Finite Group Databasebeta

← C2×#11731054 #13520259

Subgroups — C2×#11731054 #13520259

Order 1792.

2654 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×#89985C211yesmaximal, characteristic, complemented
3C2×#89985C211yesmaximal, characteristic, complemented
4C2×#89731C211yesmaximal, characteristic, complemented
5C2×#89731C211yesmaximal, characteristic, complemented
6C2×#89732C211yesmaximal, characteristic
7C2×#89720C211yesmaximal, characteristic, complemented
8C2×#89711C211yesmaximal, characteristic, complemented
9C2×#89712C211yesmaximal, characteristic, complemented
10C2×#89712C211yesmaximal, characteristic, complemented
11C2×#89705C211yesmaximal, characteristic, complemented
12#11731054C2116yesmaximal, direct product factor
13C2×#89447C211yesmaximal, characteristic, complemented
14C2×#89447C211yesmaximal, characteristic, complemented
15C2×#89432C211yesmaximal, characteristic, complemented
16C2×#89444C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×D28C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C22×C42×C7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
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×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×C4⋊Dic7C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C4×C7×C22⋊C4C2218yescomplemented
43C2×C7×#95C2211yescharacteristic
44C2×C7×#95C2211yescharacteristic
45#89985C2218yescomplemented
46#89985C2218yescomplemented
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55#89732C2218yes—
56#89731C2218yescomplemented
57#89731C2218yescomplemented
58#89720C2218yescomplemented
59#89712C2218yescomplemented
60#89712C2218yescomplemented
61#89711C2218yescomplemented
62#89705C2218yescomplemented
63#89447C2218yescomplemented
64#89447C2218yescomplemented
65#89444C2218yescomplemented
66#89432C2218yescomplemented
67C2×#2648—71nomaximal, Sylow
68C25×C7C2311yescharacteristic
69C24×D7C2311yescharacteristic
70C24×D7C2311yescharacteristic
71C23×C4×C7—24no—
72C23×C4×C7—42no—
73C23×C4×C7—42no—
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2314yes—
81C22×C22⋊D7—24no—
82C22×C22⋊D7—24no—
83C22×C22⋊D7—42no—
84C22×C22⋊D7—42no—
85C22×C22⋊D7—42no—
86C22×C22⋊D7—42no—
87C22×C22⋊D7C2314yes—
88C22×C22⋊D7C2314yes—
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C22×D28—24no—
96C22×D28—42no—
97C22×D28—42no—
98C22×D28C2314yes—
99C2×C7×C22⋊C4—24no—
100C2×C7×C22⋊C4—24no—
101C2×C7×C22⋊C4C2314yes—
102C2×C7×C22⋊C4C2314yes—
103C2×C42×C7—42no—
104C2×C42×C7—42no—
105C2×C42×C7C2314yes—
106C2×C42×C7C2314yes—
107C2×C22⋊Dic7—42no—
108C2×C22⋊Dic7—42no—
109C2×C22⋊Dic7C2314yes—
110C2×C22⋊Dic7C2314yes—
111C2×(C2×D7)⋊C4—24no—
112C2×(C2×D7)⋊C4—24no—
113C2×(C2×D7)⋊C4—42no—
114C2×(C2×D7)⋊C4—42no—
115C2×(C2×D7)⋊C4—42no—
116C2×(C2×D7)⋊C4—42no—
117C2×(C2×D7)⋊C4—42no—
118C2×(C2×D7)⋊C4—42no—
119C2×(C2×D7)⋊C4—42no—
120C2×(C2×D7)⋊C4—42no—
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×(C2×D7)⋊C4C2314yes—
131C2×C4⋊Dic7—42no—
132C2×C4⋊Dic7C2314yes—
133C2×Dic7⋊C4—24no—
134C2×Dic7⋊C4—42no—
135C2×Dic7⋊C4—42no—
136C2×Dic7⋊C4—42no—
137C2×Dic7⋊C4C2314yes—
