Finite Group Databasebeta

← #13524675

Subgroups — #13524675

Order 1792.

2040 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2395C211yesmaximal, characteristic, complemented
2#11739845C211yesmaximal, characteristic
3C4×#6499C211yesmaximal, characteristic, complemented
4#11739670C212yesmaximal, complemented
5#11735652C211yesmaximal, characteristic, complemented
6#11735629C211yesmaximal, characteristic, complemented
7#11735472C212yesmaximal, complemented
8#11735260C211yesmaximal, characteristic, complemented
9#11735246C211yesmaximal, characteristic, complemented
10#11734957C212yesmaximal, complemented
11#11734950C212yesmaximal, complemented
12#11734918C212yesmaximal, complemented
13#11734414C212yesmaximal, complemented
14#11734393C212yesmaximal, complemented
15#11731223C212yesmaximal, complemented
16C4×#6455C212yesmaximal, complemented
17C4×#6446C212yesmaximal, complemented
18#11731008C212yesmaximal, complemented
19C4×#6442C212yesmaximal, complemented
20C22×#1157C2211yescharacteristic
21C2×C4×C7×D4C2211yescharacteristic
22C2×C7×#117C2211yescharacteristic
23C2×#6499C2211yescharacteristic
24C2×C4×C22⋊D7C2212yes—
25C2×#6455C2212yes—
26C2×#6455C2212yes—
27C2×#6446C2212yes—
28C2×#6442C2212yes—
29C2×#6435C2212yes—
30C2×C42×D7C2212yes—
31C2×C4×Dic14C2211yescharacteristic
32C7×#400C2211yescharacteristic
33C7×#399C2211yescharacteristic
34C7×#398C2211yescharacteristic
35C7×#397C2212yes—
36C7×#397C2211yescharacteristic
37C7×#394C2212yes—
38C4×C7×C4⋊C4C2212yes—
39C4×C7×C22⋊C4C2212yes—
40C4×C7×C22⋊C4C2211yescharacteristic
41#89995C2212yes—
42#89993C2211yescharacteristic
43C4×C22⋊Dic7C2212yes—
44C4×C22⋊Dic7C2212yes—
45C4×C22⋊Dic7C2211yescharacteristic
46#89766C2212yes—
47#89764C2212yes—
48#89763C2211yescharacteristic
49#89762C2212yes—
50#89762C2212yes—
51#89752C2212yes—
52#89751C2212yes—
53#89751C2211yescharacteristic
54#89749C2211yescharacteristic
55C4⋊C4×Dic7C2212yes—
56C4⋊C4×Dic7C2212yes—
57#89746C2211yescharacteristic
58#89744C2212yes—
59#89744C2212yes—
60#89732C2211yescharacteristic
61#89731C2212yes—
62#89729C2212yes—
63#89729C2212yes—
64#89729C2212yes—
65#89729C2212yes—
66#89728C2212yes—
67#89728C2212yes—
68#89728C2212yes—
69#89723C2212yes—
70#89723C2212yes—
71#89719C2211yescharacteristic
72#89717C2212yes—
73#89717C2212yes—
74#89717C2212yes—
75#89717C2212yes—
76#89717C2212yes—
77#89717C2212yes—
78#89716C2212yes—
79C4×(C2×D7)⋊C4C2212yes—
80C4×(C2×D7)⋊C4C2212yes—
81C4×(C2×D7)⋊C4C2212yes—
82C4×C4⋊Dic7C2212yes—
83C4×Dic7⋊C4C2212yes—
84C4×Dic7⋊C4C2212yes—
85C42×Dic7C2212yes—
86C42×Dic7C2211yescharacteristic
87#89448C2212yes—
88#89445C2212yes—
89#89440C2212yes—
90#89438C2212yes—
91#89438C2212yes—
92#89437C2212yes—
93#89437C2212yes—
94#89436C2212yes—
95#89430C2212yes—
96#89429C2212yes—
97#89427C2212yes—
98#89426C2212yes—
99#89425C2212yes—
