Finite Group Databasebeta

← C2×#11740555 #13523959

Subgroups — C2×#11740555 #13523959

Order 1792.

2898 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#126C211yesmaximal, characteristic, complemented
2C22×#6459C211yesmaximal, characteristic, complemented
3#11740555C2116yesmaximal, direct product factor
4C2×#89765C211yesmaximal, characteristic, complemented
5C2×#89756C211yesmaximal, characteristic, complemented
6C2×#89746C211yesmaximal, characteristic, complemented
7C2×#89762C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
9C2×#89728C211yesmaximal, characteristic
10C2×#89733C211yesmaximal, characteristic
11C2×#89719C211yesmaximal, characteristic, complemented
12C2×#89729C211yesmaximal, characteristic
13C2×#89717C211yesmaximal, characteristic, complemented
14C2×#89717C211yesmaximal, characteristic, complemented
15C2×#89705C211yesmaximal, characteristic, complemented
16C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C23×Dic14C2211yescharacteristic
20C2×C7×#126—28no—
21C2×C7×#126C2218yescomplemented
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C42×C7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
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×C4×Dic7C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6459—28no—
45C2×#6459C2218yescomplemented
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
55C2×C7⋊#95C2211yescharacteristic
56#89765C2218yescomplemented
57#89762C2218yescomplemented
58#89756C2218yescomplemented
59C4⋊C4×Dic7C2218yescomplemented
60#89746C2218yescomplemented
61#89733C2218yes—
62#89729C2218yes—
63#89728C2218yes—
64#89719C2218yescomplemented
65#89717C2218yescomplemented
66#89717C2218yescomplemented
67C4×(C2×D7)⋊C4C2218yescomplemented
68#89705C2218yescomplemented
69C2×#2560—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—
93C22×Dic14—24no—
94C22×Dic14—24no—
95C22×Dic14—42no—
96C22×Dic14C2314yes—
97C7×#126—232no—
98C2×C7×C4⋊C4—24no—
99C2×C7×C4⋊C4—24no—
100C2×C7×C4⋊C4D418yescomplemented
101C2×C7×C4⋊C4C2314yes—
102C2×C7×C4⋊C4C2314yes—
103C2×C7×C4⋊C4C2314yes—
104C2×C7×C22⋊C4—24no—
105C2×C7×C22⋊C4—24no—
106C2×C7×C22⋊C4—24no—
107C2×C7×C22⋊C4C2314yes—
108C2×C7×C22⋊C4C2314yes—
109C2×C7×C22⋊C4C2314yes—
110C2×C42×C7—24no—
111C2×C42×C7C2314yes—
112C2×C22⋊Dic7—24no—
113C2×C22⋊Dic7—24no—
114C2×C22⋊Dic7—42no—
115C2×C22⋊Dic7C2314yes—
116C2×C22⋊Dic7C2314yes—
117C2×C22⋊Dic7C2314yes—
118C2×(C2×D7)⋊C4—24no—
119C2×(C2×D7)⋊C4—24no—
120C2×(C2×D7)⋊C4—24no—
121C2×(C2×D7)⋊C4—24no—
122C2×(C2×D7)⋊C4—24no—
123C2×(C2×D7)⋊C4C2314yes—
124C2×(C2×D7)⋊C4C2314yes—
125C2×(C2×D7)⋊C4C2314yes—
126C2×(C2×D7)⋊C4C2314yes—
127C2×(C2×D7)⋊C4C2314yes—
128C2×C4⋊Dic7—24no—
129C2×C4⋊Dic7C2314yes—
130C2×Dic7⋊C4—24no—
131C2×Dic7⋊C4—24no—
132C2×Dic7⋊C4—24no—
133C2×Dic7⋊C4C2314yes—
134C2×Dic7⋊C4C2314yes—
135C2×Dic7⋊C4C2314yes—
136C2×C4×Dic7—24no—
137C2×C4×Dic7—42no—
138C2×C4×Dic7—42no—
139C2×C4×Dic7C2314yes—
140C2×C4×Dic7C2314yes—
141C2×C4×Dic7C2314yes—
142#6459—232no—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×#126D711yescharacteristic, complemented
154C22×C22⋊Q8—71no—
155#2560—716no—
156C2×#398—71no—
157C2×#397—71no—
158C2×#394—71no—
159C2×#393—71no—
160C2×#391—71no—
161C2×#390—71no—
162C2×#388—71no—
163C2×#388—71no—