138C2×Dic7⋊C4C2314yes—
139C2×Dic7⋊C4C2314yes—
140C2×Dic7⋊C4C2314yes—
141C7×#95C2314yes—
142C7×#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151#2648—716no—
152C2×#400—71no—
153C2×#397—71no—
154C2×#397—71no—
155C2×#396—71no—
156C2×#394—71no—
157C2×#394—71no—
158C2×#394—71no—
159C2×#392—71no—
160C2×#390—71no—
161C2×#388—71no—
162C2×#388—71no—
163C2×#387—71no—
164C2×#386—71no—
165C2×#386—71no—
166C2×C4×C22⋊C4D711yescharacteristic, complemented
167C24×C7—22no—
168C24×C7—22no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7#4114yes—
174C24×C7C2412yes—
175C24×C7C2411yescharacteristic
176C23×D7—22no—
177C23×D7—22no—
178C23×D7—22no—
179C23×D7—22no—
180C23×D7—22no—
181C23×D7—22no—
182C23×D7—22no—
183C23×D7—22no—
184C23×D7—22no—
185C23×D7—22no—
186C23×D7—22no—
187C23×D7—22no—
188C23×D7—22no—
189C23×D7—22no—
190C23×D7C2412yes—
191C23×D7C2412yes—
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×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—28no—
209C22×C4×C7—44no—
210C22×C4×C7—44no—
211C22×C4×C7—416no—
212C22×C4×C7#4114yes—
213C22×C4×C7#4114yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2412yes—
216C22×C4×C7C2412yes—
217C22×C4×C7C2412yes—
218C22×C4×C7C2412yes—
219C22×C4×C7C2412yes—
220C2×C22⋊D7—28no—
221C2×C22⋊D7—28no—
222C2×C22⋊D7—44no—
223C2×C22⋊D7—44no—
224C2×C22⋊D7—44no—
225C2×C22⋊D7—44no—
226C2×C22⋊D7—416no—
227C2×C22⋊D7—416no—
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×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7—22no—
239C22×Dic7—22no—
240C22×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7C2412yes—
247C22×Dic7C2412yes—
248C22×Dic7C2412yes—
249C22×Dic7C2412yes—
250C22×Dic7C2412yes—
251C22×Dic7C2412yes—
252C2×D28—28no—
253C2×D28—44no—
254C2×D28—44no—
255C2×D28—416no—
256C7×C22⋊C4—28no—
257C7×C22⋊C4—28no—
258C42×C7—44no—
259C42×C7—44no—
260C22⋊Dic7—44no—
261C22⋊Dic7—44no—
262(C2×D7)⋊C4—28no—
263(C2×D7)⋊C4—28no—
264(C2×D7)⋊C4—44no—
265(C2×D7)⋊C4—44no—
266(C2×D7)⋊C4—44no—
267(C2×D7)⋊C4—44no—
268(C2×D7)⋊C4—44no—
269(C2×D7)⋊C4—44no—
270(C2×D7)⋊C4—44no—
271(C2×D7)⋊C4—44no—
272C4⋊Dic7—44no—
273Dic7⋊C4—28no—
274Dic7⋊C4—44no—
275Dic7⋊C4—44no—
276Dic7⋊C4—44no—
277C23×D4—71no—
278C23×D4—71no—
279C23×D4—71no—
280C24×C4C2×D711yescharacteristic
281C22×C4⋊C4—71no—
282C22×C4⋊C4—71no—
283C22×C4⋊C4—71no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C22⋊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⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C22⋊C4C2×D711yescharacteristic
299C22×C22⋊C4C2×D711yescharacteristic
300C22×C42C2×D711yescharacteristic
301C22×C42C2×D711yescharacteristic
302#400—78no—
303#397—78no—
304#397—78no—
305#396—78no—
306#394—78no—
307#394—78no—
308#394—78no—
309#392—78no—
310#390—78no—
311#388—78no—
312#388—78no—
313#387—78no—
314#386—78no—
315#386—78no—
316C4×C22⋊C4C2×D718yescomplemented
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95C2×D711yescharacteristic
326C2×#95C2×D711yescharacteristic
327C23×C7—28no—
328C23×C7—28no—
329C23×C7—28no—
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—44no—
