Finite Group Databasebeta

← C2×#11733773 #13521493

Subgroups — C2×#11733773 #13521493

Order 1792.

3330 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6442C211yesmaximal, characteristic, complemented
2C22×(C22⋊D7)⋊C4C211yesmaximal, characteristic, complemented
3C2×C7×#390C211yesmaximal, characteristic, complemented
4C2×#89995C211yesmaximal, characteristic
5C2×#89992C211yesmaximal, characteristic, complemented
6C2×#89764C211yesmaximal, characteristic, complemented
7C2×#89753C211yesmaximal, characteristic, complemented
8C2×#89731C211yesmaximal, characteristic, complemented
9C2×#89728C211yesmaximal, characteristic, complemented
10C2×#89733C211yesmaximal, characteristic, complemented
11C2×#89717C211yesmaximal, characteristic, complemented
12C2×#89716C211yesmaximal, characteristic, complemented
13C2×#89714C211yesmaximal, characteristic, complemented
14C2×#89705C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
16#11733773C2116yesmaximal, direct product factor
17C23×C7×D4C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C24×Dic7C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C42×C7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
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
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×(C22⋊D7)⋊C4—28no—
45C2×(C22⋊D7)⋊C4C2218yescomplemented
46C2×#6442—28no—
47C2×#6442C2218yescomplemented
48C7×#390C2218yescomplemented
49#89995C2218yes—
50#89992C2218yescomplemented
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59#89764C2218yescomplemented
60#89753C2218yescomplemented
61#89733C2218yescomplemented
62#89731C2218yescomplemented
63#89728C2218yescomplemented
64#89717C2218yescomplemented
65#89716C2218yescomplemented
66#89714C2218yescomplemented
67C4×(C2×D7)⋊C4C2218yescomplemented
68#89705C2218yescomplemented
69C2×#2467—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C25×C7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C22×C7×D4—24no—
74C22×C7×D4—24no—
75C22×C7×D4—42no—
76C22×C7×D4C2314yes—
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C22×C22⋊D7—24no—
83C22×C22⋊D7—24no—
84C22×C22⋊D7—24no—
85C22×C22⋊D7—24no—
86C22×C22⋊D7—42no—
87C22×C22⋊D7—42no—
88C22×C22⋊D7C2314yes—
89C22×C22⋊D7C2314yes—
90C23×Dic7—24no—
91C23×Dic7—24no—
92C23×Dic7—42no—
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2314yes—
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C22×C4×D7—24no—
102C22×C4×D7—24no—
103C22×C4×D7—42no—
104C22×C4×D7C2314yes—
105C2×C7×C4⋊C4—24no—
106C2×C7×C4⋊C4C2314yes—
107C2×C7×C22⋊C4—24no—
108C2×C7×C22⋊C4—24no—
109C2×C7×C22⋊C4—42no—
110C2×C7×C22⋊C4—42no—
111C2×C7×C22⋊C4C2314yes—
112C2×C7×C22⋊C4C2314yes—
113C2×C7×C22⋊C4C2314yes—
114C2×C7×C22⋊C4C2314yes—
115C2×C42×C7—42no—
116C2×C42×C7C2314yes—
117C2×C22⋊Dic7—24no—
118C2×C22⋊Dic7—24no—
119C2×C22⋊Dic7—24no—
120C2×C22⋊Dic7—24no—
121C2×C22⋊Dic7—42no—
122C2×C22⋊Dic7C2314yes—
123C2×C22⋊Dic7C2314yes—
