Finite Group Databasebeta

← C2×#11740525 #13522349

Subgroups — C2×#11740525 #13522349

Order 1792.

2898 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#126C211yesmaximal, characteristic, complemented
2C22×#6455C211yesmaximal, characteristic, complemented
3#11740525C2116yesmaximal, direct product factor
4C2×#89764C211yesmaximal, characteristic, complemented
5C2×#89761C211yesmaximal, characteristic, complemented
6C2×#89755C211yesmaximal, characteristic, complemented
7C2×#89745C211yesmaximal, characteristic, complemented
8C2×#89753C211yesmaximal, characteristic, complemented
9C2×#89728C211yesmaximal, characteristic
10C2×#89721C211yesmaximal, characteristic, complemented
11C2×#89733C211yesmaximal, characteristic
12C2×#89729C211yesmaximal, characteristic
13C2×#89716C211yesmaximal, characteristic, complemented
14C2×#89716C211yesmaximal, characteristic, complemented
15C2×#89712C211yesmaximal, characteristic, complemented
16C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C2×C7×#126—28no—
20C2×C7×#126C2218yescomplemented
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C42×C7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×C4⋊Dic7C2211yescharacteristic
37C22×C4⋊Dic7C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C2×#6455—28no—
47C2×#6455C2218yescomplemented
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56#89764C2218yescomplemented
57#89761C2218yescomplemented
58#89755C2218yescomplemented
59#89753C2218yescomplemented
60#89745C2218yescomplemented
61#89733C2218yes—
62#89729C2218yes—
63#89728C2218yes—
64#89721C2218yescomplemented
65#89716C2218yescomplemented
66#89716C2218yescomplemented
67#89712C2218yescomplemented
68C4×Dic7⋊C4C2218yescomplemented
69C2×#2479—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C22×C22⋊D7—24no—
79C22×C22⋊D7—24no—
80C22×C22⋊D7—42no—
81C22×C22⋊D7C2314yes—
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C22×C4×D7—24no—
90C22×C4×D7—24no—
91C22×C4×D7—24no—
92C22×C4×D7C2314yes—
93C7×#126—232no—
94C2×C7×C4⋊C4—24no—
95C2×C7×C4⋊C4—24no—
96C2×C7×C4⋊C4D418yescomplemented
97C2×C7×C4⋊C4C2314yes—
98C2×C7×C4⋊C4C2314yes—
99C2×C7×C4⋊C4C2314yes—
100C2×C7×C22⋊C4—24no—
101C2×C7×C22⋊C4—24no—
102C2×C7×C22⋊C4—24no—
103C2×C7×C22⋊C4C2314yes—
104C2×C7×C22⋊C4C2314yes—
105C2×C7×C22⋊C4C2314yes—
106C2×C42×C7—24no—
107C2×C42×C7C2314yes—
108C2×C22⋊Dic7—24no—
109C2×C22⋊Dic7—24no—
110C2×C22⋊Dic7—42no—
111C2×C22⋊Dic7C2314yes—
112C2×C22⋊Dic7C2314yes—
113C2×C22⋊Dic7C2314yes—
114C2×(C2×D7)⋊C4—24no—
115C2×(C2×D7)⋊C4—24no—
116C2×(C2×D7)⋊C4—24no—
117C2×(C2×D7)⋊C4—24no—
118C2×(C2×D7)⋊C4—42no—
119C2×(C2×D7)⋊C4C2314yes—
120C2×(C2×D7)⋊C4C2314yes—
121C2×(C2×D7)⋊C4C2314yes—
122C2×(C2×D7)⋊C4C2314yes—
123C2×(C2×D7)⋊C4C2314yes—
124C2×C4⋊Dic7—24no—
125C2×C4⋊Dic7—24no—
126C2×C4⋊Dic7C2314yes—
127C2×C4⋊Dic7C2314yes—
128C2×Dic7⋊C4—24no—
129C2×Dic7⋊C4—24no—
130C2×Dic7⋊C4—42no—
131C2×Dic7⋊C4—42no—
132C2×Dic7⋊C4—42no—
133C2×Dic7⋊C4C2314yes—
134C2×Dic7⋊C4C2314yes—
135C2×Dic7⋊C4C2314yes—