100#89424C2212yes—
101#89424C2212yes—
102#89423C2212yes—
103#89420C2212yes—
104#89420C2212yes—
105#89418C2212yes—
106#89418C2212yes—
107#34871—71nomaximal, Sylow
108C22×C7×D4C2311yescharacteristic
109C23×C4×C7C2311yescharacteristic
110C23×C4×C7C2311yescharacteristic
111C22×C22⋊D7C2312yes—
112C22×C22⋊D7C2312yes—
113C2×#1157—28no—
114C2×#1157—42no—
115C22×D28C2311yescharacteristic
116C22×C4×D7C2312yes—
117C22×C4×D7C2312yes—
118C22×C4×D7C2312yes—
119C22×Dic14C2311yescharacteristic
120C22×Dic14C2311yescharacteristic
121C4×C7×D4—42no—
122C7×#117—42no—
123C2×C7×C4⋊C4C2312yes—
124C2×C7×C4⋊C4C2312yes—
125C2×C7×C4⋊C4C2311yescharacteristic
126C2×C7×C4⋊C4C2311yescharacteristic
127C2×C7×C4⋊C4C2311yescharacteristic
128C2×C7×C22⋊C4C2312yes—
129C2×C7×C22⋊C4C2312yes—
130C2×C7×C22⋊C4C2312yes—
131C2×C7×C22⋊C4C2311yescharacteristic
132C2×C7×C22⋊C4C2312yes—
133C2×C7×C22⋊C4C2311yescharacteristic
134C2×C42×C7C2311yescharacteristic
135C2×C42×C7C2312yes—
136C2×C42×C7C2312yes—
137C2×C22⋊Dic7C2312yes—
138C2×C22⋊Dic7C2312yes—
139C2×C22⋊Dic7C2312yes—
140C2×C22⋊Dic7C2312yes—
141C2×C22⋊Dic7C2312yes—
142C2×C22⋊Dic7C2312yes—
143#6499—24no—
144C4×C22⋊D7—28no—
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×(C2×D7)⋊C4C2312yes—
152C2×(C2×D7)⋊C4C2312yes—
153C2×(C2×D7)⋊C4C2312yes—
154C2×C4⋊Dic7C2312yes—
155C2×C4⋊Dic7C2311yescharacteristic
156C2×C4⋊Dic7C2312yes—
157C2×Dic7⋊C4C2312yes—
158C2×Dic7⋊C4C2312yes—
159C2×Dic7⋊C4C2312yes—
160C2×Dic7⋊C4C2312yes—
161C2×Dic7⋊C4C2312yes—
162C2×Dic7⋊C4C2312yes—
163C2×Dic7⋊C4C2312yes—
164C2×Dic7⋊C4C2312yes—
165C2×C4×Dic7C2312yes—
166C2×C4×Dic7C2312yes—
167C2×C4×Dic7C2312yes—
168C2×C4×Dic7C2312yes—
169C2×C4×Dic7C2312yes—
170C2×C4×Dic7C2312yes—
171C2×C4×Dic7C2312yes—
172C2×C4×Dic7C2312yes—
173C2×C4×Dic7C2312yes—
174C2×C4×Dic7C2312yes—
175C2×C4×Dic7C2311yescharacteristic
176C2×C4×Dic7C2311yescharacteristic
177#6455—28no—
178#6455—28no—
179#6446—28no—
180#6442—28no—
181#6435—44no—
182C42×D7—28no—
183C4×Dic14—42no—
184C7×#95C2312yes—
185C7×#95C2312yes—
186C7×#95C2312yes—
187C7×#95C2312yes—
188C7×#95C2311yescharacteristic
189C7×#95C2311yescharacteristic
190C7⋊#95C2312yes—
191C7⋊#95C2312yes—
192C7⋊#95C2312yes—
193C7⋊#95C2312yes—
194C7⋊#95C2312yes—
195C7⋊#95C2312yes—
196C7⋊#95C2312yes—
197C7⋊#95C2312yes—
198C7⋊#95C2312yes—
199C7⋊#95C2312yes—
200C7⋊#95C2311yescharacteristic
201C7⋊#95C2312yes—
202C7⋊#95C2312yes—
203C7⋊#95C2311yescharacteristic
204C7⋊#95C2312yes—
205C7⋊#95C2312yes—
206C7⋊#95C2312yes—
207C7⋊#95C2312yes—
208#2612—71no—
209#2610—72no—
210#2609—71no—
211#2586—71no—
212#2572—71no—
213#2554—72no—
214#2532—72no—
215#2526—72no—
216#2479—72no—
217#2471—72no—
218#2396—72no—
219#2395D711yescharacteristic, complemented
220#2388—71no—
221C4×#126—72no—
222C4×#124—71no—
223C4×#123—72no—
224#2297—72no—
225#2293—72no—
226C4×#117—72no—
