Finite Group Databasebeta

← C2×#11732220 #13524422

Subgroups — C2×#11732220 #13524422

Order 1792.

3502 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×#6489C211yesmaximal, characteristic, complemented
2C22×(C22⋊D7)⋊C4C211yesmaximal, characteristic, complemented
3C2×C7×#386C211yesmaximal, characteristic, complemented
4C2×#89995C211yesmaximal, characteristic
5C2×#89992C211yesmaximal, characteristic, complemented
6C2×#89985C211yesmaximal, characteristic, complemented
7C2×#89728C211yesmaximal, characteristic, complemented
8C2×#89721C211yesmaximal, characteristic, complemented
9C2×#89733C211yesmaximal, characteristic, complemented
10C2×#89716C211yesmaximal, characteristic, complemented
11C2×#89722C211yesmaximal, characteristic, complemented
12#11732220C2116yesmaximal, direct product factor
13C2×#89440C211yesmaximal, characteristic, complemented
14C2×#89432C211yesmaximal, characteristic, complemented
15C2×#89442C211yesmaximal, characteristic, complemented
16C2×#89423C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C23×C4×D7C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C2×#6489—28no—
36C2×#6489C2218yescomplemented
37C22×C4⋊Dic7C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×(C22⋊D7)⋊C4—28no—
45C2×(C22⋊D7)⋊C4C2218yescomplemented
46C7×#386C2218yescomplemented
47C2×C7×#95C2211yescharacteristic
48C2×C7×#95C2211yescharacteristic
49#89995C2218yes—
50#89992C2218yescomplemented
51#89985C2218yescomplemented
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60#89733C2218yescomplemented
61#89728C2218yescomplemented
62#89722C2218yescomplemented
63#89721C2218yescomplemented
64#89716C2218yescomplemented
65#89442C2218yescomplemented
66#89440C2218yescomplemented
67#89432C2218yescomplemented
68#89423C2218yescomplemented
69C2×#2598—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×C7—24no—
78C23×C4×C7—24no—
79C23×C4×C7—24no—
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2314yes—
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C22×C22⋊D7—24no—
87C22×C22⋊D7—24no—
88C22×C22⋊D7—24no—
89C22×C22⋊D7—24no—
90C22×C22⋊D7—24no—
91C22×C22⋊D7—42no—
92C22×C22⋊D7C2314yes—
93C22×C22⋊D7C2314yes—
94C23×Dic7—24no—
95C23×Dic7—42no—
96C23×Dic7—42no—
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2314yes—
105C22×C4×D7—24no—
106C22×C4×D7—42no—
107C22×C4×D7—42no—
108C22×C4×D7C2314yes—
109C2×C7×C22⋊C4—24no—
110C2×C7×C22⋊C4—24no—
111C2×C7×C22⋊C4—42no—
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⋊Dic7—42no—
119C2×C22⋊Dic7—42no—
120C2×C22⋊Dic7C2314yes—
121C2×C22⋊Dic7C2314yes—
122C2×C22⋊Dic7C2314yes—
123C2×C22⋊Dic7C2314yes—
124C2×C22⋊Dic7C2314yes—
125C2×(C2×D7)⋊C4—24no—
126C2×(C2×D7)⋊C4—24no—
127C2×(C2×D7)⋊C4—24no—
128C2×(C2×D7)⋊C4—42no—
129C2×(C2×D7)⋊C4C2314yes—
130C2×(C2×D7)⋊C4C2314yes—
131C2×(C2×D7)⋊C4C2314yes—
132C2×(C2×D7)⋊C4C2314yes—
133#6489—232no—
134C2×C4⋊Dic7—24no—
135C2×C4⋊Dic7—24no—
136C2×C4⋊Dic7—42no—
137C2×C4⋊Dic7C2314yes—
138C2×C4⋊Dic7C2314yes—
139C2×C4⋊Dic7C2314yes—
140C2×Dic7⋊C4—24no—
141C2×Dic7⋊C4—42no—
142C2×Dic7⋊C4C2314yes—
143C2×Dic7⋊C4C2314yes—
144C2×C4×Dic7—24no—
145C2×C4×Dic7D418yescomplemented
146C2×C4×Dic7C2314yes—
147C2×C4×Dic7C2314yes—
148(C22⋊D7)⋊C4—232no—
149C7×#95C2314yes—
150C7×#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×C4×D4—71no—
160C22×#117—71no—
161#2598—716no—
162C2×#400—71no—
163C2×#399—71no—
164C2×#394—71no—
165C2×#392—71no—
166C2×#388—71no—
167C2×#388—71no—
168C2×#386—71no—
169C2×#386—71no—
170C2×#386—71no—
171C2×#386D711yescharacteristic, complemented
172C2×#385—71no—
