Finite Group Databasebeta

← C2×#11734230 #13522015

Subgroups — C2×#11734230 #13522015

Order 1792.

2962 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×Q8×Dic7C211yesmaximal, characteristic, complemented
2C22×#6446C211yesmaximal, characteristic
3C2×C7×#393C211yesmaximal, characteristic, complemented
4C2×#90003C211yesmaximal, characteristic, complemented
5C2×#89733C211yesmaximal, characteristic
6C2×#89729C211yesmaximal, characteristic
7C2×#89716C211yesmaximal, characteristic, complemented
8C2×#89723C211yesmaximal, characteristic, complemented
9C2×#89723C211yesmaximal, characteristic, complemented
10#11734230C2116yesmaximal, direct product factor
11C2×#89440C211yesmaximal, characteristic, complemented
12C2×#89429C211yesmaximal, characteristic, complemented
13C2×#89442C211yesmaximal, characteristic, complemented
14C2×#89426C211yesmaximal, characteristic, complemented
15C2×#89425C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic, complemented
17C23×C7×Q8C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C4×D7C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C2×Q8×Dic7—28no—
27C2×Q8×Dic7C2218yescomplemented
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×C4⋊Dic7C2211yescharacteristic
34C22×C4⋊Dic7C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×C4⋊Dic7C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×C4×Dic7C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6446—28no—
45C2×#6446C2218yes—
46C7×#393C2218yescomplemented
47C2×C7×#95C2211yescharacteristic
48C2×C7×#95C2211yescharacteristic
49C2×C7×#95C2211yescharacteristic
50#90003C2218yescomplemented
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58#89733C2218yes—
59#89729C2218yes—
60#89723C2218yescomplemented
61#89723C2218yescomplemented
62#89716C2218yescomplemented
63#89442C2218yescomplemented
64#89440C2218yescomplemented
65#89438C2218yescomplemented
66#89429C2218yescomplemented
67#89426C2218yescomplemented
68#89425C2218yescomplemented
69C2×#2458—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C22×C7×Q8—24no—
73C22×C7×Q8—24no—
74C22×C7×Q8—24no—
75C22×C7×Q8C2314yes—
76C23×C4×C7C2311yescharacteristic
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—42no—
85C22×C22⋊D7C2314yes—
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C22×C4×D7—24no—
94C22×C4×D7—24no—
95C22×C4×D7—42no—
96C22×C4×D7C2314yes—
97C2×C7×C22⋊C4—24no—
98C2×C7×C22⋊C4—24no—
99C2×C7×C22⋊C4—24no—
100C2×C7×C22⋊C4C2314yes—
101C2×C7×C22⋊C4C2314yes—
102C2×C7×C22⋊C4C2314yes—
103C2×C22⋊Dic7—24no—
104C2×C22⋊Dic7—24no—
105C2×C22⋊Dic7—42no—
106C2×C22⋊Dic7C2314yes—
107C2×C22⋊Dic7C2314yes—
108C2×C22⋊Dic7C2314yes—
109Q8×Dic7—232no—
110C2×(C2×D7)⋊C4—24no—
111C2×(C2×D7)⋊C4—24no—
112C2×(C2×D7)⋊C4—24no—
113C2×(C2×D7)⋊C4—24no—
114C2×(C2×D7)⋊C4—24no—
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—24no—
122C2×C4⋊Dic7—24no—
123C2×C4⋊Dic7D418yes—
124C2×C4⋊Dic7C2314yes—
125C2×C4⋊Dic7C2314yes—
126C2×C4⋊Dic7C2314yes—
127C2×C4⋊Dic7C2314yes—
128C2×Dic7⋊C4—24no—
129C2×Dic7⋊C4—42no—
130C2×Dic7⋊C4—42no—
131C2×Dic7⋊C4C2314yes—
132C2×Dic7⋊C4C2314yes—
133C2×Dic7⋊C4C2314yes—
134C2×C4×Dic7—24no—
135C2×C4×Dic7—24no—
136C2×C4×Dic7—24no—
137C2×C4×Dic7—42no—
138C2×C4×Dic7C2314yes—
139C2×C4×Dic7C2314yes—
140C2×C4×Dic7C2314yes—
141C2×C4×Dic7C2314yes—
142#6446—232no—
143C7×#95C2314yes—
144C7×#95C2314yes—
145C7×#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×#123—71no—
154C22×C4×Q8—71no—
155#2458—716no—
156C2×#398—71no—
157C2×#394—71no—
158C2×#393—71no—
159C2×#393D711yescharacteristic, complemented
160C2×#390—71no—
161C2×#388—71no—
162C2×#388—71no—
163C2×#388—71no—
164C2×#388—71no—
165C2×#387—71no—
