Finite Group Databasebeta

← C2×#11732915 #13512697

Subgroups — C2×#11732915 #13512697

Order 1792.

2982 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6446C211yesmaximal, characteristic
2C2×C7×#388C211yesmaximal, characteristic, complemented
3C2×#89759C211yesmaximal, characteristic, complemented
4C2×#89744C211yesmaximal, characteristic, complemented
5C2×#89729C211yesmaximal, characteristic
6C2×#89716C211yesmaximal, characteristic, complemented
7C2×#89730C211yesmaximal, characteristic
8C2×#89722C211yesmaximal, characteristic, complemented
9C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
10C2×#89712C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
12#11732915C2116yesmaximal, direct product factor
13C2×#89442C211yesmaximal, characteristic, complemented
14C2×#89427C211yesmaximal, characteristic, complemented
15C2×#89426C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C24×Dic7C2211yescharacteristic
19C23×C4×D7C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C42×C7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×C4⋊Dic7C2211yescharacteristic
33C22×C4⋊Dic7C2211yescharacteristic
34C22×C4⋊Dic7C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×C4×Dic7C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C22×C4×Dic7C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C2×#6446C4116yescomplemented
43C2×#6446C2218yes—
44C7×#388C2218yescomplemented
45C2×C7×#95C2211yescharacteristic
46C2×C7×#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55#89759C2218yescomplemented
56#89744C2218yescomplemented
57#89730C2218yes—
58#89729C2218yes—
59#89722C2218yescomplemented
60#89716C2218yescomplemented
61C22⋊C4×Dic7C2218yescomplemented
62#89712C2218yescomplemented
63C4×C4⋊Dic7C2218yescomplemented
64#89442C2218yescomplemented
65#89438C2218yescomplemented
66#89427C2218yescomplemented
67#89426C2218yescomplemented
68C2×#2335—71nomaximal, Sylow
69C25×C7C2311yescharacteristic
70C24×D7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C22×C22⋊D7—42no—
78C22×C22⋊D7—42no—
79C22×C22⋊D7C2×C418yes—
80C22×C22⋊D7C2314yes—
81C23×Dic7—24no—
82C23×Dic7—42no—
83C23×Dic7—42no—
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2314yes—
92C22×C4×D7—42no—
93C22×C4×D7—42no—
94C22×C4×D7C2×C418yescomplemented
95C22×C4×D7C2314yes—
96C2×C7×C4⋊C4—42no—
97C2×C7×C4⋊C4C2314yes—
98C2×C7×C22⋊C4—24no—
99C2×C7×C22⋊C4—42no—
100C2×C7×C22⋊C4C2×C418yes—
101C2×C7×C22⋊C4C2314yes—
102C2×C7×C22⋊C4C2314yes—
103C2×C7×C22⋊C4C2314yes—
104C2×C42×C7—24no—
105C2×C42×C7C2314yes—
106C2×C22⋊Dic7—42no—
107C2×C22⋊Dic7C2×C418yes—
108C2×C22⋊Dic7C2314yes—
109C2×C22⋊Dic7C2314yes—
