Finite Group Databasebeta

← C2×#11740507 #13523943

Subgroups — C2×#11740507 #13523943

Order 1792.

2834 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×#125C211yesmaximal, characteristic, complemented
2C22×#6457C211yesmaximal, characteristic
3#11740507C2116yesmaximal, direct product factor
4C2×#89766C211yesmaximal, characteristic, complemented
5C2×#89766C211yesmaximal, characteristic, complemented
6C2×#89763C211yesmaximal, characteristic
7C2×#89761C211yesmaximal, characteristic, complemented
8C2×#89754C211yesmaximal, characteristic, complemented
9C2×#89760C211yesmaximal, characteristic
10C2×#89744C211yesmaximal, characteristic, complemented
11C2×#89762C211yesmaximal, characteristic, complemented
12C2×#89762C211yesmaximal, characteristic, complemented
13C2×#89762C211yesmaximal, characteristic, complemented
14C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
15C2×#89712C211yesmaximal, characteristic, complemented
16C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
17C23×D28C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C2×C7×#125—28no—
20C2×C7×#125C2218yescomplemented
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C4⋊C4C2211yescharacteristic
27C22×C42×C7C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×(C2×D7)⋊C4C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C2×#6457—28no—
47C2×#6457C2218yes—
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#89766C2218yescomplemented
57#89766C2218yescomplemented
58#89763C2218yes—
59#89762C2218yescomplemented
60#89762C2218yescomplemented
61#89762C2218yescomplemented
62#89761C2218yescomplemented
63#89760C2218yes—
64#89754C2218yescomplemented
65C4⋊C4×Dic7C2218yescomplemented
66#89744C2218yescomplemented
67#89712C2218yescomplemented
68C4×(C2×D7)⋊C4C2218yescomplemented
69C2×#2558—71nomaximal, Sylow
70C24×D7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C22×D28—24no—
86C22×D28—24no—
87C22×D28—42no—
88C22×D28C2314yes—
89C22×C4×D7—24no—
90C22×C4×D7—24no—
91C22×C4×D7—42no—
92C22×C4×D7C2314yes—
93C7×#125—232no—
94C2×C7×C4⋊C4—24no—
95C2×C7×C4⋊C4—24no—
96C2×C7×C4⋊C4—24no—
97C2×C7×C4⋊C4—24no—
98C2×C7×C4⋊C4—24no—
99C2×C7×C4⋊C4D418yes—
100C2×C7×C4⋊C4C2314yes—
101C2×C7×C4⋊C4C2314yes—
102C2×C7×C4⋊C4C2314yes—
103C2×C7×C4⋊C4C2314yes—
104C2×C7×C4⋊C4C2314yes—
105C2×C7×C4⋊C4C2314yes—
106C2×C42×C7—24no—
107C2×C42×C7C2314yes—
108C2×(C2×D7)⋊C4—24no—
109C2×(C2×D7)⋊C4—24no—
110C2×(C2×D7)⋊C4—24no—
111C2×(C2×D7)⋊C4—24no—
112C2×(C2×D7)⋊C4—24no—
113C2×(C2×D7)⋊C4—24no—
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×(C2×D7)⋊C4C2314yes—
125C2×(C2×D7)⋊C4C2314yes—
126C2×(C2×D7)⋊C4C2314yes—
127C2×(C2×D7)⋊C4C2314yes—
128C2×(C2×D7)⋊C4C2314yes—
129C2×(C2×D7)⋊C4C2314yes—
130C2×C4⋊Dic7—24no—
131C2×C4⋊Dic7C2314yes—
132C2×Dic7⋊C4—24no—
133C2×Dic7⋊C4—24no—
134C2×Dic7⋊C4—42no—
135C2×Dic7⋊C4C2314yes—
136C2×Dic7⋊C4C2314yes—
137C2×Dic7⋊C4C2314yes—
138C2×C4×Dic7—24no—
139C2×C4×Dic7—42no—
140C2×C4×Dic7—42no—
141C2×C4×Dic7C2314yes—
142C2×C4×Dic7C2314yes—
143C2×C4×Dic7C2314yes—
144#6457—232no—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×#125D711yescharacteristic, complemented
154C22×#123—71no—
155#2558—716no—
156C2×#400—71no—
157C2×#396—71no—
158C2×#396—71no—
159C2×#394—71no—
160C2×#390—71no—
161C2×#389—71no—
162C2×#388—71no—
163C2×#388—71no—
164C2×#388—71no—
165C2×#388—71no—
166C2×#385—71no—