136C2×Dic7⋊C4C2314yes—
137C2×Dic7⋊C4C2314yes—
138C2×C4×Dic7—24no—
139C2×C4×Dic7—24no—
140C2×C4×Dic7—24no—
141C2×C4×Dic7C2314yes—
142C2×C4×Dic7C2314yes—
143C2×C4×Dic7C2314yes—
144#6455—232no—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×#126D711yescharacteristic, complemented
154C22×#117—71no—
155#2479—716no—
156C2×#399—71no—
157C2×#399—71no—
158C2×#398—71no—
159C2×#394—71no—
160C2×#390—71no—
161C2×#389—71no—
162C2×#388—71no—
163C2×#388—71no—
164C2×#388—71no—
165C2×#387—71no—
166C2×#386—71no—
167C2×#385—71no—
168C2×C4×C4⋊C4—71no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7—22no—
174C24×C7—22no—
175C24×C7—22no—
176C24×C7C2412yes—
177C24×C7C2411yescharacteristic
178C23×D7—22no—
179C23×D7—22no—
180C23×D7—22no—
181C23×D7—22no—
182C23×D7—22no—
183C23×D7—22no—
184C23×D7#4114yes—
185C23×D7C2412yes—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7C2×D414yes—
202C22×C4×C7C2×D414yes—
203C22×C4×C7C2×D414yes—
204C22×C4×C7C2412yes—
205C22×C4×C7C2412yes—
206C22×C4×C7C2412yes—
207C22×C4×C7C2412yes—
208C22×C4×C7C2412yes—
209C22×C4×C7C2412yes—
210C2×C22⋊D7—28no—
211C2×C22⋊D7—28no—
212C2×C22⋊D7—44no—
213C2×C22⋊D7—416no—
214C22×Dic7—22no—
215C22×Dic7—22no—
216C22×Dic7—22no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7—22no—
222C22×Dic7—22no—
223C22×Dic7—22no—
224C22×Dic7—22no—
225C22×Dic7—22no—
226C22×Dic7—22no—
227C22×Dic7—22no—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7—22no—
231C22×Dic7—22no—
232C22×Dic7#4114yes—
233C22×Dic7#4114yes—
234C22×Dic7#4114yes—
235C22×Dic7C2412yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C22×Dic7C2412yes—
239C22×Dic7C2412yes—
240C22×Dic7C2412yes—
241C22×Dic7C2412yes—
242C2×C4×D7—232no—
243C2×C4×D7—28no—
244C2×C4×D7—28no—
245C2×C4×D7—28no—
246C7×C4⋊C4—28no—
247C7×C4⋊C4—28no—
248C7×C4⋊C4C2×D4116yescomplemented
249C7×C22⋊C4—28no—
250C7×C22⋊C4—28no—
251C7×C22⋊C4—28no—
252C42×C7—28no—
253C22⋊Dic7—28no—
254C22⋊Dic7—28no—
255C22⋊Dic7—44no—
256(C2×D7)⋊C4—28no—
257(C2×D7)⋊C4—28no—
258(C2×D7)⋊C4—28no—
259(C2×D7)⋊C4—28no—
260(C2×D7)⋊C4—44no—
261C4⋊Dic7—28no—
262C4⋊Dic7—28no—
263Dic7⋊C4—28no—
264Dic7⋊C4—28no—
265Dic7⋊C4—44no—
266Dic7⋊C4—44no—
267Dic7⋊C4—44no—
268C4×Dic7—28no—
269C4×Dic7—28no—
270C4×Dic7—28no—
271C23×D4—71no—
272C24×C4—71no—
273C2×#126—28no—
274C2×#126C2×D718yescomplemented
275C2×#117—78no—
276C2×#117—148no—
277C22×C4⋊C4—71no—
278C22×C4⋊C4—71no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4—71no—
282C22×C4⋊C4—71no—
283C22×C4⋊C4—71no—
284C22×C4⋊C4C2×D711yescharacteristic
285C22×C4⋊C4C2×D711yescharacteristic
286C22×C4⋊C4C2×D711yescharacteristic
287C22×C22⋊C4—71no—
288C22×C22⋊C4—71no—
289C22×C22⋊C4—71no—
290C22×C22⋊C4—71no—
291C22×C22⋊C4—71no—
292C22×C22⋊C4—71no—
293C22×C22⋊C4—71no—
294C22×C22⋊C4—71no—
295C22×C22⋊C4C2×D711yescharacteristic
296C22×C22⋊C4C2×D711yescharacteristic
297C22×C22⋊C4C2×D711yescharacteristic
298C22×C42—71no—
299C22×C42—71no—
300C22×C42—71no—
301C22×C42C2×D711yescharacteristic
302#399—78no—