110C2×(C2×D7)⋊C4—24no—
111C2×(C2×D7)⋊C4—24no—
112C2×(C2×D7)⋊C4—42no—
113C2×(C2×D7)⋊C4—42no—
114C2×(C2×D7)⋊C4C2×C418yescomplemented
115C2×(C2×D7)⋊C4C2314yes—
116C2×(C2×D7)⋊C4C2314yes—
117C2×(C2×D7)⋊C4C2314yes—
118C2×(C2×D7)⋊C4C2314yes—
119C2×(C2×D7)⋊C4C2314yes—
120C2×C4⋊Dic7—24no—
121C2×C4⋊Dic7—42no—
122C2×C4⋊Dic7C2×C418yescomplemented
123C2×C4⋊Dic7C2314yes—
124C2×C4⋊Dic7C2314yes—
125C2×C4⋊Dic7C2314yes—
126C2×Dic7⋊C4—42no—
127C2×Dic7⋊C4—42no—
128C2×Dic7⋊C4C2×C418yescomplemented
129C2×Dic7⋊C4C2314yes—
130C2×Dic7⋊C4C2314yes—
131C2×Dic7⋊C4C2314yes—
132C2×C4×Dic7—42no—
133C2×C4×Dic7—42no—
134C2×C4×Dic7—42no—
135C2×C4×Dic7—42no—
136C2×C4×Dic7C2314yes—
137C2×C4×Dic7C2314yes—
138C2×C4×Dic7C2314yes—
139C2×C4×Dic7C2314yes—
140#6446C2×C4164yescomplemented
141C7×#95C2314yes—
142C7×#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C22×#123—71no—
152#2335—716no—
153C2×#390—71no—
154C2×#389—71no—
155C2×#388—71no—
156C2×#388—71no—
157C2×#388—71no—
158C2×#388D711yescharacteristic, complemented
159C2×#387—71no—
160C2×#387—71no—
161C2×#386—71no—
162C2×#385—71no—
163C2×#380—71no—
164C2×C4×C4⋊C4—71no—
165C2×C4×C22⋊C4—71no—
166C2×C4×C22⋊C4—71no—
167C24×C7—22no—
168C24×C7—22no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7C22×C414yes—
174C24×C7C2412yes—
175C24×C7C2411yescharacteristic
176C23×D7—22no—
177C23×D7—22no—
178C23×D7—22no—
179C23×D7—22no—
180C23×D7—22no—
181C23×D7—22no—
182C23×D7C22×C414yes—
183C23×D7C2412yes—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7C22×C414yes—
200C22×C4×C7C22×C414yes—
201C22×C4×C7#4114yes—
202C22×C4×C7C2412yes—
203C22×C4×C7C2412yes—
204C22×C4×C7C2412yes—
205C22×C4×C7C2412yes—
206C22×C4×C7C2412yes—
207C22×C4×C7C2412yes—
208C2×C22⋊D7—416no—
209C2×C22⋊D7—44no—
210C2×C22⋊D7—44no—
211C2×C22⋊D7C22×C4116yes—
212C22×Dic7—22no—
213C22×Dic7—22no—
214C22×Dic7—22no—
215C22×Dic7—22no—
216C22×Dic7—22no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7—22no—
222C22×Dic7—22no—
223C22×Dic7—22no—
224C22×Dic7—22no—
225C22×Dic7—22no—
226C22×Dic7—22no—
227C22×Dic7—22no—
228C22×Dic7—22no—
229C22×Dic7—28no—
230C22×Dic7—44no—
231C22×Dic7—44no—
232C22×Dic7—416no—
233C22×Dic7C22×C414yes—
234C22×Dic7C22×C414yes—
235C22×Dic7C22×C414yes—
236C22×Dic7#4114yes—
237C22×Dic7C2412yes—
238C22×Dic7C2412yes—
239C22×Dic7C2412yes—
240C22×Dic7C2412yes—
241C22×Dic7C2412yes—
242C22×Dic7C2412yes—
243C22×Dic7C2412yes—
244C2×C4×D7—416no—
245C2×C4×D7—44no—
246C2×C4×D7—44no—
247C2×C4×D7C22×C4116yescomplemented
248C7×C4⋊C4—44no—
249C7×C22⋊C4—28no—
250C7×C22⋊C4—44no—
251C7×C22⋊C4C22×C4116yes—
252C42×C7—28no—
253C22⋊Dic7—44no—
254C22⋊Dic7C22×C4116yes—
255(C2×D7)⋊C4—28no—
