Finite Group Databasebeta

← C2×#11734697 #13521275

Subgroups — C2×#11734697 #13521275

Order 1792.

3830 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6509C211yesmaximal, characteristic, complemented
2C22×#6509C211yesmaximal, characteristic, complemented
3C22×D7×C4⋊C4C211yesmaximal, characteristic, complemented
4C22×#6456C211yesmaximal, characteristic
5C2×C7×#395C211yesmaximal, characteristic, complemented
6C2×#89764C211yesmaximal, characteristic, complemented
7C2×#89766C211yesmaximal, characteristic, complemented
8C2×#89761C211yesmaximal, characteristic, complemented
9C2×#89756C211yesmaximal, characteristic, complemented
10#11734697C2116yesmaximal, direct product factor
11C2×#89437C211yesmaximal, characteristic
12C2×#89437C211yesmaximal, characteristic
13C2×#89440C211yesmaximal, characteristic, complemented
14C2×#89440C211yesmaximal, characteristic, complemented
15C2×#89419C211yesmaximal, characteristic, complemented
16C2×#89427C211yesmaximal, characteristic, complemented
17C23×C7×Q8C2211yescharacteristic
18C23×D28C2211yescharacteristic
19C23×C4×D7C2211yescharacteristic
20C23×C4×D7C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C23×C4×D7C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C4⋊C4C2211yescharacteristic
26C2×#6509—28no—
27C2×#6509—28no—
28C2×#6509C2218yescomplemented
29C2×#6509C2218yescomplemented
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×(C2×D7)⋊C4C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×C4⋊Dic7C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×Dic7⋊C4C2211yescharacteristic
45C22×Dic7⋊C4C2211yescharacteristic
46C22×Dic7⋊C4C2211yescharacteristic
47C22×C4×Dic7C2211yescharacteristic
48C2×#6456—28no—
49C2×#6456C2218yes—
50C2×D7×C4⋊C4—28no—
51C2×D7×C4⋊C4C2218yescomplemented
52C7×#395C2218yescomplemented
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#89766C2218yescomplemented
62#89764C2218yescomplemented
63#89761C2218yescomplemented
64#89756C2218yescomplemented
65#89440C2218yescomplemented
66#89440C2218yescomplemented
67#89437C2218yes—
68#89437C2218yes—
69#89427C2218yescomplemented
70#89419C2218yescomplemented
71C2×#2449—71nomaximal, Sylow
72C24×D7C2311yescharacteristic
73C24×D7C2311yescharacteristic
74C22×C7×Q8—24no—
75C22×C7×Q8—24no—
76C22×C7×Q8—42no—
77C22×C7×Q8C2314yes—
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C22×D28—24no—
92C22×D28—24no—
93C22×D28Q818yescomplemented
94C22×D28C2314yes—
95C22×C4×D7—24no—
96C22×C4×D7—24no—
97C22×C4×D7—24no—
98C22×C4×D7—24no—
99C22×C4×D7—24no—
100C22×C4×D7—24no—
101C22×C4×D7—24no—
102C22×C4×D7—24no—
103C22×C4×D7—24no—
104C22×C4×D7—42no—
105C22×C4×D7—42no—
106C22×C4×D7—42no—
107C22×C4×D7C2314yes—
108C22×C4×D7C2314yes—
109C22×C4×D7C2314yes—
110C22×C4×D7C2314yes—
111C2×C7×C4⋊C4—24no—
112C2×C7×C4⋊C4—24no—
113C2×C7×C4⋊C4—42no—
