Finite Group Databasebeta

← C2×#11730982 #13523937

Subgroups — C2×#11730982 #13523937

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×#6492C211yesmaximal, characteristic
2C22×#6433C211yesmaximal, characteristic, complemented
3C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×#89982C211yesmaximal, characteristic, complemented
5C2×#89720C211yesmaximal, characteristic, complemented
6C2×#89733C211yesmaximal, characteristic
7C2×#89729C211yesmaximal, characteristic
8C2×#89716C211yesmaximal, characteristic, complemented
9C2×#89712C211yesmaximal, characteristic, complemented
10C2×#89712C211yesmaximal, characteristic, complemented
11C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
12#11730982C2116yesmaximal, direct product factor
13C2×#89448C211yesmaximal, characteristic, complemented
14C2×#89430C211yesmaximal, characteristic, complemented
15C2×#89419C211yesmaximal, characteristic, complemented
16C2×#89442C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C42×C7C2211yescharacteristic
22C22×C42×C7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C2×#6492—28no—
27C2×#6492C2218yes—
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×C4⋊Dic7C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C2×#6433—28no—
47C2×#6433C2218yescomplemented
48C4×C7×C22⋊C4C2218yescomplemented
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51#89982C2218yescomplemented
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58#89733C2218yes—
59#89729C2218yes—
60#89720C2218yescomplemented
61#89716C2218yescomplemented
62#89712C2218yescomplemented
63#89712C2218yescomplemented
64C4×Dic7⋊C4C2218yescomplemented
65#89448C2218yescomplemented
66#89442C2218yescomplemented
67#89430C2218yescomplemented
68#89419C2218yescomplemented
69C2×#2558—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C23×C4×C7—24no—
73C23×C4×C7—24no—
74C23×C4×C7—42no—
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2314yes—
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C22×C22⋊D7—24no—
83C22×C22⋊D7—24no—
84C22×C22⋊D7—42no—
85C22×C22⋊D7C2314yes—
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C2×C7×C22⋊C4—24no—
94C2×C7×C22⋊C4—24no—
95C2×C7×C22⋊C4C2314yes—
96C2×C7×C22⋊C4C2314yes—
97C2×C42×C7—24no—
98C2×C42×C7—42no—
99C2×C42×C7C2314yes—
100C2×C42×C7C2314yes—
101C2×C22⋊Dic7—24no—
102C2×C22⋊Dic7—24no—
103C2×C22⋊Dic7—24no—
104C2×C22⋊Dic7C2314yes—
105C2×C22⋊Dic7C2314yes—
106C2×C22⋊Dic7C2314yes—
107#6492—232no—
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—42no—
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×C4⋊Dic7—24no—
121C2×C4⋊Dic7—24no—
122C2×C4⋊Dic7C2314yes—
123C2×C4⋊Dic7C2314yes—
124C2×Dic7⋊C4—24no—
125C2×Dic7⋊C4—24no—
126C2×Dic7⋊C4—24no—
127C2×Dic7⋊C4—24no—
128C2×Dic7⋊C4—24no—
129C2×Dic7⋊C4—24no—
130C2×Dic7⋊C4—42no—
131C2×Dic7⋊C4D418yes—
132C2×Dic7⋊C4C2314yes—
133C2×Dic7⋊C4C2314yes—
134C2×Dic7⋊C4C2314yes—
135C2×Dic7⋊C4C2314yes—
136C2×Dic7⋊C4C2314yes—
137C2×Dic7⋊C4C2314yes—
138C2×Dic7⋊C4C2314yes—
139C2×Dic7⋊C4C2314yes—
140C2×C4×Dic7—24no—
141C2×C4×Dic7—42no—