173C2×#385—71no—
174C2×#383—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#4114yes—
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—232no—
205C22×C4×C7—22no—
206C22×C4×C7—28no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—28no—
211C22×C4×C7—28no—
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×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7C2×D414yes—
222C22×C4×C7#4114yes—
223C22×C4×C7C2412yes—
224C22×C4×C7C2412yes—
225C22×C4×C7C2412yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2412yes—
228C2×C22⋊D7—232no—
229C2×C22⋊D7—28no—
230C2×C22⋊D7—28no—
231C2×C22⋊D7—28no—
232C2×C22⋊D7—28no—
233C2×C22⋊D7—28no—
234C2×C22⋊D7—44no—
235C2×C22⋊D7—416no—
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—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—28no—
256C22×Dic7—44no—
257C22×Dic7—44no—
258C22×Dic7—416no—
259C22×Dic7C2×D414yes—
260C22×Dic7C2×D414yes—
261C22×Dic7C2412yes—
262C22×Dic7C2412yes—
263C22×Dic7C2412yes—
264C22×Dic7C2412yes—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C2×C4×D7—28no—
269C2×C4×D7—44no—
270C2×C4×D7—44no—
271C2×C4×D7—416no—
272C7×C22⋊C4—28no—
273C7×C22⋊C4—28no—
274C7×C22⋊C4—44no—
275C22⋊Dic7—28no—
276C22⋊Dic7—28no—
277C22⋊Dic7—28no—
278C22⋊Dic7—44no—
279C22⋊Dic7—44no—
280(C2×D7)⋊C4—28no—
281(C2×D7)⋊C4—28no—
282(C2×D7)⋊C4—28no—
283(C2×D7)⋊C4—44no—
284C4⋊Dic7—28no—
285C4⋊Dic7—28no—
286C4⋊Dic7—44no—
287Dic7⋊C4—28no—
288Dic7⋊C4—44no—
289C4×Dic7—28no—
290C4×Dic7C2×D4116yescomplemented
291C23×D4—71no—
292C23×D4—71no—
293C23×D4C2×D711yescharacteristic
294C24×C4—71no—
295C24×C4—71no—
296C24×C4C2×D711yescharacteristic
297C2×C4×D4—78no—
298C2×C4×D4—148no—
299C2×#117—78no—
300C2×#117—148no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C4⋊C4—71no—
305C22×C4⋊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×C22⋊C4C2×D711yescharacteristic
318C22×C42—71no—
319C22×C42—71no—
320#400—78no—
321#399—78no—
322#394—78no—
323#392—78no—
324#388—78no—
325#388—78no—
326#386—78no—
327#386—78no—
328#386—78no—
329#386C2×D718yescomplemented
330#385—78no—
331#385—78no—
332#383—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×#95C2×D711yescharacteristic
342C2×#95C2×D711yescharacteristic
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×D412yes—
370C23×C7C2×#4114yes—
371C23×C7C2×#4112yes—
372C23×C7C2×#4114yes—
373C23×C7C2×#4112yes—
374C23×C7C2×#4112yes—
375C23×C7C2×#4112yes—
376C23×C7H(5,𝔽2)12yes—
377C23×C7H(5,𝔽2)12yes—
378C23×C7C2511yescharacteristic
379C22×D7—28no—
380C22×D7—28no—
381C22×D7—28no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—22no—
385C22×D7—22no—
386C22×D7—22no—
387C22×D7—22no—
388C22×D7—44no—
389C22×D7—44no—
390C22×D7—44no—
391C22×D7—44no—
392C22×D7C2×#4114yes—
393C7×D4—416no—
394C2×C4×C7—232no—
395C2×C4×C7—28no—
396C2×C4×C7—28no—
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—22no—
409C2×C4×C7—22no—
410C2×C4×C7—44no—
411C2×C4×C7—44no—
412C2×C4×C7—44no—
413C2×C4×C7C22×D414yes—
414C2×C4×C7C2×#4114yes—
415C22⋊D7—232no—
416C22⋊D7—416no—
417C2×Dic7—28no—
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—416no—
439C2×Dic7—44no—
440C2×Dic7—44no—
441C2×Dic7—44no—
442C2×Dic7—44no—
443C2×Dic7—44no—
444C2×Dic7C22×D414yes—
445C2×Dic7C22×D414yes—
446C4×D7—416no—
447C25—71no—
448C25C22×D711yescharacteristic
449C25C22×D711yescharacteristic
450C22×D4—24no—
451C22×D4—24no—
452C22×D4—42no—
453C22×D4—74no—
454C22×D4—74no—
455C22×D4—144no—
456C22×D4—144no—
457C22×D4—144no—
458C22×D4—144no—
459C22×D4—144no—
460C22×D4—282no—
461C22×D4C22×D714yes—