114C2×C7×C4⋊C4C2314yes—
115C2×C7×C4⋊C4C2314yes—
116C2×C7×C4⋊C4C2314yes—
117#6509—232no—
118#6509—232no—
119C2×(C2×D7)⋊C4—24no—
120C2×(C2×D7)⋊C4—24no—
121C2×(C2×D7)⋊C4—24no—
122C2×(C2×D7)⋊C4—24no—
123C2×(C2×D7)⋊C4—24no—
124C2×(C2×D7)⋊C4—24no—
125C2×(C2×D7)⋊C4—42no—
126C2×(C2×D7)⋊C4D418yes—
127C2×(C2×D7)⋊C4C2314yes—
128C2×(C2×D7)⋊C4C2314yes—
129C2×(C2×D7)⋊C4C2314yes—
130C2×(C2×D7)⋊C4C2314yes—
131C2×(C2×D7)⋊C4C2314yes—
132C2×(C2×D7)⋊C4C2314yes—
133C2×(C2×D7)⋊C4C2314yes—
134C2×(C2×D7)⋊C4C2314yes—
135C2×C4⋊Dic7—24no—
136C2×C4⋊Dic7—24no—
137C2×C4⋊Dic7—24no—
138C2×C4⋊Dic7C2314yes—
139C2×C4⋊Dic7C2314yes—
140C2×C4⋊Dic7C2314yes—
141C2×Dic7⋊C4—24no—
142C2×Dic7⋊C4—24no—
143C2×Dic7⋊C4—24no—
144C2×Dic7⋊C4—24no—
145C2×Dic7⋊C4—24no—
146C2×Dic7⋊C4D418yescomplemented
147C2×Dic7⋊C4C2314yes—
148C2×Dic7⋊C4C2314yes—
149C2×Dic7⋊C4C2314yes—
150C2×Dic7⋊C4C2314yes—
151C2×Dic7⋊C4C2314yes—
152C2×Dic7⋊C4C2314yes—
153C2×C4×Dic7—24no—
154C2×C4×Dic7C2314yes—
155#6456—232no—
156D7×C4⋊C4—232no—
157C7×#95C2314yes—
158C7×#95C2314yes—
159C7×#95C2314yes—
160C7⋊#95C2314yes—
161C7⋊#95C2314yes—
162C7⋊#95C2314yes—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C22×C22⋊Q8—71no—
166C22×C22⋊Q8—71no—
167C22×C4×D4—71no—
168C23×C4⋊C4—71no—
169#2449—716no—
170C2×#399—71no—
171C2×#398—71no—
172C2×#396—71no—
173C2×#395D711yescharacteristic, complemented
174C2×#389—71no—
175C2×#387—71no—
176C2×#386—71no—
177C2×#386—71no—
178C2×#385—71no—
179C2×#385—71no—
180C2×#385—71no—
181C24×C7C2411yescharacteristic
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×D7—22no—
191C23×D7—22no—
192C23×D7C2×D414yes—
193C23×D7C2×Q814yes—
194C23×D7C2×Q814yes—
195C23×D7#4114yes—
196C23×D7C2412yes—
197C23×D7C2412yes—
198C2×C7×Q8—28no—
199C2×C7×Q8—28no—
200C2×C7×Q8—44no—
201C2×C7×Q8—416no—
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×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7C2×D414yes—
220C22×C4×C7C2×D414yes—
221C22×C4×C7C2×Q814yes—
222C22×C4×C7#4114yes—
223C22×C4×C7C2412yes—
224C22×C4×C7C2412yes—
225C22×C4×C7C2412yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2412yes—
228C22×C4×C7C2412yes—
229C22×C4×C7C2412yes—
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×Dic7C2×D414yes—
246C22×Dic7C2×D414yes—
247C22×Dic7C2×D414yes—
248C22×Dic7C2412yes—
249C22×Dic7C2412yes—
250C22×Dic7C2412yes—
251C22×Dic7C2412yes—
252C22×Dic7C2412yes—
253C22×Dic7C2412yes—
254C2×D28—232no—
255C2×D28—28no—
256C2×D28—28no—
257C2×D28C2×Q8116yescomplemented
258C2×C4×D7—232no—
259C2×C4×D7—28no—
260C2×C4×D7—28no—
261C2×C4×D7—28no—
262C2×C4×D7—28no—
263C2×C4×D7—28no—
264C2×C4×D7—28no—
265C2×C4×D7—28no—
266C2×C4×D7—28no—
267C2×C4×D7—28no—
268C2×C4×D7—44no—
269C2×C4×D7—44no—
270C2×C4×D7—44no—
271C2×C4×D7—416no—
272C2×C4×D7—416no—
273C2×C4×D7—416no—
274C7×C4⋊C4—28no—
275C7×C4⋊C4—28no—
276C7×C4⋊C4—44no—
