Finite Group Databasebeta

← #13560438

Subgroups — #13560438

Order 1792.

1664 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2820C211yesmaximal, characteristic, complemented
2#11740516C211yesmaximal, characteristic, complemented
3Dic7×#125C211yesmaximal, characteristic, complemented
4#11740452C211yesmaximal, characteristic
5Dic7×#124C211yesmaximal, characteristic, complemented
6#11735541C212yesmaximal, complemented
7#11735462C212yesmaximal, complemented
8#11735181C212yesmaximal, complemented
9#11734904C212yesmaximal, complemented
10#11734900C212yesmaximal, complemented
11#11734850C212yesmaximal, complemented
12#11734727C212yesmaximal, complemented
13#11734726C212yesmaximal, complemented
14#11734723C212yesmaximal, complemented
15#11734615C212yesmaximal, complemented
16#11734613C212yesmaximal, complemented
17#11734335C212yesmaximal, complemented
18#11731664C211yesmaximal, characteristic, complemented
19#11731594C211yesmaximal, characteristic, complemented
20C2×C7×#125C2211yescharacteristic
21C2×C7×#124C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C2×D4×Dic7C2211yescharacteristic
24C2×#6456C2211yescharacteristic
25C2×#6455C2212yes—
26C2×#6450C2211yescharacteristic
27C2×(C22⋊D7)⋊C4C2212yes—
28C2×(C22⋊D7)⋊C4C2212yes—
29C2×#6440C2212yes—
30C2×#6438C2211yescharacteristic
31C7×#399C2212yes—
32C7×#397C2212yes—
33C7×#396C2212yes—
34C7×#396C2212yes—
35C7×#395C2212yes—
36C7×#394C2212yes—
37C7×#382C2211yescharacteristic
38#90003C2212yes—
39#90002C2211yescharacteristic
40#89995C2212yes—
41#89993C2211yescharacteristic
42#89766C2212yes—
43#89766C2212yes—
44#89766C2212yes—
45#89766C2212yes—
46#89765C2212yes—
47#89765C2212yes—
48#89764C2212yes—
49#89763C2212yes—
50#89760C2211yescharacteristic
51#89758C2212yes—
52#89757C2211yescharacteristic
53#89757C2211yescharacteristic
54#89756C2212yes—
55#89756C2212yes—
56#89755C2212yes—
57#89754C2212yes—
58#89753C2212yes—
59#89753C2212yes—
60#89751C2212yes—
61C4⋊C4×Dic7C2212yes—
62C4⋊C4×Dic7C2211yescharacteristic
63C4⋊C4×Dic7C2211yescharacteristic
64C4⋊C4×Dic7C2212yes—
65C4⋊C4×Dic7C2212yes—
66#89746C2211yescharacteristic
67#89733C2212yes—
68#89733C2212yes—
69#89733C2212yes—
70#89733C2212yes—
71#89733C2212yes—
72#89733C2212yes—
73#89732C2212yes—
74#89731C2212yes—
75#89731C2212yes—
76#89725C2212yes—
77#89724C2212yes—
78#89724C2212yes—
79#89723C2212yes—
80#89723C2212yes—
81#89721C2212yes—
82#89720C2212yes—
83#89720C2212yes—
84#89719C2212yes—
85C22⋊C4×Dic7C2212yes—
86C22⋊C4×Dic7C2212yes—
87C22⋊C4×Dic7C2212yes—
88#89708C2211yescharacteristic
89#89708C2211yescharacteristic
90C42×Dic7C2211yescharacteristic
91#89449C2212yes—
92#89447C2212yes—
93#89447C2212yes—
