Finite Group Databasebeta

← C2×#11734860 #13522495

Subgroups — C2×#11734860 #13522495

Order 1792.

3570 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D7×C4⋊C4C211yesmaximal, characteristic, complemented
2C22×#6455C211yesmaximal, characteristic, complemented
3C22×#6446C211yesmaximal, characteristic
4C22×#6446C211yesmaximal, characteristic
5C2×C7×#396C211yesmaximal, characteristic, complemented
6C2×#89761C211yesmaximal, characteristic, complemented
7C2×#89755C211yesmaximal, characteristic, complemented
8C2×#89756C211yesmaximal, characteristic, complemented
9C2×#89757C211yesmaximal, characteristic, complemented
10C2×#89728C211yesmaximal, characteristic
11C2×#89720C211yesmaximal, characteristic, complemented
12C2×#89716C211yesmaximal, characteristic, complemented
13C2×#89723C211yesmaximal, characteristic, complemented
14#11734860C2116yesmaximal, direct product factor
15C2×#89436C211yesmaximal, characteristic, complemented
16C2×#89419C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C23×C4×D7C2211yescharacteristic
20C23×C4×D7C2211yescharacteristic
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×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
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×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6455—28no—
45C2×#6455C2218yescomplemented
46C2×D7×C4⋊C4—28no—
47C2×D7×C4⋊C4C2218yescomplemented
48C2×#6446—28no—
49C2×#6446—28no—
50C2×#6446C2218yes—
51C2×#6446C2218yes—
52C7×#396C2218yescomplemented
53C2×C7×#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61#89761C2218yescomplemented
62#89757C2218yescomplemented
63#89756C2218yescomplemented
64#89755C2218yescomplemented
65#89728C2218yes—
66#89723C2218yescomplemented
67#89720C2218yescomplemented
68#89716C2218yescomplemented
69#89436C2218yescomplemented
70#89419C2218yescomplemented
71C2×#2413—71nomaximal, Sylow
72C25×C7C2311yescharacteristic
73C24×D7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C22×C22⋊D7—24no—
81C22×C22⋊D7—24no—
82C22×C22⋊D7—24no—
83C22×C22⋊D7C2314yes—
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C22×C4×D7—24no—
92C22×C4×D7—24no—
93C22×C4×D7—24no—
94C22×C4×D7—24no—
95C22×C4×D7—24no—
96C22×C4×D7—24no—
97C22×C4×D7—24no—
98C22×C4×D7—24no—
99C22×C4×D7D418yes—
100C22×C4×D7C2314yes—
101C22×C4×D7C2314yes—
102C22×C4×D7C2314yes—
103C2×C7×C4⋊C4—24no—
104C2×C7×C4⋊C4—24no—
105C2×C7×C4⋊C4—24no—
106C2×C7×C4⋊C4C2314yes—
107C2×C7×C4⋊C4C2314yes—
108C2×C7×C4⋊C4C2314yes—
109C2×C7×C22⋊C4—24no—
110C2×C7×C22⋊C4—24no—
111C2×C7×C22⋊C4—24no—
112C2×C7×C22⋊C4C2314yes—
113C2×C7×C22⋊C4C2314yes—
114C2×C7×C22⋊C4C2314yes—
115C2×C22⋊Dic7—24no—
116C2×C22⋊Dic7—24no—
117C2×C22⋊Dic7—24no—
118C2×C22⋊Dic7C2314yes—
119C2×C22⋊Dic7C2314yes—
120C2×C22⋊Dic7C2314yes—
121C2×(C2×D7)⋊C4—24no—
122C2×(C2×D7)⋊C4—24no—
123C2×(C2×D7)⋊C4D418yes—
124C2×(C2×D7)⋊C4C2314yes—
125C2×(C2×D7)⋊C4C2314yes—
126C2×(C2×D7)⋊C4C2314yes—
127C2×C4⋊Dic7—24no—
128C2×C4⋊Dic7—24no—
129C2×C4⋊Dic7—24no—
130C2×C4⋊Dic7—24no—
131C2×C4⋊Dic7C2314yes—