164C2×#388—71no—
165C2×#387—71no—
166C2×#386—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×C7C2×D414yes—
203C22×C4×C7C2×D414yes—
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×Dic7#4114yes—
233C22×Dic7#4114yes—
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—
246C2×Dic14—28no—
247C2×Dic14—28no—
248C2×Dic14—44no—
249C2×Dic14—416no—
250C7×C4⋊C4—28no—
251C7×C4⋊C4—28no—
252C7×C4⋊C4C2×D4116yescomplemented
253C7×C22⋊C4—28no—
254C7×C22⋊C4—28no—
255C7×C22⋊C4—28no—
256C42×C7—28no—
257C22⋊Dic7—28no—
258C22⋊Dic7—28no—
259C22⋊Dic7—44no—
260(C2×D7)⋊C4—28no—
261(C2×D7)⋊C4—28no—
262(C2×D7)⋊C4—28no—
263(C2×D7)⋊C4—28no—
264(C2×D7)⋊C4—28no—
265C4⋊Dic7—28no—
266Dic7⋊C4—28no—
267Dic7⋊C4—28no—
268Dic7⋊C4—28no—
269C4×Dic7—28no—
270C4×Dic7—44no—
271C4×Dic7—44no—
272C23×Q8—71no—
273C23×D4—71no—
274C24×C4—71no—
275C2×#126—28no—
276C2×#126C2×D718yescomplemented
277C2×C22⋊Q8—78no—
278C2×C22⋊Q8—148no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4—71no—
282C22×C4⋊C4—71no—
283C22×C4⋊C4C2×D711yescharacteristic
284C22×C4⋊C4C2×D711yescharacteristic
285C22×C4⋊C4C2×D711yescharacteristic
286C22×C22⋊C4—71no—
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⋊C4C2×D711yescharacteristic
295C22×C22⋊C4C2×D711yescharacteristic
296C22×C22⋊C4C2×D711yescharacteristic
297C22×C42—71no—
298C22×C42—71no—
299C22×C42—71no—
300C22×C42C2×D711yescharacteristic
301#398—78no—
302#397—78no—
303#394—78no—
304#393—78no—
305#391—78no—
306#390—78no—
307#388—78no—
308#388—78no—
309#388—78no—
310#387—78no—
311#386—78no—
312C4×C4⋊C4—78no—
313C4×C22⋊C4—78no—
314C2×#95—71no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C23×C7—22no—
325C23×C7—22no—
326C23×C7—22no—
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
331C23×C7—44no—
332C23×C7—44no—
333C23×C7—44no—
334C23×C7—44no—
335C23×C7—44no—
336C23×C7—44no—
337C23×C7—44no—
338C23×C7C22×D412yes—
339C23×C7C2×#4112yes—
340C23×C7C2×#4112yes—
341C23×C7C2×#4112yes—
342C23×C7C2×#4112yes—
343C23×C7H(5,𝔽2)12yes—
344C23×C72−1+412yes—
345C23×C7C2511yescharacteristic
346C22×D7—28no—
347C22×D7—28no—
348C22×D7—28no—
349C22×D7—22no—
350C22×D7—22no—
351C22×D7—22no—
352C22×D7—22no—
353C22×D7—22no—
354C22×D7—22no—
355C22×D7—44no—
356C22×D7—44no—
357C22×D7—44no—
358C22×D7—44no—
359C22×D7C2×#4114yes—
360C2×C4×C7—28no—
361C2×C4×C7—28no—
362C2×C4×C7—28no—
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—22no—
378C2×C4×C7—44no—
379C2×C4×C7—44no—
380C2×C4×C7—44no—
381C2×C4×C7C22×D414yes—
382C2×C4×C7C22×D414yes—
383C2×C4×C7C22×D414yes—
384C22⋊D7—416no—
385C2×Dic7—28no—
386C2×Dic7—28no—
387C2×Dic7—28no—
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—22no—
406C2×Dic7—44no—
407C2×Dic7—44no—
408C2×Dic7—44no—
409C2×Dic7—44no—
410C2×Dic7C2×#4114yes—
411C2×Dic7C2×#4114yes—
412C2×Dic7C2×#4114yes—
413C4×D7—416no—
414Dic14—416no—
415C25—71no—
416C25C22×D711yescharacteristic
417C22×Q8—74no—
418C22×Q8—144no—
419C22×Q8—144no—
420C22×Q8—282no—
421C22×D4—74no—
422C22×D4—144no—
423C22×D4—144no—
424C22×D4—282no—
425C23×C4—71no—
426C23×C4—71no—
427C23×C4—71no—
428C23×C4—71no—
429C23×C4—71no—
430C23×C4—71no—
431C23×C4—71no—
432C23×C4—74no—
433C23×C4—144no—
434C23×C4—144no—
435C23×C4—282no—
436C23×C4C22×D711yescharacteristic
