Finite Group Databasebeta

← #13560402

Subgroups — #13560402

Order 1792.

1716 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2392C211yesmaximal, characteristic, complemented
2#11739846C212yesmaximal, complemented
3#11739792C211yesmaximal, characteristic, complemented
4#11739790C212yesmaximal, complemented
5#11739764C211yesmaximal, characteristic, complemented
6#11739718C211yesmaximal, characteristic, complemented
7#11739674C211yesmaximal, characteristic, complemented
8#11735459C212yesmaximal, complemented
9#11735181C212yesmaximal, complemented
10#11734900C212yesmaximal, complemented
11#11734852C212yesmaximal, complemented
12#11734613C212yesmaximal, complemented
13#11734612C212yesmaximal, complemented
14#11734547C212yesmaximal, complemented
15#11734194C212yesmaximal, complemented
16#11731116C211yesmaximal, characteristic, complemented
17#11731062C211yesmaximal, characteristic, complemented
18#11731028C212yesmaximal, complemented
19#11731027C212yesmaximal, complemented
20C2×C4×C7×D4C2211yescharacteristic
21C2×C4×C7×D4C2212yes—
22C2×C7×#117C2211yescharacteristic
23C2×C4×C22⋊D7C2212yes—
24C2×C4×C22⋊D7C2212yes—
25C2×C4×C22⋊D7C2212yes—
26C2×#6489C2212yes—
27C2×C4×D28C2211yescharacteristic
28C2×#6435C2212yes—
29C7×#398C2211yescharacteristic
30C7×#397C2211yescharacteristic
31C7×#396C2212yes—
32C7×#394C2212yes—
33C7×#394C2211yescharacteristic
34C7×#392C2211yescharacteristic
35C4×C7×C4⋊C4C2211yescharacteristic
36C4×C7×C22⋊C4C2212yes—
37#89995C2212yes—
38#89995C2212yes—
39#89995C2212yes—
40#89994C2212yes—
41#89994C2212yes—
42#89993C2212yes—
43C4×C22⋊Dic7C2211yescharacteristic
44C4×C22⋊Dic7C2211yescharacteristic
45C4×C22⋊Dic7C2212yes—
46#89766C2212yes—
47#89766C2212yes—
48#89765C2212yes—
49#89764C2212yes—
50#89763C2211yescharacteristic
51#89760C2212yes—
52#89758C2212yes—
53#89757C2212yes—
54#89756C2212yes—
55#89756C2212yes—
56#89755C2211yescharacteristic
57#89753C2212yes—
58#89753C2212yes—
59#89752C2212yes—
60#89745C2212yes—
61#89733C2212yes—
62#89733C2212yes—
63#89733C2212yes—
64#89733C2212yes—
65#89733C2212yes—
66#89733C2212yes—
67#89733C2212yes—
68#89732C2211yescharacteristic
69#89732C2212yes—
70#89731C2212yes—
71#89731C2212yes—
72#89725C2211yescharacteristic
73#89725C2212yes—
74#89725C2212yes—
75#89724C2212yes—
76#89724C2212yes—
77#89723C2212yes—
78#89723C2212yes—
79#89723C2212yes—
80#89723C2212yes—
81#89721C2212yes—
82#89721C2212yes—
83#89720C2212yes—
84#89720C2212yes—
85#89720C2212yes—
86C4×(C2×D7)⋊C4C2212yes—
87C4×(C2×D7)⋊C4C2212yes—
88C4×C4⋊Dic7C2211yescharacteristic
89C4×C4⋊Dic7C2211yescharacteristic
90C4×C4⋊Dic7C2211yescharacteristic
91C4×C4⋊Dic7C2212yes—
92#89704C2211yescharacteristic
93C4×Dic7⋊C4C2212yes—
94C42×Dic7C2211yescharacteristic
95#89449C2212yes—
96#89447C2212yes—
97#89446C2212yes—
98#89446C2212yes—
99#89441C2212yes—