124C2×C22⋊Dic7C2314yes—
125C2×C22⋊Dic7C2314yes—
126C2×C22⋊Dic7C2314yes—
127C2×(C2×D7)⋊C4—24no—
128C2×(C2×D7)⋊C4—24no—
129C2×(C2×D7)⋊C4—24no—
130C2×(C2×D7)⋊C4—42no—
131C2×(C2×D7)⋊C4C2314yes—
132C2×(C2×D7)⋊C4C2314yes—
133C2×(C2×D7)⋊C4C2314yes—
134C2×(C2×D7)⋊C4C2314yes—
135C2×C4⋊Dic7—24no—
136C2×C4⋊Dic7C2314yes—
137C2×Dic7⋊C4—24no—
138C2×Dic7⋊C4—42no—
139C2×Dic7⋊C4—42no—
140C2×Dic7⋊C4D418yescomplemented
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(C22⋊D7)⋊C4—232no—
150#6442—232no—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#126—71no—
160C22×C4×D4—71no—
161#2467—716no—
162C2×#399—71no—
163C2×#394—71no—
164C2×#394—71no—
165C2×#392—71no—
166C2×#390D711yescharacteristic, complemented
167C2×#388—71no—
168C2×#388—71no—
169C2×#387—71no—
170C2×#387—71no—
171C2×#386—71no—
172C2×#386—71no—
173C2×#380—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×C7—22no—
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#4114yes—
199C23×D7C2412yes—
200C2×C7×D4—28no—
201C2×C7×D4—28no—
202C2×C7×D4—44no—
203C2×C7×D4—416no—
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×C7C2×D414yes—
218C22×C4×C7#4114yes—
219C22×C4×C7C2412yes—
220C22×C4×C7C2412yes—
221C22×C4×C7C2412yes—
222C22×C4×C7C2412yes—
223C22×C4×C7C2412yes—
224C2×C22⋊D7—232no—
225C2×C22⋊D7—28no—
226C2×C22⋊D7—28no—
227C2×C22⋊D7—28no—
228C2×C22⋊D7—28no—
229C2×C22⋊D7—44no—
230C2×C22⋊D7—44no—
231C2×C22⋊D7—416no—
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×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—28no—
251C22×Dic7—28no—
252C22×Dic7—44no—
253C22×Dic7—416no—
254C22×Dic7C2×D414yes—
255C22×Dic7C2×D414yes—
256C22×Dic7#4114yes—
257C22×Dic7C2412yes—
258C22×Dic7C2412yes—
259C22×Dic7C2412yes—
260C22×Dic7C2412yes—
261C22×Dic7C2412yes—
262C22×Dic7C2412yes—
263C22×Dic7C2412yes—
264C2×C4×D7—28no—
265C2×C4×D7—28no—
266C2×C4×D7—44no—
267C2×C4×D7—416no—
268C7×C4⋊C4—28no—
269C7×C22⋊C4—28no—
270C7×C22⋊C4—28no—
271C7×C22⋊C4—44no—
272C7×C22⋊C4—44no—
273C42×C7—44no—
274C22⋊Dic7—28no—
275C22⋊Dic7—28no—
276C22⋊Dic7—28no—
277C22⋊Dic7—28no—
278C22⋊Dic7—44no—
279(C2×D7)⋊C4—28no—
280(C2×D7)⋊C4—28no—
281(C2×D7)⋊C4—28no—
282(C2×D7)⋊C4—44no—
283C4⋊Dic7—28no—
284Dic7⋊C4—28no—
285Dic7⋊C4—44no—
286Dic7⋊C4—44no—
287Dic7⋊C4C2×D4116yescomplemented
288C4×Dic7—28no—
289C4×Dic7—28no—
290C23×D4—71no—
291C23×D4—71no—
292C23×D4C2×D711yescharacteristic
293C24×C4—71no—
294C24×C4—71no—
295C2×#126—78no—
296C2×#126—148no—
297C2×C4×D4—78no—
298C2×C4×D4—148no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C4⋊C4C2×D711yescharacteristic
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⋊C4C2×D711yescharacteristic
315C22×C22⋊C4C2×D711yescharacteristic
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C42—71no—
319C22×C42—71no—
320C22×C42C2×D711yescharacteristic
321#399—78no—
322#394—78no—
323#394—78no—
324#392—78no—
325#390C2×D718yescomplemented
326#388—78no—
327#388—78no—
328#387—78no—
329#387—78no—
330#386—78no—