462C23×C4—24no—
463C23×C4—24no—
464C23×C4—24no—
465C23×C4—71no—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—71no—
470C23×C4—71no—
471C23×C4—71no—
472C23×C4—74no—
473C23×C4—74no—
474C23×C4—144no—
475C23×C4—144no—
476C23×C4—282no—
477C23×C4—282no—
478C23×C4—282no—
479C23×C4—282no—
480C23×C4C22×D714yes—
481C23×C4C22×D711yescharacteristic
482C23×C4C22×D711yescharacteristic
483C23×C4C22×D711yescharacteristic
484C23×C4C22×D711yescharacteristic
485C23×C4C22×D711yescharacteristic
486C4×D4—1432no—
487#117—1432no—
488C2×C4⋊C4—74no—
489C2×C4⋊C4—74no—
490C2×C4⋊C4—74no—
491C2×C4⋊C4—74no—
492C2×C4⋊C4—74no—
493C2×C4⋊C4—144no—
494C2×C4⋊C4—144no—
495C2×C4⋊C4—144no—
496C2×C4⋊C4—282no—
497C2×C4⋊C4—282no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—42no—
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—74no—
508C2×C22⋊C4—74no—
509C2×C22⋊C4—74no—
510C2×C22⋊C4—144no—
511C2×C22⋊C4—144no—
512C2×C22⋊C4—144no—
513C2×C22⋊C4—144no—
514C2×C22⋊C4—144no—
515C2×C22⋊C4—144no—
516C2×C22⋊C4—282no—
517C2×C22⋊C4—282no—
518C2×C22⋊C4—282no—
519C2×C22⋊C4C22×D714yes—
520C2×C22⋊C4C22×D714yes—
521C2×C22⋊C4C22×D714yes—
522C2×C42—78no—
523C2×C42—74no—
524C2×C42—74no—
525C2×C42—144no—
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#95C22×D714yes—
535#95C22×D714yes—
536C22×C7—24no—
537C22×C7—24no—
538C22×C7—24no—
539C22×C7—24no—
540C22×C7—24no—
541C22×C7—24no—
542C22×C7—416no—
543C22×C7—416no—
544C22×C7—42no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7—42no—
552C22×C7#52514yes—
553C22×C7#52514yes—
554C22×C7#53514yes—
555C22×C7#55114yes—
556C22×C7#55114yes—
557C22×C7#55314yes—
558C22×C7#55314yes—
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—24no—
567C2×D7—24no—
568C2×D7—24no—
569C2×D7—416no—
570C2×D7—42no—
571C2×D7—42no—
572C2×D7—42no—
573C2×D7—42no—
574C4×C7—24no—
575C4×C7—24no—
576C4×C7—42no—
577C4×C7—42no—
578C4×C7—42no—
579Dic7—24no—
580Dic7—24no—
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—74no—
599C24—72no—
600C24—142no—
601C24—142no—
602C24—142no—
603C24—142no—
604C24—142no—
605C24—142no—
606C24#115714yes—
607C24#115914yes—
608C24C23×D712yes—
609C24C23×D712yes—
610C24C23×D711yescharacteristic
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—44no—
614C2×D4—416no—
615C2×D4—148no—
616C2×D4—148no—
617C2×D4—1432no—
618C2×D4—148no—
619C2×D4—148no—
620C2×D4—148no—
621C2×D4—284no—
622C2×D4—2816no—
623C22×C4—232no—
624C22×C4—22no—
625C22×C4—28no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—28no—
630C22×C4—28no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—74no—
641C22×C4—74no—
642C22×C4—72no—
643C22×C4—72no—
644C22×C4—72no—
645C22×C4—72no—
646C22×C4—72no—
647C22×C4—72no—
648C22×C4—72no—
649C22×C4—148no—
650C22×C4—148no—
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—142no—
666C22×C4—142no—
667C22×C4—142no—
668C22×C4—142no—
669C22×C4—142no—
670C22×C4—284no—
671C22×C4—284no—
672C22×C4—2816no—
673C22×C4—284no—
674C22×C4—284no—
675C22×C4—2816no—
676C22×C4D4×D714yes—
677C22×C4#115914yes—
678C22×C4C23×D712yes—
679C22×C4C23×D712yes—
680C22×C4C23×D712yes—
681C22×C4C23×D712yes—
682C22×C4C23×D712yes—
683C4⋊C4—148no—
684C4⋊C4—148no—
685C4⋊C4—148no—
686C4⋊C4—284no—
687C4⋊C4—284no—
688C22⋊C4—28no—
689C22⋊C4—28no—
690C22⋊C4—44no—
691C22⋊C4—148no—
692C22⋊C4—148no—
693C22⋊C4—148no—
694C22⋊C4—148no—
695C22⋊C4—148no—
696C22⋊C4—148no—
697C22⋊C4—284no—
698C22⋊C4—284no—
699C22⋊C4—284no—
700C42—716no—
701C42—148no—
702C2×C7—44no—
703C2×C7—44no—
704C2×C7#259818yescomplemented
705C2×C7C2×#52511yescharacteristic