337C23×C7—44no—
338C23×C7—44no—
339C23×C7—44no—
340C23×C7C2×#4114yes—
341C23×C7C2×#4112yes—
342C23×C7C2×#4112yes—
343C23×C7C2×#4112yes—
344C23×C7H(5,𝔽2)12yes—
345C23×C7H(5,𝔽2)12yes—
346C23×C7H(5,𝔽2)12yes—
347C23×C7H(5,𝔽2)12yes—
348C23×C7C2511yescharacteristic
349C22×D7—22no—
350C22×D7—22no—
351C22×D7—22no—
352C22×D7—22no—
353C22×D7—22no—
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—44no—
364C22×D7—44no—
365C22×D7—44no—
366C22×D7—44no—
367C22×D7—44no—
368C22×D7—44no—
369C22×D7—44no—
370C22×D7—44no—
371C22×D7—44no—
372C22×D7—44no—
373C22×D7—44no—
374C22×D7—44no—
375C22×D7—44no—
376C22×D7—44no—
377C2×C4×C7—28no—
378C2×C4×C7—28no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—416no—
396C2×C4×C7—44no—
397C2×C4×C7—44no—
398C2×C4×C7—44no—
399C2×C4×C7—44no—
400C2×C4×C7C2×#4114yes—
401C2×C4×C7C2×#4114yes—
402C22⋊D7—416no—
403C22⋊D7—416no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—44no—
423C2×Dic7—44no—
424C2×Dic7—44no—
425C2×Dic7—44no—
426C2×Dic7—44no—
427C2×Dic7—44no—
428D28—416no—
429C25—71no—
430C25—71no—
431C25C22×D711yescharacteristic
432C22×D4—74no—
433C22×D4—74no—
434C22×D4—74no—
435C22×D4—144no—
436C22×D4—144no—
437C22×D4—144no—
438C22×D4—282no—
439C22×D4—282no—
440C22×D4—282no—
441C22×D4—282no—
442C22×D4—282no—
443C22×D4—282no—
444C23×C4—24no—
445C23×C4—42no—
446C23×C4—42no—
447C23×C4—71no—
448C23×C4—71no—
449C23×C4—71no—
450C23×C4—71no—
451C23×C4—71no—
452C23×C4—71no—
453C23×C4C22×D711yescharacteristic
454C23×C4C22×D711yescharacteristic
455C23×C4C22×D711yescharacteristic
456C23×C4C22×D711yescharacteristic
457C23×C4C22×D711yescharacteristic
458C23×C4C22×D711yescharacteristic
459C23×C4C22×D714yes—
460C2×C4⋊C4—74no—
461C2×C4⋊C4—74no—
462C2×C4⋊C4—74no—
463C2×C4⋊C4—74no—
464C2×C4⋊C4—74no—
465C2×C4⋊C4—144no—
466C2×C4⋊C4—282no—
467C2×C4⋊C4—282no—
468C2×C4⋊C4—282no—
469C2×C4⋊C4—282no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—74no—
473C2×C22⋊C4—74no—
474C2×C22⋊C4—74no—
475C2×C22⋊C4—74no—
476C2×C22⋊C4—74no—
477C2×C22⋊C4—74no—
478C2×C22⋊C4—74no—
479C2×C22⋊C4—74no—
480C2×C22⋊C4—74no—
481C2×C22⋊C4—74no—
482C2×C22⋊C4—74no—
483C2×C22⋊C4—74no—
484C2×C22⋊C4—144no—
485C2×C22⋊C4—144no—
486C2×C22⋊C4—282no—
487C2×C22⋊C4—282no—
488C2×C22⋊C4—282no—
489C2×C22⋊C4—282no—
490C2×C22⋊C4—282no—
491C2×C22⋊C4—282no—
492C2×C22⋊C4—282no—
493C2×C22⋊C4—282no—
494C2×C22⋊C4—282no—
495C2×C22⋊C4—282no—
496C2×C22⋊C4C22×D714yes—
497C2×C22⋊C4C22×D714yes—
498C2×C42—42no—
499C2×C42—42no—
500C2×C42C22×D714yes—
501C2×C42C22×D714yes—
502#95—74no—
503#95—74no—
504#95—74no—
505#95—74no—
506#95—74no—
507#95—74no—
508#95—74no—
509#95—74no—
510#95C22×D714yes—
511#95C22×D714yes—
512C22×C7—24no—
513C22×C7—24no—
514C22×C7—24no—
515C22×C7—416no—
516C22×C7—42no—
517C22×C7—42no—
518C22×C7—42no—
519C22×C7—42no—
520C22×C7#52914yes—
521C22×C7#53814yes—
522C22×C7#53814yes—
523C22×C7#53814yes—
524C22×C7#53814yes—
525C22×C7#54014yes—
526C22×C7#54014yes—
527C22×C7C22×#4111yescharacteristic
528C22×C7C22×#4111yescharacteristic
529C22×C7C22×#4111yescharacteristic
530C22×C7C2×H(5,𝔽2)11yescharacteristic
531C22×C7C2×H(5,𝔽2)11yescharacteristic