303#399—78no—
304#398—78no—
305#394—78no—
306#390—78no—
307#389—78no—
308#388—78no—
309#388—78no—
310#388—78no—
311#387—78no—
312#386—78no—
313#385—78no—
314C4×C4⋊C4—78no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C23×C7—22no—
324C23×C7—22no—
325C23×C7—22no—
326C23×C7—22no—
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—44no—
331C23×C7—44no—
332C23×C7—44no—
333C23×C7—44no—
334C23×C7—44no—
335C23×C7—44no—
336C23×C7—44no—
337C23×C7C22×D412yes—
338C23×C7C2×#4112yes—
339C23×C7C2×#4112yes—
340C23×C7C2×#4112yes—
341C23×C7C2×#4112yes—
342C23×C7H(5,𝔽2)12yes—
343C23×C72−1+412yes—
344C23×C7C2511yescharacteristic
345C22×D7—28no—
346C22×D7—28no—
347C22×D7—28no—
348C22×D7—22no—
349C22×D7—22no—
350C22×D7—22no—
351C22×D7—22no—
352C22×D7—22no—
353C22×D7—22no—
354C22×D7—44no—
355C22×D7—44no—
356C22×D7—44no—
357C22×D7—44no—
358C22×D7C2×#4114yes—
359C2×C4×C7—28no—
360C2×C4×C7—28no—
361C2×C4×C7—28no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—44no—
378C2×C4×C7—44no—
379C2×C4×C7—44no—
380C2×C4×C7C22×D414yes—
381C2×C4×C7C22×D414yes—
382C2×C4×C7C22×D414yes—
383C22⋊D7—416no—
384C2×Dic7—28no—
385C2×Dic7—28no—
386C2×Dic7—28no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—44no—
406C2×Dic7—44no—
407C2×Dic7—44no—
408C2×Dic7—44no—
409C2×Dic7C2×#4114yes—
410C2×Dic7C2×#4114yes—
411C2×Dic7C2×#4114yes—
412C4×D7—232no—
413C25—71no—
414C25C22×D711yescharacteristic
415C22×D4—74no—
416C22×D4—144no—
417C22×D4—144no—
418C22×D4—282no—
419C23×C4—71no—
420C23×C4—71no—
421C23×C4—71no—
422C23×C4—71no—
423C23×C4—71no—
424C23×C4—71no—
425C23×C4—71no—
426C23×C4—74no—
427C23×C4—144no—
428C23×C4—144no—
429C23×C4—144no—
430C23×C4C22×D711yescharacteristic
431C23×C4C22×D711yescharacteristic
432C23×C4C22×D711yescharacteristic
433C23×C4C22×D711yescharacteristic
434C23×C4C22×D711yescharacteristic
435C23×C4C22×D711yescharacteristic
436#126—232no—
437#117—1432no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—74no—
441C2×C4⋊C4—74no—
442C2×C4⋊C4—74no—
443C2×C4⋊C4—74no—
444C2×C4⋊C4—74no—
445C2×C4⋊C4—74no—
446C2×C4⋊C4—74no—
447C2×C4⋊C4—144no—
448C2×C4⋊C4—144no—
449C2×C4⋊C4—144no—
450C2×C4⋊C4—144no—
451C2×C4⋊C4—282no—
452C2×C4⋊C4—282no—
453C2×C4⋊C4—282no—
454C2×C4⋊C4C22⋊D718yescomplemented
455C2×C4⋊C4C22×D714yes—
456C2×C4⋊C4C22×D714yes—
457C2×C4⋊C4C22×D714yes—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—74no—
462C2×C22⋊C4—74no—
463C2×C22⋊C4—74no—
464C2×C22⋊C4—74no—
465C2×C22⋊C4—74no—
466C2×C22⋊C4—74no—
467C2×C22⋊C4—74no—
468C2×C22⋊C4—74no—
469C2×C22⋊C4—144no—
470C2×C22⋊C4—144no—
471C2×C22⋊C4—144no—
472C2×C22⋊C4—144no—
473C2×C22⋊C4—144no—
474C2×C22⋊C4—144no—
475C2×C22⋊C4—282no—
476C2×C22⋊C4—282no—
477C2×C22⋊C4C22×D714yes—
478C2×C22⋊C4C22×D714yes—
479C2×C22⋊C4C22×D714yes—
480C2×C42—24no—
481C2×C42—74no—
482C2×C42—74no—
483C2×C42—74no—
484C2×C42—144no—
485C2×C42—144no—
486C2×C42—144no—
487C2×C42C22×D714yes—
488#95—74no—
489#95—74no—
490#95—74no—
491#95—74no—
492#95—74no—
493#95—74no—
494#95—74no—
495#95—74no—