227C24×C7C2411yescharacteristic
228C24×C7C2411yescharacteristic
229C23×D7C2412yes—
230C2×C7×D4—22no—
231C2×C7×D4—41no—
232C2×C7×D4—41no—
233C22×C4×C7—24no—
234C22×C4×C7—24no—
235C22×C4×C7—22no—
236C22×C4×C7—22no—
237C22×C4×C7C2411yescharacteristic
238C22×C4×C7C2412yes—
239C22×C4×C7C2411yescharacteristic
240C22×C4×C7C2412yes—
241C22×C4×C7C2411yescharacteristic
242C22×C4×C7C2412yes—
243C22×C4×C7C2411yescharacteristic
244C22×C4×C7C2412yes—
245C22×C4×C7C2411yescharacteristic
246C2×C22⋊D7—24no—
247C2×C22⋊D7—24no—
248C2×C22⋊D7—24no—
249C2×C22⋊D7—24no—
250C2×C22⋊D7—42no—
251C2×C22⋊D7—42no—
252C22×Dic7C2412yes—
253C22×Dic7C2412yes—
254C22×Dic7C2412yes—
255C22×Dic7C2412yes—
256C22×Dic7C2412yes—
257C22×Dic7C2412yes—
258C22×Dic7C2412yes—
259#1157—416no—
260C2×D28—24no—
261C2×D28—41no—
262C2×C4×D7—24no—
263C2×C4×D7—24no—
264C2×C4×D7—24no—
265C2×C4×D7—24no—
266C2×C4×D7—24no—
267C2×C4×D7—24no—
268C2×C4×D7—24no—
269C2×C4×D7—42no—
270C2×C4×D7#4118yes—
271C2×Dic14—22no—
272C2×Dic14—24no—
273C2×Dic14—41no—
274C2×Dic14—41no—
275C2×Dic14—41no—
276C7×C4⋊C4—24no—
277C7×C4⋊C4—24no—
278C7×C4⋊C4—41no—
279C7×C4⋊C4—41no—
280C7×C4⋊C4—41no—
281C7×C22⋊C4—24no—
282C7×C22⋊C4—24no—
283C7×C22⋊C4—42no—
284C7×C22⋊C4—42no—
285C7×C22⋊C4—41no—
286C7×C22⋊C4—41no—
287C42×C7—24no—
288C42×C7—22no—
289C42×C7—24no—
290C22⋊Dic7—24no—
291C22⋊Dic7—24no—
292C22⋊Dic7—24no—
293C22⋊Dic7—24no—
294C22⋊Dic7—24no—
295C22⋊Dic7—24no—
296(C2×D7)⋊C4—24no—
297(C2×D7)⋊C4—24no—
298(C2×D7)⋊C4—24no—
299(C2×D7)⋊C4—24no—
300(C2×D7)⋊C4—24no—
301(C2×D7)⋊C4—24no—
302(C2×D7)⋊C4—42no—
303(C2×D7)⋊C4—42no—
304(C2×D7)⋊C4—42no—
305C4⋊Dic7—24no—
306C4⋊Dic7—41no—
307C4⋊Dic7#4118yescomplemented
308Dic7⋊C4—24no—
309Dic7⋊C4—24no—
310Dic7⋊C4—24no—
311Dic7⋊C4—24no—
312Dic7⋊C4—42no—
313Dic7⋊C4—42no—
314Dic7⋊C4—42no—
315Dic7⋊C4—42no—
316C4×Dic7—24no—
317C4×Dic7—24no—
318C4×Dic7—24no—
319C4×Dic7—24no—
320C4×Dic7—24no—
321C4×Dic7—24no—
322C4×Dic7—24no—
323C4×Dic7—24no—
324C4×Dic7—24no—
325C4×Dic7—41no—
326C4×Dic7—42no—
327C4×Dic7#4114yescomplemented
328C22×#41—71no—
329C2×#126—72no—
330C2×#124—71no—
331C2×#123—72no—
332C2×C4×Q8—71no—
333C2×C4×D4—72no—
334C2×C4×D4C2×D711yescharacteristic
335C2×#117—72no—
336C2×#117—72no—
337C2×#117—72no—
338C2×#117C2×D711yescharacteristic
339C22×C42—72no—
340#400—72no—
341#400C2×D711yescharacteristic
342#399—72no—
343#399C2×D711yescharacteristic
344#398—72no—
345#398—72no—
346#398C2×D711yescharacteristic
347#397C2×D712yes—
348#397C2×D711yescharacteristic
349#396—72no—
350#396—72no—
351#395—72no—
352#395—71no—
353#394—71no—
354#394—72no—
355#394C2×D712yes—
356#393—71no—
357#393—72no—
358#392—72no—
359#392—71no—
360#391—71no—
361#391—72no—
362#391—72no—
363#390—71no—
364#390—72no—
365#390—72no—
366#390—72no—
367#390—72no—
368#389—72no—
369#389—72no—
370#388—72no—
371#388—72no—
372#388—72no—