256(C2×D7)⋊C4—28no—
257(C2×D7)⋊C4—44no—
258(C2×D7)⋊C4—44no—
259(C2×D7)⋊C4C22×C4116yescomplemented
260C4⋊Dic7—28no—
261C4⋊Dic7—44no—
262C4⋊Dic7C22×C4116yescomplemented
263Dic7⋊C4—44no—
264Dic7⋊C4—44no—
265Dic7⋊C4C22×C4116yescomplemented
266C4×Dic7—44no—
267C4×Dic7—44no—
268C4×Dic7—44no—
269C4×Dic7—44no—
270C23×D4—71no—
271C24×C4—71no—
272C24×C4—71no—
273C2×#123—716no—
274C2×#123—78no—
275C22×C4⋊C4—71no—
276C22×C4⋊C4—71no—
277C22×C4⋊C4—71no—
278C22×C4⋊C4—71no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4C2×D711yescharacteristic
282C22×C22⋊C4—71no—
283C22×C22⋊C4—71no—
284C22×C22⋊C4—71no—
285C22×C22⋊C4—71no—
286C22×C22⋊C4—71no—
287C22×C22⋊C4—71no—
288C22×C22⋊C4—71no—
289C22×C22⋊C4C2×D711yescharacteristic
290C22×C22⋊C4C2×D711yescharacteristic
291C22×C22⋊C4C2×D711yescharacteristic
292C22×C42—71no—
293C22×C42—71no—
294C22×C42—71no—
295C22×C42—71no—
296C22×C42C2×D711yescharacteristic
297#390—78no—
298#389—78no—
299#388—78no—
300#388—78no—
301#388—78no—
302#388C2×D718yescomplemented
303#387—78no—
304#387—78no—
305#386—78no—
306#385—78no—
307#380—78no—
308C4×C4⋊C4—78no—
309C4×C22⋊C4—78no—
310C4×C22⋊C4—78no—
311C2×#95—71no—
312C2×#95—71no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95C2×D711yescharacteristic
320C2×#95C2×D711yescharacteristic
321C23×C7—28no—
322C23×C7—28no—
323C23×C7—28no—
324C23×C7—22no—
325C23×C7—22no—
326C23×C7—22no—
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—44no—
331C23×C7—44no—
332C23×C7—44no—
333C23×C7—44no—
334C23×C7C23×C414yes—
335C23×C7C23×C412yes—
336C23×C7C2×#4112yes—
337C23×C7C2×#4112yes—
338C23×C7H(5,𝔽2)12yes—
339C23×C7H(5,𝔽2)12yes—
340C23×C7H(5,𝔽2)12yes—
341C23×C72−1+412yes—
342C23×C7C2511yescharacteristic
343C22×D7—28no—
344C22×D7—28no—
345C22×D7—28no—
346C22×D7—22no—
347C22×D7—22no—
348C22×D7—22no—
349C22×D7—22no—
350C22×D7—22no—
351C22×D7—22no—
352C22×D7—44no—
353C22×D7—44no—
354C22×D7—44no—
355C22×D7—44no—
356C22×D7C23×C414yes—
357C2×C4×C7—28no—
358C2×C4×C7—28no—
359C2×C4×C7—28no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—44no—
376C2×C4×C7—44no—
377C2×C4×C7—44no—
378C2×C4×C7C23×C414yes—
379C2×C4×C7C23×C414yes—
380C2×C4×C7C2×#4114yes—
381C22⋊D7—416no—
382C2×Dic7—28no—
383C2×Dic7—28no—
384C2×Dic7—28no—
385C2×Dic7—28no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—416no—
404C2×Dic7—44no—
405C2×Dic7—44no—
406C2×Dic7—44no—
407C2×Dic7C23×C414yes—
408C2×Dic7C23×C414yes—
409C2×Dic7C23×C414yes—
410C2×Dic7C2×#4114yes—
411C4×D7—416no—
412C25—71no—
413C25C22×D711yescharacteristic
414C22×D4—78no—
415C22×D4—74no—
416C22×D4—282no—
417C22×D4—282no—
418C23×C4—71no—
419C23×C4—71no—
420C23×C4—71no—
421C23×C4—71no—