331#386—78no—
332#380—78no—
333C4×C22⋊C4—78no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95—71no—
342C23×C7—28no—
343C23×C7—28no—
344C23×C7—28no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
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—44no—
359C23×C7—44no—
360C23×C7—44no—
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×D412yes—
370C23×C7C2×#4114yes—
371C23×C7C2×#4112yes—
372C23×C7C2×#4112yes—
373C23×C7C2×#4112yes—
374C23×C7C2×#4112yes—
375C23×C7H(5,𝔽2)12yes—
376C23×C7H(5,𝔽2)12yes—
377C23×C7C2511yescharacteristic
378C22×D7—28no—
379C22×D7—28no—
380C22×D7—28no—
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—22no—
385C22×D7—22no—
386C22×D7—22no—
387C22×D7—44no—
388C22×D7—44no—
389C22×D7—44no—
390C22×D7—44no—
391C22×D7C2×#4114yes—
392C7×D4—416no—
393C2×C4×C7—28no—
394C2×C4×C7—28no—
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—22no—
408C2×C4×C7—44no—
409C2×C4×C7—44no—
410C2×C4×C7—44no—
411C2×C4×C7C22×D414yes—
412C2×C4×C7C2×#4114yes—
413C22⋊D7—232no—
414C22⋊D7—416no—
415C2×Dic7—28no—
416C2×Dic7—28no—
417C2×Dic7—28no—
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—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—416no—
437C2×Dic7—44no—
438C2×Dic7—44no—
439C2×Dic7—44no—
440C2×Dic7—44no—
441C2×Dic7C22×D414yes—
442C2×Dic7C22×D414yes—
443C2×Dic7C2×#4114yes—
444C4×D7—416no—
445C25—71no—
446C25C22×D711yescharacteristic
447C25C22×D711yescharacteristic
448C22×D4—24no—
449C22×D4—24no—
450C22×D4—42no—
451C22×D4—74no—
452C22×D4—74no—
453C22×D4—144no—
454C22×D4—144no—
455C22×D4—144no—
456C22×D4—144no—
457C22×D4—282no—
458C22×D4—282no—
459C22×D4C22×D714yes—
460C23×C4—71no—
461C23×C4—71no—
462C23×C4—71no—
463C23×C4—71no—
464C23×C4—71no—
465C23×C4—71no—
466C23×C4—71no—
467C23×C4—74no—
468C23×C4—74no—
469C23×C4—144no—
470C23×C4—144no—
471C23×C4—144no—
472C23×C4—144no—
473C23×C4—282no—
474C23×C4—282no—
475C23×C4C22×D711yescharacteristic
476C23×C4C22×D711yescharacteristic
477C23×C4C22×D711yescharacteristic
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D711yescharacteristic
480#126—1432no—
481C4×D4—1432no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—78no—
484C2×C4⋊C4—74no—
485C2×C4⋊C4—74no—
486C2×C4⋊C4—74no—
487C2×C4⋊C4—74no—
488C2×C4⋊C4—74no—
489C2×C4⋊C4—144no—
490C2×C4⋊C4—144no—
491C2×C4⋊C4—282no—
492C2×C4⋊C4—282no—
493C2×C4⋊C4C22×D714yes—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—42no—
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—74no—
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—144no—
514C2×C22⋊C4—282no—
515C2×C22⋊C4—282no—
516C2×C22⋊C4C22×D714yes—
517C2×C22⋊C4C22×D714yes—
518C2×C22⋊C4C22×D714yes—
519C2×C22⋊C4C22×D714yes—
520C2×C42—42no—
521C2×C42—74no—
522C2×C42—74no—
523C2×C42—144no—
524C2×C42—144no—
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—
534C22×C7—24no—
535C22×C7—24no—
536C22×C7—24no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—42no—
