Finite Group Databasebeta

← C2×#11733046 #13523948

Subgroups — C2×#11733046 #13523948

Order 1792.

2834 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×#6453C211yesmaximal, characteristic, complemented
2C22×#6446C211yesmaximal, characteristic
3C2×C7×#388C211yesmaximal, characteristic, complemented
4C2×#89766C211yesmaximal, characteristic, complemented
5C2×#89720C211yesmaximal, characteristic, complemented
6C2×#89733C211yesmaximal, characteristic
7C2×#89729C211yesmaximal, characteristic
8C2×#89717C211yesmaximal, characteristic, complemented
9C2×#89723C211yesmaximal, characteristic, complemented
10C2×#89712C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
12#11733046C2116yesmaximal, direct product factor
13C2×#89440C211yesmaximal, characteristic, complemented
14C2×#89430C211yesmaximal, characteristic, complemented
15C2×#89419C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
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×C4⋊Dic7C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6453—28no—
45C2×#6453C2218yescomplemented
46C2×#6446—28no—
47C2×#6446C2218yes—
48C7×#388C2218yescomplemented
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57#89766C2218yescomplemented
58#89733C2218yes—
59#89729C2218yes—
60#89723C2218yescomplemented
61#89720C2218yescomplemented
62#89717C2218yescomplemented
63#89712C2218yescomplemented
64C4×C4⋊Dic7C2218yescomplemented
65#89440C2218yescomplemented
66#89438C2218yescomplemented
67#89430C2218yescomplemented
68#89419C2218yescomplemented
69C2×#2558—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C22×C22⋊D7—24no—
79C22×C22⋊D7—24no—
80C22×C22⋊D7—42no—
81C22×C22⋊D7C2314yes—
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C22×C4×D7—24no—
90C22×C4×D7—24no—
91C22×C4×D7—42no—
92C22×C4×D7C2314yes—
93C2×C7×C4⋊C4—24no—
94C2×C7×C4⋊C4C2314yes—
95C2×C7×C22⋊C4—24no—
96C2×C7×C22⋊C4—24no—
97C2×C7×C22⋊C4—24no—
98C2×C7×C22⋊C4C2314yes—
99C2×C7×C22⋊C4C2314yes—
100C2×C7×C22⋊C4C2314yes—
101C2×C42×C7—24no—
102C2×C42×C7C2314yes—
103C2×C22⋊Dic7—24no—
104C2×C22⋊Dic7—24no—
105C2×C22⋊Dic7—42no—
106C2×C22⋊Dic7C2314yes—
107C2×C22⋊Dic7C2314yes—
108C2×C22⋊Dic7C2314yes—
109C2×(C2×D7)⋊C4—24no—
110C2×(C2×D7)⋊C4—24no—
111C2×(C2×D7)⋊C4—24no—
112C2×(C2×D7)⋊C4—24no—
113C2×(C2×D7)⋊C4—24no—
114C2×(C2×D7)⋊C4C2314yes—
115C2×(C2×D7)⋊C4C2314yes—
116C2×(C2×D7)⋊C4C2314yes—
117C2×(C2×D7)⋊C4C2314yes—
118C2×(C2×D7)⋊C4C2314yes—
119C2×C4⋊Dic7—24no—
120C2×C4⋊Dic7—24no—
121C2×C4⋊Dic7—24no—
122C2×C4⋊Dic7D418yes—
123C2×C4⋊Dic7C2314yes—
124C2×C4⋊Dic7C2314yes—
125C2×C4⋊Dic7C2314yes—
126C2×C4⋊Dic7C2314yes—
127C2×Dic7⋊C4—24no—
128C2×Dic7⋊C4—24no—
129C2×Dic7⋊C4—24no—
130C2×Dic7⋊C4—24no—
131C2×Dic7⋊C4—42no—
132C2×Dic7⋊C4C2314yes—
133C2×Dic7⋊C4C2314yes—
134C2×Dic7⋊C4C2314yes—
135C2×Dic7⋊C4C2314yes—
136C2×Dic7⋊C4C2314yes—
137C2×C4×Dic7—24no—
