Finite Group Databasebeta

← C2×#11733037 #13525060

Subgroups — C2×#11733037 #13525060

Order 1792.

3526 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×#6459C211yesmaximal, characteristic, complemented
2C22×#6441C211yesmaximal, characteristic, complemented
3C22×(C22⋊D7)⋊C4C211yesmaximal, characteristic
4C22×C4×Dic14C211yesmaximal, characteristic, complemented
5C2×C7×#388C211yesmaximal, characteristic, complemented
6C2×#89756C211yesmaximal, characteristic, complemented
7C2×#89731C211yesmaximal, characteristic
8C2×#89733C211yesmaximal, characteristic
9C2×#89716C211yesmaximal, characteristic, complemented
10C2×#89714C211yesmaximal, characteristic, complemented
11C2×#89712C211yesmaximal, characteristic, complemented
12#11733037C2116yesmaximal, direct product factor
13C2×#89439C211yesmaximal, characteristic, complemented
14C2×#89429C211yesmaximal, characteristic, complemented
15C2×#89442C211yesmaximal, characteristic, complemented
16C2×#89422C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C24×Dic7C2211yescharacteristic
19C23×C4×D7C2211yescharacteristic
20C23×Dic14C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C42×C7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
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×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6459—28no—
45C2×#6459C2218yescomplemented
46C2×(C22⋊D7)⋊C4—28no—
47C2×(C22⋊D7)⋊C4C2218yes—
48C2×#6441—28no—
49C2×#6441C2218yescomplemented
50C2×C4×Dic14—28no—
51C2×C4×Dic14C2218yescomplemented
52C7×#388C2218yescomplemented
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#89756C2218yescomplemented
62#89733C2218yes—
63#89731C2218yes—
64#89716C2218yescomplemented
65#89714C2218yescomplemented
66#89712C2218yescomplemented
67#89442C2218yescomplemented
68#89439C2218yescomplemented
69#89429C2218yescomplemented
70#89422C2218yescomplemented
71C2×#2536—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×Dic7—24no—
85C23×Dic7—24no—
86C23×Dic7—24no—
87C23×Dic7C2314yes—
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C22×C4×D7—24no—
96C22×C4×D7—24no—
97C22×C4×D7—24no—
98C22×C4×D7C2314yes—
99C22×Dic14—24no—
100C22×Dic14—24no—
101C22×Dic14D418yescomplemented
102C22×Dic14C2314yes—
103C2×C7×C4⋊C4—24no—
104C2×C7×C4⋊C4C2314yes—
105C2×C7×C22⋊C4—24no—
106C2×C7×C22⋊C4—24no—
107C2×C7×C22⋊C4—24no—
108C2×C7×C22⋊C4C2314yes—
109C2×C7×C22⋊C4C2314yes—
110C2×C7×C22⋊C4C2314yes—
111C2×C42×C7—24no—
112C2×C42×C7C2314yes—
113C2×C22⋊Dic7—24no—
114C2×C22⋊Dic7—24no—
115C2×C22⋊Dic7C2314yes—
116C2×C22⋊Dic7C2314yes—
117C2×(C2×D7)⋊C4—24no—
118C2×(C2×D7)⋊C4—24no—
119C2×(C2×D7)⋊C4—24no—
120C2×(C2×D7)⋊C4—24no—
121C2×(C2×D7)⋊C4—24no—
122C2×(C2×D7)⋊C4C2314yes—
123C2×(C2×D7)⋊C4C2314yes—
124C2×(C2×D7)⋊C4C2314yes—
125C2×(C2×D7)⋊C4C2314yes—
126C2×(C2×D7)⋊C4C2314yes—
127C2×C4⋊Dic7—24no—