100#89441C2212yes—
101#89433C2212yes—
102#89433C2212yes—
103#89432C2212yes—
104#89431C2212yes—
105#89430C2212yes—
106#89429C2212yes—
107#36692—71nomaximal, Sylow
108C22×C7×D4C2311yescharacteristic
109C22×C7×D4C2312yes—
110C23×C4×C7C2312yes—
111C23×C4×C7C2311yescharacteristic
112C22×C22⋊D7C2312yes—
113C22×C22⋊D7C2312yes—
114C22×C22⋊D7C2312yes—
115C22×D28C2311yescharacteristic
116C22×C4×D7C2312yes—
117C4×C7×D4—24no—
118C4×C7×D4—44no—
119C7×#117—24no—
120C2×C7×C4⋊C4C2311yescharacteristic
121C2×C7×C4⋊C4C2311yescharacteristic
122C2×C7×C4⋊C4C2311yescharacteristic
123C2×C7×C4⋊C4C2312yes—
124C2×C7×C4⋊C4C2312yes—
125C2×C7×C22⋊C4C2312yes—
126C2×C7×C22⋊C4C2311yescharacteristic
127C2×C7×C22⋊C4C2311yescharacteristic
128C2×C7×C22⋊C4C2312yes—
129C2×C7×C22⋊C4C2312yes—
130C2×C7×C22⋊C4C2312yes—
131C2×C7×C22⋊C4C2312yes—
132C2×C42×C7C2312yes—
133C2×C42×C7C2311yescharacteristic
134C2×C42×C7C2311yescharacteristic
135C2×C22⋊Dic7C2312yes—
136C2×C22⋊Dic7C2312yes—
137C2×C22⋊Dic7C2312yes—
138C2×C22⋊Dic7C2312yes—
139C2×C22⋊Dic7C2312yes—
140C2×C22⋊Dic7C2312yes—
141C2×C22⋊Dic7C2312yes—
142C2×C22⋊Dic7C2312yes—
143C2×C22⋊Dic7C2312yes—
144C4×C22⋊D7—44no—
145C4×C22⋊D7—44no—
146C4×C22⋊D7—44no—
147C2×(C2×D7)⋊C4C2312yes—
148C2×(C2×D7)⋊C4C2312yes—
149C2×(C2×D7)⋊C4C2312yes—
150C2×(C2×D7)⋊C4C2312yes—
151C2×(C2×D7)⋊C4C2312yes—
152C2×(C2×D7)⋊C4C2312yes—
153C2×(C2×D7)⋊C4C2312yes—
154C2×(C2×D7)⋊C4C2312yes—
155C2×(C2×D7)⋊C4C2312yes—
156C2×(C2×D7)⋊C4C2312yes—
157#6489—44no—
158C2×C4⋊Dic7C2311yescharacteristic
159C2×C4⋊Dic7C2312yes—
160C2×C4⋊Dic7C2312yes—
161C2×C4⋊Dic7C2312yes—
162C2×C4⋊Dic7C2312yes—
163C2×C4⋊Dic7C2312yes—
164C2×C4⋊Dic7C2312yes—
165C2×C4⋊Dic7C2312yes—
166C2×Dic7⋊C4C2312yes—
167C2×Dic7⋊C4C2312yes—
168C2×Dic7⋊C4C2312yes—
169C2×Dic7⋊C4C2312yes—
170C2×Dic7⋊C4C2312yes—
171C2×Dic7⋊C4C2312yes—
172C2×Dic7⋊C4C2312yes—
173C2×C4×Dic7C2311yescharacteristic
174C2×C4×Dic7C2311yescharacteristic
175C2×C4×Dic7C2311yescharacteristic
176C2×C4×Dic7C2312yes—
177C2×C4×Dic7C2311yescharacteristic
178C2×C4×Dic7C2312yes—
179C2×C4×Dic7C2312yes—
180C4×D28—24no—
181#6435—44no—
182C7×#95C2312yes—
183C7×#95C2312yes—
184C7×#95C2311yescharacteristic
185C7×#95C2311yescharacteristic
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⋊#95C2311yescharacteristic
201C7⋊#95C2311yescharacteristic
202C7⋊#95C2312yes—
203C7⋊#95C2312yes—
204#2837—72no—
205#2837—72no—
206#2836—72no—
207#2836—72no—
208#2829—72no—
209#2829—72no—
210#2828—72no—
211#2828—72no—
212#2402—71no—
213#2397—71no—
214#2395—72no—
215#2395—72no—
216#2392—72no—
217#2392—72no—
218#2392—71no—
219#2392D711yescharacteristic, complemented
220#2298—71no—
221#2293—71no—
222#2293—71no—
223C24×C7C2411yescharacteristic
224C24×C7C2412yes—
225C23×D7C2412yes—
226C2×C7×D4—22no—
227C2×C7×D4—42no—
228C2×C7×D4—42no—
229C2×C7×D4—42no—
230C2×C7×D4—42no—