277(C2×D7)⋊C4—28no—
278(C2×D7)⋊C4—28no—
279(C2×D7)⋊C4—28no—
280(C2×D7)⋊C4—28no—
281(C2×D7)⋊C4—28no—
282(C2×D7)⋊C4—28no—
283(C2×D7)⋊C4—44no—
284(C2×D7)⋊C4C2×D4116yes—
285C4⋊Dic7—28no—
286C4⋊Dic7—28no—
287C4⋊Dic7—28no—
288Dic7⋊C4—28no—
289Dic7⋊C4—28no—
290Dic7⋊C4—28no—
291Dic7⋊C4—28no—
292Dic7⋊C4—28no—
293Dic7⋊C4C2×D4116yescomplemented
294C4×Dic7—28no—
295C23×Q8C2×D711yescharacteristic
296C23×D4—71no—
297C24×C4—71no—
298C24×C4—71no—
299C24×C4—71no—
300C24×C4—71no—
301C2×C22⋊Q8—78no—
302C2×C22⋊Q8—78no—
303C2×C22⋊Q8—148no—
304C2×C22⋊Q8—148no—
305C2×C4×D4—78no—
306C2×C4×D4—148no—
307C22×C4⋊C4—71no—
308C22×C4⋊C4—71no—
309C22×C4⋊C4—71no—
310C22×C4⋊C4—71no—
311C22×C4⋊C4—71no—
312C22×C4⋊C4—71no—
313C22×C4⋊C4—71no—
314C22×C4⋊C4—71no—
315C22×C4⋊C4—71no—
316C22×C4⋊C4—78no—
317C22×C4⋊C4—148no—
318C22×C4⋊C4C2×D711yescharacteristic
319C22×C4⋊C4C2×D711yescharacteristic
320C22×C4⋊C4C2×D711yescharacteristic
321C22×C22⋊C4—71no—
322C22×C22⋊C4—71no—
323C22×C22⋊C4—71no—
324C22×C22⋊C4—71no—
325C22×C22⋊C4—71no—
326C22×C22⋊C4—71no—
327C22×C22⋊C4—71no—
328C22×C22⋊C4—71no—
329C22×C42—71no—
330#399—78no—
331#398—78no—
332#396—78no—
333#395C2×D718yescomplemented
334#389—78no—
335#387—78no—
336#386—78no—
337#386—78no—
338#385—78no—
339#385—78no—
340#385—78no—
341C2×#95—71no—
342C2×#95—71no—
343C2×#95—71no—
344C2×#95—71no—
345C2×#95—71no—
346C2×#95C2×D711yescharacteristic
347C2×#95C2×D711yescharacteristic
348C2×#95C2×D711yescharacteristic
349C23×C7C22×D412yes—
350C23×C7C22×D412yes—
351C23×C7C22×Q812yes—
352C23×C7C2×#4112yes—
353C23×C7C2×#4112yes—
354C23×C7H(5,𝔽2)12yes—
355C23×C72−1+412yes—
356C23×C7C2511yescharacteristic
357C22×D7—28no—
358C22×D7—28no—
359C22×D7—28no—
360C22×D7—28no—
361C22×D7—28no—
362C22×D7—28no—
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—28no—
368C22×D7—28no—
369C22×D7—28no—
370C22×D7—22no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—44no—
377C22×D7—44no—
378C22×D7—44no—
379C22×D7—44no—
380C22×D7C22⋊Q8116yescomplemented
381C22×D7C22×D414yes—
382C22×D7C22×Q814yes—
383C22×D7C22×Q814yes—
384C22×D7C2×#4114yes—
385C7×Q8—416no—
386C2×C4×C7—28no—
387C2×C4×C7—28no—
388C2×C4×C7—28no—
389C2×C4×C7—28no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—44no—
408C2×C4×C7—44no—
409C2×C4×C7—44no—
410C2×C4×C7C22×D414yes—
411C2×C4×C7C22×D414yes—
412C2×C4×C7C22×Q814yes—
413C2×C4×C7C2×#4114yes—
414C2×Dic7—28no—
415C2×Dic7—28no—
416C2×Dic7—28no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—22no—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—22no—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—44no—
433C2×Dic7—44no—
434C2×Dic7—44no—
435C2×Dic7C22×D414yes—
436C2×Dic7C22×D414yes—
437C2×Dic7C22×D414yes—
438D28—232no—
439C4×D7—232no—
440C4×D7—416no—
441C4×D7—416no—
442C4×D7—416no—
443C25—71no—
444C25—71no—
445C22×Q8—24no—