422C23×C4—78no—
423C23×C4—74no—
424C23×C4—71no—
425C23×C4—71no—
426C23×C4—71no—
427C23×C4—74no—
428C23×C4—144no—
429C23×C4—282no—
430C23×C4—282no—
431C23×C4—282no—
432C23×C4—282no—
433C23×C4C22×D711yescharacteristic
434C23×C4C22×D711yescharacteristic
435C23×C4C22×D711yescharacteristic
436C23×C4C22×D711yescharacteristic
437C23×C4C22×D711yescharacteristic
438C23×C4C22×D711yescharacteristic
439#123—764no—
440C2×C4⋊C4—42no—
441C2×C4⋊C4—78no—
442C2×C4⋊C4—78no—
443C2×C4⋊C4—74no—
444C2×C4⋊C4—74no—
445C2×C4⋊C4—74no—
446C2×C4⋊C4—74no—
447C2×C4⋊C4—74no—
448C2×C4⋊C4—74no—
449C2×C4⋊C4—144no—
450C2×C4⋊C4—282no—
451C2×C4⋊C4—282no—
452C2×C4⋊C4—282no—
453C2×C4⋊C4C22×D714yes—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—78no—
457C2×C22⋊C4—74no—
458C2×C22⋊C4—78no—
459C2×C22⋊C4—74no—
460C2×C22⋊C4—74no—
461C2×C22⋊C4—74no—
462C2×C22⋊C4—74no—
463C2×C22⋊C4—74no—
464C2×C22⋊C4—74no—
465C2×C22⋊C4—144no—
466C2×C22⋊C4—144no—
467C2×C22⋊C4—282no—
468C2×C22⋊C4—282no—
469C2×C22⋊C4—282no—
470C2×C22⋊C4C4×D718yes—
471C2×C22⋊C4C22×D714yes—
472C2×C22⋊C4C22×D714yes—
473C2×C22⋊C4C22×D714yes—
474C2×C42—24no—
475C2×C42—74no—
476C2×C42—74no—
477C2×C42—74no—
478C2×C42—74no—
479C2×C42—282no—
480C2×C42—282no—
481C2×C42—282no—
482C2×C42—282no—
483C2×C42C22×D714yes—
484#95—74no—
485#95—74no—
486#95—74no—
487#95—74no—
488#95—74no—
489#95—74no—
490#95—74no—
491#95—74no—
492#95C22×D714yes—
493#95C22×D714yes—
494C22×C7—24no—
495C22×C7—24no—
496C22×C7—24no—
497C22×C7—416no—
498C22×C7—42no—
499C22×C7—42no—
500C22×C7—42no—
501C22×C7—42no—
502C22×C7C4×#4114yes—
503C22×C7#51814yes—
504C22×C7#52014yes—
505C22×C7#53814yes—
506C22×C7#53914yes—
507C22×C7#54014yes—
508C22×C7#54214yes—
509C22×C7C24×C411yescharacteristic
510C22×C7C22×#4111yescharacteristic
511C22×C7C22×#4111yescharacteristic
512C22×C7C2×H(5,𝔽2)11yescharacteristic
513C22×C7C2×H(5,𝔽2)11yescharacteristic
514C22×C7C2×H(5,𝔽2)11yescharacteristic
515C22×C7C2×2−1+411yescharacteristic
516C2×D7—24no—
517C2×D7—24no—
518C2×D7—24no—
519C2×D7—416no—
520C2×D7—42no—
521C2×D7—42no—
522C2×D7—42no—
523C2×D7—42no—
524C4×C7—24no—
525C4×C7—24no—
526C4×C7—24no—
527C4×C7—42no—
528C4×C7—42no—
529C4×C7—42no—
530Dic7—24no—
531Dic7—24no—
532Dic7—24no—
533Dic7—24no—
534Dic7—42no—
535Dic7—42no—
536Dic7—42no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—74no—
544C24—72no—
545C24—142no—
546C24—142no—
547C24—142no—
548C24—142no—
549C24—142no—
550C24—142no—
551C24C2×C4×D714yes—
552C24C23×D712yes—
553C24C23×D711yescharacteristic
554C2×D4—716no—
555C2×D4—2816no—
556C2×D4—284no—
557C2×D4—284no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—74no—
574C22×C4—74no—