532C22×C7C2×H(5,𝔽2)11yescharacteristic
533C22×C7C2×H(5,𝔽2)11yescharacteristic
534C2×D7—42no—
535C2×D7—42no—
536C2×D7—42no—
537C2×D7—42no—
538C2×D7—42no—
539C2×D7—42no—
540C2×D7—42no—
541C2×D7—42no—
542C2×D7—42no—
543C2×D7—42no—
544C2×D7—42no—
545C2×D7—42no—
546C2×D7—42no—
547C2×D7—42no—
548C2×D7—88no—
549C2×D7—88no—
550C4×C7—24no—
551C4×C7—24no—
552C4×C7—42no—
553C4×C7—42no—
554C4×C7—42no—
555C4×C7—42no—
556Dic7—42no—
557Dic7—42no—
558Dic7—42no—
559Dic7—42no—
560Dic7—42no—
561Dic7—42no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—72no—
569C24—72no—
570C24—142no—
571C24—142no—
572C24—142no—
573C24—142no—
574C24—142no—
575C24—142no—
576C24—142no—
577C24—142no—
578C24—142no—
579C24—142no—
580C24—142no—
581C24—142no—
582C24—142no—
583C24—142no—
584C24#115714yes—
585C24C23×D712yes—
586C24C23×D711yescharacteristic
587C2×D4—148no—
588C2×D4—148no—
589C2×D4—148no—
590C2×D4—284no—
591C2×D4—284no—
592C2×D4—2816no—
593C2×D4—284no—
594C2×D4—284no—
595C2×D4—284no—
596C2×D4—284no—
597C2×D4—2816no—
598C2×D4—2816no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—28no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—416no—
619C22×C4—72no—
620C22×C4—72no—
621C22×C4—72no—
622C22×C4—72no—
623C22×C4—72no—
624C22×C4—72no—
625C22×C4—142no—
626C22×C4—142no—
627C22×C4—142no—
628C22×C4—142no—
629C22×C4—142no—
630C22×C4—142no—
631C22×C4—142no—
632C22×C4—142no—
633C22×C4—142no—
634C22×C4—142no—
635C22×C4—142no—
636C22×C4—142no—
637C22×C4—142no—
638C22×C4—142no—
639C22×C4—142no—
640C22×C4—142no—
641C22×C4—142no—
642C22×C4—142no—
643C22×C4#115714yes—
644C22×C4#115714yes—
645C22×C4C23×D712yes—
646C22×C4C23×D712yes—
647C22×C4C23×D712yes—
648C22×C4C23×D712yes—
649C22×C4C23×D712yes—
650C22×C4C23×D712yes—
651C4⋊C4—148no—
652C4⋊C4—284no—
653C4⋊C4—284no—
654C4⋊C4—284no—
655C4⋊C4—284no—
656C22⋊C4—28no—
657C22⋊C4—28no—
658C22⋊C4—148no—
659C22⋊C4—148no—
660C22⋊C4—284no—
661C22⋊C4—284no—
662C22⋊C4—284no—
663C22⋊C4—284no—
664C22⋊C4—284no—
665C22⋊C4—284no—
666C22⋊C4—284no—
667C22⋊C4—284no—
668C22⋊C4—284no—
669C22⋊C4—284no—
670C42—44no—
671C42—44no—
672C2×C7—44no—
673C2×C7#264818yescomplemented
674C2×C7C2×#52911yescharacteristic
675C2×C7C2×#53811yescharacteristic
676C2×C7C2×#53811yescharacteristic
677C2×C7C2×#53811yescharacteristic
678C2×C7C2×#53811yescharacteristic
679C2×C7C2×#54011yescharacteristic
680C2×C7C2×#54011yescharacteristic
681D7—82no—
682D7—82no—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—142no—
697C23—142no—
698C23—142no—
699C23—142no—
700C23—142no—
701C23—142no—
702C23—142no—
703C23—142no—
704C23—142no—
705C23—142no—
706C23—142no—
707C23—142no—
708C23—142no—
709C23—142no—
710C23—284no—
711C23—284no—
712C23—284no—
713C23—284no—
714C23—284no—
715C23—284no—
716C23—284no—
717C23—284no—
718C23—284no—
719C23—284no—
720C23—284no—
721C23—284no—
722C23—284no—
723C23—284no—
724C23C2×#115714yes—
725C23C2×#115712yes—
726C23C2×#115712yes—
727C23C2×#115712yes—
728C23#654812yes—
729C23#654812yes—
730C23#655312yes—
731C23#655312yes—
732C23C24×D711yescharacteristic
733D4—2816no—
734D4—2816no—