446C22×Q8—24no—
447C22×Q8—42no—
448C22×Q8C22×D714yes—
449C22×D4—78no—
450C22×D4—74no—
451C22×D4—144no—
452C22×D4—144no—
453C23×C4—71no—
454C23×C4—71no—
455C23×C4—71no—
456C23×C4—71no—
457C23×C4—71no—
458C23×C4—71no—
459C23×C4—74no—
460C23×C4—74no—
461C23×C4—74no—
462C23×C4—74no—
463C23×C4—144no—
464C23×C4—144no—
465C23×C4—144no—
466C23×C4—144no—
467C23×C4—144no—
468C23×C4—144no—
469C23×C4—144no—
470C23×C4—144no—
471C23×C4—144no—
472C23×C4—282no—
473C23×C4—282no—
474C23×C4—282no—
475C23×C4C22×D711yescharacteristic
476C23×C4C22×D711yescharacteristic
477C23×C4C22×D711yescharacteristic
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D711yescharacteristic
480C23×C4C22×D711yescharacteristic
481C23×C4C22×D711yescharacteristic
482C22⋊Q8—1432no—
483C22⋊Q8—1432no—
484C4×D4—1432no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—78no—
489C2×C4⋊C4—74no—
490C2×C4⋊C4—74no—
491C2×C4⋊C4—74no—
492C2×C4⋊C4—74no—
493C2×C4⋊C4—74no—
494C2×C4⋊C4—74no—
495C2×C4⋊C4—74no—
496C2×C4⋊C4—74no—
497C2×C4⋊C4—74no—
498C2×C4⋊C4—1432no—
499C2×C4⋊C4—144no—
500C2×C4⋊C4—144no—
501C2×C4⋊C4—144no—
502C2×C4⋊C4—144no—
503C2×C4⋊C4—144no—
504C2×C4⋊C4—144no—
505C2×C4⋊C4—144no—
506C2×C4⋊C4—144no—
507C2×C4⋊C4C22×D714yes—
508C2×C4⋊C4C22×D714yes—
509C2×C4⋊C4C22×D714yes—
510C2×C22⋊C4—78no—
511C2×C22⋊C4—74no—
512C2×C22⋊C4—74no—
513C2×C22⋊C4—74no—
514C2×C22⋊C4—74no—
515C2×C22⋊C4—74no—
516C2×C22⋊C4—74no—
517C2×C22⋊C4—74no—
518C2×C22⋊C4—74no—
519C2×C22⋊C4—144no—
520C2×C22⋊C4—144no—
521C2×C22⋊C4—144no—
522C2×C22⋊C4—144no—
523C2×C22⋊C4—144no—
524C2×C22⋊C4—144no—
525C2×C22⋊C4—282no—
526C2×C42—74no—
527C2×C42—144no—
528#95—74no—
529#95—74no—
530#95—74no—
531#95—74no—
532#95—74no—
533#95C22×D714yes—
534#95C22×D714yes—
535#95C22×D714yes—
536C22×C7C2×C22⋊Q814yes—
537C22×C7#52514yes—
538C22×C7#53914yes—
539C22×C7D4214yes—
540C22×C7#54714yes—
541C22×C7D4×Q814yes—
542C22×C7#55414yes—
543C22×C7C23×D411yescharacteristic
544C22×C7C23×D411yescharacteristic
545C22×C7C23×Q811yescharacteristic
546C22×C7C22×#4111yescharacteristic
547C22×C7C22×#4111yescharacteristic
548C22×C7C2×H(5,𝔽2)11yescharacteristic
549C22×C7C2×2−1+411yescharacteristic
550C2×D7—24no—
551C2×D7—24no—
552C2×D7—24no—
553C2×D7—24no—
554C2×D7—24no—
555C2×D7—24no—
556C2×D7—232no—
557C2×D7—24no—
558C2×D7—24no—
559C2×D7—24no—
560C2×D7—42no—
561C2×D7—42no—
562C2×D7—42no—
563C2×D7—42no—
564C2×D7—416no—
565C2×D7C2×C22⋊Q818yescomplemented
566C4×C7—24no—
567C4×C7—24no—
568C4×C7—24no—
569C4×C7—24no—
570C4×C7—42no—
571C4×C7—42no—
572C4×C7—42no—
573Dic7—24no—
574Dic7—24no—
575Dic7—24no—
576Dic7—42no—
577Dic7—42no—
578Dic7—42no—
579C24—74no—
580C24—74no—
581C24—74no—
582C24—72no—
583C24—74no—
584C24—72no—
585C24—142no—
586C24—142no—
587C24—142no—
588C24—142no—
589C24—142no—
590C24—142no—
591C24—142no—
592C24—142no—
593C24—142no—