231C22×C4×C7—22no—
232C22×C4×C7—24no—
233C22×C4×C7—24no—
234C22×C4×C7—22no—
235C22×C4×C7—24no—
236C22×C4×C7—22no—
237C22×C4×C7C2412yes—
238C22×C4×C7C2411yescharacteristic
239C22×C4×C7C2411yescharacteristic
240C22×C4×C7C2411yescharacteristic
241C22×C4×C7C2412yes—
242C22×C4×C7C2412yes—
243C22×C4×C7C2411yescharacteristic
244C22×C4×C7C2411yescharacteristic
245C22×C4×C7C2411yescharacteristic
246C2×C22⋊D7—42no—
247C2×C22⋊D7—42no—
248C2×C22⋊D7—42no—
249C2×C22⋊D7—42no—
250C2×C22⋊D7—42no—
251C2×C22⋊D7—42no—
252C2×C22⋊D7—42no—
253C2×C22⋊D7—42no—
254C2×C22⋊D7—42no—
255C22×Dic7C2412yes—
256C22×Dic7C2412yes—
257C22×Dic7C2412yes—
258C22×Dic7C2412yes—
259C22×Dic7C2412yes—
260C22×Dic7C2412yes—
261C22×Dic7C2412yes—
262C2×D28—22no—
263C2×D28—42no—
264C2×C4×D7—24no—
265C2×C4×D7—24no—
266C2×C4×D7—24no—
267C7×C4⋊C4—22no—
268C7×C4⋊C4—22no—
269C7×C4⋊C4—22no—
270C7×C4⋊C4—42no—
271C7×C4⋊C4—42no—
272C7×C22⋊C4—22no—
273C7×C22⋊C4—22no—
274C7×C22⋊C4—24no—
275C7×C22⋊C4—42no—
276C7×C22⋊C4—42no—
277C7×C22⋊C4—42no—
278C7×C22⋊C4—42no—
279C42×C7—22no—
280C42×C7—24no—
281C42×C7#4114yes—
282C22⋊Dic7—42no—
283C22⋊Dic7—42no—
284C22⋊Dic7—42no—
285C22⋊Dic7—42no—
286C22⋊Dic7—42no—
287C22⋊Dic7—42no—
288C22⋊Dic7—42no—
289C22⋊Dic7—42no—
290C22⋊Dic7—42no—
291(C2×D7)⋊C4—24no—
292(C2×D7)⋊C4—42no—
293(C2×D7)⋊C4—42no—
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—
301C4⋊Dic7—22no—
302C4⋊Dic7—42no—
303C4⋊Dic7—42no—
304C4⋊Dic7—42no—
305C4⋊Dic7—42no—
306C4⋊Dic7—42no—
307C4⋊Dic7—42no—
308C4⋊Dic7—42no—
309Dic7⋊C4—42no—
310Dic7⋊C4—42no—
311Dic7⋊C4—42no—
312Dic7⋊C4—42no—
313Dic7⋊C4—42no—
314Dic7⋊C4—42no—
315Dic7⋊C4—42no—
316C4×Dic7—22no—
317C4×Dic7—22no—
318C4×Dic7—24no—
319C4×Dic7—22no—
320C4×Dic7—22no—
321C4×Dic7—42no—
322C4×Dic7—42no—
323C2×C4×D4—72no—
324C2×C4×D4—72no—
325C2×C4×D4—72no—
326C2×C4×D4—71no—
327C2×C4×D4C2×D711yescharacteristic
328C2×C4×D4C2×D712yes—
329C2×#117—72no—
330C2×#117—72no—
331C2×#117C2×D711yescharacteristic
332#400—72no—
333#400—72no—
334#400—72no—
335#400—72no—
336#399—72no—
337#399—72no—
338#399—72no—
339#399—72no—
340#398—72no—
341#398—72no—
342#398—71no—
343#398—72no—
344#398—72no—
345#398—72no—
346#398—72no—
347#398C2×D711yescharacteristic
348#397—72no—
349#397—72no—
350#397—72no—
351#397—72no—
352#397—72no—
353#397—71no—
354#397—72no—
355#397—72no—
356#397—72no—
357#397C2×D711yescharacteristic
358#396—72no—
359#396—72no—
360#396—72no—
361#396—72no—
362#396—72no—
363#396C2×D712yes—
364#394—72no—
365#394—72no—
366#394—71no—
367#394—72no—
368#394—72no—
369#394—72no—
370#394—72no—
371#394—72no—
372#394—72no—
373#394—72no—
374#394—72no—
375#394—72no—
376#394C2×D712yes—
377#394C2×D711yescharacteristic
378#392—72no—
379#392—72no—
380#392—72no—
381#392—71no—
382#392—72no—
383#392C2×D711yescharacteristic
384#390—72no—
385#390—72no—
386#389—72no—
387#389—72no—
388#388—72no—