142C2×C4×Dic7C2314yes—
143C2×C4×Dic7C2314yes—
144#6433—232no—
145C7×#95C2314yes—
146C7×#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×#125—71no—
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⋊C4D711yescharacteristic, complemented
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7—22no—
174C24×C7—22no—
175C24×C7#4114yes—
176C24×C7C2412yes—
177C24×C7C2411yescharacteristic
178C23×D7—22no—
179C23×D7—22no—
180C23×D7—22no—
181C23×D7—22no—
182C23×D7—22no—
183C23×D7—22no—
184C23×D7—22no—
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—28no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—28no—
203C22×C4×C7—44no—
204C22×C4×C7—416no—
205C22×C4×C7C2×D414yes—
206C22×C4×C7#4114yes—
207C22×C4×C7#4114yes—
208C22×C4×C7C2412yes—
209C22×C4×C7C2412yes—
210C22×C4×C7C2412yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C2×C22⋊D7—28no—
215C2×C22⋊D7—28no—
216C2×C22⋊D7—44no—
217C2×C22⋊D7—416no—
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—22no—
233C22×Dic7—22no—
234C22×Dic7—22no—
235C22×Dic7—22no—
236C22×Dic7C2×D414yes—
237C22×Dic7C2×D414yes—
238C22×Dic7#4114yes—
239C22×Dic7C2412yes—
240C22×Dic7C2412yes—
241C22×Dic7C2412yes—
242C22×Dic7C2412yes—
243C22×Dic7C2412yes—
244C22×Dic7C2412yes—
245C22×Dic7C2412yes—
246C7×C22⋊C4—28no—
247C7×C22⋊C4—28no—
248C42×C7—28no—
249C42×C7—44no—
250C22⋊Dic7—28no—
251C22⋊Dic7—28no—
252C22⋊Dic7—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—
259C4⋊Dic7—28no—
260C4⋊Dic7—28no—
261Dic7⋊C4—28no—
262Dic7⋊C4—28no—
263Dic7⋊C4—28no—
264Dic7⋊C4—28no—
265Dic7⋊C4—28no—
266Dic7⋊C4—28no—
267Dic7⋊C4—44no—
268Dic7⋊C4C2×D4116yes—
269C4×Dic7—28no—
270C4×Dic7—44no—
271C23×D4—71no—
272C24×C4C2×D711yescharacteristic
273C2×#125—78no—
274C2×#125—148no—
275C2×#123—78no—
276C2×#123—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⋊C4—71no—
286C22×C4⋊C4—71no—
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⋊C4C2×D711yescharacteristic
297C22×C22⋊C4C2×D711yescharacteristic
298C22×C42—71no—
299C22×C42—71no—
300C22×C42C2×D711yescharacteristic
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⋊C4C2×D718yescomplemented
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95C2×D711yescharacteristic
322C2×#95C2×D711yescharacteristic
323C23×C7—28no—
324C23×C7—28no—
325C23×C7—28no—
326C23×C7—22no—
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—44no—
333C23×C7—44no—
334C23×C7—44no—
335C23×C7—44no—
336C23×C7C22×D412yes—
337C23×C7C2×#4114yes—
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—22no—
346C22×D7—22no—
347C22×D7—22no—
348C22×D7—22no—
349C22×D7—22no—
350C22×D7—22no—
351C22×D7—22no—
352C22×D7—44no—
353C22×D7—44no—
354C22×D7—44no—
355C22×D7—44no—
356C22×D7—44no—
357C22×D7—44no—
358C22×D7—44no—
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—416no—
378C2×C4×C7—44no—
379C2×C4×C7—44no—
380C2×C4×C7—44no—
381C2×C4×C7C22×D414yes—
382C2×C4×C7C2×#4114yes—
383C2×C4×C7C2×#4114yes—
384C22⋊D7—416no—
385C2×Dic7—28no—
386C2×Dic7—28no—
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—22no—