132C2×C4⋊Dic7C2314yes—
133C2×C4⋊Dic7C2314yes—
134C2×C4⋊Dic7C2314yes—
135C2×Dic7⋊C4—24no—
136C2×Dic7⋊C4—24no—
137C2×Dic7⋊C4—24no—
138C2×Dic7⋊C4—24no—
139C2×Dic7⋊C4—24no—
140C2×Dic7⋊C4C2314yes—
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C2×Dic7⋊C4C2314yes—
144C2×Dic7⋊C4C2314yes—
145C2×C4×Dic7—24no—
146C2×C4×Dic7—24no—
147C2×C4×Dic7C2314yes—
148C2×C4×Dic7C2314yes—
149#6455—232no—
150D7×C4⋊C4—232no—
151#6446—232no—
152#6446—232no—
153C7×#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C7⋊#95C2314yes—
160C7⋊#95C2314yes—
161C22×#123—71no—
162C22×#123—71no—
163C22×#117—71no—
164C23×C4⋊C4—71no—
165#2413—716no—
166C2×#398—71no—
167C2×#398—71no—
168C2×#396—71no—
169C2×#396D711yescharacteristic, complemented
170C2×#389—71no—
171C2×#389—71no—
172C2×#388—71no—
173C2×#388—71no—
174C2×#386—71no—
175C2×#385—71no—
176C2×#381—71no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7—22no—
182C24×C7—22no—
183C24×C7—22no—
184C24×C7C2412yes—
185C24×C7C2411yescharacteristic
186C23×D7—22no—
187C23×D7—22no—
188C23×D7—22no—
189C23×D7—22no—
190C23×D7C2×D414yes—
191C23×D7C2×D414yes—
192C23×D7#4114yes—
193C23×D7C2412yes—
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—22no—
209C22×C4×C7C2×D414yes—
210C22×C4×C7C2×D414yes—
211C22×C4×C7#4114yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2412yes—
216C22×C4×C7C2412yes—
217C22×C4×C7C2412yes—
218C2×C22⋊D7—28no—
219C2×C22⋊D7—28no—
220C2×C22⋊D7—28no—
221C2×C22⋊D7—416no—
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×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7—22no—
239C22×Dic7—22no—
240C22×Dic7C2×D414yes—
241C22×Dic7C2×D414yes—
242C22×Dic7#4114yes—
243C22×Dic7C2412yes—
244C22×Dic7C2412yes—
245C22×Dic7C2412yes—
246C22×Dic7C2412yes—
247C22×Dic7C2412yes—
248C22×Dic7C2412yes—
249C22×Dic7C2412yes—
250C2×C4×D7—232no—
251C2×C4×D7—232no—
252C2×C4×D7—28no—
253C2×C4×D7—28no—
254C2×C4×D7—28no—
255C2×C4×D7—28no—
256C2×C4×D7—28no—
257C2×C4×D7—28no—
258C2×C4×D7—28no—
259C2×C4×D7—28no—
260C2×C4×D7—416no—
261C2×C4×D7C2×D4116yes—
262C7×C4⋊C4—28no—
263C7×C4⋊C4—28no—
264C7×C4⋊C4—28no—
265C7×C22⋊C4—28no—
266C7×C22⋊C4—28no—
267C7×C22⋊C4—28no—
268C22⋊Dic7—28no—
269C22⋊Dic7—28no—
270C22⋊Dic7—28no—
271(C2×D7)⋊C4—28no—
272(C2×D7)⋊C4—28no—
273(C2×D7)⋊C4C2×D4116yes—
274C4⋊Dic7—28no—
275C4⋊Dic7—28no—
276C4⋊Dic7—28no—
277C4⋊Dic7—28no—
278Dic7⋊C4—28no—
279Dic7⋊C4—28no—
280Dic7⋊C4—28no—
281Dic7⋊C4—28no—
282Dic7⋊C4—28no—
283C4×Dic7—28no—
284C4×Dic7—28no—
285C23×D4—71no—
286C24×C4—71no—
287C24×C4—71no—
288C24×C4—71no—
289C2×#123—78no—
290C2×#123—78no—
291C2×#123—148no—
292C2×#123—148no—
293C2×#117—78no—
294C2×#117—148no—
295C22×C4⋊C4—71no—
296C22×C4⋊C4—71no—
297C22×C4⋊C4—71no—
298C22×C4⋊C4—71no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C4⋊C4—78no—
305C22×C4⋊C4—148no—
306C22×C4⋊C4C2×D711yescharacteristic
307C22×C4⋊C4C2×D711yescharacteristic
308C22×C4⋊C4C2×D711yescharacteristic
309C22×C22⋊C4—71no—
310C22×C22⋊C4—71no—
311C22×C22⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4—71no—