166C2×#387—71no—
167C2×#385—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—
186C2×C7×Q8—232no—
187C2×C7×Q8—28no—
188C2×C7×Q8—28no—
189C2×C7×Q8—28no—
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×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7C2×D414yes—
206C22×C4×C7#4114yes—
207C22×C4×C7#4114yes—
208C22×C4×C7C2412yes—
209C22×C4×C7C2412yes—
210C22×C4×C7C2412yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C2×C22⋊D7—28no—
215C2×C22⋊D7—28no—
216C2×C22⋊D7—44no—
217C2×C22⋊D7—416no—
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—22no—
233C22×Dic7—22no—
234C22×Dic7—22no—
235C22×Dic7—22no—
236C22×Dic7C2×D414yes—
237C22×Dic7C2×D414yes—
238C22×Dic7#4114yes—
239C22×Dic7C2412yes—
240C22×Dic7C2412yes—
241C22×Dic7C2412yes—
242C22×Dic7C2412yes—
243C22×Dic7C2412yes—
244C22×Dic7C2412yes—
245C22×Dic7C2412yes—
246C2×C4×D7—28no—
247C2×C4×D7—28no—
248C2×C4×D7—44no—
249C2×C4×D7—416no—
250C7×C22⋊C4—28no—
251C7×C22⋊C4—28no—
252C7×C22⋊C4—28no—
253C22⋊Dic7—28no—
254C22⋊Dic7—28no—
255C22⋊Dic7—44no—
256(C2×D7)⋊C4—28no—
257(C2×D7)⋊C4—28no—
258(C2×D7)⋊C4—28no—
259(C2×D7)⋊C4—28no—
260(C2×D7)⋊C4—28no—
261C4⋊Dic7—28no—
262C4⋊Dic7—28no—
263C4⋊Dic7—28no—
264C4⋊Dic7C2×D4116yes—
265Dic7⋊C4—28no—
266Dic7⋊C4—44no—
267Dic7⋊C4—44no—
268C4×Dic7—28no—
269C4×Dic7—28no—
270C4×Dic7—28no—
271C4×Dic7—44no—
272C23×Q8C2×D711yescharacteristic
273C23×D4—71no—
274C24×C4—71no—
275C2×#123—78no—
276C2×#123—148no—
277C2×C4×Q8—78no—
278C2×C4×Q8—148no—
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×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×C42—71no—
301#398—78no—
302#394—78no—
303#393—78no—
304#393C2×D718yescomplemented
305#390—78no—
306#388—78no—
307#388—78no—
308#388—78no—
309#388—78no—
310#387—78no—
311#387—78no—
312#385—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×#95C2×D711yescharacteristic
322C2×#95C2×D711yescharacteristic
323C2×#95C2×D711yescharacteristic
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—
360C7×Q8—232no—
361C2×C4×C7—28no—
362C2×C4×C7—28no—
363C2×C4×C7—28no—
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—22no—
379C2×C4×C7—44no—
380C2×C4×C7—44no—
381C2×C4×C7—44no—
382C2×C4×C7C22×D414yes—
383C2×C4×C7C2×#4114yes—
384C2×C4×C7C2×#4114yes—
385C22⋊D7—416no—
386C2×Dic7—28no—
387C2×Dic7—28no—
388C2×Dic7—28no—
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—22no—
407C2×Dic7—44no—
408C2×Dic7—44no—
409C2×Dic7—44no—
410C2×Dic7—44no—
411C2×Dic7C22×D414yes—
412C2×Dic7C22×D414yes—
413C2×Dic7C2×#4114yes—
414C4×D7—416no—
415C25—71no—
416C25C22×D711yescharacteristic
417C22×Q8—24no—
418C22×Q8—24no—
419C22×Q8—24no—
420C22×Q8C22×D714yes—
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#123—1432no—
443C4×Q8—1432no—
444C2×C4⋊C4—78no—
445C2×C4⋊C4—74no—
446C2×C4⋊C4—74no—
447C2×C4⋊C4—74no—
448C2×C4⋊C4—74no—
449C2×C4⋊C4—74no—
450C2×C4⋊C4—74no—
451C2×C4⋊C4—74no—
452C2×C4⋊C4—144no—
453C2×C4⋊C4—144no—
454C2×C4⋊C4—144no—
455C2×C4⋊C4—144no—
456C2×C4⋊C4—282no—
457C2×C4⋊C4—282no—
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—74no—
481C2×C42—74no—
482C2×C42—74no—
483C2×C42—74no—
484C2×C42—144no—
485C2×C42—144no—
486C2×C42—144no—
487C2×C42—282no—
488#95—74no—
489#95—74no—
490#95—74no—
491#95—74no—
492#95—74no—
493#95—74no—
494#95—74no—
495#95C22×D714yes—
496#95C22×D714yes—
497#95C22×D714yes—
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#52514yes—
507C22×C7#52914yes—
508C22×C7#54214yes—
509C22×C7#54614yes—
510C22×C7#54814yes—
511C22×C7#55214yes—
512C22×C7#55914yes—
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—42no—
524C2×D7—42no—
525C2×D7—42no—
526C2×D7—42no—
527C2×D7—416no—