406C2×Dic7—44no—
407C2×Dic7—44no—
408C2×Dic7—44no—
409C2×Dic7—44no—
410C2×Dic7C22×D414yes—
411C2×Dic7C22×D414yes—
412C2×Dic7C2×#4114yes—
413C25—71no—
414C25C22×D711yescharacteristic
415C22×D4—74no—
416C22×D4—144no—
417C22×D4—144no—
418C22×D4—282no—
419C23×C4—24no—
420C23×C4—24no—
421C23×C4—42no—
422C23×C4—71no—
423C23×C4—71no—
424C23×C4—71no—
425C23×C4—71no—
426C23×C4—71no—
427C23×C4—71no—
428C23×C4—71no—
429C23×C4C22×D711yescharacteristic
430C23×C4C22×D711yescharacteristic
431C23×C4C22×D711yescharacteristic
432C23×C4C22×D714yes—
433C23×C4C22×D711yescharacteristic
434C23×C4C22×D711yescharacteristic
435C23×C4C22×D711yescharacteristic
436#125—1432no—
437#123—1432no—
438C2×C4⋊C4—78no—
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—74no—
448C2×C4⋊C4—74no—
449C2×C4⋊C4—144no—
450C2×C4⋊C4—144no—
451C2×C4⋊C4—144no—
452C2×C4⋊C4—144no—
453C2×C4⋊C4—144no—
454C2×C4⋊C4—144no—
455C2×C4⋊C4—144no—
456C2×C4⋊C4—144no—
457C2×C4⋊C4—282no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
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—282no—
478C2×C22⋊C4C22×D714yes—
479C2×C22⋊C4C22×D714yes—
480C2×C42—24no—
481C2×C42—42no—
482C2×C42—74no—
483C2×C42—74no—
484C2×C42—144no—
485C2×C42—282no—
486C2×C42C22×D714yes—
487C2×C42C22×D714yes—
488#95—74no—
489#95—74no—
490#95—74no—
491#95—74no—
492#95—74no—
493#95—74no—
494#95C22×D714yes—
495#95C22×D714yes—
496C22×C7—24no—
497C22×C7—24no—
498C22×C7—24no—
499C22×C7—42no—
500C22×C7—42no—
501C22×C7—42no—
502C22×C7—42no—
503C22×C7—416no—
504C22×C7#52914yes—
505C22×C7#53214yes—
506C22×C7#53914yes—
507C22×C7#54614yes—
508C22×C7#54814yes—
509C22×C7#55214yes—
510C22×C7#55314yes—
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—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—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—72no—
546C24—142no—
547C24—142no—
548C24—142no—
549C24—142no—
550C24—142no—
551C24—142no—
552C24—142no—
553C24#115714yes—
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—28no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—28no—
577C22×C4—44no—
578C22×C4—416no—
579C22×C4—74no—
580C22×C4—74no—
581C22×C4—74no—
582C22×C4—72no—
583C22×C4—72no—
584C22×C4—72no—
585C22×C4—72no—
586C22×C4—72no—
587C22×C4—72no—
588C22×C4—72no—
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×C4—142no—
605C22×C4—142no—
606C22×C4—142no—
607C22×C4#115714yes—
608C22×C4#115714yes—
609C22×C4D4×D714yes—
610C22×C4C23×D712yes—
611C22×C4C23×D712yes—
612C22×C4C23×D712yes—
613C22×C4C23×D712yes—
614C22×C4C23×D712yes—
615C22×C4C23×D712yes—
616C4⋊C4—716no—
617C4⋊C4—148no—
618C4⋊C4—148no—
619C4⋊C4—148no—
620C4⋊C4—148no—
621C4⋊C4—148no—
622C4⋊C4—148no—
623C4⋊C4—148no—
624C4⋊C4—148no—
625C4⋊C4—284no—
626C22⋊C4—28no—
627C22⋊C4—28no—
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—44no—
639C42—148no—
640C42—284no—
641C2×C7—44no—
642C2×C7#255818yescomplemented
643C2×C7C2×#52911yescharacteristic
644C2×C7C2×#53211yescharacteristic
645C2×C7C2×#53911yescharacteristic
646C2×C7C2×#54611yescharacteristic
