Finite Group Databasebeta

← C2×#11732463 #13522353

Subgroups — C2×#11732463 #13522353

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×#6461C211yesmaximal, characteristic, complemented
2C22×#6455C211yesmaximal, characteristic, complemented
3C2×C7×#387C211yesmaximal, characteristic, complemented
4C2×#89763C211yesmaximal, characteristic
5C2×#89757C211yesmaximal, characteristic, complemented
6C2×#89711C211yesmaximal, characteristic
7C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
8#11732463C2116yesmaximal, direct product factor
9C2×#89449C211yesmaximal, characteristic, complemented
10C2×#89449C211yesmaximal, characteristic, complemented
11C2×#89437C211yesmaximal, characteristic
12C2×#89440C211yesmaximal, characteristic, complemented
13C2×#89433C211yesmaximal, characteristic, complemented
14C2×#89442C211yesmaximal, characteristic, complemented
15C2×#89442C211yesmaximal, characteristic, complemented
16C2×#89442C211yesmaximal, characteristic, complemented
17C23×D28C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C42×C7C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×C4⋊Dic7C2211yescharacteristic
34C22×C4⋊Dic7C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×C4⋊Dic7C2211yescharacteristic
37C22×C4⋊Dic7C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6461—28no—
45C2×#6461C2218yescomplemented
46C2×#6455—28no—
47C2×#6455C2218yescomplemented
48C7×#387C2218yescomplemented
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51C2×C7×#95C2211yescharacteristic
52C2×C7×#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57#89763C2218yes—
58#89757C2218yescomplemented
59#89711C2218yes—
60C4×C4⋊Dic7C2218yescomplemented
61#89449C2218yescomplemented
62#89449C2218yescomplemented
63#89442C2218yescomplemented
64#89442C2218yescomplemented
65#89442C2218yescomplemented
66#89440C2218yescomplemented
67#89437C2218yes—
68#89433C2218yescomplemented
69C2×#2479—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—24no—
92C22×C4×D7C2314yes—
93C2×C7×C4⋊C4—24no—
94C2×C7×C4⋊C4D418yescomplemented
95C2×C7×C4⋊C4C2314yes—
96C2×C7×C4⋊C4C2314yes—
97C2×C42×C7—24no—
98C2×C42×C7C2314yes—
99C2×(C2×D7)⋊C4—24no—
100C2×(C2×D7)⋊C4—24no—
101C2×(C2×D7)⋊C4—24no—
102C2×(C2×D7)⋊C4—24no—
103C2×(C2×D7)⋊C4—24no—
104C2×(C2×D7)⋊C4—24no—
105C2×(C2×D7)⋊C4—24no—
106C2×(C2×D7)⋊C4—24no—
107C2×(C2×D7)⋊C4—24no—
108C2×(C2×D7)⋊C4—42no—
109C2×(C2×D7)⋊C4—42no—
110C2×(C2×D7)⋊C4C2314yes—
111C2×(C2×D7)⋊C4C2314yes—
112C2×(C2×D7)⋊C4C2314yes—
113C2×(C2×D7)⋊C4C2314yes—
114C2×(C2×D7)⋊C4C2314yes—
115C2×(C2×D7)⋊C4C2314yes—
116C2×(C2×D7)⋊C4C2314yes—
117C2×(C2×D7)⋊C4C2314yes—
118C2×(C2×D7)⋊C4C2314yes—
119C2×(C2×D7)⋊C4C2314yes—
120C2×(C2×D7)⋊C4C2314yes—
121C2×C4⋊Dic7—24no—
122C2×C4⋊Dic7—24no—
123C2×C4⋊Dic7—24no—
124C2×C4⋊Dic7—24no—
125C2×C4⋊Dic7—42no—
126C2×C4⋊Dic7—42no—
127C2×C4⋊Dic7—42no—
128C2×C4⋊Dic7C2314yes—
129C2×C4⋊Dic7C2314yes—
130C2×C4⋊Dic7C2314yes—
131C2×C4⋊Dic7C2314yes—
132C2×C4⋊Dic7C2314yes—
133C2×C4⋊Dic7C2314yes—
134C2×C4⋊Dic7C2314yes—
135C2×Dic7⋊C4—24no—
136C2×Dic7⋊C4C2314yes—
137C2×C4×Dic7—24no—
138C2×C4×Dic7—24no—
139C2×C4×Dic7—24no—
140C2×C4×Dic7C2314yes—
141C2×C4×Dic7C2314yes—
142C2×C4×Dic7C2314yes—
143#6461—232no—
144#6455—232no—
145C7×#95C2314yes—
146C7×#95C2314yes—
147C7×#95C2314yes—
148C7×#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×#126—71no—
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×#387D711yescharacteristic, complemented