94#89441C2212yes—
95#89441C2212yes—
96#89438C2212yes—
97#89438C2212yes—
98#89438C2212yes—
99#89433C2212yes—
100#89433C2212yes—
101#89433C2212yes—
102#89430C2212yes—
103#89430C2212yes—
104#89429C2212yes—
105#89429C2212yes—
106#89421C2212yes—
107#36695—71nomaximal, Sylow
108C22×C7×Q8C2311yescharacteristic
109C22×C7×D4C2311yescharacteristic
110C22×C22⋊D7C2312yes—
111C22×C22⋊D7C2312yes—
112C23×Dic7C2312yes—
113C22×D28C2311yescharacteristic
114C22×C4×D7C2312yes—
115C22×Dic14C2311yescharacteristic
116C7×#125—24no—
117C7×#124—24no—
118C2×C7×C4⋊C4C2312yes—
119C2×C7×C4⋊C4C2312yes—
120C2×C7×C4⋊C4C2311yescharacteristic
121C2×C7×C4⋊C4C2311yescharacteristic
122C2×C7×C4⋊C4C2311yescharacteristic
123C2×C7×C4⋊C4C2312yes—
124C2×C7×C4⋊C4C2311yescharacteristic
125C2×C7×C4⋊C4C2312yes—
126C2×C7×C22⋊C4C2312yes—
127C2×C7×C22⋊C4C2312yes—
128C2×C7×C22⋊C4C2312yes—
129C2×C7×C22⋊C4C2312yes—
130C2×C7×C22⋊C4C2312yes—
131C2×C7×C22⋊C4C2312yes—
132C2×C42×C7C2311yescharacteristic
133C2×C22⋊Dic7C2312yes—
134C2×C22⋊Dic7C2312yes—
135C2×C22⋊Dic7C2312yes—
136C2×C22⋊Dic7C2312yes—
137C2×C22⋊Dic7C2312yes—
138Q8×Dic7—42no—
139D4×Dic7—42no—
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×(C2×D7)⋊C4C2312yes—
150C2×(C2×D7)⋊C4C2312yes—
151C2×C4⋊Dic7C2312yes—
152C2×C4⋊Dic7C2311yescharacteristic
153C2×C4⋊Dic7C2311yescharacteristic
154C2×C4⋊Dic7C2312yes—
155C2×C4⋊Dic7C2311yescharacteristic
156C2×C4⋊Dic7C2311yescharacteristic
157C2×C4⋊Dic7C2312yes—
158C2×C4⋊Dic7C2312yes—
159C2×C4⋊Dic7C2312yes—
160C2×Dic7⋊C4C2312yes—
161C2×Dic7⋊C4C2312yes—
162C2×Dic7⋊C4C2312yes—
163C2×Dic7⋊C4C2312yes—
164C2×Dic7⋊C4C2312yes—
165C2×Dic7⋊C4C2312yes—
166C2×Dic7⋊C4C2312yes—
167C2×C4×Dic7C2312yes—
168C2×C4×Dic7C2312yes—
169C2×C4×Dic7C2312yes—
170C2×C4×Dic7C2311yescharacteristic
171C2×C4×Dic7C2312yes—
172C2×C4×Dic7C2311yescharacteristic
173C2×C4×Dic7C2311yescharacteristic
174C2×C4×Dic7C2311yescharacteristic
175C2×C4×Dic7C2311yescharacteristic
176C2×C4×Dic7C2311yescharacteristic
177#6456—42no—
178#6455—44no—
179#6450—42no—
180(C22⋊D7)⋊C4—44no—
181(C22⋊D7)⋊C4—44no—
182#6440—44no—
183#6438—24no—
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#2845—71no—
207#2837—72no—
208#2837—72no—
209#2831—72no—
210#2831—72no—
211#2829—72no—
212#2829—72no—
213#2820—71no—
214#2820D711yescharacteristic, complemented
215#2819—71no—
216#2396—72no—
217#2396—72no—
218#2395—72no—
219#2395—72no—
220#2392—72no—
221#2392—72no—
222C4×#125—71no—
223C4×#124—71no—
224C4×#124—71no—
225C24×C7C2412yes—
226C23×D7C2412yes—
227C2×C7×Q8—22no—
228C2×C7×Q8—41no—
229C2×C7×Q8—41no—
230C2×C7×D4—22no—
231C2×C7×D4—41no—
232C2×C7×D4—41no—
233C22×C4×C7C2412yes—
234C22×C4×C7C2412yes—
235C22×C4×C7C2412yes—