167C2×C4×C4⋊C4—71no—
168C2×C4×C22⋊C4—71no—
169C24×C7C2411yescharacteristic
170C23×D7—22no—
171C23×D7—22no—
172C23×D7—22no—
173C23×D7—22no—
174C23×D7—22no—
175C23×D7—22no—
176C23×D7—22no—
177C23×D7—22no—
178C23×D7—22no—
179C23×D7—22no—
180C23×D7—22no—
181C23×D7—22no—
182C23×D7—22no—
183C23×D7#4114yes—
184C23×D7C2412yes—
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×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7C2×D414yes—
204C22×C4×C7C2×D414yes—
205C22×C4×C7C2×D414yes—
206C22×C4×C7#4114yes—
207C22×C4×C7C2412yes—
208C22×C4×C7C2412yes—
209C22×C4×C7C2412yes—
210C22×C4×C7C2412yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
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#4114yes—
231C22×Dic7#4114yes—
232C22×Dic7C2412yes—
233C22×Dic7C2412yes—
234C22×Dic7C2412yes—
235C22×Dic7C2412yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C2×D28—28no—
239C2×D28—28no—
240C2×D28—44no—
241C2×D28—416no—
242C2×C4×D7—28no—
243C2×C4×D7—28no—
244C2×C4×D7—44no—
245C2×C4×D7—416no—
246C7×C4⋊C4—28no—
247C7×C4⋊C4—28no—
248C7×C4⋊C4—28no—
249C7×C4⋊C4—28no—
250C7×C4⋊C4—28no—
251C7×C4⋊C4C2×D4116yes—
252C42×C7—28no—
253(C2×D7)⋊C4—28no—
254(C2×D7)⋊C4—28no—
255(C2×D7)⋊C4—28no—
256(C2×D7)⋊C4—28no—
257(C2×D7)⋊C4—28no—
258(C2×D7)⋊C4—28no—
259(C2×D7)⋊C4—28no—
260(C2×D7)⋊C4—28no—
261(C2×D7)⋊C4—28no—
262(C2×D7)⋊C4—28no—
263(C2×D7)⋊C4—44no—
264C4⋊Dic7—28no—
265Dic7⋊C4—28no—
266Dic7⋊C4—28no—
267Dic7⋊C4—44no—
268C4×Dic7—28no—
269C4×Dic7—44no—
270C4×Dic7—44no—
271C23×D4—71no—
272C24×C4—71no—
273C2×#125—28no—
274C2×#125C2×D718yescomplemented
275C2×#123—78no—
276C2×#123—148no—
277C22×C4⋊C4—71no—
278C22×C4⋊C4—71no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4C2×D711yescharacteristic
282C22×C4⋊C4C2×D711yescharacteristic
283C22×C4⋊C4C2×D711yescharacteristic
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⋊C4—71no—
296C22×C22⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C42—71no—
299C22×C42—71no—
300C22×C42—71no—
301C22×C42C2×D711yescharacteristic
302#400—78no—
303#396—78no—
304#396—78no—
305#394—78no—
306#390—78no—
307#389—78no—
308#388—78no—
309#388—78no—
310#388—78no—
311#388—78no—
312#385—78no—
313C4×C4⋊C4—78no—
314C4×C22⋊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×C7C22×D412yes—
324C23×C7C2×#4112yes—
325C23×C7C2×#4112yes—
326C23×C7C2×#4112yes—
327C23×C7C2×#4112yes—
328C23×C7H(5,𝔽2)12yes—
329C23×C72−1+412yes—
330C23×C7C2511yescharacteristic
331C22×D7—28no—
332C22×D7—28no—
333C22×D7—28no—
334C22×D7—22no—
335C22×D7—22no—
336C22×D7—22no—
337C22×D7—22no—
338C22×D7—22no—
339C22×D7—22no—
340C22×D7—22no—
341C22×D7—22no—
342C22×D7—22no—
343C22×D7—22no—
344C22×D7—22no—
345C22×D7—22no—
346C22×D7—22no—
347C22×D7—44no—
348C22×D7—44no—
349C22×D7—44no—
350C22×D7—44no—
351C22×D7—44no—
352C22×D7—44no—
353C22×D7—44no—
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—28no—
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—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—44no—
381C2×C4×C7—44no—
382C2×C4×C7—44no—
383C2×C4×C7C22×D414yes—
384C2×C4×C7C22×D414yes—
385C2×C4×C7C22×D414yes—
386C2×C4×C7C2×#4114yes—
387C2×Dic7—28no—
388C2×Dic7—28no—
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—
411D28—416no—
412C4×D7—416no—
413C25—71no—
414C25—71no—
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—74no—
426C23×C4—144no—