315C22×C22⋊C4C2×D711yescharacteristic
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C42—71no—
319C22×C42—71no—
320#398—78no—
321#398—78no—
322#396—78no—
323#396C2×D718yescomplemented
324#389—78no—
325#389—78no—
326#388—78no—
327#388—78no—
328#386—78no—
329#385—78no—
330#381—78no—
331C2×#95—71no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95C2×D711yescharacteristic
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—44no—
347C23×C7—44no—
348C23×C7—44no—
349C23×C7—44no—
350C23×C7—44no—
351C23×C7—44no—
352C23×C7—44no—
353C23×C7C22×D412yes—
354C23×C7C22×D412yes—
355C23×C7C2×#4112yes—
356C23×C7C2×#4112yes—
357C23×C7C2×#4112yes—
358C23×C72−1+412yes—
359C23×C72−1+412yes—
360C23×C7C2511yescharacteristic
361C22×D7—28no—
362C22×D7—28no—
363C22×D7—28no—
364C22×D7—28no—
365C22×D7—28no—
366C22×D7—28no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—22no—
371C22×D7#121116yes—
372C22×D7C22×D414yes—
373C22×D7C22×D414yes—
374C22×D7C2×#4114yes—
375C2×C4×C7—28no—
376C2×C4×C7—28no—
377C2×C4×C7—28no—
378C2×C4×C7—22no—
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—44no—
394C2×C4×C7—44no—
395C2×C4×C7—44no—
396C2×C4×C7C22×D414yes—
397C2×C4×C7C22×D414yes—
398C2×C4×C7C2×#4114yes—
399C22⋊D7—416no—
400C2×Dic7—28no—
401C2×Dic7—28no—
402C2×Dic7—28no—
403C2×Dic7—22no—
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—44no—
422C2×Dic7—44no—
423C2×Dic7—44no—
424C2×Dic7—44no—
425C2×Dic7C22×D414yes—
426C2×Dic7C22×D414yes—
427C2×Dic7C2×#4114yes—
428C4×D7—232no—
429C4×D7—232no—
430C4×D7—416no—
431C25—71no—
432C25C22×D711yescharacteristic
433C22×D4—74no—
434C22×D4—144no—
435C22×D4—144no—
436C22×D4—144no—
437C23×C4—71no—
438C23×C4—71no—
439C23×C4—71no—
440C23×C4—78no—
441C23×C4—74no—
442C23×C4—71no—
443C23×C4—71no—
444C23×C4—71no—
445C23×C4—71no—
446C23×C4—74no—
447C23×C4—74no—
448C23×C4—144no—
449C23×C4—144no—
450C23×C4—144no—
451C23×C4—144no—
452C23×C4—144no—
453C23×C4—144no—
454C23×C4—144no—
455C23×C4—144no—
456C23×C4C22×D711yescharacteristic
457C23×C4C22×D711yescharacteristic
458C23×C4C22×D711yescharacteristic
459C23×C4C22×D711yescharacteristic
460C23×C4C22×D711yescharacteristic
461C23×C4C22×D711yescharacteristic
462#123—1432no—
463#123—1432no—
464#117—1432no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—74no—
469C2×C4⋊C4—74no—
470C2×C4⋊C4—74no—
471C2×C4⋊C4—74no—
472C2×C4⋊C4—74no—
473C2×C4⋊C4—74no—
474C2×C4⋊C4—74no—
475C2×C4⋊C4—74no—
476C2×C4⋊C4—74no—
477C2×C4⋊C4—1432no—
478C2×C4⋊C4—144no—
479C2×C4⋊C4—144no—
480C2×C4⋊C4—144no—
481C2×C4⋊C4—144no—
482C2×C4⋊C4—144no—
483C2×C4⋊C4—144no—
484C2×C4⋊C4—144no—
485C2×C4⋊C4—144no—
486C2×C4⋊C4—144no—
487C2×C4⋊C4C22×D714yes—
488C2×C4⋊C4C22×D714yes—
489C2×C4⋊C4C22×D714yes—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—78no—
494C2×C22⋊C4—74no—
495C2×C22⋊C4—74no—
496C2×C22⋊C4—74no—
497C2×C22⋊C4—74no—
498C2×C22⋊C4—74no—
499C2×C22⋊C4—74no—
500C2×C22⋊C4—144no—
501C2×C22⋊C4—144no—
502C2×C22⋊C4—144no—
503C2×C22⋊C4—144no—
504C2×C22⋊C4—144no—
505C2×C22⋊C4C22×D714yes—