540C22×C7—42no—
541C22×C7—416no—
542C22×C7—42no—
543C22×C7—42no—
544C22×C7—42no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—88no—
550C22×C7#52514yes—
551C22×C7#52914yes—
552C22×C7#53814yes—
553C22×C7#54614yes—
554C22×C7#55014yes—
555C22×C7#55114yes—
556C22×C7#55314yes—
557C22×C7C23×D411yescharacteristic
558C22×C7C22×#4111yescharacteristic
559C22×C7C22×#4111yescharacteristic
560C22×C7C22×#4111yescharacteristic
561C22×C7C22×#4111yescharacteristic
562C22×C7C2×H(5,𝔽2)11yescharacteristic
563C22×C7C2×H(5,𝔽2)11yescharacteristic
564C2×D7—24no—
565C2×D7—24no—
566C2×D7—24no—
567C2×D7—42no—
568C2×D7—42no—
569C2×D7—42no—
570C2×D7—42no—
571C2×D7—416no—
572C4×C7—24no—
573C4×C7—24no—
574C4×C7—42no—
575C4×C7—42no—
576C4×C7—42no—
577Dic7—24no—
578Dic7—24no—
579Dic7—24no—
580Dic7—42no—
581Dic7—42no—
582Dic7—42no—
583Dic7—42no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—74no—
598C24—72no—
599C24—142no—
600C24—142no—
601C24—142no—
602C24—142no—
603C24—142no—
604C24—142no—
605C24#115714yes—
606C24C23×D712yes—
607C24C23×D712yes—
608C24C23×D711yescharacteristic
609C2×D4—28no—
610C2×D4—28no—
611C2×D4—44no—
612C2×D4—416no—
613C2×D4—148no—
614C2×D4—148no—
615C2×D4—1432no—
616C2×D4—148no—
617C2×D4—148no—
618C2×D4—284no—
619C2×D4—284no—
620C2×D4—2816no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—74no—
635C22×C4—74no—
636C22×C4—74no—
637C22×C4—72no—
638C22×C4—72no—
639C22×C4—72no—
640C22×C4—72no—
641C22×C4—72no—
642C22×C4—72no—
643C22×C4—72no—
644C22×C4—148no—
645C22×C4—148no—
646C22×C4—148no—
647C22×C4—142no—
648C22×C4—142no—
649C22×C4—142no—
650C22×C4—142no—
651C22×C4—142no—
652C22×C4—142no—
653C22×C4—142no—
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—148no—
666C22×C4—284no—
667C22×C4—2816no—
668C22×C4—284no—
669C22×C4—2816no—
670C22×C4D4×D714yes—
671C22×C4#115914yes—
672C22×C4C23×D712yes—
673C22×C4C23×D712yes—
674C22×C4C23×D712yes—
675C22×C4C23×D712yes—
676C22×C4C23×D712yes—
677C4⋊C4—28no—
678C4⋊C4—716no—
679C4⋊C4—148no—
680C4⋊C4—148no—
681C4⋊C4—284no—
682C4⋊C4—284no—
683C22⋊C4—28no—
684C22⋊C4—28no—
685C22⋊C4—44no—
686C22⋊C4—44no—
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—
696C42—44no—
697C42—148no—
698C42—148no—
699C2×C7—44no—
700C2×C7—82no—
701C2×C7#246718yescomplemented
702C2×C7C2×#52511yescharacteristic
703C2×C7C2×#52911yescharacteristic
704C2×C7C2×#53811yescharacteristic
705C2×C7C2×#54611yescharacteristic
706C2×C7C2×#55011yescharacteristic
707C2×C7C2×#55111yescharacteristic
708C2×C7C2×#55311yescharacteristic
709D7—44no—
710C23—28no—
711C23—28no—
712C23—28no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—74no—
738C23—148no—
739C23—148no—
740C23—148no—
741C23—142no—
742C23—142no—
743C23—142no—
744C23—142no—
745C23—142no—
746C23—142no—
747C23—284no—
748C23—284no—
749C23—284no—
750C23—284no—
751C23C2×#115714yes—
752C23C2×#115712yes—
753C23C2×D4×D712yes—
754C23C2×#115912yes—
755C23#654812yes—