427C23×C4—144no—
428C23×C4—282no—
429C23×C4C22×D711yescharacteristic
430C23×C4C22×D711yescharacteristic
431C23×C4C22×D711yescharacteristic
432C23×C4C22×D711yescharacteristic
433C23×C4C22×D711yescharacteristic
434C23×C4C22×D711yescharacteristic
435C23×C4C22×D711yescharacteristic
436#125—232no—
437#123—1432no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
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—282no—
451C2×C4⋊C4C22⋊D718yes—
452C2×C4⋊C4C22×D714yes—
453C2×C4⋊C4C22×D714yes—
454C2×C4⋊C4C22×D714yes—
455C2×C4⋊C4C22×D714yes—
456C2×C4⋊C4C22×D714yes—
457C2×C4⋊C4C22×D714yes—
458C2×C22⋊C4—74no—
459C2×C22⋊C4—74no—
460C2×C22⋊C4—74no—
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—144no—
476C2×C22⋊C4—144no—
477C2×C22⋊C4—144no—
478C2×C22⋊C4—144no—
479C2×C22⋊C4—282no—
480C2×C42—24no—
481C2×C42—74no—
482C2×C42—74no—
483C2×C42—74no—
484C2×C42—144no—
485C2×C42—282no—
486C2×C42—282no—
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#52914yes—
497C22×C7#53214yes—
498C22×C7#53914yes—
499C22×C7#54614yes—
500C22×C7#54814yes—
501C22×C7#55214yes—
502C22×C7#55314yes—
503C22×C7C23×D411yescharacteristic
504C22×C7C22×#4111yescharacteristic
505C22×C7C22×#4111yescharacteristic
506C22×C7C22×#4111yescharacteristic
507C22×C7C22×#4111yescharacteristic
508C22×C7C2×H(5,𝔽2)11yescharacteristic
509C22×C7C2×2−1+411yescharacteristic
510C2×D7—24no—
511C2×D7—24no—
512C2×D7—24no—
513C2×D7—42no—
514C2×D7—42no—
515C2×D7—42no—
516C2×D7—42no—
517C2×D7—416no—
518C2×D7—42no—
519C2×D7—42no—
520C2×D7—42no—
521C2×D7—42no—
522C2×D7—42no—
523C2×D7—42no—
524C2×D7—42no—
525C2×D7—88no—
526C4×C7—24no—
527C4×C7—24no—
528C4×C7—24no—
529C4×C7—24no—
530C4×C7—42no—
531C4×C7—42no—
532C4×C7—42no—
533Dic7—24no—
534Dic7—24no—
535Dic7—42no—
536Dic7—42no—
537Dic7—42no—
538Dic7—42no—
539C24—74no—
540C24—72no—
541C24—72no—
542C24—142no—
543C24—142no—
544C24—142no—
545C24—142no—
546C24—142no—
547C24—142no—
548C24—142no—
549C24—142no—
550C24—142no—
551C24—142no—
552C24—142no—
553C24—142no—
554C24—142no—
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—22no—
576C22×C4—22no—
577C22×C4—74no—
578C22×C4—74no—
579C22×C4—72no—
580C22×C4—72no—
581C22×C4—72no—
582C22×C4—72no—
583C22×C4—72no—
584C22×C4—72no—
585C22×C4—148no—
586C22×C4—142no—
587C22×C4—142no—
588C22×C4—142no—
589C22×C4—142no—
590C22×C4—142no—
591C22×C4—142no—
592C22×C4—142no—
593C22×C4—142no—
594C22×C4—142no—
595C22×C4—142no—
596C22×C4—142no—
597C22×C4—142no—
598C22×C4—142no—
599C22×C4—142no—
600C22×C4—142no—
601C22×C4—142no—
602C22×C4—148no—
603C22×C4—284no—
604C22×C4—2816no—
605C22×C4#116114yes—
606C22×C4C2×C22⋊D714yes—
607C22×C4C2×C22⋊D714yes—
608C22×C4C2×C22⋊D714yes—
609C22×C4C23×D712yes—
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—28no—
619C4⋊C4—28no—
620C4⋊C4—28no—
621C4⋊C4—148no—
622C4⋊C4—148no—
623C4⋊C4—148no—
624C4⋊C4—284no—
625C4⋊C4C2×C22⋊D7116yes—
626C22⋊C4—148no—
627C22⋊C4—148no—
628C22⋊C4—148no—
629C22⋊C4—148no—
630C22⋊C4—148no—
631C22⋊C4—148no—
632C22⋊C4—148no—
633C22⋊C4—148no—
634C22⋊C4—148no—
635C22⋊C4—148no—
636C22⋊C4—284no—
637C42—28no—
638C42—148no—
639C42—284no—
640C42—284no—
641C2×C7#255818yescomplemented
642C2×C7C2×#52911yescharacteristic
643C2×C7C2×#53211yescharacteristic
644C2×C7C2×#53911yescharacteristic
645C2×C7C2×#54611yescharacteristic
646C2×C7C2×#54811yescharacteristic
647C2×C7C2×#55211yescharacteristic