236C22×C4×C7C2412yes—
237C22×C4×C7C2412yes—
238C22×C4×C7C2411yescharacteristic
239C22×C4×C7C2411yescharacteristic
240C22×C4×C7C2411yescharacteristic
241C2×C22⋊D7—42no—
242C2×C22⋊D7—42no—
243C2×C22⋊D7—42no—
244C2×C22⋊D7—42no—
245C2×C22⋊D7—42no—
246C2×C22⋊D7—42no—
247C22×Dic7—24no—
248C22×Dic7—24no—
249C22×Dic7—24no—
250C22×Dic7C2411yescharacteristic
251C22×Dic7C2412yes—
252C22×Dic7C2412yes—
253C22×Dic7C2412yes—
254C22×Dic7C2412yes—
255C22×Dic7C2411yescharacteristic
256C22×Dic7C2411yescharacteristic
257C22×Dic7C2412yes—
258C22×Dic7C2411yescharacteristic
259C2×D28—22no—
260C2×D28—41no—
261C2×D28—41no—
262C2×C4×D7—24no—
263C2×C4×D7—24no—
264C2×C4×D7—24no—
265C2×Dic14—22no—
266C2×Dic14—41no—
267C2×Dic14—41no—
268C7×C4⋊C4—22no—
269C7×C4⋊C4—22no—
270C7×C4⋊C4—24no—
271C7×C4⋊C4—24no—
272C7×C4⋊C4—41no—
273C7×C4⋊C4—42no—
274C7×C4⋊C4—41no—
275C7×C4⋊C4—42no—
276C7×C22⋊C4—24no—
277C7×C22⋊C4—24no—
278C7×C22⋊C4—42no—
279C7×C22⋊C4—42no—
280C7×C22⋊C4—42no—
281C7×C22⋊C4—42no—
282C42×C7#4114yes—
283C22⋊Dic7—42no—
284C22⋊Dic7—42no—
285C22⋊Dic7—42no—
286C22⋊Dic7—42no—
287C22⋊Dic7—42no—
288(C2×D7)⋊C4—24no—
289(C2×D7)⋊C4—24no—
290(C2×D7)⋊C4—42no—
291(C2×D7)⋊C4—42no—
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—
299C4⋊Dic7—42no—
300C4⋊Dic7—42no—
301C4⋊Dic7—42no—
302C4⋊Dic7—42no—
303C4⋊Dic7—41no—
304C4⋊Dic7—41no—
305C4⋊Dic7—41no—
306C4⋊Dic7—41no—
307C4⋊Dic7—42no—
308Dic7⋊C4—42no—
309Dic7⋊C4—42no—
310Dic7⋊C4—42no—
311Dic7⋊C4—42no—
312Dic7⋊C4—42no—
313Dic7⋊C4—42no—
314Dic7⋊C4—42no—
315C4×Dic7—24no—
316C4×Dic7—24no—
317C4×Dic7—24no—
318C4×Dic7—22no—
319C4×Dic7—24no—
320C4×Dic7—22no—
321C4×Dic7—22no—
322C4×Dic7—41no—
323C4×Dic7—41no—
324C4×Dic7—41no—
325C2×#125C2×D711yescharacteristic
326C2×#124—71no—
327C2×#124C2×D711yescharacteristic
328C2×C4×Q8—71no—
329C2×C4×Q8—71no—
330C2×C4×D4—71no—
331C2×C4×D4—71no—
332C2×C4×D4—72no—
333C2×C4×D4—72no—
334C2×#117—72no—
335C2×#117—72no—
336#400—72no—
337#400—72no—
338#400—72no—
339#400—72no—
340#399—72no—
341#399—72no—
342#399—72no—
343#399C2×D712yes—
344#398—72no—
345#398—72no—
346#398—72no—
347#398—72no—
348#398—72no—
349#398—72no—
350#398—72no—
351#398—72no—
352#397—72no—
353#397—72no—
354#397—72no—
355#397—72no—
356#397—72no—
357#397—72no—
358#397—72no—
359#397C2×D712yes—
360#396—72no—
361#396—72no—
362#396—72no—
363#396—72no—
364#396—72no—
365#396—72no—
366#396C2×D712yes—
367#396C2×D712yes—
368#395—72no—
369#395C2×D712yes—
370#394—72no—
371#394—72no—
372#394—72no—
373#394—72no—
374#394—72no—
375#394—72no—
376#394—72no—
377#394—72no—
378#394—72no—
379#394C2×D712yes—
380#393—72no—
381#393—72no—
382#392—72no—
383#392—72no—
384#391—71no—
385#391—71no—
386#390—71no—