166C2×#386—71no—
167C2×#385—71no—
168C2×C4×C4⋊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×C7C2×D414yes—
203C22×C4×C7C2×D414yes—
204C22×C4×C7C2×D414yes—
205C22×C4×C7#4114yes—
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—22no—
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—232no—
243C2×C4×D7—28no—
244C2×C4×D7—28no—
245C2×C4×D7—28no—
246C7×C4⋊C4—28no—
247C7×C4⋊C4C2×D4116yescomplemented
248C42×C7—28no—
249(C2×D7)⋊C4—28no—
250(C2×D7)⋊C4—28no—
251(C2×D7)⋊C4—28no—
252(C2×D7)⋊C4—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—44no—
259(C2×D7)⋊C4—44no—
260C4⋊Dic7—28no—
261C4⋊Dic7—28no—
262C4⋊Dic7—28no—
263C4⋊Dic7—28no—
264C4⋊Dic7—44no—
265C4⋊Dic7—44no—
266C4⋊Dic7—44no—
267Dic7⋊C4—28no—
268C4×Dic7—28no—
269C4×Dic7—28no—
270C4×Dic7—28no—
271C23×D4—71no—
272C24×C4—71no—
273C2×#126—78no—
274C2×#126—148no—
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⋊C4—71no—
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#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#387C2×D718yescomplemented
312#386—78no—
313#385—78no—
314C4×C4⋊C4—78no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95C2×D711yescharacteristic
320C2×#95C2×D711yescharacteristic
321C2×#95C2×D711yescharacteristic
322C2×#95C2×D711yescharacteristic
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—28no—
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×C7C22×D414yes—
383C2×C4×C7C22×D414yes—
384C2×C4×C7C22×D414yes—
385C2×C4×C7C2×#4114yes—
386C2×C4×C7C2×#4114yes—
387C2×Dic7—28no—
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×Dic7—44no—
410C2×Dic7C2×#4114yes—
411D28—416no—
412C4×D7—232no—
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—144no—
429C23×C4C22×D711yescharacteristic
430C23×C4C22×D711yescharacteristic
431C23×C4C22×D711yescharacteristic
432C23×C4C22×D711yescharacteristic
433C23×C4C22×D711yescharacteristic
434C23×C4C22×D711yescharacteristic
435C23×C4C22×D711yescharacteristic
436#126—1432no—
437#117—1432no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—74no—
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—144no—
452C2×C4⋊C4—282no—
453C2×C4⋊C4—282no—
454C2×C4⋊C4—282no—
455C2×C4⋊C4D2818yescomplemented
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—282no—
479C2×C22⋊C4—282no—
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#95C22×D714yes—
493#95C22×D714yes—
494#95C22×D714yes—
495#95C22×D714yes—
496C22×C7#52514yes—
497C22×C7#52914yes—
498C22×C7#54214yes—
499C22×C7#54714yes—
500C22×C7#55014yes—
501C22×C7#55114yes—
502C22×C7#55214yes—
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—24no—
531C4×C7—42no—
532C4×C7—42no—
533Dic7—24no—
534Dic7—42no—
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—74no—
577C22×C4—72no—
578C22×C4—72no—
579C22×C4—72no—
580C22×C4—72no—
581C22×C4—72no—
582C22×C4—72no—
583C22×C4—148no—
584C22×C4—148no—
585C22×C4—1432no—
586C22×C4—142no—
587C22×C4—142no—
588C22×C4—148no—
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—142no—
603C22×C4—142no—
604C22×C4C2×D2814yes—
605C22×C4C2×D2814yes—
606C22×C4C2×D2814yes—
607C22×C4#115914yes—
608C22×C4#116114yes—
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—148no—
618C4⋊C4—148no—
619C4⋊C4—148no—
620C4⋊C4—148no—
621C4⋊C4—148no—
622C4⋊C4—284no—
623C4⋊C4—284no—
624C4⋊C4—284no—
625C4⋊C4C2×D28116yescomplemented
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—284no—