735D4—2816no—
736C2×C4—28no—
737C2×C4—28no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—416no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—142no—
760C2×C4—142no—
761C2×C4—142no—
762C2×C4—142no—
763C2×C4—142no—
764C2×C4—142no—
765C2×C4—142no—
766C2×C4—142no—
767C2×C4—142no—
768C2×C4—142no—
769C2×C4—142no—
770C2×C4—142no—
771C2×C4—142no—
772C2×C4—142no—
773C2×C4—142no—
774C2×C4—142no—
775C2×C4—142no—
776C2×C4—142no—
777C2×C4—284no—
778C2×C4—284no—
779C2×C4—284no—
780C2×C4—284no—
781C2×C4—284no—
782C2×C4—284no—
783C2×C4C2×#115714yes—
784C2×C4C2×#115714yes—
785C7C2×#264811yescharacteristic, complemented, Sylow
786C22—24no—
787C22—24no—
788C22—24no—
789C22—42no—
790C22—42no—
791C22—416no—
792C22—42no—
793C22—42no—
794C22—282no—
795C22—282no—
796C22—282no—
797C22—282no—
798C22—282no—
799C22—282no—
800C22—282no—
801C22—282no—
802C22—282no—
803C22—282no—
804C22—282no—
805C22—282no—
806C22—282no—
807C22—282no—
808C22—568no—
809C22—568no—
810C22#9017014yes—
811C22#9018514yes—
812C22#9022614yes—
813C22#9025114yes—
814C22#9025114yes—
815C22#9025114yes—
816C22#9025314yes—
817C22C22×#115711yescharacteristic
818C22C22×#115711yescharacteristic
819C22C22×#115711yescharacteristic
820C22C2×#654811yescharacteristic
821C22C2×#654811yescharacteristic
822C22C2×#655311yescharacteristic
823C22C2×#655311yescharacteristic
824C4—24no—
825C4—24no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—282no—
831C4—282no—
832C4—282no—
833C4—282no—
834C4—282no—
835C4—282no—
836C2—44no—
837C2—562no—
838C2—562no—
839C2#1173105418yesdirect product factor
840C2C2×#9017011yescharacteristic
841C2C2×#9018511yescharacteristic
842C2C2×#9022611yescharacteristic
843C2C2×#9025111yescharacteristic
844C2C2×#9025111yescharacteristic
845C2C2×#9025111yescharacteristic
846C2C2×#9025311yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C4×C7×C22⋊C4C2
socleC24×C7C24
prime radicalC2×#89732C2
hypercenterC2×C4×C22⋊C4D7
hypocenterC7C2×#2648
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C7×C22⋊C4C2semidirect
2. C2×#89985C2semidirect
3. C2×#89985C2semidirect
4. C2×#89731C2semidirect
5. C2×#89731C2semidirect
7. C2×#89720C2semidirect
8. C2×#89711C2semidirect
9. C2×#89712C2semidirect
10. C2×#89712C2semidirect
11. C2×#89705C2semidirect
12. #11731054C2direct (N × H)
13. C2×#89447C2semidirect
14. C2×#89447C2semidirect
15. C2×#89432C2semidirect
16. C2×#89444C2semidirect
42. C4×C7×C22⋊C4C22semidirect
45. #89985C22semidirect
46. #89985C22semidirect
56. #89731C22semidirect
57. #89731C22semidirect
58. #89720C22semidirect
59. #89712C22semidirect
60. #89712C22semidirect
61. #89711C22semidirect
62. #89705C22semidirect
63. #89447C22semidirect
64. #89447C22semidirect
65. #89444C22semidirect
66. #89432C22semidirect
166. C2×C4×C22⋊C4D7semidirect
316. C4×C22⋊C4C2×D7semidirect
673. C2×C7#2648semidirect
785. C7C2×#2648semidirect
839. C2#11731054direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C7×C22⋊C42
C2×#899852
C2×#897312
C2×#897322
C2×#897202
C2×#897112
C2×#897122
C2×#897052
#117310542
C2×#894472
C2×#894322
C2×#894442
C2×#26487