138C2×C4×Dic7—42no—
139C2×C4×Dic7—42no—
140C2×C4×Dic7C2314yes—
141C2×C4×Dic7C2314yes—
142C2×C4×Dic7C2314yes—
143#6453—232no—
144#6446—232no—
145C7×#95C2314yes—
146C7×#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×#125—71no—
154C22×#123—71no—
155#2558—716no—
156C2×#400—71no—
157C2×#396—71no—
158C2×#396—71no—
159C2×#394—71no—
160C2×#390—71no—
161C2×#389—71no—
162C2×#388—71no—
163C2×#388—71no—
164C2×#388—71no—
165C2×#388D711yescharacteristic, complemented
166C2×#385—71no—
167C2×C4×C4⋊C4—71no—
168C2×C4×C22⋊C4—71no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7—22no—
174C24×C7—22no—
175C24×C7—22no—
176C24×C7C2412yes—
177C24×C7C2411yescharacteristic
178C23×D7—22no—
179C23×D7—22no—
180C23×D7—22no—
181C23×D7—22no—
182C23×D7—22no—
183C23×D7—22no—
184C23×D7#4114yes—
185C23×D7C2412yes—
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×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7C2×D414yes—
202C22×C4×C7#4114yes—
203C22×C4×C7#4114yes—
204C22×C4×C7C2412yes—
205C22×C4×C7C2412yes—
206C22×C4×C7C2412yes—
207C22×C4×C7C2412yes—
208C22×C4×C7C2412yes—
209C22×C4×C7C2412yes—
210C2×C22⋊D7—28no—
211C2×C22⋊D7—28no—
212C2×C22⋊D7—44no—
213C2×C22⋊D7—416no—
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—22no—
230C22×Dic7—22no—
231C22×Dic7—22no—
232C22×Dic7C2×D414yes—
233C22×Dic7C2×D414yes—
234C22×Dic7#4114yes—
235C22×Dic7C2412yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C22×Dic7C2412yes—
239C22×Dic7C2412yes—
240C22×Dic7C2412yes—
241C22×Dic7C2412yes—
242C2×C4×D7—28no—
243C2×C4×D7—28no—
244C2×C4×D7—44no—
245C2×C4×D7—416no—
246C7×C4⋊C4—28no—
247C7×C22⋊C4—28no—
248C7×C22⋊C4—28no—
249C7×C22⋊C4—28no—
250C42×C7—28no—
251C22⋊Dic7—28no—
252C22⋊Dic7—28no—
253C22⋊Dic7—44no—
254(C2×D7)⋊C4—28no—
255(C2×D7)⋊C4—28no—
256(C2×D7)⋊C4—28no—
257(C2×D7)⋊C4—28no—
258(C2×D7)⋊C4—28no—
259C4⋊Dic7—28no—
260C4⋊Dic7—28no—
261C4⋊Dic7—28no—
262C4⋊Dic7C2×D4116yes—
263Dic7⋊C4—28no—
264Dic7⋊C4—28no—
265Dic7⋊C4—28no—
266Dic7⋊C4—28no—
267Dic7⋊C4—44no—
268C4×Dic7—28no—
269C4×Dic7—44no—
270C4×Dic7—44no—
271C23×D4—71no—
272C24×C4—71no—
273C2×#125—78no—
274C2×#125—148no—
275C2×#123—78no—
276C2×#123—148no—
277C22×C4⋊C4—71no—
278C22×C4⋊C4—71no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4—71no—
282C22×C4⋊C4—71no—
283C22×C4⋊C4—71no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C4⋊C4C2×D711yescharacteristic
287C22×C22⋊C4—71no—
288C22×C22⋊C4—71no—
289C22×C22⋊C4—71no—
290C22×C22⋊C4—71no—
291C22×C22⋊C4—71no—
292C22×C22⋊C4—71no—
293C22×C22⋊C4—71no—
294C22×C22⋊C4—71no—
295C22×C22⋊C4C2×D711yescharacteristic
296C22×C22⋊C4C2×D711yescharacteristic
297C22×C22⋊C4C2×D711yescharacteristic
298C22×C42—71no—
299C22×C42—71no—
300C22×C42—71no—
301C22×C42C2×D711yescharacteristic
302#400—78no—
303#396—78no—
304#396—78no—
305#394—78no—
306#390—78no—
307#389—78no—
308#388—78no—