128C2×C4⋊Dic7—24no—
129C2×C4⋊Dic7C2314yes—
130C2×C4⋊Dic7C2314yes—
131C2×Dic7⋊C4—24no—
132C2×Dic7⋊C4—24no—
133C2×Dic7⋊C4—24no—
134C2×Dic7⋊C4—24no—
135C2×Dic7⋊C4—24no—
136C2×Dic7⋊C4—24no—
137C2×Dic7⋊C4—24no—
138C2×Dic7⋊C4C2314yes—
139C2×Dic7⋊C4C2314yes—
140C2×Dic7⋊C4C2314yes—
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C2×Dic7⋊C4C2314yes—
144C2×Dic7⋊C4C2314yes—
145C2×C4×Dic7—24no—
146C2×C4×Dic7D418yes—
147C2×C4×Dic7C2314yes—
148C2×C4×Dic7C2314yes—
149#6459—232no—
150(C22⋊D7)⋊C4—232no—
151#6441—232no—
152C4×Dic14—232no—
153C7×#95C2314yes—
154C7×#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C7⋊#95C2314yes—
160C7⋊#95C2314yes—
161C22×C22⋊Q8—71no—
162C22×C22⋊Q8—71no—
163C22×C4×Q8—71no—
164C22×C4×D4—71no—
165#2536—716no—
166C2×#398—71no—
167C2×#398—71no—
168C2×#394—71no—
169C2×#394—71no—
170C2×#388—71no—
171C2×#388—71no—
172C2×#388—71no—
173C2×#388D711yescharacteristic, complemented
174C2×#382—71no—
175C2×#380—71no—
176C2×#380—71no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7—22no—
182C24×C7—22no—
183C24×C7#4114yes—
184C24×C7C2412yes—
185C24×C7C2411yescharacteristic
186C23×D7—22no—
187C23×D7—22no—
188C23×D7—22no—
189C23×D7—22no—
190C23×D7—22no—
191C23×D7—22no—
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×C7—22no—
210C22×C4×C7C2×D414yes—
211C22×C4×C7C2×D414yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2412yes—
216C22×C4×C7C2412yes—
217C22×C4×C7C2412yes—
218C2×C22⋊D7—232no—
219C2×C22⋊D7—28no—
220C2×C22⋊D7—28no—
221C2×C22⋊D7—28no—
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—28no—
239C22×Dic7—28no—
240C22×Dic7—28no—
241C22×Dic7—416no—
242C22×Dic7C2×D414yes—
243C22×Dic7C2×D414yes—
244C22×Dic7C2×D414yes—
245C22×Dic7C2×D414yes—
246C22×Dic7#4114yes—
247C22×Dic7C2412yes—
248C22×Dic7C2412yes—
249C22×Dic7C2412yes—
250C22×Dic7C2412yes—
251C22×Dic7C2412yes—
252C22×Dic7C2412yes—
253C22×Dic7C2412yes—
254C2×C4×D7—28no—
255C2×C4×D7—28no—
256C2×C4×D7—28no—
257C2×C4×D7—416no—
258C2×Dic14—232no—
259C2×Dic14—28no—
260C2×Dic14—28no—
261C2×Dic14C2×D4116yescomplemented
262C7×C4⋊C4—28no—
263C7×C22⋊C4—28no—
264C7×C22⋊C4—28no—
265C7×C22⋊C4—28no—
266C42×C7—28no—
267C22⋊Dic7—28no—
268C22⋊Dic7—28no—
269(C2×D7)⋊C4—28no—
270(C2×D7)⋊C4—28no—
271(C2×D7)⋊C4—28no—
272(C2×D7)⋊C4—28no—
273(C2×D7)⋊C4—28no—
274C4⋊Dic7—28no—
275C4⋊Dic7—28no—
276Dic7⋊C4—28no—
277Dic7⋊C4—28no—
278Dic7⋊C4—28no—
279Dic7⋊C4—28no—
280Dic7⋊C4—28no—
281Dic7⋊C4—28no—
282Dic7⋊C4—28no—
283C4×Dic7—28no—
284C4×Dic7C2×D4116yes—
285C23×Q8—71no—
286C23×D4—71no—
287C24×C4—71no—
288C24×C4—71no—
289C2×C22⋊Q8—78no—
290C2×C22⋊Q8—78no—
291C2×C22⋊Q8—148no—
292C2×C22⋊Q8—148no—
293C2×C4×Q8—78no—
294C2×C4×Q8—148no—
295C2×C4×D4—78no—
296C2×C4×D4—148no—
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—71no—
305C22×C4⋊C4—71no—
306C22×C4⋊C4C2×D711yescharacteristic