389#388—72no—
390#388—72no—
391#388—72no—
392#388—72no—
393#388—72no—
394#387—72no—
395#387—72no—
396C4×C4⋊C4—72no—
397C4×C4⋊C4—72no—
398C4×C4⋊C4—71no—
399C4×C4⋊C4—71no—
400C4×C4⋊C4—71no—
401C4×C4⋊C4C2×D711yescharacteristic
402C4×C22⋊C4—71no—
403C4×C22⋊C4—71no—
404C4×C22⋊C4—72no—
405C4×C22⋊C4—72no—
406C4×C22⋊C4—72no—
407C4×C22⋊C4C2×D712yes—
408#376—71no—
409C43—71no—
410C23×C7—21no—
411C23×C7—22no—
412C23×C7—22no—
413C23×C7—21no—
414C23×C7—22no—
415C23×C7—21no—
416C23×C7—22no—
417C23×C7—22no—
418C23×C7—22no—
419C23×C7—22no—
420C23×C7—22no—
421C23×C7—22no—
422C23×C7C2511yescharacteristic
423C22×D7—22no—
424C22×D7—22no—
425C22×D7—22no—
426C22×D7—22no—
427C22×D7—22no—
428C22×D7—22no—
429C22×D7—22no—
430C7×D4—44no—
431C7×D4—48no—
432C2×C4×C7—22no—
433C2×C4×C7—22no—
434C2×C4×C7—21no—
435C2×C4×C7—21no—
436C2×C4×C7—22no—
437C2×C4×C7—21no—
438C2×C4×C7—21no—
439C2×C4×C7—22no—
440C2×C4×C7—22no—
441C2×C4×C7—22no—
442C2×C4×C7—22no—
443C2×C4×C7—21no—
444C2×C4×C7—22no—
445C2×C4×C7—22no—
446C2×C4×C7—22no—
447C2×C4×C7—22no—
448C2×C4×C7—22no—
449C2×C4×C7—22no—
450C2×C4×C7—44no—
451C2×C4×C7—48no—
452C2×C4×C7C2×#4112yes—
453C2×C4×C7C2×#4112yes—
454C2×C4×C7C2×#4112yes—
455C2×C4×C7H(5,𝔽2)12yes—
456C2×C4×C7H(5,𝔽2)12yes—
457C22⋊D7—48no—
458C22⋊D7—48no—
459C22⋊D7—48no—
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—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—
481D28—44no—
482C4×D7—48no—
483C22×D4—72no—
484C22×D4—72no—
485C22×D4—72no—
486C22×D4—71no—
487C22×D4C22×D711yescharacteristic
488C22×D4C22×D712yes—
489C23×C4—72no—
490C23×C4C22×D712yes—
491C23×C4C22×D711yescharacteristic
492C4×D4—24no—
493C4×D4—44no—
494C4×D4—144no—
495C4×D4—284no—
496C4×D4—284no—
497C4×D4—284no—
498#117—24no—
499#117—284no—
500#117—284no—
501C2×C4⋊C4—71no—
502C2×C4⋊C4—72no—
503C2×C4⋊C4—72no—
504C2×C4⋊C4—72no—
505C2×C4⋊C4—72no—
506C2×C4⋊C4—72no—
507C2×C4⋊C4—72no—
508C2×C4⋊C4—72no—
509C2×C4⋊C4—72no—
510C2×C4⋊C4—72no—
511C2×C4⋊C4—72no—
512C2×C4⋊C4—72no—
513C2×C4⋊C4—72no—
514C2×C4⋊C4—72no—
515C2×C4⋊C4—72no—
516C2×C4⋊C4C22×D711yescharacteristic
517C2×C4⋊C4C22×D711yescharacteristic
518C2×C4⋊C4C22×D711yescharacteristic
519C2×C4⋊C4C22×D712yes—
520C2×C4⋊C4C22×D712yes—
521C2×C22⋊C4—72no—
522C2×C22⋊C4—72no—
523C2×C22⋊C4—72no—
524C2×C22⋊C4—72no—
525C2×C22⋊C4—72no—
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⋊C4—72no—
535C2×C22⋊C4—72no—
536C2×C22⋊C4—72no—
537C2×C22⋊C4—72no—
538C2×C22⋊C4—72no—
539C2×C22⋊C4—72no—
540C2×C22⋊C4C22×D711yescharacteristic
541C2×C22⋊C4C22×D711yescharacteristic
542C2×C22⋊C4C22×D712yes—
543C2×C22⋊C4C22×D712yes—
544C2×C22⋊C4C22×D712yes—
545C2×C22⋊C4C22×D712yes—
546C2×C22⋊C4C22×D712yes—
547C2×C42—71no—
548C2×C42—71no—
549C2×C42—72no—
550C2×C42—71no—
551C2×C42—71no—
552C2×C42—72no—
553C2×C42—72no—
554C2×C42C22×D712yes—
555C2×C42C22×D711yescharacteristic