309#388—78no—
310#388—78no—
311#388C2×D718yescomplemented
312#385—78no—
313C4×C4⋊C4—78no—
314C4×C22⋊C4—78no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95C2×D711yescharacteristic
322C2×#95C2×D711yescharacteristic
323C23×C7—22no—
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×C7—44no—
335C23×C7—44no—
336C23×C7—44no—
337C23×C7C22×D412yes—
338C23×C7C2×#4112yes—
339C23×C7C2×#4112yes—
340C23×C7C2×#4112yes—
341C23×C7C2×#4112yes—
342C23×C7H(5,𝔽2)12yes—
343C23×C72−1+412yes—
344C23×C7C2511yescharacteristic
345C22×D7—28no—
346C22×D7—28no—
347C22×D7—28no—
348C22×D7—22no—
349C22×D7—22no—
350C22×D7—22no—
351C22×D7—22no—
352C22×D7—22no—
353C22×D7—22no—
354C22×D7—44no—
355C22×D7—44no—
356C22×D7—44no—
357C22×D7—44no—
358C22×D7C2×#4114yes—
359C2×C4×C7—28no—
360C2×C4×C7—28no—
361C2×C4×C7—28no—
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—22no—
376C2×C4×C7—22no—
377C2×C4×C7—44no—
378C2×C4×C7—44no—
379C2×C4×C7—44no—
380C2×C4×C7C22×D414yes—
381C2×C4×C7C2×#4114yes—
382C2×C4×C7C2×#4114yes—
383C22⋊D7—416no—
384C2×Dic7—28no—
385C2×Dic7—28no—
386C2×Dic7—28no—
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—22no—
404C2×Dic7—22no—
405C2×Dic7—44no—
406C2×Dic7—44no—
407C2×Dic7—44no—
408C2×Dic7—44no—
409C2×Dic7C22×D414yes—
410C2×Dic7C22×D414yes—
411C2×Dic7C2×#4114yes—
412C4×D7—416no—
413C25—71no—
414C25C22×D711yescharacteristic
415C22×D4—74no—
416C22×D4—144no—
417C22×D4—144no—
418C22×D4—282no—
419C23×C4—71no—
420C23×C4—71no—
421C23×C4—71no—
422C23×C4—71no—
423C23×C4—71no—
424C23×C4—71no—
425C23×C4—71no—
426C23×C4—74no—
427C23×C4—144no—
428C23×C4—144no—
429C23×C4—282no—
430C23×C4C22×D711yescharacteristic
431C23×C4C22×D711yescharacteristic
432C23×C4C22×D711yescharacteristic
433C23×C4C22×D711yescharacteristic
434C23×C4C22×D711yescharacteristic
435C23×C4C22×D711yescharacteristic
436#125—1432no—
437#123—1432no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—78no—
440C2×C4⋊C4—74no—
441C2×C4⋊C4—74no—
442C2×C4⋊C4—74no—
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—144no—
451C2×C4⋊C4—144no—
452C2×C4⋊C4—144no—
453C2×C4⋊C4—144no—
454C2×C4⋊C4—144no—
455C2×C4⋊C4—144no—
456C2×C4⋊C4—282no—
457C2×C4⋊C4C22×D714yes—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—74no—
462C2×C22⋊C4—74no—
463C2×C22⋊C4—74no—
464C2×C22⋊C4—74no—
465C2×C22⋊C4—74no—
466C2×C22⋊C4—74no—
467C2×C22⋊C4—74no—
468C2×C22⋊C4—74no—
469C2×C22⋊C4—144no—
470C2×C22⋊C4—144no—
471C2×C22⋊C4—144no—
472C2×C22⋊C4—144no—
473C2×C22⋊C4—144no—
474C2×C22⋊C4—144no—
475C2×C22⋊C4—144no—
476C2×C22⋊C4—282no—
477C2×C22⋊C4C22×D714yes—
478C2×C22⋊C4C22×D714yes—
479C2×C22⋊C4C22×D714yes—
480C2×C42—24no—
481C2×C42—74no—
482C2×C42—74no—
483C2×C42—74no—
484C2×C42—144no—
485C2×C42—282no—
486C2×C42—282no—
487C2×C42C22×D714yes—
488#95—74no—
489#95—74no—
490#95—74no—
491#95—74no—
492#95—74no—
