Finite Group Databasebeta

← C2×#11739810 #13521434

Subgroups — C2×#11739810 #13521434

Order 1792.

3394 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×D4C211yesmaximal, characteristic, complemented
2C22×#6448C211yesmaximal, characteristic, complemented
3C2×#89995C211yesmaximal, characteristic
4C2×#89994C211yesmaximal, characteristic, complemented
5C2×#89985C211yesmaximal, characteristic, complemented
6C2×#89985C211yesmaximal, characteristic, complemented
7C2×#89983C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
9#11739810C2116yesmaximal, direct product factor
10C2×#89762C211yesmaximal, characteristic, complemented
11C2×#89750C211yesmaximal, characteristic, complemented
12C2×#89733C211yesmaximal, characteristic, complemented
13C2×#89719C211yesmaximal, characteristic, complemented
14C2×#89723C211yesmaximal, characteristic, complemented
15C2×#89701C211yesmaximal, characteristic, complemented
16C2×#89712C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C24×C4×C7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C23×C22⋊D7C2211yescharacteristic
22C23×Dic14C2211yescharacteristic
23C2×C4×C7×D4—28no—
24C2×C4×C7×D4C2218yescomplemented
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C42×C7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C22×C22⋊Dic7C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×(C2×D7)⋊C4C2211yescharacteristic
39C22×(C2×D7)⋊C4C2211yescharacteristic
40C22×C4⋊Dic7C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6448—28no—
45C2×#6448C2218yescomplemented
46#89995C2218yes—
47#89994C2218yescomplemented
48#89985C2218yescomplemented
49#89985C2218yescomplemented
50#89983C2218yescomplemented
51C4×C22⋊Dic7C2218yescomplemented
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61C2×C7⋊#95C2211yescharacteristic
62#89762C2218yescomplemented
63#89750C2218yescomplemented
64#89733C2218yescomplemented
65#89723C2218yescomplemented
66#89719C2218yescomplemented
67#89712C2218yescomplemented
68#89701C2218yescomplemented
69C2×#2459—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C25×C7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C22×C7×D4—24no—
74C22×C7×D4—24no—
75C22×C7×D4—24no—
76C22×C7×D4C2314yes—
77C23×C4×C7—24no—
78C23×C4×C7—24no—
79C23×C4×C7—24no—
80C23×C4×C7—24no—
81C23×C4×C7—42no—
82C23×C4×C7—42no—
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2314yes—
85C23×C4×C7C2314yes—
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C23×C4×C7C2311yescharacteristic
89C23×C4×C7C2311yescharacteristic
90C22×C22⋊D7—24no—
91C22×C22⋊D7—24no—
92C22×C22⋊D7—24no—
93C22×C22⋊D7—42no—
94C22×C22⋊D7—42no—
95C22×C22⋊D7—42no—
96C22×C22⋊D7C2314yes—
97C22×C22⋊D7C2314yes—
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2311yescharacteristic