373#388—72no—
374#388—72no—
375#388—72no—
376#388—72no—
377#388—72no—
378#388—72no—
379#388—72no—
380#388—72no—
381#387—72no—
382#387—72no—
383#387—72no—
384#387—72no—
385#387—72no—
386#386—72no—
387#386—72no—
388#386—72no—
389#386—72no—
390#386—72no—
391#385—72no—
392#383—72no—
393#382—71no—
394#381—72no—
395C4×C4⋊C4—72no—
396C4×C4⋊C4—72no—
397C4×C4⋊C4—72no—
398C4×C4⋊C4—72no—
399C4×C4⋊C4—72no—
400C4×C4⋊C4C2×D712yes—
401C4×C22⋊C4—71no—
402C4×C22⋊C4—72no—
403C4×C22⋊C4—72no—
404C4×C22⋊C4—72no—
405C4×C22⋊C4—72no—
406C4×C22⋊C4—72no—
407C4×C22⋊C4—72no—
408C4×C22⋊C4—72no—
409C4×C22⋊C4C2×D712yes—
410C4×C22⋊C4C2×D711yescharacteristic
411#376—72no—
412#376—72no—
413C43—72no—
414C43—71no—
415C23×C7—22no—
416C23×C7—21no—
417C23×C7—21no—
418C23×C7—22no—
419C23×C7—22no—
420C23×C7—22no—
421C23×C7—21no—
422C23×C7—21no—
423C23×C7—21no—
424C23×C7—21no—
425C23×C7C2511yescharacteristic
426C22×D7—22no—
427C22×D7—22no—
428C22×D7—22no—
429C22×D7—22no—
430C22×D7—22no—
431C22×D7—22no—
432C22×D7C2×#4114yes—
433C7×D4—44no—
434C2×C4×C7—22no—
435C2×C4×C7—22no—
436C2×C4×C7—21no—
437C2×C4×C7—21no—
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—21no—
447C2×C4×C7—22no—
448C2×C4×C7—22no—
449C2×C4×C7—21no—
450C2×C4×C7—21no—
451C2×C4×C7—22no—
452C2×C4×C7—22no—
453C2×C4×C7—44no—
454C2×C4×C7—44no—
455C2×C4×C7C2×#4112yes—
456C2×C4×C7C2×#4114yes—
457C2×C4×C7C2×#4114yes—
458C2×C4×C7H(5,𝔽2)12yes—
459C22⋊D7—48no—
460C22⋊D7—48no—
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×Dic7C2×#4114yes—
479C2×Dic7C2×#4114yes—
480C2×Dic7C2×#4114yes—
481C2×Dic7C2×#4114yes—
482D28—44no—
483C4×D7—216no—
484C4×D7—216no—
485C4×D7—48no—
486Dic14—44no—
487Dic14—44no—
488C2×#41—148no—
489C2×#41—282no—
490C22×Q8—71no—
491C22×Q8—71no—
492C22×D4—72no—
493C22×D4—72no—
494C22×D4—71no—
495C22×D4C22×D711yescharacteristic
496C23×C4—72no—
497C23×C4—72no—
498C23×C4—72no—
499C23×C4C22×D711yescharacteristic
500C23×C4C22×D711yescharacteristic
501#126—148no—
502#124—144no—
503#123—148no—
504C4×Q8—282no—
505C4×D4—42no—
506C4×D4—148no—
507#117—42no—
508#117—148no—
509#117—148no—
510#117—284no—
511C2×C4⋊C4—72no—
512C2×C4⋊C4—72no—
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—71no—
521C2×C4⋊C4—72no—
522C2×C4⋊C4C22×D712yes—
523C2×C4⋊C4C22×D712yes—
524C2×C4⋊C4C22×D711yescharacteristic
525C2×C4⋊C4C22×D711yescharacteristic
526C2×C4⋊C4C22×D711yescharacteristic
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⋊C4—72no—
541C2×C22⋊C4—72no—
542C2×C22⋊C4C22×D712yes—
543C2×C22⋊C4C22×D712yes—
544C2×C22⋊C4C22×D712yes—
545C2×C22⋊C4C22×D711yescharacteristic
546C2×C22⋊C4C22×D711yescharacteristic
547C2×C22⋊C4C22×D712yes—
548C2×C42—71no—
549C2×C42—72no—
550C2×C42—72no—
551C2×C42—72no—
552C2×C42—72no—
553C2×C42—72no—
554C2×C42—72no—
555C2×C42—72no—
556C2×C42—72no—
557C2×C42—72no—
558C2×C42—71no—