556C2×C42C22×D711yescharacteristic
557#95—72no—
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—71no—
570#95—71no—
571#95—72no—
572#95—72no—
573#95—72no—
574#95—72no—
575#95C22×D712yes—
576#95C22×D712yes—
577#95C22×D711yescharacteristic
578#95C22×D711yescharacteristic
579C22×C7—41no—
580C22×C7—42no—
581C22×C7—42no—
582C22×C7—41no—
583C22×C7—42no—
584C22×C7—41no—
585C22×C7—42no—
586C22×C7—42no—
587C22×C7—42no—
588C22×C7—42no—
589C22×C7—42no—
590C22×C7—42no—
591C22×C7C22×#4111yescharacteristic
592C22×C7C2×H(5,𝔽2)11yescharacteristic
593C22×C7C2×H(5,𝔽2)11yescharacteristic
594C22×C7#58512yes—
595C22×C7#58512yes—
596C2×D7—42no—
597C2×D7—42no—
598C2×D7—42no—
599C2×D7—42no—
600C2×D7—42no—
601C2×D7—42no—
602C2×D7—42no—
603C4×C7—22no—
604C4×C7—22no—
605C4×C7—42no—
606C4×C7—41no—
607C4×C7—41no—
608C4×C7—41no—
609C4×C7—42no—
610C4×C7—42no—
611C4×C7#54014yes—
612Dic7—42no—
613Dic7—42no—
614Dic7—42no—
615Dic7—42no—
616Dic7—42no—
617Dic7—42no—
618Dic7—42no—
619C24—72no—
620C24C23×D711yescharacteristic
621C24C23×D712yes—
622C2×D4—22no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—142no—
628C2×D4—282no—
629C2×D4—282no—
630C2×D4—282no—
631C2×D4—282no—
632C2×D4—282no—
633C2×D4—282no—
634C2×D4—282no—
635C2×D4—282no—
636C2×D4—282no—
637C2×D4—282no—
638C22×C4—22no—
639C22×C4—24no—
640C22×C4—22no—
641C22×C4—24no—
642C22×C4—24no—
643C22×C4—22no—
644C22×C4—72no—
645C22×C4—72no—
646C22×C4—72no—
647C22×C4—72no—
648C22×C4—72no—
649C22×C4—72no—
650C22×C4—72no—
651C22×C4—144no—
652C22×C4—144no—
653C22×C4—144no—
654C22×C4C23×D711yescharacteristic
655C22×C4C23×D711yescharacteristic
656C22×C4C23×D712yes—
657C22×C4C23×D711yescharacteristic
658C22×C4C23×D712yes—
659C22×C4C23×D712yes—
660C22×C4C23×D711yescharacteristic
661C22×C4C23×D711yescharacteristic
662C22×C4C23×D711yescharacteristic
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—142no—
669C4⋊C4—282no—
670C4⋊C4—282no—
671C4⋊C4—282no—
672C4⋊C4—282no—
673C4⋊C4—282no—
674C4⋊C4—282no—
675C4⋊C4—282no—
676C4⋊C4—282no—
677C4⋊C4—282no—
678C4⋊C4—282no—
679C4⋊C4—282no—
680C4⋊C4—282no—
681C4⋊C4—282no—
682C4⋊C4—282no—
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—24no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—144no—
691C22⋊C4—282no—
692C22⋊C4—282no—
693C22⋊C4—282no—
694C22⋊C4—282no—
695C22⋊C4—282no—
696C22⋊C4—282no—
697C22⋊C4—282no—
698C22⋊C4—282no—
699C22⋊C4—282no—
700C22⋊C4—282no—
701C22⋊C4—282no—
702C22⋊C4—282no—
703C22⋊C4—282no—
704C22⋊C4—282no—
705C22⋊C4—282no—
706C22⋊C4—282no—
707C22⋊C4—282no—
708C22⋊C4—282no—
709C42—22no—
710C42—24no—
711C42—142no—
712C42—142no—
713C42—142no—
714C42—144no—
715C42—142no—
716C42—282no—
717C42—282no—
718C42#115914yes—
719C2×C7—82no—
720C2×C7—81no—
721C2×C7C2×#54011yescharacteristic
722C2×C7#345511yescharacteristic
723C2×C7#345511yescharacteristic