105C22×Dic14—24no—
106C22×Dic14—24no—
107C22×Dic14—42no—
108C22×Dic14C2314yes—
109C4×C7×D4—232no—
110C2×C7×C4⋊C4—24no—
111C2×C7×C4⋊C4C2314yes—
112C2×C7×C22⋊C4—24no—
113C2×C7×C22⋊C4D418yescomplemented
114C2×C7×C22⋊C4C2314yes—
115C2×C7×C22⋊C4C2314yes—
116C2×C42×C7—24no—
117C2×C42×C7C2314yes—
118C2×C22⋊Dic7—24no—
119C2×C22⋊Dic7—24no—
120C2×C22⋊Dic7—24no—
121C2×C22⋊Dic7—42no—
122C2×C22⋊Dic7—42no—
123C2×C22⋊Dic7—42no—
124C2×C22⋊Dic7C2314yes—
125C2×C22⋊Dic7C2314yes—
126C2×C22⋊Dic7C2314yes—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130C2×(C2×D7)⋊C4—24no—
131C2×(C2×D7)⋊C4—24no—
132C2×(C2×D7)⋊C4—24no—
133C2×(C2×D7)⋊C4—24no—
134C2×(C2×D7)⋊C4—42no—
135C2×(C2×D7)⋊C4C2314yes—
136C2×(C2×D7)⋊C4C2314yes—
137C2×(C2×D7)⋊C4C2314yes—
138C2×(C2×D7)⋊C4C2314yes—
139C2×(C2×D7)⋊C4C2314yes—
140C2×C4⋊Dic7—42no—
141C2×C4⋊Dic7C2314yes—
142C2×Dic7⋊C4—24no—
143C2×Dic7⋊C4C2314yes—
144C2×C4×Dic7—24no—
145C2×C4×Dic7—42no—
146C2×C4×Dic7C2314yes—
147C2×C4×Dic7C2314yes—
148#6448—232no—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#124—71no—
160C22×C4×D4D711yescharacteristic, complemented
161#2459—716no—
162C2×#394—71no—
163C2×#394—71no—
164C2×#393—71no—
165C2×#392—71no—
166C2×#391—71no—
167C2×#388—71no—
168C2×#388—71no—
169C2×#388—71no—
170C2×#387—71no—
171C2×#386—71no—
172C2×#386—71no—
173C2×#381—71no—
174C2×C4×C22⋊C4—71no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7—22no—
182C24×C7—22no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7C2×D414yes—
188C24×C7#4114yes—
189C24×C7C2412yes—
190C24×C7C2412yes—
191C24×C7C2411yescharacteristic
192C23×D7—22no—
193C23×D7—22no—
194C23×D7—22no—
195C23×D7—22no—
196C23×D7—22no—
197C23×D7—22no—
198C23×D7—22no—
199C23×D7C2412yes—
200C2×C7×D4—232no—
201C2×C7×D4—28no—
202C2×C7×D4—28no—
203C2×C7×D4—28no—
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—28no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—28no—
217C22×C4×C7—28no—
218C22×C4×C7—28no—
219C22×C4×C7—44no—
220C22×C4×C7—44no—
221C22×C4×C7—416no—
222C22×C4×C7—416no—
223C22×C4×C7C2×D414yes—
224C22×C4×C7C2×D414yes—
225C22×C4×C7#4114yes—
226C22×C4×C7#4114yes—
227C22×C4×C7C2412yes—
228C22×C4×C7C2412yes—
229C22×C4×C7C2412yes—
230C22×C4×C7C2412yes—
231C22×C4×C7C2412yes—
232C2×C22⋊D7—28no—
233C2×C22⋊D7—28no—
234C2×C22⋊D7—28no—
235C2×C22⋊D7—44no—
236C2×C22⋊D7—44no—
237C2×C22⋊D7—44no—
238C2×C22⋊D7—416no—
239C2×C22⋊D7—416no—
240C22×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—22no—
256C22×Dic7—22no—
257C22×Dic7—22no—
258C22×Dic7—22no—
259C22×Dic7—22no—
260C22×Dic7#4114yes—
261C22×Dic7C2412yes—
262C22×Dic7C2412yes—
263C22×Dic7C2412yes—
264C22×Dic7C2412yes—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C2×Dic14—28no—
269C2×Dic14—28no—
270C2×Dic14—44no—
271C2×Dic14—416no—
272C7×C4⋊C4—28no—