647C2×C7C2×#54811yescharacteristic
648C2×C7C2×#55211yescharacteristic
649C2×C7C2×#55311yescharacteristic
650D7—82no—
651C23—28no—
652C23—28no—
653C23—28no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—142no—
665C23—142no—
666C23—142no—
667C23—142no—
668C23—142no—
669C23—142no—
670C23—142no—
671C23—284no—
672C23—284no—
673C23—284no—
674C23—284no—
675C23—284no—
676C23—284no—
677C23—284no—
678C23C2×#115714yes—
679C23C2×#115712yes—
680C23C2×#115712yes—
681C23C2×#115712yes—
682C23C2×D4×D712yes—
683C23#654812yes—
684C23D7×#4112yes—
685C23#655412yes—
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—416no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—74no—
711C2×C4—74no—
712C2×C4—74no—
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×C4C2×#115714yes—
739C2×C4C2×#115714yes—
740C2×C4C2×D4×D714yes—
741C7C2×#255811yescharacteristic, complemented, Sylow
742C22—24no—
743C22—24no—
744C22—24no—
745C22—416no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—282no—
751C22—282no—
752C22—282no—
753C22—282no—
754C22—282no—
755C22—282no—
756C22—282no—
757C22—568no—
758C22#9017014yes—
759C22#9018114yes—
760C22#9022214yes—
761C22#9023914yes—
762C22#9024314yes—
763C22#9024914yes—
764C22#9025514yes—
765C22C22×#115711yescharacteristic
766C22C22×#115711yescharacteristic
767C22C22×#115711yescharacteristic
768C22C22×D4×D711yescharacteristic
769C22C2×#654811yescharacteristic
770C22C2×D7×#4111yescharacteristic
771C22C2×#655411yescharacteristic
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—44no—
786C2—562no—
787C2#1173098218yesdirect product factor
788C2C2×#9017011yescharacteristic
789C2C2×#9018111yescharacteristic
790C2C2×#9022211yescharacteristic
791C2C2×#9025511yescharacteristic
792C2C2×#9024311yescharacteristic
793C2C2×#9023911yescharacteristic
794C2C2×#9024911yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C4×C7×C22⋊C4C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×C4×C22⋊C4D7
hypocenterC7C2×#2558
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#6433C2semidirect
3. C2×C4×C7×C22⋊C4C2semidirect
4. C2×#89982C2semidirect
5. C2×#89720C2semidirect
8. C2×#89716C2semidirect
9. C2×#89712C2semidirect
10. C2×#89712C2semidirect
11. C2×C4×Dic7⋊C4C2semidirect
12. #11730982C2direct (N × H)
13. C2×#89448C2semidirect
14. C2×#89430C2semidirect
15. C2×#89419C2semidirect
16. C2×#89442C2semidirect
47. C2×#6433C22semidirect
48. C4×C7×C22⋊C4C22semidirect
51. #89982C22semidirect
60. #89720C22semidirect
61. #89716C22semidirect
62. #89712C22semidirect
63. #89712C22semidirect
64. C4×Dic7⋊C4C22semidirect
65. #89448C22semidirect
66. #89442C22semidirect
67. #89430C22semidirect
68. #89419C22semidirect
168. C2×C4×C22⋊C4D7semidirect
314. C4×C22⋊C4C2×D7semidirect
642. C2×C7#2558semidirect
741. C7C2×#2558semidirect
787. C2#11730982direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64922
C22×#64332
C2×C4×C7×C22⋊C42
C2×#899822
C2×#897202
C2×#897332
C2×#897292
C2×#897162
C2×#897122
C2×C4×Dic7⋊C42
#117309822
C2×#894482
C2×#894302
C2×#894192
C2×#894422
C2×#25587