648C2×C7C2×#55311yescharacteristic
649D7—44no—
650D7—82no—
651C23—74no—
652C23—148no—
653C23—148no—
654C23—148no—
655C23—142no—
656C23—142no—
657C23—142no—
658C23—142no—
659C23—142no—
660C23—142no—
661C23—142no—
662C23—142no—
663C23—142no—
664C23—142no—
665C23—142no—
666C23—142no—
667C23—142no—
668C23—284no—
669C23—284no—
670C23—284no—
671C23—284no—
672C23—284no—
673C23—284no—
674C23—284no—
675C23—284no—
676C23—284no—
677C23—284no—
678C23—284no—
679C23C2×#116112yes—
680C23#655112yes—
681C23D7×#4112yes—
682C23D7×#4112yes—
683C23D7×#4112yes—
684C23#655312yes—
685C23C22×C22⋊D712yes—
686C23C24×D711yescharacteristic
687D4—2816no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—28no—
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—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—74no—
713C2×C4—74no—
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—2816no—
733C2×C4—284no—
734C2×C4—284no—
735C2×C4—284no—
736C2×C4—284no—
737C2×C4C2×#116114yes—
738C2×C4C22×C22⋊D714yes—
739C2×C4C22×C22⋊D714yes—
740C2×C4C22×C22⋊D714yes—
741C7C2×#255811yescharacteristic, complemented, Sylow
742C22—144no—
743C22—144no—
744C22—144no—
745C22—282no—
746C22—282no—
747C22—2816no—
748C22—282no—
749C22—282no—
750C22—282no—
751C22—282no—
752C22—282no—
753C22—282no—
754C22—282no—
755C22—282no—
756C22—282no—
757C22—568no—
758C22#9038214yes—
759C22#9038314yes—
760C22#9038414yes—
761C22#9038614yes—
762C22#9050814yes—
763C22#9052014yes—
764C22#9052314yes—
765C22C22×#116111yescharacteristic
766C22C2×#655111yescharacteristic
767C22C2×D7×#4111yescharacteristic
768C22C2×D7×#4111yescharacteristic
769C22C2×D7×#4111yescharacteristic
770C22C2×#655311yescharacteristic
771C22C23×C22⋊D711yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—144no—
780C4—144no—
781C4—282no—
782C4—282no—
783C4—282no—
784C4—282no—
785C2—284no—
786C2—562no—
787C2#1174050718yesdirect product factor
788C2C2×#9038211yescharacteristic
789C2C2×#9038311yescharacteristic
790C2C2×#9038411yescharacteristic
791C2C2×#9038611yescharacteristic
792C2C2×#9050811yescharacteristic
793C2C2×#9052311yescharacteristic
794C2C2×#9052011yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C7×#125C2
socleC24×C7C24
prime radicalC23×D28C22
hypercenterC22×#125D7
hypocenterC7C2×#2558
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. C22×C7×#125C2semidirect
3. #11740507C2direct (N × H)
4. C2×#89766C2semidirect
5. C2×#89766C2semidirect
7. C2×#89761C2semidirect
8. C2×#89754C2semidirect
10. C2×#89744C2semidirect
11. C2×#89762C2semidirect
12. C2×#89762C2semidirect
13. C2×#89762C2semidirect
14. C2×C4⋊C4×Dic7C2semidirect
15. C2×#89712C2semidirect
16. C2×C4×(C2×D7)⋊C4C2semidirect
20. C2×C7×#125C22semidirect
56. #89766C22semidirect
57. #89766C22semidirect
59. #89762C22semidirect
60. #89762C22semidirect
61. #89762C22semidirect
62. #89761C22semidirect
64. #89754C22semidirect
65. C4⋊C4×Dic7C22semidirect
66. #89744C22semidirect
67. #89712C22semidirect
68. C4×(C2×D7)⋊C4C22semidirect
153. C22×#125D7semidirect
274. C2×#125C2×D7semidirect
641. C2×C7#2558semidirect
741. C7C2×#2558semidirect
787. C2#11740507direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1252
C22×#64572
#117405072
C2×#897662
C2×#897632
C2×#897612
C2×#897542
C2×#897602
C2×#897442
C2×#897622
C2×C4⋊C4×Dic72
C2×#897122
C2×C4×(C2×D7)⋊C42
C2×#25587