273C7×C22⋊C4—28no—
274C7×C22⋊C4C2×D4116yescomplemented
275C42×C7—28no—
276C22⋊Dic7—28no—
277C22⋊Dic7—28no—
278C22⋊Dic7—28no—
279C22⋊Dic7—44no—
280C22⋊Dic7—44no—
281C22⋊Dic7—44no—
282(C2×D7)⋊C4—28no—
283(C2×D7)⋊C4—28no—
284(C2×D7)⋊C4—28no—
285(C2×D7)⋊C4—28no—
286(C2×D7)⋊C4—44no—
287C4⋊Dic7—44no—
288Dic7⋊C4—28no—
289C4×Dic7—28no—
290C4×Dic7—44no—
291C23×Q8—71no—
292C23×D4—71no—
293C23×D4—71no—
294C23×D4C2×D711yescharacteristic
295C24×C4C2×D711yescharacteristic
296C24×C4C2×D711yescharacteristic
297C2×#124—78no—
298C2×#124—148no—
299C2×C4×D4—28no—
300C2×C4×D4C2×D718yescomplemented
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4C2×D711yescharacteristic
304C22×C22⋊C4—71no—
305C22×C22⋊C4—71no—
306C22×C22⋊C4—71no—
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⋊C4—71no—
315C22×C22⋊C4C2×D711yescharacteristic
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C42—71no—
318C22×C42—71no—
319C22×C42C2×D711yescharacteristic
320#394—78no—
321#394—78no—
322#393—78no—
323#392—78no—
324#391—78no—
325#388—78no—
326#388—78no—
327#388—78no—
328#387—78no—
329#386—78no—
330#386—78no—
331#381—78no—
332C4×C22⋊C4—78no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95—71no—
342C2×#95—71no—
343C23×C7—28no—
344C23×C7—28no—
345C23×C7—28no—
346C23×C7—28no—
347C23×C7—28no—
348C23×C7—28no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—44no—
362C23×C7—44no—
363C23×C7—44no—
364C23×C7—44no—
365C23×C7—44no—
366C23×C7—44no—
367C23×C7—44no—
368C23×C7—44no—
369C23×C7C22×D414yes—
370C23×C7C22×D412yes—
371C23×C7C2×#4114yes—
372C23×C7C2×#4112yes—
373C23×C7C2×#4112yes—
374C23×C7C2×#4112yes—
375C23×C7C2×#4112yes—
376C23×C7H(5,𝔽2)12yes—
377C23×C7H(5,𝔽2)12yes—
378C23×C7C2511yescharacteristic
379C22×D7—22no—
380C22×D7—22no—
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—22no—
385C22×D7—22no—
386C22×D7—44no—
387C22×D7—44no—
388C22×D7—44no—
389C22×D7—44no—
390C22×D7—44no—
391C22×D7—44no—
392C22×D7—44no—
393C7×D4—232no—
394C2×C4×C7—28no—
395C2×C4×C7—28no—
396C2×C4×C7—28no—
397C2×C4×C7—28no—
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—22no—
408C2×C4×C7—22no—
409C2×C4×C7—416no—
410C2×C4×C7—416no—
411C2×C4×C7—44no—
412C2×C4×C7C22×D414yes—
413C2×C4×C7C22×D414yes—
414C2×C4×C7C2×#4114yes—
415C2×C4×C7C2×#4114yes—
416C22⋊D7—416no—
417C22⋊D7—416no—
418C2×Dic7—28no—
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—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—44no—
440C2×Dic7—44no—
441C2×Dic7—44no—
442C2×Dic7—44no—
443C2×Dic7—44no—
444C2×Dic7—44no—
445C2×Dic7C2×#4114yes—
446Dic14—416no—
447C25—71no—
448C25C22×D711yescharacteristic
449C25C22×D711yescharacteristic
450C22×Q8—74no—
451C22×Q8—144no—
452C22×Q8—144no—
453C22×Q8—282no—
454C22×D4—24no—
455C22×D4—24no—
456C22×D4—24no—
457C22×D4—74no—