575C22×C4—74no—
576C22×C4—74no—
577C22×C4—72no—
578C22×C4—72no—
579C22×C4—72no—
580C22×C4—72no—
581C22×C4—716no—
582C22×C4—72no—
583C22×C4—72no—
584C22×C4—72no—
585C22×C4—148no—
586C22×C4—142no—
587C22×C4—142no—
588C22×C4—142no—
589C22×C4—142no—
590C22×C4—142no—
591C22×C4—142no—
592C22×C4—142no—
593C22×C4—142no—
594C22×C4—142no—
595C22×C4—142no—
596C22×C4—142no—
597C22×C4—142no—
598C22×C4—142no—
599C22×C4—142no—
600C22×C4—142no—
601C22×C4—142no—
602C22×C4—142no—
603C22×C4—2816no—
604C22×C4—284no—
605C22×C4—284no—
606C22×C4—284no—
607C22×C4—284no—
608C22×C4—2816no—
609C22×C4C2×C4×D714yes—
610C22×C4C2×C4×D714yes—
611C22×C4#115914yes—
612C22×C4C23×D712yes—
613C22×C4C23×D712yes—
614C22×C4C23×D712yes—
615C22×C4C23×D712yes—
616C22×C4C23×D712yes—
617C22×C4C23×D712yes—
618C4⋊C4—44no—
619C4⋊C4—716no—
620C4⋊C4—716no—
621C4⋊C4—148no—
622C4⋊C4—284no—
623C4⋊C4—284no—
624C4⋊C4—284no—
625C22⋊C4—28no—
626C22⋊C4—44no—
627C22⋊C4—716no—
628C22⋊C4—716no—
629C22⋊C4—148no—
630C22⋊C4—148no—
631C22⋊C4—284no—
632C22⋊C4—284no—
633C22⋊C4—284no—
634C22⋊C4C2×C4×D7116yes—
635C42—28no—
636C42—284no—
637C42—284no—
638C42—284no—
639C42—284no—
640C2×C7—44no—
641C2×C7#233518yescomplemented
642C2×C7C2×C4×#4111yescharacteristic
643C2×C7C2×#51811yescharacteristic
644C2×C7C2×#52011yescharacteristic
645C2×C7C2×#53811yescharacteristic
646C2×C7C2×#53911yescharacteristic
647C2×C7C2×#54011yescharacteristic
648C2×C7C2×#54211yescharacteristic
649D7—44no—
650C23—28no—
651C23—28no—
652C23—28no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—74no—
664C23—148no—
665C23—148no—
666C23—148no—
667C23—142no—
668C23—142no—
669C23—142no—
670C23—142no—
671C23—142no—
672C23—142no—
673C23—284no—
674C23—284no—
675C23—284no—
676C23—284no—
677C23C22×C4×D714yes—
678C23C22×C4×D712yes—
679C23C2×#115912yes—
680C23#654812yes—
681C23D7×#4112yes—
682C23#655312yes—
683C23#655312yes—
684C23#655412yes—
685C23C24×D711yescharacteristic
686D4—2816no—
687C2×C4—28no—
688C2×C4—28no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—28no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—74no—
709C2×C4—74no—
710C2×C4—74no—
711C2×C4—74no—
712C2×C4—148no—
713C2×C4—148no—
714C2×C4—148no—
715C2×C4—148no—
716C2×C4—142no—
717C2×C4—142no—
718C2×C4—142no—
719C2×C4—142no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—142no—
724C2×C4—142no—
725C2×C4—142no—
726C2×C4—142no—
727C2×C4—142no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—2816no—
734C2×C4—2816no—
735C2×C4—284no—
736C2×C4—284no—
737C2×C4—284no—
738C2×C4C22×C4×D714yes—
739C2×C4C22×C4×D714yes—
740C2×C4C2×#115914yes—
741C7C2×#233511yescharacteristic, complemented, Sylow