387#390—71no—
388#389—71no—
389#389—71no—
390#388—72no—
391#388—72no—
392#388—72no—
393#388—72no—
394#387—72no—
395#387—72no—
396#382—71no—
397#382—71no—
398#382C2×D711yescharacteristic
399C4×C4⋊C4—72no—
400C4×C4⋊C4—72no—
401C4×C4⋊C4—71no—
402C4×C4⋊C4—71no—
403C4×C4⋊C4—72no—
404C4×C4⋊C4—72no—
405C4×C22⋊C4—72no—
406C4×C22⋊C4—72no—
407C4×C22⋊C4—72no—
408C4×C22⋊C4—72no—
409C4×C22⋊C4—72no—
410C4×C22⋊C4—72no—
411C43—71no—
412C23×C7—22no—
413C23×C7—22no—
414C23×C7—22no—
415C23×C7—22no—
416C23×C7—22no—
417C23×C7—22no—
418C23×C7—22no—
419C23×C7C2511yescharacteristic
420C22×D7—22no—
421C22×D7—22no—
422C22×D7—22no—
423C22×D7—22no—
424C22×D7—22no—
425C22×D7—22no—
426C22×D7—22no—
427C7×Q8—44no—
428C7×D4—44no—
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—22no—
440C2×C4×C7—22no—
441C2×C4×C7—22no—
442C2×C4×C7—22no—
443C2×C4×C7—22no—
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×C7C2×#4112yes—
451C2×C4×C7C2×#4112yes—
452C2×C4×C7C2×#4112yes—
453C22⋊D7—48no—
454C22⋊D7—48no—
455C2×Dic7—22no—
456C2×Dic7—21no—
457C2×Dic7—22no—
458C2×Dic7—22no—
459C2×Dic7—22no—
460C2×Dic7—22no—
461C2×Dic7—21no—
462C2×Dic7—22no—
463C2×Dic7—22no—
464C2×Dic7—21no—
465C2×Dic7—22no—
466C2×Dic7—21no—
467C2×Dic7—21no—
468C2×Dic7—21no—
469C2×Dic7—21no—
470C2×Dic7—21no—
471C2×Dic7—21no—
472C2×Dic7—22no—
473C2×Dic7—22no—
474C2×Dic7—22no—
475C2×Dic7—22no—
476C2×Dic7—22no—
477C2×Dic7—22no—
478C2×Dic7—22no—
479C2×Dic7—48no—
480C2×Dic7H(5,𝔽2)12yes—
481C2×Dic7H(5,𝔽2)12yes—
482C2×Dic72−1+412yes—
483D28—44no—
484C4×D7—48no—
485Dic14—44no—
486C22×Q8—71no—
487C22×Q8C22×D711yescharacteristic
488C22×D4—72no—
489C22×D4—72no—
490C22×D4—71no—
491C22×D4C22×D711yescharacteristic
492C23×C4—72no—
493C23×C4—72no—
494#125—24no—
495#124—24no—
496#124—144no—
497C4×Q8—282no—
498C4×Q8—282no—
499C4×D4—284no—
500C4×D4—284no—
501C4×D4—282no—
502C4×D4—282no—
503#117—284no—
504#117—284no—
505C2×C4⋊C4—72no—
506C2×C4⋊C4—72no—
507C2×C4⋊C4—72no—
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—71no—
517C2×C4⋊C4—71no—
518C2×C4⋊C4—72no—
519C2×C4⋊C4—72no—
520C2×C4⋊C4—72no—
521C2×C4⋊C4C22×D712yes—
522C2×C4⋊C4C22×D712yes—
523C2×C4⋊C4C22×D711yescharacteristic
524C2×C4⋊C4C22×D711yescharacteristic
525C2×C4⋊C4C22×D712yes—
526C2×C4⋊C4C22×D711yescharacteristic
527C2×C4⋊C4C22×D711yescharacteristic
528C2×C4⋊C4C22×D712yes—
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⋊C4—72no—
541C2×C22⋊C4—72no—
542C2×C22⋊C4—72no—
543C2×C22⋊C4—72no—
544C2×C22⋊C4—72no—
545C2×C22⋊C4C22×D712yes—
546C2×C22⋊C4C22×D712yes—
547C2×C22⋊C4C22×D712yes—
548C2×C22⋊C4C22×D712yes—
549C2×C22⋊C4C22×D712yes—
550C2×C22⋊C4C22×D712yes—
551C2×C42—72no—
552C2×C42—72no—
553C2×C42—72no—
554C2×C42—72no—