559C2×C42—72no—
560C2×C42—148no—
561C2×C42C22×D712yes—
562C2×C42C22×D711yescharacteristic
563C2×C42C22×D712yes—
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—71no—
574#95—72no—
575#95—72no—
576#95—72no—
577#95—71no—
578#95—72no—
579#95—72no—
580#95—72no—
581#95—72no—
582#95C22×D712yes—
583#95C22×D712yes—
584#95C22×D711yescharacteristic
585#95C22×D712yes—
586#95C22×D711yescharacteristic
587#95C22×D712yes—
588C22×C7—42no—
589C22×C7—42no—
590C22×C7—41no—
591C22×C7—41no—
592C22×C7—41no—
593C22×C7—41no—
594C22×C7—42no—
595C22×C7—42no—
596C22×C7—41no—
597C22×C7—41no—
598C22×C7C22×#4111yescharacteristic
599C22×C7C22×#4112yes—
600C22×C7C22×#4112yes—
601C22×C7C2×H(5,𝔽2)11yescharacteristic
602C22×C7#58511yescharacteristic
603C2×D7—24no—
604C2×D7—24no—
605C2×D7—24no—
606C2×D7—42no—
607C2×D7—42no—
608C2×D7—42no—
609C2×D7—42no—
610C4×C7—24no—
611C4×C7—22no—
612C4×C7—42no—
613C4×C7—41no—
614C4×C7—41no—
615C4×C7—42no—
616C4×C7—42no—
617C4×C7—41no—
618C4×C7#55114yes—
619Dic7—24no—
620Dic7—24no—
621Dic7—24no—
622Dic7—24no—
623Dic7—42no—
624Dic7—42no—
625Dic7—42no—
626C24—72no—
627C24C23×D711yescharacteristic
628C24C23×D711yescharacteristic
629#41—2816no—
630C2×Q8—144no—
631C2×Q8—142no—
632C2×Q8—281no—
633C2×Q8—281no—
634C2×Q8—281no—
635C2×D4—22no—
636C2×D4—41no—
637C2×D4—41no—
638C2×D4—144no—
639C2×D4—144no—
640C2×D4—144no—
641C2×D4—144no—
642C2×D4—144no—
643C2×D4—281no—
644C2×D4—282no—
645C2×D4—282no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—72no—
651C22×C4—72no—
652C22×C4—72no—
653C22×C4—72no—
654C22×C4—78no—
655C22×C4—72no—
656C22×C4—72no—
657C22×C4—72no—
658C22×C4—144no—
659C22×C4—144no—
660C22×C4—144no—
661C22×C4—144no—
662C22×C4—144no—
663C22×C4—144no—
664C22×C4—144no—
665C22×C4—282no—
666C22×C4C23×D711yescharacteristic
667C22×C4C23×D712yes—
668C22×C4C23×D711yescharacteristic
669C22×C4C23×D711yescharacteristic
670C22×C4C23×D712yes—
671C22×C4C23×D712yes—
672C22×C4C23×D711yescharacteristic
673C22×C4C23×D712yes—
674C22×C4C23×D711yescharacteristic
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—41no—
678C4⋊C4—41no—
679C4⋊C4—41no—
680C4⋊C4—78no—
681C4⋊C4—144no—
682C4⋊C4—144no—
683C4⋊C4—144no—
684C4⋊C4—144no—
685C4⋊C4—144no—
686C4⋊C4—282no—
687C4⋊C4—282no—
688C4⋊C4—282no—
689C4⋊C4—282no—
690C4⋊C4—281no—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—42no—
694C22⋊C4—41no—
695C22⋊C4—41no—
696C22⋊C4—42no—
697C22⋊C4—144no—
698C22⋊C4—144no—
699C22⋊C4—144no—
700C22⋊C4—144no—
701C22⋊C4—144no—
702C22⋊C4—144no—
703C22⋊C4—144no—
704C22⋊C4—144no—
705C22⋊C4—144no—
706C22⋊C4—144no—
707C22⋊C4—144no—
708C22⋊C4—144no—
709C22⋊C4—282no—
710C22⋊C4—282no—
711C22⋊C4—282no—
712C42—24no—
713C42—22no—
714C42—24no—
715C42—74no—
716C42—144no—
717C42—144no—
718C42—144no—
719C42—144no—
720C42—144no—
721C42—144no—
722C42—144no—
723C42—144no—
724C42—144no—