493#95—74no—
494#95C22×D714yes—
495#95C22×D714yes—
496C22×C7—42no—
497C22×C7—42no—
498C22×C7—42no—
499C22×C7—42no—
500C22×C7—42no—
501C22×C7—42no—
502C22×C7—42no—
503C22×C7—88no—
504C22×C7#52914yes—
505C22×C7#53214yes—
506C22×C7#53914yes—
507C22×C7#54614yes—
508C22×C7#54814yes—
509C22×C7#55214yes—
510C22×C7#55314yes—
511C22×C7C23×D411yescharacteristic
512C22×C7C22×#4111yescharacteristic
513C22×C7C22×#4111yescharacteristic
514C22×C7C22×#4111yescharacteristic
515C22×C7C22×#4111yescharacteristic
516C22×C7C2×H(5,𝔽2)11yescharacteristic
517C22×C7C2×2−1+411yescharacteristic
518C2×D7—24no—
519C2×D7—24no—
520C2×D7—24no—
521C2×D7—42no—
522C2×D7—42no—
523C2×D7—42no—
524C2×D7—42no—
525C2×D7—416no—
526C4×C7—24no—
527C4×C7—24no—
528C4×C7—24no—
529C4×C7—42no—
530C4×C7—42no—
531C4×C7—42no—
532Dic7—24no—
533Dic7—24no—
534Dic7—24no—
535Dic7—42no—
536Dic7—42no—
537Dic7—42no—
538Dic7—42no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—74no—
547C24—72no—
548C24—142no—
549C24—142no—
550C24—142no—
551C24—142no—
552C24—142no—
553C24—142no—
554C24C23×D712yes—
555C24C23×D711yescharacteristic
556C2×D4—148no—
557C2×D4—148no—
558C2×D4—284no—
559C2×D4—2816no—
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—22no—
574C22×C4—22no—
575C22×C4—74no—
576C22×C4—74no—
577C22×C4—74no—
578C22×C4—72no—
579C22×C4—72no—
580C22×C4—72no—
581C22×C4—72no—
582C22×C4—72no—
583C22×C4—72no—
584C22×C4—72no—
585C22×C4—148no—
586C22×C4—148no—
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—142no—
604C22×C4—142no—
605C22×C4—284no—
606C22×C4—2816no—
607C22×C4#115714yes—
608C22×C4D4×D714yes—
609C22×C4#115914yes—
610C22×C4C23×D712yes—
611C22×C4C23×D712yes—
612C22×C4C23×D712yes—
613C22×C4C23×D712yes—
614C22×C4C23×D712yes—
615C22×C4C23×D712yes—
616C4⋊C4—28no—
617C4⋊C4—716no—
618C4⋊C4—148no—
619C4⋊C4—148no—
620C4⋊C4—148no—
621C4⋊C4—148no—
622C4⋊C4—148no—
623C4⋊C4—148no—
624C4⋊C4—148no—
625C4⋊C4—284no—
626C22⋊C4—28no—
627C22⋊C4—28no—
628C22⋊C4—28no—
629C22⋊C4—148no—
630C22⋊C4—148no—
631C22⋊C4—148no—
632C22⋊C4—148no—
633C22⋊C4—148no—
634C22⋊C4—148no—
635C22⋊C4—148no—
636C22⋊C4—284no—
637C42—28no—
638C42—148no—
639C42—284no—
640C42—284no—
641C2×C7—82no—
642C2×C7#255818yescomplemented
643C2×C7C2×#52911yescharacteristic
644C2×C7C2×#53211yescharacteristic
645C2×C7C2×#53911yescharacteristic
646C2×C7C2×#54611yescharacteristic
647C2×C7C2×#54811yescharacteristic
648C2×C7C2×#55211yescharacteristic
649C2×C7C2×#55311yescharacteristic
650D7—44no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—74no—
666C23—148no—
667C23—148no—
668C23—142no—
669C23—142no—
670C23—142no—
671C23—142no—
672C23—142no—
673C23—142no—
674C23—148no—
675C23—284no—
676C23—284no—
677C23—284no—
678C23—284no—
679C23C2×#115712yes—
680C23C2×D4×D712yes—
681C23C2×#115912yes—
682C23D7×#4112yes—
683C23D7×#4112yes—
684C23#655312yes—