307C22×C22⋊C4—71no—
308C22×C22⋊C4—71no—
309C22×C22⋊C4—71no—
310C22×C22⋊C4—71no—
311C22×C22⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4C2×D711yescharacteristic
315C22×C22⋊C4C2×D711yescharacteristic
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C42—71no—
318C22×C42—71no—
319C22×C42C2×D711yescharacteristic
320#398—78no—
321#398—78no—
322#394—78no—
323#394—78no—
324#388—78no—
325#388—78no—
326#388—78no—
327#388C2×D718yescomplemented
328#382—78no—
329#380—78no—
330#380—78no—
331C2×#95—71no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95C2×D711yescharacteristic
338C2×#95C2×D711yescharacteristic
339C23×C7—28no—
340C23×C7—28no—
341C23×C7—28no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—44no—
349C23×C7—44no—
350C23×C7—44no—
351C23×C7—44no—
352C23×C7C22×D412yes—
353C23×C7C22×D412yes—
354C23×C7C2×#4114yes—
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—22no—
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—44no—
371C22×D7—44no—
372C22×D7—44no—
373C22×D7—44no—
374C22×D7C2×#4114yes—
375C2×C4×C7—28no—
376C2×C4×C7—28no—
377C2×C4×C7—22no—
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×C7—44no—
397C2×C4×C7C22×D414yes—
398C2×C4×C7C22×D414yes—
399C22⋊D7—232no—
400C2×Dic7—28no—
401C2×Dic7—28no—
402C2×Dic7—22no—
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—44no—
419C2×Dic7—44no—
420C2×Dic7—44no—
421C2×Dic7—44no—
422C2×Dic7—416no—
423C2×Dic7#121116yes—
424C2×Dic7C22×D414yes—
425C2×Dic7C22×D414yes—
426C2×Dic7C22×D414yes—
427C2×Dic7C22×D414yes—
428C2×Dic7C2×#4114yes—
429C4×D7—416no—
430Dic14—232no—
431C25—71no—
432C25C22×D711yescharacteristic
433C22×Q8—78no—
434C22×Q8—74no—
435C22×Q8—144no—
436C22×Q8—144no—
437C22×D4—74no—
438C22×D4—144no—
439C22×D4—144no—
440C22×D4—144no—
441C23×C4—71no—
442C23×C4—71no—
443C23×C4—71no—
444C23×C4—74no—
445C23×C4—71no—
446C23×C4—71no—
447C23×C4—71no—
448C23×C4—71no—
449C23×C4—74no—
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
462C22⋊Q8—1432no—
463C22⋊Q8—1432no—
464C4×Q8—1432no—
465C4×D4—1432no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—74no—
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—144no—
477C2×C4⋊C4—144no—
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⋊C4C22×D714yes—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—74no—
490C2×C22⋊C4—74no—
491C2×C22⋊C4—74no—
492C2×C22⋊C4—74no—
493C2×C22⋊C4—74no—
494C2×C22⋊C4—74no—
495C2×C22⋊C4—74no—
496C2×C22⋊C4—144no—
497C2×C22⋊C4—144no—
498C2×C22⋊C4—144no—
499C2×C22⋊C4—144no—
500C2×C22⋊C4—144no—
501C2×C22⋊C4—144no—
502C2×C22⋊C4—144no—
503C2×C22⋊C4C22×D714yes—
504C2×C22⋊C4C22×D714yes—
505C2×C22⋊C4C22×D714yes—
506C2×C42—24no—
507C2×C42—78no—
508C2×C42—74no—
509C2×C42—74no—
510C2×C42—144no—
511C2×C42C22×D714yes—
512#95—74no—
513#95—74no—
514#95—74no—
515#95—74no—
516#95—74no—