506C2×C22⋊C4C22×D714yes—
507C2×C22⋊C4C22×D714yes—
508C2×C42—74no—
509C2×C42—74no—
510C2×C42—144no—
511C2×C42—144no—
512#95—74no—
513#95—74no—
514#95—74no—
515#95—74no—
516#95—74no—
517#95—74no—
518#95—74no—
519#95C22×D714yes—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7—42no—
526C22×C7—42no—
527C22×C7—88no—
528C22×C7C2×#12114yes—
529C22×C7#52514yes—
530C22×C7#53614yes—
531C22×C7#54714yes—
532C22×C7#54714yes—
533C22×C7#55214yes—
534C22×C7#55214yes—
535C22×C7C23×D411yescharacteristic
536C22×C7C23×D411yescharacteristic
537C22×C7C22×#4111yescharacteristic
538C22×C7C22×#4111yescharacteristic
539C22×C7C22×#4111yescharacteristic
540C22×C7C2×2−1+411yescharacteristic
541C22×C7C2×2−1+411yescharacteristic
542C2×D7—24no—
543C2×D7—232no—
544C2×D7—24no—
545C2×D7—24no—
546C2×D7—24no—
547C2×D7—24no—
548C2×D7—24no—
549C2×D7C2×#12118yes—
550C4×C7—24no—
551C4×C7—24no—
552C4×C7—24no—
553C4×C7—42no—
554C4×C7—42no—
555C4×C7—42no—
556Dic7—24no—
557Dic7—24no—
558Dic7—24no—
559Dic7—42no—
560Dic7—42no—
561Dic7—42no—
562Dic7—42no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—74no—
571C24—74no—
572C24—74no—
573C24—72no—
574C24—142no—
575C24—142no—
576C24—142no—
577C24—142no—
578C24C23×D712yes—
579C24C23×D711yescharacteristic
580C2×D4—148no—
581C2×D4—148no—
582C2×D4—148no—
583C2×D4—2816no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—74no—
600C22×C4—74no—
601C22×C4—74no—
602C22×C4—72no—
603C22×C4—72no—
604C22×C4—72no—
605C22×C4—716no—
606C22×C4—72no—
607C22×C4—72no—
608C22×C4—72no—
609C22×C4—72no—
610C22×C4—148no—
611C22×C4—148no—
612C22×C4—148no—
613C22×C4—1432no—
614C22×C4—148no—
615C22×C4—1432no—
616C22×C4—148no—
617C22×C4—148no—
618C22×C4—148no—
619C22×C4—142no—
620C22×C4—142no—
621C22×C4—142no—
622C22×C4—142no—
623C22×C4—142no—
624C22×C4—142no—
625C22×C4—148no—
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—2816no—
639C22×C4D4×D714yes—
640C22×C4D4×D714yes—
641C22×C4#115914yes—
642C22×C4C23×D712yes—
643C22×C4C23×D712yes—
644C22×C4C23×D712yes—
645C22×C4C23×D712yes—
646C22×C4C23×D712yes—
647C22×C4C23×D712yes—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—148no—
652C4⋊C4—148no—
653C4⋊C4—148no—
654C4⋊C4—148no—
655C4⋊C4—148no—
656C4⋊C4—148no—
657C4⋊C4—148no—
658C4⋊C4—148no—
659C4⋊C4—148no—
660C22⋊C4—28no—
661C22⋊C4—28no—
662C22⋊C4—28no—
663C22⋊C4—716no—
664C22⋊C4—148no—
665C22⋊C4—148no—
666C22⋊C4—148no—
667C22⋊C4—148no—
668C22⋊C4—148no—
669C42—148no—
670C42—148no—
671C2×C7—82no—
672C2×C7#241318yescomplemented
673C2×C7C22×#12111yescharacteristic
674C2×C7C2×#52511yescharacteristic
675C2×C7C2×#53611yescharacteristic
676C2×C7C2×#54711yescharacteristic
677C2×C7C2×#54711yescharacteristic
678C2×C7C2×#55211yescharacteristic
679C2×C7C2×#55211yescharacteristic
680D7—28no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—716no—
696C23—74no—
697C23—74no—
698C23—74no—
699C23—148no—
700C23—148no—
701C23—148no—
702C23—148no—
703C23—148no—
704C23—148no—
705C23—142no—
706C23—142no—
707C23—142no—
708C23—142no—