724C2×C7#352912yes—
725C2×C7#352912yes—
726D7—82no—
727C23—21no—
728C23—22no—
729C23—21no—
730C23—22no—
731C23—22no—
732C23—21no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—142no—
740C23—142no—
741C23—142no—
742C23—142no—
743C23—142no—
744C23—142no—
745C23—142no—
746C23C24×D711yescharacteristic
747D4—44no—
748D4—48no—
749D4—284no—
750D4—288no—
751D4—288no—
752D4—288no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—44no—
772C2×C4—48no—
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—142no—
782C2×C4—142no—
783C2×C4—142no—
784C2×C4—142no—
785C2×C4—142no—
786C2×C4—142no—
787C2×C4—142no—
788C2×C4—142no—
789C2×C4—142no—
790C2×C4—142no—
791C2×C4—142no—
792C2×C4—142no—
793C2×C4—142no—
794C2×C4—288no—
795C2×C4C2×#115912yes—
796C2×C4C2×#115912yes—
797C2×C4C2×#115912yes—
798C2×C4#654812yes—
799C2×C4#655312yes—
800C7#3669211yescharacteristic, complemented, Sylow
801C22—42no—
802C22—42no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—42no—
809C22—41no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—282no—
814C22—282no—
815C22—282no—
816C22—282no—
817C22—282no—
818C22—282no—
819C22—282no—
820C22C22×#115911yescharacteristic
821C22C2×#654811yescharacteristic
822C22C2×#655311yescharacteristic
823C22#9061612yes—
824C22#9061612yes—
825C4—22no—
826C4—22no—
827C4—42no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—42no—
832C4—42no—
833C4—282no—
834C4—282no—
835C4—282no—
836C4—282no—
837C4—282no—
838C4—282no—
839C4—282no—
840C4#9031014yes—
841C2—81no—
842C2—82no—
843C2—562no—
844C2C2×#9031011yescharacteristic
845C2#1174308711yescharacteristic
846C2#1174311612yes—
847C2#1174323912yes—
848C2#1174330411yescharacteristic
subgroupG/H
centerC22×C4C23×D7
commutator, socle, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC7×#2392C2
hypercenter#2392D7
hypocenterC7#36692
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ #2392

Complements

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

NH ≅ G/Ntype
1. C7×#2392C2semidirect
2. #11739846C2semidirect
3. #11739792C2semidirect
4. #11739790C2semidirect
5. #11739764C2semidirect
6. #11739718C2semidirect
7. #11739674C2semidirect
8. #11735459C2semidirect
9. #11735181C2semidirect
10. #11734900C2semidirect
11. #11734852C2semidirect
12. #11734613C2semidirect
13. #11734612C2semidirect
14. #11734547C2semidirect
15. #11734194C2semidirect
16. #11731116C2semidirect
17. #11731062C2semidirect
18. #11731028C2semidirect
19. #11731027C2semidirect
219. #2392D7semidirect
800. C7#36692semidirect

Maximal subgroups

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

subgroupindex
C7×#23922
#117398462
#117397922
#117397902
#117397642
#117397182
#117396742
#117354592
#117351812
#117349002
#117348522
#117346132
#117346122
#117345472
#117341942
#117311162
#117310622
#117310282
#117310272
#366927