555C2×C42—71no—
556C2×C42—71no—
557C2×C42—71no—
558C2×C42—71no—
559C2×C42—71no—
560C2×C42—71no—
561C2×C42C22×D711yescharacteristic
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—
584C22×C7—42no—
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×C7C2×2−1+411yescharacteristic
595C22×C7#58511yescharacteristic
596C22×C7#58511yescharacteristic
597C22×C7#58511yescharacteristic
598C2×D7—42no—
599C2×D7—42no—
600C2×D7—42no—
601C2×D7—42no—
602C2×D7—42no—
603C2×D7—42no—
604C2×D7—42no—
605C4×C7—22no—
606C4×C7—22no—
607C4×C7—22no—
608C4×C7—42no—
609C4×C7—42no—
610C4×C7—42no—
611C4×C7—42no—
612C4×C7—42no—
613Dic7—42no—
614Dic7—42no—
615Dic7—41no—
616Dic7—42no—
617Dic7—41no—
618Dic7—42no—
619Dic7—42no—
620Dic7—41no—
621Dic7#56214yes—
622C24—72no—
623C24C23×D712yes—
624C2×Q8—22no—
625C2×Q8—41no—
626C2×Q8—41no—
627C2×Q8—142no—
628C2×Q8—281no—
629C2×Q8—281no—
630C2×D4—22no—
631C2×D4—41no—
632C2×D4—41no—
633C2×D4—142no—
634C2×D4—281no—
635C2×D4—281no—
636C2×D4—282no—
637C2×D4—282no—
638C2×D4—282no—
639C2×D4—282no—
640C2×D4—282no—
641C2×D4—282no—
642C22×C4—71no—
643C22×C4—71no—
644C22×C4—72no—
645C22×C4—72no—
646C22×C4—72no—
647C22×C4—72no—
648C22×C4—71no—
649C22×C4—71no—
650C22×C4—72no—
651C22×C4—144no—
652C22×C4—144no—
653C22×C4—144no—
654C22×C4—144no—
655C22×C4—144no—
656C22×C4—144no—
657C22×C4C23×D712yes—
658C22×C4C23×D712yes—
659C22×C4C23×D712yes—
660C22×C4C23×D712yes—
661C22×C4C23×D712yes—
662C22×C4C23×D711yescharacteristic
663C22×C4C23×D711yescharacteristic
664C22×C4C23×D711yescharacteristic
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—24no—
668C4⋊C4—24no—
669C4⋊C4—42no—
670C4⋊C4—41no—
671C4⋊C4—41no—
672C4⋊C4—42no—
673C4⋊C4—282no—
674C4⋊C4—282no—
675C4⋊C4—282no—
676C4⋊C4—282no—
677C4⋊C4—282no—
678C4⋊C4—282no—
679C4⋊C4—282no—
680C4⋊C4—281no—
681C4⋊C4—281no—
682C4⋊C4—282no—
683C4⋊C4—282no—
684C4⋊C4—282no—
685C4⋊C4—282no—
686C4⋊C4—281no—
687C4⋊C4—281no—
688C4⋊C4—282no—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—144no—
696C22⋊C4—144no—
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—
709C22⋊C4—282no—
710C22⋊C4—282no—
711C42—142no—
712C42—144no—
713C42—144no—
714C42—144no—
715C42—144no—
716C42—142no—
717C42—142no—
718C42—281no—
719C42—281no—
720C42—281no—
721C42#115914yes—
722C2×C7—82no—
723C2×C7#346011yescharacteristic
724C2×C7#346011yescharacteristic
725C2×C7#346111yescharacteristic
726C2×C7C2×#56211yescharacteristic
727C2×C7#352911yescharacteristic
728C2×C7#352911yescharacteristic
729C2×C7#353111yescharacteristic
730D7—82no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—142no—
739C23—142no—
740C23—142no—
741C23—142no—
742C23—142no—
743C23—142no—
744C23—142no—