458C22×D4—74no—
459C22×D4—144no—
460C22×D4—144no—
461C22×D4—144no—
462C22×D4—282no—
463C22×D4—282no—
464C22×D4—282no—
465C22×D4C22×D714yes—
466C23×C4—24no—
467C23×C4—24no—
468C23×C4—24no—
469C23×C4—24no—
470C23×C4—42no—
471C23×C4—42no—
472C23×C4—71no—
473C23×C4—71no—
474C23×C4—71no—
475C23×C4—71no—
476C23×C4—71no—
477C23×C4—71no—
478C23×C4—71no—
479C23×C4C22×D711yescharacteristic
480C23×C4C22×D714yes—
481C23×C4C22×D714yes—
482C23×C4C22×D711yescharacteristic
483C23×C4C22×D711yescharacteristic
484C23×C4C22×D711yescharacteristic
485C23×C4C22×D711yescharacteristic
486#124—1432no—
487C4×D4—232no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—74no—
490C2×C4⋊C4—74no—
491C2×C4⋊C4—144no—
492C2×C4⋊C4—282no—
493C2×C4⋊C4C22×D714yes—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—74no—
496C2×C22⋊C4—74no—
497C2×C22⋊C4—74no—
498C2×C22⋊C4—74no—
499C2×C22⋊C4—74no—
500C2×C22⋊C4—74no—
501C2×C22⋊C4—74no—
502C2×C22⋊C4—74no—
503C2×C22⋊C4—74no—
504C2×C22⋊C4—74no—
505C2×C22⋊C4—74no—
506C2×C22⋊C4—144no—
507C2×C22⋊C4—144no—
508C2×C22⋊C4—144no—
509C2×C22⋊C4—144no—
510C2×C22⋊C4—144no—
511C2×C22⋊C4—144no—
512C2×C22⋊C4—144no—
513C2×C22⋊C4—282no—
514C2×C22⋊C4—282no—
515C2×C22⋊C4—282no—
516C2×C22⋊C4—282no—
517C2×C22⋊C4C22⋊D718yescomplemented
518C2×C22⋊C4C22×D714yes—
519C2×C22⋊C4C22×D714yes—
520C2×C42—24no—
521C2×C42—74no—
522C2×C42—74no—
523C2×C42—144no—
524C2×C42—282no—
525C2×C42C22×D714yes—
526#95—74no—
527#95—74no—
528#95—74no—
529#95—74no—
530#95—74no—
531#95—74no—
532#95—74no—
533#95—74no—
534#95—74no—
535#95—74no—
536C22×C7—24no—
537C22×C7—24no—
538C22×C7—24no—
539C22×C7—24no—
540C22×C7—24no—
541C22×C7—24no—
542C22×C7—42no—
543C22×C7—42no—
544C22×C7—42no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—42no—
550C22×C7—416no—
551C22×C7—416no—
552C22×C7#52514yes—
553C22×C7#52914yes—
554C22×C7#53814yes—
555C22×C7#54614yes—
556C22×C7#54614yes—
557C22×C7#55514yes—
558C22×C7#55914yes—
559C22×C7C23×D411yescharacteristic
560C22×C7C22×#4111yescharacteristic
561C22×C7C22×#4111yescharacteristic
562C22×C7C22×#4111yescharacteristic
563C22×C7C22×#4111yescharacteristic
564C22×C7C2×H(5,𝔽2)11yescharacteristic
565C22×C7C2×H(5,𝔽2)11yescharacteristic
566C2×D7—42no—
567C2×D7—42no—
568C2×D7—42no—
569C2×D7—42no—
570C2×D7—42no—
571C2×D7—42no—
572C2×D7—42no—
573C2×D7—88no—
574C4×C7—24no—
575C4×C7—24no—
576C4×C7—24no—
577C4×C7—24no—
578C4×C7—42no—
579Dic7—24no—
580Dic7—42no—
581Dic7—42no—
582Dic7—42no—
583Dic7—42no—
584Dic7—42no—
585Dic7—42no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—72no—
599C24—142no—
600C24—142no—
601C24—142no—
602C24—142no—
603C24—142no—
604C24—142no—
605C24—142no—
606C24#115714yes—
607C24C2×C22⋊D714yes—
608C24C23×D712yes—
609C24C23×D712yes—
610C24C23×D711yescharacteristic
611C2×Q8—148no—