594C24—142no—
595C24C23×D711yescharacteristic
596C2×Q8—28no—
597C2×Q8—28no—
598C2×Q8—44no—
599C2×Q8—416no—
600C2×D4—716no—
601C2×D4—148no—
602C2×D4—1432no—
603C2×D4—148no—
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—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—74no—
622C22×C4—74no—
623C22×C4—74no—
624C22×C4—72no—
625C22×C4—72no—
626C22×C4—72no—
627C22×C4—72no—
628C22×C4—72no—
629C22×C4—72no—
630C22×C4—148no—
631C22×C4—148no—
632C22×C4—148no—
633C22×C4—148no—
634C22×C4—1432no—
635C22×C4—148no—
636C22×C4—148no—
637C22×C4—142no—
638C22×C4—142no—
639C22×C4—142no—
640C22×C4—142no—
641C22×C4—142no—
642C22×C4—142no—
643C22×C4—148no—
644C22×C4—142no—
645C22×C4—142no—
646C22×C4—142no—
647C22×C4—142no—
648C22×C4—142no—
649C22×C4—142no—
650C22×C4—142no—
651C22×C4—142no—
652C22×C4—142no—
653C22×C4—148no—
654C22×C4—148no—
655C22×C4—284no—
656C22×C4—284no—
657C22×C4—284no—
658C22×C4—2816no—
659C22×C4—2816no—
660C22×C4—2816no—
661C22×C4D4×D714yes—
662C22×C4D4×D714yes—
663C22×C4Q8×D714yes—
664C22×C4#116114yes—
665C22×C4C23×D712yes—
666C22×C4C23×D712yes—
667C22×C4C23×D712yes—
668C22×C4C23×D712yes—
669C22×C4C23×D712yes—
670C22×C4C23×D712yes—
671C22×C4C23×D712yes—
672C4⋊C4—28no—
673C4⋊C4—28no—
674C4⋊C4—44no—
675C4⋊C4—716no—
676C4⋊C4—148no—
677C4⋊C4—148no—
678C4⋊C4—148no—
679C4⋊C4—148no—
680C4⋊C4—148no—
681C4⋊C4—148no—
682C4⋊C4—148no—
683C4⋊C4—148no—
684C22⋊C4—716no—
685C22⋊C4—148no—
686C22⋊C4—148no—
687C22⋊C4—148no—
688C22⋊C4—148no—
689C22⋊C4—148no—
690C22⋊C4—148no—
691C22⋊C4—284no—
692C42—148no—
693C2×C7#244918yescomplemented
694C2×C7C22×C22⋊Q811yescharacteristic
695C2×C7C2×#52511yescharacteristic
696C2×C7C2×#53911yescharacteristic
697C2×C7C2×D4211yescharacteristic
698C2×C7C2×#54711yescharacteristic
699C2×C7C2×D4×Q811yescharacteristic
700C2×C7C2×#55411yescharacteristic
701D7—28no—
702D7—44no—
703C23—716no—
704C23—74no—
705C23—74no—
706C23—74no—
707C23—74no—
708C23—148no—
709C23—148no—
710C23—148no—
711C23—148no—
712C23—148no—
713C23—148no—
714C23—142no—
715C23—142no—
716C23—142no—
717C23—142no—
718C23—148no—
719C23—148no—
720C23—148no—
721C23—142no—
722C23—142no—
723C23—142no—
724C23—142no—
725C23—142no—
726C23—142no—
727C23—284no—
728C23—284no—
729C23—284no—
730C23—284no—
731C23C2×D4×D712yes—
732C23C2×D4×D712yes—
733C23#654812yes—
734C23C2×Q8×D712yes—
735C23C2×#116112yes—
736C23#655112yes—
737C23D7×#4112yes—
738C23C24×D711yescharacteristic
739Q8—416no—
740D4—1432no—
741C2×C4—28no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—28no—
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—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—74no—
766C2×C4—74no—
767C2×C4—74no—
768C2×C4—1432no—
769C2×C4—148no—
770C2×C4—148no—
771C2×C4—148no—
772C2×C4—142no—
773C2×C4—142no—
774C2×C4—142no—
775C2×C4—142no—
776C2×C4—142no—
777C2×C4—142no—