517#95—74no—
518#95C22×D714yes—
519#95C22×D714yes—
520C22×C7—24no—
521C22×C7—24no—
522C22×C7—24no—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7—42no—
526C22×C7—42no—
527C22×C7—416no—
528C22×C7C2×#12114yes—
529C22×C7#52514yes—
530C22×C7#53614yes—
531C22×C7#54814yes—
532C22×C7#54814yes—
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—24no—
544C2×D7—24no—
545C2×D7—42no—
546C2×D7—42no—
547C2×D7—42no—
548C2×D7—42no—
549C2×D7—416no—
550C4×C7—24no—
551C4×C7—24no—
552C4×C7—42no—
553C4×C7—42no—
554C4×C7—42no—
555C4×C7—42no—
556Dic7—24no—
557Dic7—24no—
558Dic7—42no—
559Dic7—42no—
560Dic7—42no—
561Dic7—42no—
562Dic7C2×#12118yes—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—74no—
570C24—72no—
571C24—142no—
572C24—142no—
573C24—142no—
574C24—142no—
575C24—142no—
576C24—142no—
577C24#115714yes—
578C24C23×D712yes—
579C24C23×D711yescharacteristic
580C2×Q8—716no—
581C2×Q8—148no—
582C2×Q8—1432no—
583C2×Q8—148no—
584C2×D4—148no—
585C2×D4—148no—
586C2×D4—1432no—
587C2×D4—148no—
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—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—74no—
605C22×C4—74no—
606C22×C4—74no—
607C22×C4—72no—
608C22×C4—74no—
609C22×C4—74no—
610C22×C4—72no—
611C22×C4—72no—
612C22×C4—72no—
613C22×C4—72no—
614C22×C4—72no—
615C22×C4—72no—
616C22×C4—148no—
617C22×C4—148no—
618C22×C4—148no—
619C22×C4—148no—
620C22×C4—148no—
621C22×C4—148no—
622C22×C4—142no—
623C22×C4—142no—
624C22×C4—142no—
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—2816no—
639C22×C4—2816no—
640C22×C4D4×D714yes—
641C22×C4D4×D714yes—
642C22×C4C23×D712yes—
643C22×C4C23×D712yes—
644C22×C4C23×D712yes—
645C22×C4C23×D712yes—
646C22×C4C23×D712yes—
647C22×C4C23×D712yes—
648C4⋊C4—28no—
649C4⋊C4—148no—
650C4⋊C4—148no—
651C4⋊C4—148no—
652C4⋊C4—148no—
653C4⋊C4—148no—
654C4⋊C4—148no—
655C4⋊C4—148no—
656C4⋊C4—148no—
657C4⋊C4—148no—
658C22⋊C4—28no—
659C22⋊C4—28no—
660C22⋊C4—28no—
661C22⋊C4—148no—
662C22⋊C4—148no—
663C22⋊C4—148no—
664C22⋊C4—148no—
665C22⋊C4—148no—
666C22⋊C4—148no—
667C22⋊C4—148no—
668C42—28no—
669C42—716no—
670C42—148no—
671C2×C7—44no—
672C2×C7#253618yescomplemented
673C2×C7C22×#12111yescharacteristic
674C2×C7C2×#52511yescharacteristic
675C2×C7C2×#53611yescharacteristic
676C2×C7C2×#54811yescharacteristic
677C2×C7C2×#54811yescharacteristic
678C2×C7C2×#55211yescharacteristic
679C2×C7C2×#55211yescharacteristic
680D7—44no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—74no—
695C23—148no—
696C23—148no—
697C23—148no—
698C23—142no—
699C23—142no—
700C23—142no—
701C23—142no—
702C23—142no—
703C23—142no—
704C23—284no—
705C23—284no—
706C23—284no—
707C23—284no—
708C23C2×#115714yes—
709C23C2×#115712yes—
710C23C2×D4×D712yes—
711C23C2×D4×D712yes—
712C23D7×#4112yes—
713C23D7×#4112yes—
714C23#655412yes—
715C23#655412yes—
716C23C24×D711yescharacteristic