496C22×C7—42no—
497C22×C7—42no—
498C22×C7—42no—
499C22×C7—42no—
500C22×C7—42no—
501C22×C7—42no—
502C22×C7—42no—
503C22×C7—88no—
504C22×C7#52514yes—
505C22×C7#52914yes—
506C22×C7#54214yes—
507C22×C7#54714yes—
508C22×C7#55014yes—
509C22×C7#55114yes—
510C22×C7#55214yes—
511C22×C7C23×D411yescharacteristic
512C22×C7C22×#4111yescharacteristic
513C22×C7C22×#4111yescharacteristic
514C22×C7C22×#4111yescharacteristic
515C22×C7C22×#4111yescharacteristic
516C22×C7C2×H(5,𝔽2)11yescharacteristic
517C22×C7C2×2−1+411yescharacteristic
518C2×D7—24no—
519C2×D7—24no—
520C2×D7—24no—
521C2×D7—42no—
522C2×D7—42no—
523C2×D7—42no—
524C2×D7—42no—
525C2×D7—416no—
526C4×C7—24no—
527C4×C7—24no—
528C4×C7—24no—
529C4×C7—42no—
530C4×C7—42no—
531C4×C7—42no—
532Dic7—24no—
533Dic7—24no—
534Dic7—24no—
535Dic7—42no—
536Dic7—42no—
537Dic7—42no—
538Dic7—42no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—74no—
547C24—72no—
548C24—142no—
549C24—142no—
550C24—142no—
551C24—142no—
552C24—142no—
553C24—142no—
554C24C23×D712yes—
555C24C23×D711yescharacteristic
556C2×D4—148no—
557C2×D4—148no—
558C2×D4—284no—
559C2×D4—2816no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—74no—
576C22×C4—74no—
577C22×C4—74no—
578C22×C4—72no—
579C22×C4—72no—
580C22×C4—72no—
581C22×C4—72no—
582C22×C4—72no—
583C22×C4—72no—
584C22×C4—72no—
585C22×C4—148no—
586C22×C4—148no—
587C22×C4—1432no—
588C22×C4—142no—
589C22×C4—142no—
590C22×C4—142no—
591C22×C4—142no—
592C22×C4—142no—
593C22×C4—142no—
594C22×C4—148no—
595C22×C4—142no—
596C22×C4—142no—
597C22×C4—142no—
598C22×C4—142no—
599C22×C4—142no—
600C22×C4—142no—
601C22×C4—142no—
602C22×C4—142no—
603C22×C4—142no—
604C22×C4—142no—
605C22×C4—142no—
606C22×C4—142no—
607C22×C4C2×C22⋊D714yes—
608C22×C4C2×C22⋊D714yes—
609C22×C4C2×C22⋊D714yes—
610C22×C4C23×D712yes—
611C22×C4C23×D712yes—
612C22×C4C23×D712yes—
613C22×C4C23×D712yes—
614C22×C4C23×D712yes—
615C22×C4C23×D712yes—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—148no—
619C4⋊C4—148no—
620C4⋊C4—148no—
621C4⋊C4—148no—
622C4⋊C4—284no—
623C4⋊C4—284no—
624C4⋊C4—284no—
625C4⋊C4C2×C22⋊D7116yescomplemented
626C22⋊C4—28no—
627C22⋊C4—28no—
628C22⋊C4—28no—
629C22⋊C4—148no—
630C22⋊C4—148no—
631C22⋊C4—148no—
632C22⋊C4—148no—
633C22⋊C4—148no—
634C22⋊C4—148no—
635C22⋊C4—284no—
636C22⋊C4—284no—
637C42—28no—
638C42—148no—
639C42—148no—
640C42—148no—
641C2×C7—82no—
642C2×C7#247918yescomplemented
643C2×C7C2×#52511yescharacteristic
644C2×C7C2×#52911yescharacteristic
645C2×C7C2×#54211yescharacteristic
646C2×C7C2×#54711yescharacteristic
647C2×C7C2×#55011yescharacteristic
648C2×C7C2×#55111yescharacteristic
649C2×C7C2×#55211yescharacteristic
650D7—44no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—74no—
666C23—148no—
667C23—148no—
668C23—148no—
669C23—142no—
670C23—142no—
671C23—142no—
672C23—142no—
673C23—142no—
674C23—142no—
675C23—284no—
676C23—284no—
677C23—284no—
678C23—284no—
679C23D7×#4112yes—
680C23D7×#4112yes—
681C23D7×#4112yes—
682C23D7×#4112yes—