612C2×Q8—148no—
613C2×Q8—284no—
614C2×Q8—2816no—
615C2×D4—232no—
616C2×D4—28no—
617C2×D4—28no—
618C2×D4—28no—
619C2×D4—148no—
620C2×D4—148no—
621C2×D4—148no—
622C2×D4—284no—
623C2×D4—284no—
624C2×D4—284no—
625C2×D4—2816no—
626C2×D4—2816no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—28no—
639C22×C4—28no—
640C22×C4—28no—
641C22×C4—28no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—416no—
645C22×C4—416no—
646C22×C4—74no—
647C22×C4—72no—
648C22×C4—72no—
649C22×C4—72no—
650C22×C4—72no—
651C22×C4—72no—
652C22×C4—72no—
653C22×C4—72no—
654C22×C4—142no—
655C22×C4—142no—
656C22×C4—142no—
657C22×C4—142no—
658C22×C4—142no—
659C22×C4—142no—
660C22×C4—142no—
661C22×C4—142no—
662C22×C4—142no—
663C22×C4—142no—
664C22×C4—142no—
665C22×C4—142no—
666C22×C4—142no—
667C22×C4—142no—
668C22×C4—142no—
669C22×C4—142no—
670C22×C4—142no—
671C22×C4—142no—
672C22×C4—142no—
673C22×C4—142no—
674C22×C4#115714yes—
675C22×C4#115914yes—
676C22×C4C2×C22⋊D714yes—
677C22×C4C2×C22⋊D714yes—
678C22×C4C23×D712yes—
679C22×C4C23×D712yes—
680C22×C4C23×D712yes—
681C22×C4C23×D712yes—
682C22×C4C23×D712yes—
683C4⋊C4—28no—
684C4⋊C4—148no—
685C4⋊C4—284no—
686C22⋊C4—28no—
687C22⋊C4—148no—
688C22⋊C4—148no—
689C22⋊C4—148no—
690C22⋊C4—148no—
691C22⋊C4—148no—
692C22⋊C4—148no—
693C22⋊C4—148no—
694C22⋊C4—284no—
695C22⋊C4—284no—
696C22⋊C4—284no—
697C22⋊C4—284no—
698C22⋊C4C2×C22⋊D7116yescomplemented
699C42—28no—
700C42—148no—
701C42—284no—
702C2×C7—44no—
703C2×C7—44no—
704C2×C7#245918yescomplemented
705C2×C7C2×#52511yescharacteristic
706C2×C7C2×#52911yescharacteristic
707C2×C7C2×#53811yescharacteristic
708C2×C7C2×#54611yescharacteristic
709C2×C7C2×#54611yescharacteristic
710C2×C7C2×#55511yescharacteristic
711C2×C7C2×#55911yescharacteristic
712D7—82no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—28no—
717C23—28no—
718C23—28no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—142no—
740C23—142no—
741C23—142no—
742C23—142no—
743C23—142no—
744C23—142no—
745C23—142no—
746C23—284no—
747C23—284no—
748C23—284no—
749C23—284no—
750C23—284no—
751C23—284no—
752C23—284no—
753C23C2×#115714yes—
754C23C2×#115712yes—
755C23C2×#115712yes—
756C23C2×#115912yes—
757C23#654812yes—
758C23D7×#4112yes—
759C23#655312yes—
760C23C22×C22⋊D714yes—
761C23C22×C22⋊D712yes—
762C23C24×D711yescharacteristic
763Q8—2816no—
764D4—232no—
765D4—2816no—
766D4—2816no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—416no—
783C2×C4—416no—
784C2×C4—44no—
785C2×C4—74no—
786C2×C4—148no—
787C2×C4—142no—
788C2×C4—142no—
789C2×C4—142no—
790C2×C4—142no—
791C2×C4—142no—
792C2×C4—142no—
793C2×C4—142no—
794C2×C4—142no—
795C2×C4—142no—
796C2×C4—142no—
797C2×C4—142no—
798C2×C4—142no—
799C2×C4—142no—
800C2×C4—142no—
801C2×C4—142no—
802C2×C4—142no—
803C2×C4—142no—