745C23C24×D711yescharacteristic
746Q8—44no—
747Q8—284no—
748D4—44no—
749D4—284no—
750D4—288no—
751D4—288no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—72no—
774C2×C4—72no—
775C2×C4—72no—
776C2×C4—142no—
777C2×C4—141no—
778C2×C4—141no—
779C2×C4—142no—
780C2×C4—142no—
781C2×C4—142no—
782C2×C4—142no—
783C2×C4—142no—
784C2×C4—142no—
785C2×C4—141no—
786C2×C4—141no—
787C2×C4—142no—
788C2×C4—141no—
789C2×C4—142no—
790C2×C4—141no—
791C2×C4—141no—
792C2×C4—141no—
793C2×C4—141no—
794C2×C4—142no—
795C2×C4—142no—
796C2×C4—142no—
797C2×C4—142no—
798C2×C4—142no—
799C2×C4—142no—
800C2×C4—288no—
801C2×C4—288no—
802C2×C4C2×#115912yes—
803C2×C4C2×#115912yes—
804C2×C4C2×#115912yes—
805C7#3669511yescharacteristic, complemented, Sylow
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—282no—
814C22—282no—
815C22—282no—
816C22—282no—
817C22—282no—
818C22—282no—
819C22—282no—
820C22C22×#115911yescharacteristic
821C22D7×H(5,𝔽2)11yescharacteristic
822C22D7×H(5,𝔽2)11yescharacteristic
823C22#9061811yescharacteristic
824C22D7×2−1+411yescharacteristic
825C22#9062011yescharacteristic
826C22#9062011yescharacteristic
827C4—22no—
828C4—22no—
829C4—22no—
830C4—42no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—74no—
836C4—282no—
837C4—281no—
838C4—282no—
839C4—282no—
840C4—281no—
841C4—282no—
842C4—281no—
843C4—282no—
844C2—82no—
845C2—562no—
846C2#1174338211yescharacteristic
847C2#1174340711yescharacteristic
848C2#1174343211yescharacteristic
849C2#1174416111yescharacteristic
850C2D7×#56211yescharacteristic
851C2#1174418311yescharacteristic
852C2#1174418411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2820C2
prime radical#11740452C2
hypercenter#2820D7
hypocenterC7#36695
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2820

Complements

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

NH ≅ G/Ntype
1. C7×#2820C2semidirect
2. #11740516C2semidirect
3. Dic7×#125C2semidirect
5. Dic7×#124C2semidirect
6. #11735541C2semidirect
7. #11735462C2semidirect
8. #11735181C2semidirect
9. #11734904C2semidirect
10. #11734900C2semidirect
11. #11734850C2semidirect
12. #11734727C2semidirect
13. #11734726C2semidirect
14. #11734723C2semidirect
15. #11734615C2semidirect
16. #11734613C2semidirect
17. #11734335C2semidirect
18. #11731664C2semidirect
19. #11731594C2semidirect
214. #2820D7semidirect
805. C7#36695semidirect

Maximal subgroups

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

subgroupindex
C7×#28202
#117405162
Dic7×#1252
#117404522
Dic7×#1242
#117355412
#117354622
#117351812
#117349042
#117349002
#117348502
#117347272
#117347262
#117347232
#117346152
#117346132
#117343352
#117316642
#117315942
#366957