683C23#655312yes—
684C23#655412yes—
685C23C22×C22⋊D712yes—
686C23C24×D711yescharacteristic
687D4—2816no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—74no—
710C2×C4—74no—
711C2×C4—74no—
712C2×C4—1432no—
713C2×C4—148no—
714C2×C4—148no—
715C2×C4—148no—
716C2×C4—142no—
717C2×C4—142no—
718C2×C4—142no—
719C2×C4—142no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—142no—
724C2×C4—142no—
725C2×C4—142no—
726C2×C4—142no—
727C2×C4—142no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—284no—
735C2×C4—284no—
736C2×C4—284no—
737C2×C4—284no—
738C2×C4C22×C22⋊D714yes—
739C2×C4C22×C22⋊D714yes—
740C2×C4C22×C22⋊D714yes—
741C7C2×#247911yescharacteristic, complemented, Sylow
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—88no—
750C22—144no—
751C22—144no—
752C22—144no—
753C22—282no—
754C22—282no—
755C22—2816no—
756C22—282no—
757C22—282no—
758C22#9039614yes—
759C22#9039714yes—
760C22#9039914yes—
761C22#9040114yes—
762C22#9051514yes—
763C22#9051914yes—
764C22#9052514yes—
765C22C2×D7×#4111yescharacteristic
766C22C2×D7×#4111yescharacteristic
767C22C2×D7×#4111yescharacteristic
768C22C2×D7×#4111yescharacteristic
769C22C2×#655311yescharacteristic
770C22C2×#655411yescharacteristic
771C22C23×C22⋊D711yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—144no—
779C4—144no—
780C4—144no—
781C4—282no—
782C4—282no—
783C4—282no—
784C4—282no—
785C2—82no—
786C2—284no—
787C2#1174052518yesdirect product factor
788C2C2×#9039711yescharacteristic
789C2C2×#9040111yescharacteristic
790C2C2×#9039611yescharacteristic
791C2C2×#9039911yescharacteristic
792C2C2×#9051511yescharacteristic
793C2C2×#9051911yescharacteristic
794C2C2×#9052511yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C7×#126C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC22×#126D7
hypocenterC7C2×#2479
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. C22×C7×#126C2semidirect
2. C22×#6455C2semidirect
3. #11740525C2direct (N × H)
4. C2×#89764C2semidirect
5. C2×#89761C2semidirect
6. C2×#89755C2semidirect
7. C2×#89745C2semidirect
8. C2×#89753C2semidirect
10. C2×#89721C2semidirect
13. C2×#89716C2semidirect
14. C2×#89716C2semidirect
15. C2×#89712C2semidirect
16. C2×C4×Dic7⋊C4C2semidirect
20. C2×C7×#126C22semidirect
47. C2×#6455C22semidirect
56. #89764C22semidirect
57. #89761C22semidirect
58. #89755C22semidirect
59. #89753C22semidirect
60. #89745C22semidirect
64. #89721C22semidirect
65. #89716C22semidirect
66. #89716C22semidirect
67. #89712C22semidirect
68. C4×Dic7⋊C4C22semidirect
96. C2×C7×C4⋊C4D4semidirect
153. C22×#126D7semidirect
248. C7×C4⋊C4C2×D4semidirect
274. C2×#126C2×D7semidirect
454. C2×C4⋊C4C22⋊D7semidirect
625. C4⋊C4C2×C22⋊D7semidirect
642. C2×C7#2479semidirect
741. C7C2×#2479semidirect
787. C2#11740525direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1262
C22×#64552
#117405252
C2×#897642
C2×#897612
C2×#897552
C2×#897452
C2×#897532
C2×#897282
C2×#897212
C2×#897332
C2×#897292
C2×#897162
C2×#897122
C2×C4×Dic7⋊C42
C2×#24797