725C42—281no—
726C42—282no—
727C2×C7—81no—
728C2×C7—81no—
729C2×C7#344412yes—
730C2×C7#346011yescharacteristic
731C2×C7C2×#55111yescharacteristic
732C2×C7#347512yes—
733C2×C7#348311yescharacteristic
734D7—44no—
735C23—21no—
736C23—21no—
737C23—22no—
738C23—22no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—22no—
743C23—21no—
744C23—21no—
745C23—74no—
746C23—142no—
747C23—142no—
748C23—142no—
749C23—142no—
750C23—142no—
751C23—142no—
752C23C24×D711yescharacteristic
753Q8—284no—
754Q8—284no—
755D4—44no—
756D4—284no—
757D4—288no—
758D4—288no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—74no—
781C2×C4—74no—
782C2×C4—74no—
783C2×C4—74no—
784C2×C4—1416no—
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—1416no—
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—288no—
804C2×C4#654812yes—
805C2×C4D7×#4112yes—
806C2×C4D7×#4114yes—
807C2×C4D7×#4114yes—
808C7#3487111yescharacteristic, complemented, Sylow
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—144no—
820C22—144no—
821C22—144no—
822C22—282no—
823C22—282no—
824C22—282no—
825C22—282no—
826C22C2×#654811yescharacteristic
827C22C2×D7×#4112yes—
828C22C2×D7×#4112yes—
829C22C2×D7×#4111yescharacteristic
830C22#9061611yescharacteristic
831C4—22no—
832C4—24no—
833C4—41no—
834C4—42no—
835C4—41no—
836C4—41no—
837C4—42no—
838C4—42no—
839C4—144no—
840C4—144no—
841C4—144no—
842C4—144no—
843C4—282no—
844C4—282no—
845C4—282no—
846C4#9035014yes—
847C2—81no—
848C2—81no—
849C2—284no—
850C2C2×#9035011yescharacteristic
851C2#1174308811yescharacteristic
852C2#1174318712yes—
853C2#1174321912yes—
854C2#1174328911yescharacteristic
subgroupG/H
centerC22×C4C23×D7
commutator, socle, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC7×#2395C2
prime radical#11739845C2
hypercenter#2395D7
hypocenterC7#34871
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ #2395

Complements

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

NH ≅ G/Ntype
1. C7×#2395C2semidirect
3. C4×#6499C2semidirect
4. #11739670C2semidirect
5. #11735652C2semidirect
6. #11735629C2semidirect
7. #11735472C2semidirect
8. #11735260C2semidirect
9. #11735246C2semidirect
10. #11734957C2semidirect
11. #11734950C2semidirect
12. #11734918C2semidirect
13. #11734414C2semidirect
14. #11734393C2semidirect
15. #11731223C2semidirect
16. C4×#6455C2semidirect
17. C4×#6446C2semidirect
18. #11731008C2semidirect
19. C4×#6442C2semidirect
219. #2395D7semidirect
307. C4⋊Dic7#41semidirect
327. C4×Dic7#41semidirect
808. C7#34871semidirect

Maximal subgroups

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

subgroupindex
C7×#23952
#117398452
C4×#64992
#117396702
#117356522
#117356292
#117354722
#117352602
#117352462
#117349572
#117349502
#117349182
#117344142
#117343932
#117312232
C4×#64552
C4×#64462
#117310082
C4×#64422
#348717