804C2×C4—142no—
805C2×C4—142no—
806C2×C4—142no—
807C2×C4—284no—
808C2×C4—284no—
809C2×C4—284no—
810C2×C4—284no—
811C2×C4—284no—
812C2×C4—284no—
813C2×C4C2×#115714yes—
814C2×C4C2×#115914yes—
815C2×C4C22×C22⋊D714yes—
816C2×C4C22×C22⋊D714yes—
817C7C2×#245911yescharacteristic, complemented, Sylow
818C22—24no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—416no—
833C22—416no—
834C22—282no—
835C22—282no—
836C22—282no—
837C22—282no—
838C22—282no—
839C22—282no—
840C22—282no—
841C22—568no—
842C22#9022914yes—
843C22#9025014yes—
844C22#9025114yes—
845C22#9025414yes—
846C22#9048214yes—
847C22#9049714yes—
848C22#9052014yes—
849C22C22×#115711yescharacteristic
850C22C22×#115711yescharacteristic
851C22C22×#115911yescharacteristic
852C22C2×#654811yescharacteristic
853C22C2×D7×#4111yescharacteristic
854C22C2×#655311yescharacteristic
855C22C23×C22⋊D711yescharacteristic
856C4—24no—
857C4—24no—
858C4—24no—
859C4—24no—
860C4—42no—
861C4—144no—
862C4—282no—
863C4—282no—
864C4—282no—
865C4—282no—
866C4—282no—
867C4—282no—
868C2—44no—
869C2—44no—
870C2—562no—
871C2#1173981018yesdirect product factor
872C2C2×#9022911yescharacteristic
873C2C2×#9025411yescharacteristic
874C2C2×#9025011yescharacteristic
875C2C2×#9025111yescharacteristic
876C2C2×#9048211yescharacteristic
877C2C2×#9049711yescharacteristic
878C2C2×#9052011yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C4×C7×D4C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC22×C4×D4D7
hypocenterC7C2×#2459
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C7×D4C2semidirect
2. C22×#6448C2semidirect
4. C2×#89994C2semidirect
5. C2×#89985C2semidirect
6. C2×#89985C2semidirect
7. C2×#89983C2semidirect
8. C2×C4×C22⋊Dic7C2semidirect
9. #11739810C2direct (N × H)
10. C2×#89762C2semidirect
11. C2×#89750C2semidirect
12. C2×#89733C2semidirect
13. C2×#89719C2semidirect
14. C2×#89723C2semidirect
15. C2×#89701C2semidirect
16. C2×#89712C2semidirect
24. C2×C4×C7×D4C22semidirect
45. C2×#6448C22semidirect
47. #89994C22semidirect
48. #89985C22semidirect
49. #89985C22semidirect
50. #89983C22semidirect
51. C4×C22⋊Dic7C22semidirect
62. #89762C22semidirect
63. #89750C22semidirect
64. #89733C22semidirect
65. #89723C22semidirect
66. #89719C22semidirect
67. #89712C22semidirect
68. #89701C22semidirect
113. C2×C7×C22⋊C4D4semidirect
160. C22×C4×D4D7semidirect
274. C7×C22⋊C4C2×D4semidirect
300. C2×C4×D4C2×D7semidirect
517. C2×C22⋊C4C22⋊D7semidirect
698. C22⋊C4C2×C22⋊D7semidirect
704. C2×C7#2459semidirect
817. C7C2×#2459semidirect
871. C2#11739810direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C7×D42
C22×#64482
C2×#899952
C2×#899942
C2×#899852
C2×#899832
C2×C4×C22⋊Dic72
#117398102
C2×#897622
C2×#897502
C2×#897332
C2×#897192
C2×#897232
C2×#897012
C2×#897122
C2×#24597