685C23#655412yes—
686C23C24×D711yescharacteristic
687D4—2816no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—28no—
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—22no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—74no—
710C2×C4—74no—
711C2×C4—74no—
712C2×C4—148no—
713C2×C4—142no—
714C2×C4—142no—
715C2×C4—142no—
716C2×C4—142no—
717C2×C4—142no—
718C2×C4—142no—
719C2×C4—148no—
720C2×C4—148no—
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—284no—
735C2×C4—284no—
736C2×C4—284no—
737C2×C4—284no—
738C2×C4C2×#115714yes—
739C2×C4C2×D4×D714yes—
740C2×C4C2×#115914yes—
741C7C2×#255811yescharacteristic, complemented, Sylow
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—88no—
750C22—144no—
751C22—144no—
752C22—144no—
753C22—282no—
754C22—2816no—
755C22—282no—
756C22—282no—
757C22—282no—
758C22#9022114yes—
759C22#9024314yes—
760C22#9024814yes—
761C22#9028714yes—
762C22#9035614yes—
763C22#9036714yes—
764C22#9039914yes—
765C22C22×#115711yescharacteristic
766C22C22×D4×D711yescharacteristic
767C22C22×#115911yescharacteristic
768C22C2×D7×#4111yescharacteristic
769C22C2×D7×#4111yescharacteristic
770C22C2×#655311yescharacteristic
771C22C2×#655411yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—144no—
779C4—144no—
780C4—144no—
781C4—282no—
782C4—282no—
783C4—282no—
784C4—282no—
785C2—82no—
786C2—284no—
787C2#1173304618yesdirect product factor
788C2C2×#9022111yescharacteristic
789C2C2×#9024311yescharacteristic
790C2C2×#9024811yescharacteristic
791C2C2×#9028711yescharacteristic
792C2C2×#9035611yescharacteristic
793C2C2×#9036711yescharacteristic
794C2C2×#9039911yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#388C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#388D7
hypocenterC7C2×#2558
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#6453C2semidirect
3. C2×C7×#388C2semidirect
4. C2×#89766C2semidirect
5. C2×#89720C2semidirect
8. C2×#89717C2semidirect
9. C2×#89723C2semidirect
10. C2×#89712C2semidirect
11. C2×C4×C4⋊Dic7C2semidirect
12. #11733046C2direct (N × H)
13. C2×#89440C2semidirect
14. C2×#89430C2semidirect
15. C2×#89419C2semidirect
16. C2×#89438C2semidirect
45. C2×#6453C22semidirect
48. C7×#388C22semidirect
57. #89766C22semidirect
60. #89723C22semidirect
61. #89720C22semidirect
62. #89717C22semidirect
63. #89712C22semidirect
64. C4×C4⋊Dic7C22semidirect
65. #89440C22semidirect
66. #89438C22semidirect
67. #89430C22semidirect
68. #89419C22semidirect
165. C2×#388D7semidirect
311. #388C2×D7semidirect
642. C2×C7#2558semidirect
741. C7C2×#2558semidirect
787. C2#11733046direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64532
C22×#64462
C2×C7×#3882
C2×#897662
C2×#897202
C2×#897332
C2×#897292
C2×#897172
C2×#897232
C2×#897122
C2×C4×C4⋊Dic72
#117330462
C2×#894402
C2×#894302
C2×#894192
C2×#894382
C2×#25587