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—232no—
559C2×Q8—28no—
560C2×Q8—28no—
561C2×Q8—28no—
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—148no—
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—142no—
611C22×C4—284no—
612C22×C4—2816no—
613C22×C4D4×D714yes—
614C22×C4#115914yes—
615C22×C4#115914yes—
616C22×C4C23×D712yes—
617C22×C4C23×D712yes—
618C22×C4C23×D712yes—
619C22×C4C23×D712yes—
620C22×C4C23×D712yes—
621C22×C4C23×D712yes—
622C4⋊C4—716no—
623C4⋊C4—148no—
624C4⋊C4—148no—
625C4⋊C4—148no—
626C4⋊C4—148no—
627C4⋊C4—284no—
628C4⋊C4—284no—
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—148no—
641C42—148no—
642C42—148no—
643C42—284no—
644C2×C7—82no—
645C2×C7#245818yescomplemented
646C2×C7C2×#52511yescharacteristic
647C2×C7C2×#52911yescharacteristic
648C2×C7C2×#54211yescharacteristic
649C2×C7C2×#54611yescharacteristic
650C2×C7C2×#54811yescharacteristic
651C2×C7C2×#55211yescharacteristic
652C2×C7C2×#55911yescharacteristic
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—142no—
672C23—142no—
673C23—142no—
674C23—142no—
675C23—142no—
676C23—142no—
677C23—148no—
678C23—284no—
679C23—284no—
680C23—284no—
681C23—284no—
682C23C2×D4×D712yes—
683C23C2×#115912yes—
684C23C2×#115912yes—
685C23#655112yes—
686C23D7×#4112yes—
687C23D7×#4112yes—
688C23#655312yes—
689C23C24×D711yescharacteristic
690Q8—232no—
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—142no—
718C2×C4—142no—
719C2×C4—142no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—148no—
724C2×C4—148no—
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×C4C2×D4×D714yes—
743C2×C4C2×#115914yes—
744C2×C4C2×#115914yes—
745C7C2×#245811yescharacteristic, 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—282no—
760C22—282no—
761C22—2816no—
762C22#9027714yes—
763C22#9032414yes—
764C22#9033014yes—
765C22#9033414yes—
766C22#9036714yes—
767C22#9037114yes—
768C22#9037214yes—
769C22C22×D4×D711yescharacteristic
770C22C22×#115911yescharacteristic
771C22C22×#115911yescharacteristic
772C22C2×#655111yescharacteristic
773C22C2×D7×#4111yescharacteristic
774C22C2×D7×#4111yescharacteristic
775C22C2×#655311yescharacteristic
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#1173423018yesdirect product factor
792C2C2×#9027711yescharacteristic
793C2C2×#9033411yescharacteristic
794C2C2×#9032411yescharacteristic
795C2C2×#9033011yescharacteristic
796C2C2×#9037111yescharacteristic
797C2C2×#9037211yescharacteristic
798C2C2×#9036711yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#393C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#393D7
hypocenterC7C2×#2458
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic7C2semidirect
3. C2×C7×#393C2semidirect
4. C2×#90003C2semidirect
7. C2×#89716C2semidirect
8. C2×#89723C2semidirect
9. C2×#89723C2semidirect
10. #11734230C2direct (N × H)
11. C2×#89440C2semidirect
12. C2×#89429C2semidirect
13. C2×#89442C2semidirect
14. C2×#89426C2semidirect
15. C2×#89425C2semidirect
16. C2×#89438C2semidirect
27. C2×Q8×Dic7C22semidirect
46. C7×#393C22semidirect
50. #90003C22semidirect
60. #89723C22semidirect
61. #89723C22semidirect
62. #89716C22semidirect
63. #89442C22semidirect
64. #89440C22semidirect
65. #89438C22semidirect
66. #89429C22semidirect
67. #89426C22semidirect
68. #89425C22semidirect
159. C2×#393D7semidirect
304. #393C2×D7semidirect
645. C2×C7#2458semidirect
745. C7C2×#2458semidirect
791. C2#11734230direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×Dic72
C22×#64462
C2×C7×#3932
C2×#900032
C2×#897332
C2×#897292
C2×#897162
C2×#897232
#117342302
C2×#894402
C2×#894292
C2×#894422
C2×#894262
C2×#894252
C2×#894382
C2×#24587