742C22—24no—
743C22—24no—
744C22—24no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—416no—
749C22—42no—
750C22—144no—
751C22—144no—
752C22—144no—
753C22—282no—
754C22—282no—
755C22—282no—
756C22—2816no—
757C22—282no—
758C22#9021414yes—
759C22C4×#115914yes—
760C22#9023614yes—
761C22#9031014yes—
762C22#9035614yes—
763C22#9036014yes—
764C22#9039514yes—
765C22C23×C4×D711yescharacteristic
766C22C22×#115911yescharacteristic
767C22C2×#654811yescharacteristic
768C22C2×D7×#4111yescharacteristic
769C22C2×#655311yescharacteristic
770C22C2×#655311yescharacteristic
771C22C2×#655411yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—144no—
779C4—144no—
780C4—144no—
781C4—144no—
782C4—282no—
783C4—282no—
784C4—282no—
785C2—44no—
786C2—284no—
787C2#1173291518yesdirect product factor
788C2C2×#9021411yescharacteristic
789C2C2×C4×#115911yescharacteristic
790C2C2×#9023611yescharacteristic
791C2C2×#9031011yescharacteristic
792C2C2×#9035611yescharacteristic
793C2C2×#9036011yescharacteristic
794C2C2×#9039511yescharacteristic
subgroupG/H
centerC24C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC2×C7×#388C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
cosocleC23×C7C25
hypercenterC2×#388D7
hypocenterC7C2×#2335
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×C7×#388C2semidirect
3. C2×#89759C2semidirect
4. C2×#89744C2semidirect
6. C2×#89716C2semidirect
8. C2×#89722C2semidirect
9. C2×C22⋊C4×Dic7C2semidirect
10. C2×#89712C2semidirect
11. C2×C4×C4⋊Dic7C2semidirect
12. #11732915C2direct (N × H)
13. C2×#89442C2semidirect
14. C2×#89427C2semidirect
15. C2×#89426C2semidirect
16. C2×#89438C2semidirect
42. C2×#6446C4semidirect
44. C7×#388C22semidirect
55. #89759C22semidirect
56. #89744C22semidirect
59. #89722C22semidirect
60. #89716C22semidirect
61. C22⋊C4×Dic7C22semidirect
62. #89712C22semidirect
63. C4×C4⋊Dic7C22semidirect
64. #89442C22semidirect
65. #89438C22semidirect
66. #89427C22semidirect
67. #89426C22semidirect
94. C22×C4×D7C2×C4semidirect
114. C2×(C2×D7)⋊C4C2×C4semidirect
122. C2×C4⋊Dic7C2×C4semidirect
128. C2×Dic7⋊C4C2×C4semidirect
140. #6446C2×C4semidirect
158. C2×#388D7semidirect
247. C2×C4×D7C22×C4semidirect
259. (C2×D7)⋊C4C22×C4semidirect
262. C4⋊Dic7C22×C4semidirect
265. Dic7⋊C4C22×C4semidirect
302. #388C2×D7semidirect
641. C2×C7#2335semidirect
741. C7C2×#2335semidirect
787. C2#11732915direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64462
C2×C7×#3882
C2×#897592
C2×#897442
C2×#897292
C2×#897162
C2×#897302
C2×#897222
C2×C22⋊C4×Dic72
C2×#897122
C2×C4×C4⋊Dic72
#117329152
C2×#894422
C2×#894272
C2×#894262
C2×#894382
C2×#23357