709C23C2×D4×D712yes—
710C23C2×D4×D712yes—
711C23C2×#115912yes—
712C23#655112yes—
713C23D7×#4112yes—
714C23D7×#4112yes—
715C23#655412yes—
716C23C24×D711yescharacteristic
717D4—2816no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—74no—
740C2×C4—74no—
741C2×C4—74no—
742C2×C4—1432no—
743C2×C4—1432no—
744C2×C4—148no—
745C2×C4—148no—
746C2×C4—148no—
747C2×C4—142no—
748C2×C4—142no—
749C2×C4—142no—
750C2×C4—142no—
751C2×C4—142no—
752C2×C4—142no—
753C2×C4—142no—
754C2×C4—142no—
755C2×C4—142no—
756C2×C4—142no—
757C2×C4—142no—
758C2×C4—142no—
759C2×C4—142no—
760C2×C4—142no—
761C2×C4—142no—
762C2×C4—142no—
763C2×C4—142no—
764C2×C4—142no—
765C2×C4—2816no—
766C2×C4—284no—
767C2×C4—284no—
768C2×C4—284no—
769C2×C4—284no—
770C2×C4C2×D4×D714yes—
771C2×C4C2×D4×D714yes—
772C2×C4C2×#115914yes—
773C7C2×#241311yescharacteristic, complemented, Sylow
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—78no—
782C22—88no—
783C22—144no—
784C22—144no—
785C22—144no—
786C22—144no—
787C22—1432no—
788C22—144no—
789C22—144no—
790C22D7×#12114yes—
791C22#9029714yes—
792C22#9030214yes—
793C22#9031914yes—
794C22#9032214yes—
795C22#9033014yes—
796C22#9039914yes—
797C22C22×D4×D711yescharacteristic
798C22C22×D4×D711yescharacteristic
799C22C22×#115911yescharacteristic
800C22C2×#655111yescharacteristic
801C22C2×D7×#4111yescharacteristic
802C22C2×D7×#4111yescharacteristic
803C22C2×#655411yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—144no—
811C4—144no—
812C4—144no—
813C4—282no—
814C4—282no—
815C4—282no—
816C4—282no—
817C2—82no—
818C2—148no—
819C2#1173486018yesdirect product factor
820C2C2×#9029711yescharacteristic
821C2C2×#9030211yescharacteristic
822C2C2×D7×#12111yescharacteristic
823C2C2×#9031911yescharacteristic
824C2C2×#9032211yescharacteristic
825C2C2×#9033011yescharacteristic
826C2C2×#9039911yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#396C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#396D7
hypocenterC7C2×#2413
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×D7×C4⋊C4C2semidirect
2. C22×#6455C2semidirect
5. C2×C7×#396C2semidirect
6. C2×#89761C2semidirect
7. C2×#89755C2semidirect
8. C2×#89756C2semidirect
9. C2×#89757C2semidirect
11. C2×#89720C2semidirect
12. C2×#89716C2semidirect
13. C2×#89723C2semidirect
14. #11734860C2direct (N × H)
15. C2×#89436C2semidirect
16. C2×#89419C2semidirect
45. C2×#6455C22semidirect
47. C2×D7×C4⋊C4C22semidirect
52. C7×#396C22semidirect
61. #89761C22semidirect
62. #89757C22semidirect
63. #89756C22semidirect
64. #89755C22semidirect
66. #89723C22semidirect
67. #89720C22semidirect
68. #89716C22semidirect
69. #89436C22semidirect
70. #89419C22semidirect
169. C2×#396D7semidirect
323. #396C2×D7semidirect
672. C2×C7#2413semidirect
773. C7C2×#2413semidirect
819. C2#11734860direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D7×C4⋊C42
C22×#64552
C22×#64462
C2×C7×#3962
C2×#897612
C2×#897552
C2×#897562
C2×#897572
C2×#897282
C2×#897202
C2×#897162
C2×#897232
#117348602
C2×#894362
C2×#894192
C2×#24137