706C2×C7C2×#52511yescharacteristic
707C2×C7C2×#53511yescharacteristic
708C2×C7C2×#55111yescharacteristic
709C2×C7C2×#55111yescharacteristic
710C2×C7C2×#55311yescharacteristic
711C2×C7C2×#55311yescharacteristic
712D7—44no—
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—74no—
740C23—148no—
741C23—148no—
742C23—148no—
743C23—142no—
744C23—142no—
745C23—142no—
746C23—142no—
747C23—142no—
748C23—142no—
749C23—284no—
750C23—284no—
751C23—284no—
752C23—284no—
753C23C2×#115714yes—
754C23C2×#115712yes—
755C23C2×D4×D712yes—
756C23C2×#115914yes—
757C23C2×#115912yes—
758C23C2×#115912yes—
759C23#654812yes—
760C23D7×#4112yes—
761C23#655312yes—
762C23C24×D711yescharacteristic
763D4—416no—
764D4—1432no—
765D4—2816no—
766C2×C4—232no—
767C2×C4—28no—
768C2×C4—28no—
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—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—74no—
786C2×C4—74no—
787C2×C4—148no—
788C2×C4—148no—
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—142no—
808C2×C4—2816no—
809C2×C4—2816no—
810C2×C4—284no—
811C2×C4—284no—
812C2×C4—284no—
813C2×C4—284no—
814C2×C4—284no—
815C2×C4C2×D4×D714yes—
816C2×C4C2×#115914yes—
817C7C2×#259811yescharacteristic, 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—144no—
835C22—144no—
836C22—144no—
837C22—282no—
838C22—282no—
839C22—282no—
840C22—282no—
841C22—2816no—
842C22#9018614yes—
843C22#9023814yes—
844C22#9025614yes—
845C22#9027714yes—
846C22#9029814yes—
847C22#9030514yes—
848C22#9034914yes—
849C22C22×#115711yescharacteristic
850C22C22×D4×D711yescharacteristic
851C22C22×#115911yescharacteristic
852C22C22×#115911yescharacteristic
853C22C2×#654811yescharacteristic
854C22C2×D7×#4111yescharacteristic
855C22C2×#655311yescharacteristic
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—144no—
862C4—144no—
863C4—282no—
864C4—282no—
865C4—282no—
866C4—282no—
867C4—282no—
868C2—44no—
869C2—44no—
870C2—284no—
871C2#1173222018yesdirect product factor
872C2C2×#9018611yescharacteristic
873C2C2×#9025611yescharacteristic
874C2C2×#9023811yescharacteristic
875C2C2×#9027711yescharacteristic
876C2C2×#9029811yescharacteristic
877C2C2×#9030511yescharacteristic
878C2C2×#9034911yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#386C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC2×#386D7
hypocenterC7C2×#2598
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#6489C2semidirect
2. C22×(C22⋊D7)⋊C4C2semidirect
3. C2×C7×#386C2semidirect
5. C2×#89992C2semidirect
6. C2×#89985C2semidirect
7. C2×#89728C2semidirect
8. C2×#89721C2semidirect
9. C2×#89733C2semidirect
10. C2×#89716C2semidirect
11. C2×#89722C2semidirect
12. #11732220C2direct (N × H)
13. C2×#89440C2semidirect
14. C2×#89432C2semidirect
15. C2×#89442C2semidirect
16. C2×#89423C2semidirect
36. C2×#6489C22semidirect
45. C2×(C22⋊D7)⋊C4C22semidirect
46. C7×#386C22semidirect
50. #89992C22semidirect
51. #89985C22semidirect
60. #89733C22semidirect
61. #89728C22semidirect
62. #89722C22semidirect
63. #89721C22semidirect
64. #89716C22semidirect
65. #89442C22semidirect
66. #89440C22semidirect
67. #89432C22semidirect
68. #89423C22semidirect
145. C2×C4×Dic7D4semidirect
171. C2×#386D7semidirect
290. C4×Dic7C2×D4semidirect
329. #386C2×D7semidirect
704. C2×C7#2598semidirect
817. C7C2×#2598semidirect
871. C2#11732220direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64892
C22×(C22⋊D7)⋊C42
C2×C7×#3862
C2×#899952
C2×#899922
C2×#899852
C2×#897282
C2×#897212
C2×#897332
C2×#897162
C2×#897222
#117322202
C2×#894402
C2×#894322
C2×#894422
C2×#894232
C2×#25987