756C23#654812yes—
757C23D7×#4112yes—
758C23D7×#4112yes—
759C23C24×D711yescharacteristic
760D4—416no—
761D4—1432no—
762D4—2816no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—74no—
782C2×C4—74no—
783C2×C4—74no—
784C2×C4—148no—
785C2×C4—148no—
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—2816no—
806C2×C4—2816no—
807C2×C4—284no—
808C2×C4—284no—
809C2×C4—284no—
810C2×C4—284no—
811C2×C4C2×D4×D714yes—
812C2×C4C2×#115914yes—
813C7C2×#246711yescharacteristic, complemented, Sylow
814C22—24no—
815C22—24no—
816C22—24no—
817C22—416no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—88no—
830C22—144no—
831C22—144no—
832C22—144no—
833C22—2816no—
834C22—282no—
835C22—282no—
836C22—282no—
837C22—282no—
838C22#9018614yes—
839C22#9023114yes—
840C22#9023814yes—
841C22#9030114yes—
842C22#9030414yes—
843C22#9037114yes—
844C22#9040914yes—
845C22C22×#115711yescharacteristic
846C22C22×D4×D711yescharacteristic
847C22C22×#115911yescharacteristic
848C22C2×#654811yescharacteristic
849C22C2×#654811yescharacteristic
850C22C2×D7×#4111yescharacteristic
851C22C2×D7×#4111yescharacteristic
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—144no—
858C4—144no—
859C4—144no—
860C4—282no—
861C4—282no—
862C4—282no—
863C4—282no—
864C2—44no—
865C2—82no—
866C2—284no—
867C2#1173377318yesdirect product factor
868C2C2×#9018611yescharacteristic
869C2C2×#9023111yescharacteristic
870C2C2×#9023811yescharacteristic
871C2C2×#9030411yescharacteristic
872C2C2×#9030111yescharacteristic
873C2C2×#9037111yescharacteristic
874C2C2×#9040911yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#390C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC2×#390D7
hypocenterC7C2×#2467
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#6442C2semidirect
2. C22×(C22⋊D7)⋊C4C2semidirect
3. C2×C7×#390C2semidirect
5. C2×#89992C2semidirect
6. C2×#89764C2semidirect
7. C2×#89753C2semidirect
8. C2×#89731C2semidirect
9. C2×#89728C2semidirect
10. C2×#89733C2semidirect
11. C2×#89717C2semidirect
12. C2×#89716C2semidirect
13. C2×#89714C2semidirect
14. C2×#89705C2semidirect
15. C2×C4×(C2×D7)⋊C4C2semidirect
16. #11733773C2direct (N × H)
45. C2×(C22⋊D7)⋊C4C22semidirect
47. C2×#6442C22semidirect
48. C7×#390C22semidirect
50. #89992C22semidirect
59. #89764C22semidirect
60. #89753C22semidirect
61. #89733C22semidirect
62. #89731C22semidirect
63. #89728C22semidirect
64. #89717C22semidirect
65. #89716C22semidirect
66. #89714C22semidirect
67. C4×(C2×D7)⋊C4C22semidirect
68. #89705C22semidirect
140. C2×Dic7⋊C4D4semidirect
166. C2×#390D7semidirect
287. Dic7⋊C4C2×D4semidirect
325. #390C2×D7semidirect
701. C2×C7#2467semidirect
813. C7C2×#2467semidirect
867. C2#11733773direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64422
C22×(C22⋊D7)⋊C42
C2×C7×#3902
C2×#899952
C2×#899922
C2×#897642
C2×#897532
C2×#897312
C2×#897282
C2×#897332
C2×#897172
C2×#897162
C2×#897142
C2×#897052
C2×C4×(C2×D7)⋊C42
#117337732
C2×#24677