437C23×C4C22×D711yescharacteristic
438C23×C4C22×D711yescharacteristic
439C23×C4C22×D711yescharacteristic
440C23×C4C22×D711yescharacteristic
441C23×C4C22×D711yescharacteristic
442#126—232no—
443C22⋊Q8—1432no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—74no—
447C2×C4⋊C4—74no—
448C2×C4⋊C4—74no—
449C2×C4⋊C4—74no—
450C2×C4⋊C4—144no—
451C2×C4⋊C4—144no—
452C2×C4⋊C4—144no—
453C2×C4⋊C4—144no—
454C2×C4⋊C4C22⋊D718yescomplemented
455C2×C4⋊C4C22×D714yes—
456C2×C4⋊C4C22×D714yes—
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#95—74no—
495#95—74no—
496#95—74no—
497#95—74no—
498C22×C7—42no—
499C22×C7—42no—
500C22×C7—42no—
501C22×C7—42no—
502C22×C7—42no—
503C22×C7—42no—
504C22×C7—42no—
505C22×C7—88no—
506C22×C7#52914yes—
507C22×C7#53214yes—
508C22×C7#53914yes—
509C22×C7#54614yes—
510C22×C7#54814yes—
511C22×C7#55114yes—
512C22×C7#55614yes—
513C22×C7C23×D411yescharacteristic
514C22×C7C22×#4111yescharacteristic
515C22×C7C22×#4111yescharacteristic
516C22×C7C22×#4111yescharacteristic
517C22×C7C22×#4111yescharacteristic
518C22×C7C2×H(5,𝔽2)11yescharacteristic
519C22×C7C2×2−1+411yescharacteristic
520C2×D7—24no—
521C2×D7—24no—
522C2×D7—24no—
523C2×D7—416no—
524C2×D7—42no—
525C2×D7—42no—
526C2×D7—42no—
527C2×D7—42no—
528C4×C7—24no—
529C4×C7—24no—
530C4×C7—24no—
531C4×C7—42no—
532C4×C7—42no—
533C4×C7—42no—
534Dic7—24no—
535Dic7—24no—
536Dic7—24no—
537Dic7—42no—
538Dic7—42no—
539Dic7—42no—
540Dic7—42no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—74no—
549C24—72no—
550C24—142no—
551C24—142no—
552C24—142no—
553C24—142no—
554C24—142no—
555C24—142no—
556C24C23×D712yes—
557C24C23×D711yescharacteristic
558C2×Q8—148no—
559C2×Q8—148no—
560C2×Q8—284no—
561C2×Q8—2816no—
562C2×D4—148no—
563C2×D4—148no—
564C2×D4—284no—
565C2×D4—2816no—
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—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—74no—
582C22×C4—74no—
583C22×C4—74no—
584C22×C4—72no—
585C22×C4—72no—
586C22×C4—72no—
587C22×C4—72no—
588C22×C4—72no—
589C22×C4—72no—
590C22×C4—72no—
591C22×C4—148no—
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—142no—
606C22×C4—142no—
607C22×C4—142no—
608C22×C4—142no—
609C22×C4—142no—
610C22×C4—148no—
611C22×C4—284no—
612C22×C4—2816no—
613C22×C4C2×C22⋊D714yes—
614C22×C4C2×C22⋊D714yes—
615C22×C4C2×C22⋊D714yes—
616C22×C4C23×D712yes—
617C22×C4C23×D712yes—
618C22×C4C23×D712yes—
619C22×C4C23×D712yes—
620C22×C4C23×D712yes—
621C22×C4C23×D712yes—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—148no—
625C4⋊C4—148no—
626C4⋊C4—148no—
627C4⋊C4—148no—
628C4⋊C4C2×C22⋊D7116yescomplemented
629C22⋊C4—28no—
630C22⋊C4—28no—
631C22⋊C4—28no—
632C22⋊C4—148no—
633C22⋊C4—148no—
634C22⋊C4—148no—
635C22⋊C4—148no—
636C22⋊C4—148no—
637C22⋊C4—148no—
638C22⋊C4—148no—
639C22⋊C4—284no—
640C42—28no—
641C42—148no—
642C42—284no—
643C42—284no—
644C2×C7—82no—
645C2×C7#256018yescomplemented
646C2×C7C2×#52911yescharacteristic
647C2×C7C2×#53211yescharacteristic
648C2×C7C2×#53911yescharacteristic
649C2×C7C2×#54611yescharacteristic
650C2×C7C2×#54811yescharacteristic
651C2×C7C2×#55111yescharacteristic
652C2×C7C2×#55611yescharacteristic
653D7—44no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—74no—
669C23—148no—
670C23—148no—
671C23—148no—
672C23—142no—