636C22⋊C4—284no—
637C42—28no—
638C42—148no—
639C42—148no—
640C42—148no—
641C2×C7#247918yescomplemented
642C2×C7C2×#52511yescharacteristic
643C2×C7C2×#52911yescharacteristic
644C2×C7C2×#54211yescharacteristic
645C2×C7C2×#54711yescharacteristic
646C2×C7C2×#55011yescharacteristic
647C2×C7C2×#55111yescharacteristic
648C2×C7C2×#55211yescharacteristic
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—
679C23C22×D2812yes—
680C23C2×#115912yes—
681C23C2×#116112yes—
682C23D7×#4112yes—
683C23D7×#4112yes—
684C23#655312yes—
685C23#655412yes—
686C23C24×D711yescharacteristic
687D4—2816no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
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—74no—
712C2×C4—1432no—
713C2×C4—148no—
714C2×C4—142no—
715C2×C4—142no—
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—284no—
732C2×C4—284no—
733C2×C4—284no—
734C2×C4—284no—
735C2×C4—284no—
736C2×C4C22×D2814yes—
737C2×C4C22×D2814yes—
738C2×C4C22×D2814yes—
739C2×C4C2×#115914yes—
740C2×C4C2×#116114yes—
741C7C2×#247911yescharacteristic, complemented, Sylow
742C22—144no—
743C22—144no—
744C22—144no—
745C22—282no—
746C22—282no—
747C22—282no—
748C22—282no—
749C22—2816no—
750C22—282no—
751C22—282no—
752C22—282no—
753C22—282no—
754C22—282no—
755C22—282no—
756C22—282no—
757C22—568no—
758C22#9021514yes—
759C22#9024614yes—
760C22#9026814yes—
761C22#9031514yes—
762C22#9034914yes—
763C22#9038514yes—
764C22#9040114yes—
765C22C23×D2811yescharacteristic
766C22C22×#115911yescharacteristic
767C22C22×#116111yescharacteristic
768C22C2×D7×#4111yescharacteristic
769C22C2×D7×#4111yescharacteristic
770C22C2×#655311yescharacteristic
771C22C2×#655411yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—24no—
777C4—42no—
778C4—42no—
779C4—144no—
780C4—282no—
781C4—282no—
782C4—282no—
783C4—282no—
784C4—282no—
785C2—284no—
786C2—562no—
787C2#1173246318yesdirect product factor
788C2C2×#9021511yescharacteristic
789C2C2×#9024611yescharacteristic
790C2C2×#9026811yescharacteristic
791C2C2×#9031511yescharacteristic
792C2C2×#9034911yescharacteristic
793C2C2×#9038511yescharacteristic
794C2C2×#9040111yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#387C2
socleC24×C7C24
prime radicalC23×D28C22
hypercenterC2×#387D7
hypocenterC7C2×#2479
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#6461C2semidirect
2. C22×#6455C2semidirect
3. C2×C7×#387C2semidirect
5. C2×#89757C2semidirect
7. C2×C4×C4⋊Dic7C2semidirect
8. #11732463C2direct (N × H)
9. C2×#89449C2semidirect
10. C2×#89449C2semidirect
12. C2×#89440C2semidirect
13. C2×#89433C2semidirect
14. C2×#89442C2semidirect
15. C2×#89442C2semidirect
16. C2×#89442C2semidirect
45. C2×#6461C22semidirect
47. C2×#6455C22semidirect
48. C7×#387C22semidirect
58. #89757C22semidirect
60. C4×C4⋊Dic7C22semidirect
61. #89449C22semidirect
62. #89449C22semidirect
63. #89442C22semidirect
64. #89442C22semidirect
65. #89442C22semidirect
66. #89440C22semidirect
68. #89433C22semidirect
94. C2×C7×C4⋊C4D4semidirect
165. C2×#387D7semidirect
247. C7×C4⋊C4C2×D4semidirect
311. #387C2×D7semidirect
455. C2×C4⋊C4D28semidirect
625. C4⋊C4C2×D28semidirect
641. C2×C7#2479semidirect
741. C7C2×#2479semidirect
787. C2#11732463direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64612
C22×#64552
C2×C7×#3872
C2×#897632
C2×#897572
C2×#897112
C2×C4×C4⋊Dic72
#117324632
C2×#894492
C2×#894372
C2×#894402
C2×#894332
C2×#894422
C2×#24797