778C2×C4—142no—
779C2×C4—142no—
780C2×C4—142no—
781C2×C4—142no—
782C2×C4—142no—
783C2×C4—142no—
784C2×C4—142no—
785C2×C4—142no—
786C2×C4—142no—
787C2×C4—2816no—
788C2×C4—2816no—
789C2×C4—2816no—
790C2×C4—284no—
791C2×C4—284no—
792C2×C4—284no—
793C2×C4C2×D4×D714yes—
794C2×C4C2×D4×D714yes—
795C2×C4C2×Q8×D714yes—
796C2×C4C2×#116114yes—
797C7C2×#244911yescharacteristic, complemented, Sylow
798C22—78no—
799C22—144no—
800C22—144no—
801C22—144no—
802C22—144no—
803C22—144no—
804C22—144no—
805C22—1432no—
806C22—144no—
807C22—144no—
808C22—144no—
809C22—282no—
810C22—282no—
811C22—282no—
812C22—282no—
813C22—2816no—
814C22#9028114yes—
815C22D7×C22⋊Q814yes—
816C22#9031814yes—
817C22#9032914yes—
818C22#9041714yes—
819C22#9041814yes—
820C22#9042114yes—
821C22C22×D4×D711yescharacteristic
822C22C22×D4×D711yescharacteristic
823C22C2×#654811yescharacteristic
824C22C22×Q8×D711yescharacteristic
825C22C22×#116111yescharacteristic
826C22C2×#655111yescharacteristic
827C22C2×D7×#4111yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—24no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—144no—
836C4—144no—
837C4—144no—
838C4—282no—
839C4—282no—
840C4—282no—
841C2—148no—
842C2—284no—
843C2#1173469718yesdirect product factor
844C2C2×#9028111yescharacteristic
845C2C2×#9031811yescharacteristic
846C2C2×D7×C22⋊Q811yescharacteristic
847C2C2×#9032911yescharacteristic
848C2C2×#9041711yescharacteristic
849C2C2×#9041811yescharacteristic
850C2C2×#9042111yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#395C2
socleC24×C7C24
prime radicalC23×D28C22
hypercenterC2×#395D7
hypocenterC7C2×#2449
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
1. C22×#6509C2semidirect
2. C22×#6509C2semidirect
3. C22×D7×C4⋊C4C2semidirect
5. C2×C7×#395C2semidirect
6. C2×#89764C2semidirect
7. C2×#89766C2semidirect
8. C2×#89761C2semidirect
9. C2×#89756C2semidirect
10. #11734697C2direct (N × H)
13. C2×#89440C2semidirect
14. C2×#89440C2semidirect
15. C2×#89419C2semidirect
16. C2×#89427C2semidirect
28. C2×#6509C22semidirect
29. C2×#6509C22semidirect
51. C2×D7×C4⋊C4C22semidirect
52. C7×#395C22semidirect
61. #89766C22semidirect
62. #89764C22semidirect
63. #89761C22semidirect
64. #89756C22semidirect
65. #89440C22semidirect
66. #89440C22semidirect
69. #89427C22semidirect
70. #89419C22semidirect
93. C22×D28Q8semidirect
146. C2×Dic7⋊C4D4semidirect
173. C2×#395D7semidirect
257. C2×D28C2×Q8semidirect
293. Dic7⋊C4C2×D4semidirect
333. #395C2×D7semidirect
380. C22×D7C22⋊Q8semidirect
565. C2×D7C2×C22⋊Q8semidirect
693. C2×C7#2449semidirect
797. C7C2×#2449semidirect
843. C2#11734697direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#65092
C22×D7×C4⋊C42
C22×#64562
C2×C7×#3952
C2×#897642
C2×#897662
C2×#897612
C2×#897562
#117346972
C2×#894372
C2×#894402
C2×#894192
C2×#894272
C2×#24497