7#58511yescharacteristic
602C2×D7—42no—
603C2×D7—42no—
604C2×D7—42no—
605C2×D7—42no—
606C2×D7—42no—
607C2×D7—42no—
608C2×D7—42no—
609C4×C7—22no—
610C4×C7—22no—
611C4×C7—22no—
612C4×C7—22no—
613C4×C7—42no—
614C4×C7—42no—
615C4×C7—41no—
616C4×C7—42no—
617C4×C7—41no—
618C4×C7—42no—
619Dic7—42no—
620Dic7—42no—
621Dic7—42no—
622Dic7—42no—
623Dic7—42no—
624Dic7—42no—
625Dic7—42no—
626C24—72no—
627C24C23×D711yescharacteristic
628C2×Q8—142no—
629C2×Q8—144no—
630C2×Q8—282no—
631C2×Q8—281no—
632C2×Q8—282no—
633C2×Q8—281no—
634C2×D4—144no—
635C2×D4—144no—
636C2×D4—144no—
637C2×D4—142no—
638C2×D4—281no—
639C2×D4—281no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—72no—
661C22×C4—72no—
662C22×C4—72no—
663C22×C4—72no—
664C22×C4—72no—
665C22×C4—72no—
666C22×C4—72no—
667C22×C4—282no—
668C22×C4—282no—
669C22×C4—282no—
670C22×C4#115714yes—
671C22×C4C23×D711yescharacteristic
672C22×C4C23×D712yes—
673C22×C4C23×D712yes—
674C22×C4C23×D712yes—
675C22×C4C23×D712yes—
676C22×C4C23×D711yescharacteristic
677C22×C4C23×D711yescharacteristic
678C22×C4C23×D711yescharacteristic
679C22×C4C23×D711yescharacteristic
680C22×C4C23×D711yescharacteristic
681C4⋊C4—24no—
682C4⋊C4—24no—
683C4⋊C4—24no—
684C4⋊C4—42no—
685C4⋊C4—144no—
686C4⋊C4—142no—
687C4⋊C4—142no—
688C4⋊C4—144no—
689C4⋊C4—282no—
690C4⋊C4—282no—
691C4⋊C4—282no—
692C4⋊C4—282no—
693C4⋊C4—282no—
694C4⋊C4—282no—
695C4⋊C4—282no—
696C4⋊C4—282no—
697C4⋊C4—282no—
698C4⋊C4—282no—
699C4⋊C4—281no—
700C4⋊C4—281no—
701C4⋊C4—282no—
702C4⋊C4—281no—
703C4⋊C4—281no—
704C22⋊C4—144no—
705C22⋊C4—144no—
706C22⋊C4—144no—
707C22⋊C4—144no—
708C22⋊C4—144no—
709C22⋊C4—144no—
710C22⋊C4—282no—
711C22⋊C4—282no—
712C22⋊C4—282no—
713C22⋊C4—282no—
714C22⋊C4—282no—
715C22⋊C4—282no—
716C22⋊C4—282no—
717C22⋊C4—282no—
718C22⋊C4—282no—
719C42—22no—
720C42—22no—
721C42—41no—
722C42—41no—
723C42—282no—
724C42—282no—
725C42—282no—
726C2×C7—24no—
727C2×C7C2×#54211yescharacteristic
728C2×C7#350511yescharacteristic
729C2×C7#350711yescharacteristic
730C2×C7#353511yescharacteristic
731C2×C7#353611yescharacteristic
732C2×C7#356011yescharacteristic
733C2×C7#356311yescharacteristic
734D7—82no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—142no—
740C23—142no—
741C23—142no—
742C23—142no—
743C23—142no—
744C23—142no—
745C23—142no—
746C23C2×#115712yes—
747C23#655312yes—
748C23#655412yes—
749C23C24×D711yescharacteristic
750Q8—564no—
751Q8—562no—
752D4—288no—
753D4—562no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—82no—
786C2×C4—82no—
787C2×C4—142no—
788C2×C4—142no—
789C2×C4—142no—
790C2×C4—142no—
791C2×C4—142no—
792C2×C4—142no—
793C2×C4—142no—
794C2×C4—142no—
795C2×C4—142no—
796C2×C4—142no—
797C2×C4—142no—
798C2×C4—142no—
799C2×C4—142no—
800C2×C4—142no—
801C2×C4—142no—
802C2×C4—142no—
803C2×C4—142no—
804C2×C4—142no—
805C2×C4—142no—
806C2×C4—142no—
807C2×C4—142no—
808C2×C4—564no—
809C2×C4C2×#115712yes—
810C2×C4C2×#115712yes—
811C2×C4#654812yes—
812C2×C4#655112yes—
813C7#3676311yescharacteristic, complemented, Sylow
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—282no—
821C22—282no—
822C22—282no—
823C22—282no—
824C22—282no—
825C22—282no—
826C22—282no—
827C22#9022514yes—
828C22C22×#115711yescharacteristic
829C22C2×#654811yescharacteristic
830C22C2×#655111yescharacteristic
831C22C2×#655311yescharacteristic
832C22C2×#655411yescharacteristic
833C22#9061611yescharacteristic
834C22#9061611yescharacteristic
835C4—22no—
836C4—22no—
837C4—22no—
838C4—22no—
839C4—41no—
840C4—42no—
841C4—41no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—282no—
846C4—282no—
847C4—282no—
848C4—282no—
849C4—282no—
850C4—282no—
851C4—282no—
852C2—24no—
853C2—562no—
854C2C2×#9022511yescharacteristic
855C2#1174285511yescharacteristic
856C2#1174288711yescharacteristic
857C2#1174305811yescharacteristic
858C2#1174307111yescharacteristic
859C2#1174315711yescharacteristic
860C2#1174318611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC2×C7×#387C2
prime radicalC2×#6493C22
hypercenterC2×#387D7
hypocenterC7#36763
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C2×C7×#387C2semidirect
3. #11739628C2semidirect
4. #11739620C2semidirect
6. #11739521C2semidirect
7. #11732883C2semidirect
8. #11732870C2semidirect
9. #11732849C2semidirect
10. #11732715C2semidirect
11. #11732664C2semidirect
12. #11732651C2semidirect
13. #11732609C2semidirect
14. #11732606C2semidirect
15. #11730820C2semidirect
16. #11730797C2semidirect
17. #11730796C2semidirect
18. #11730779C2semidirect
224. C2×#387D7semidirect
813. C7#36763semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3872
#117396442
#117396282
#117396202
#117395222
#117395212
#117328832
#117328702
#117328492
#117327152
#117326642
#117326512
#117326092
#117326062
#117308202
#117307972
#117307962
#117307792
#117307782
#367637