717Q8—1432no—
718D4—1432no—
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—22no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—716no—
742C2×C4—74no—
743C2×C4—74no—
744C2×C4—74no—
745C2×C4—74no—
746C2×C4—74no—
747C2×C4—148no—
748C2×C4—148no—
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—2816no—
767C2×C4—284no—
768C2×C4—284no—
769C2×C4—284no—
770C2×C4—284no—
771C2×C4C2×D4×D714yes—
772C2×C4C2×D4×D714yes—
773C7C2×#253611yescharacteristic, complemented, Sylow
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—416no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—144no—
783C22—144no—
784C22—144no—
785C22—282no—
786C22—2816no—
787C22—282no—
788C22—282no—
789C22—282no—
790C22#9022214yes—
791C22#9023814yes—
792C22#9024314yes—
793C22D7×#12114yes—
794C22#9033914yes—
795C22#9036814yes—
796C22#9039914yes—
797C22C22×#115711yescharacteristic
798C22C22×D4×D711yescharacteristic
799C22C22×D4×D711yescharacteristic
800C22C2×D7×#4111yescharacteristic
801C22C2×D7×#4111yescharacteristic
802C22C2×#655411yescharacteristic
803C22C2×#655411yescharacteristic
804C4—24no—
805C4—24no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—78no—
811C4—144no—
812C4—144no—
813C4—282no—
814C4—282no—
815C4—282no—
816C4—282no—
817C2—44no—
818C2—284no—
819C2#1173303718yesdirect product factor
820C2C2×#9022211yescharacteristic
821C2C2×#9024311yescharacteristic
822C2C2×#9023811yescharacteristic
823C2C2×D7×#12111yescharacteristic
824C2C2×#9033911yescharacteristic
825C2C2×#9036811yescharacteristic
826C2C2×#9039911yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#388C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#388D7
hypocenterC7C2×#2536
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#6459C2semidirect
2. C22×#6441C2semidirect
4. C22×C4×Dic14C2semidirect
5. C2×C7×#388C2semidirect
6. C2×#89756C2semidirect
9. C2×#89716C2semidirect
10. C2×#89714C2semidirect
11. C2×#89712C2semidirect
12. #11733037C2direct (N × H)
13. C2×#89439C2semidirect
14. C2×#89429C2semidirect
15. C2×#89442C2semidirect
16. C2×#89422C2semidirect
45. C2×#6459C22semidirect
49. C2×#6441C22semidirect
51. C2×C4×Dic14C22semidirect
52. C7×#388C22semidirect
61. #89756C22semidirect
64. #89716C22semidirect
65. #89714C22semidirect
66. #89712C22semidirect
67. #89442C22semidirect
68. #89439C22semidirect
69. #89429C22semidirect
70. #89422C22semidirect
101. C22×Dic14D4semidirect
173. C2×#388D7semidirect
261. C2×Dic14C2×D4semidirect
327. #388C2×D7semidirect
672. C2×C7#2536semidirect
773. C7C2×#2536semidirect
819. C2#11733037direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64592
C22×#64412
C22×(C22⋊D7)⋊C42
C22×C4×Dic142
C2×C7×#3882
C2×#897562
C2×#897312
C2×#897332
C2×#897162
C2×#897142
C2×#897122
#117330372
C2×#894392
C2×#894292
C2×#894422
C2×#894222
C2×#25367