673C23—142no—
674C23—142no—
675C23—142no—
676C23—142no—
677C23—142no—
678C23—284no—
679C23—284no—
680C23—284no—
681C23—284no—
682C23D7×#4112yes—
683C23D7×#4112yes—
684C23D7×#4112yes—
685C23D7×#4112yes—
686C23#655312yes—
687C23#655412yes—
688C23C22×C22⋊D712yes—
689C23C24×D711yescharacteristic
690Q8—2816no—
691D4—2816no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—28no—
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—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—74no—
714C2×C4—74no—
715C2×C4—74no—
716C2×C4—148no—
717C2×C4—148no—
718C2×C4—148no—
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—142no—
734C2×C4—142no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—2816no—
738C2×C4—284no—
739C2×C4—284no—
740C2×C4—284no—
741C2×C4—284no—
742C2×C4C22×C22⋊D714yes—
743C2×C4C22×C22⋊D714yes—
744C2×C4C22×C22⋊D714yes—
745C7C2×#256011yescharacteristic, complemented, Sylow
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—88no—
754C22—144no—
755C22—144no—
756C22—144no—
757C22—282no—
758C22—282no—
759C22—2816no—
760C22—282no—
761C22—282no—
762C22#9039314yes—
763C22#9039614yes—
764C22#9039714yes—
765C22#9039814yes—
766C22#9052014yes—
767C22#9052214yes—
768C22#9052314yes—
769C22C2×D7×#4111yescharacteristic
770C22C2×D7×#4111yescharacteristic
771C22C2×D7×#4111yescharacteristic
772C22C2×D7×#4111yescharacteristic
773C22C2×#655311yescharacteristic
774C22C2×#655411yescharacteristic
775C22C23×C22⋊D711yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—144no—
783C4—144no—
784C4—144no—
785C4—282no—
786C4—282no—
787C4—282no—
788C4—282no—
789C2—82no—
790C2—284no—
791C2#1174055518yesdirect product factor
792C2C2×#9039711yescharacteristic
793C2C2×#9039311yescharacteristic
794C2C2×#9039811yescharacteristic
795C2C2×#9039611yescharacteristic
796C2C2×#9052311yescharacteristic
797C2C2×#9052011yescharacteristic
798C2C2×#9052211yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C7×#126C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC22×#126D7
hypocenterC7C2×#2560
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. C22×C7×#126C2semidirect
2. C22×#6459C2semidirect
3. #11740555C2direct (N × H)
4. C2×#89765C2semidirect
5. C2×#89756C2semidirect
6. C2×#89746C2semidirect
7. C2×#89762C2semidirect
8. C2×C4⋊C4×Dic7C2semidirect
11. C2×#89719C2semidirect
13. C2×#89717C2semidirect
14. C2×#89717C2semidirect
15. C2×#89705C2semidirect
16. C2×C4×(C2×D7)⋊C4C2semidirect
21. C2×C7×#126C22semidirect
45. C2×#6459C22semidirect
56. #89765C22semidirect
57. #89762C22semidirect
58. #89756C22semidirect
59. C4⋊C4×Dic7C22semidirect
60. #89746C22semidirect
64. #89719C22semidirect
65. #89717C22semidirect
66. #89717C22semidirect
67. C4×(C2×D7)⋊C4C22semidirect
68. #89705C22semidirect
100. C2×C7×C4⋊C4D4semidirect
153. C22×#126D7semidirect
252. C7×C4⋊C4C2×D4semidirect
276. C2×#126C2×D7semidirect
454. C2×C4⋊C4C22⋊D7semidirect
628. C4⋊C4C2×C22⋊D7semidirect
645. C2×C7#2560semidirect
745. C7C2×#2560semidirect
791. C2#11740555direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1262
C22×#64592
#117405552
C2×#897652
C2×#897562
C2×#897462
C2×#897622
C2×C4⋊C4×Dic72
C2×#897282
C2×#897332
C2×#897192
C2×#897292
C2×#897172
C2×#897052
C2×C4×(C2×D7)⋊C42
C2×#25607