Finite Group Databasebeta

← C2×#11733103 #13520429

Subgroups — C2×#11733103 #13520429

Order 1792.

2222 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#388C211yesmaximal, characteristic, complemented
2C2×#89766C211yesmaximal, characteristic, complemented
3C2×#89752C211yesmaximal, characteristic, complemented
4C2×#89731C211yesmaximal, characteristic
5C2×#89731C211yesmaximal, characteristic
6C2×#89721C211yesmaximal, characteristic, complemented
7C2×#89725C211yesmaximal, characteristic, complemented
8C2×#89729C211yesmaximal, characteristic
9C2×#89716C211yesmaximal, characteristic, complemented
10C2×#89712C211yesmaximal, characteristic, complemented
11C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
12#11733103C2116yesmaximal, direct product factor
13C2×#89447C211yesmaximal, characteristic, complemented
14C2×#89429C211yesmaximal, characteristic, complemented
15C2×#89442C211yesmaximal, characteristic, complemented
16C2×#89427C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C42×C7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
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×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×C4×Dic7C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C7×#388C2218yescomplemented
43C2×C7×#95C2211yescharacteristic
44C2×C7×#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53#89766C2218yescomplemented
54#89752C2218yescomplemented
55#89731C2218yes—
56#89731C2218yes—
57#89729C2218yes—
58#89725C2218yescomplemented
59#89721C2218yescomplemented
60#89716C2218yescomplemented
61#89712C2218yescomplemented
62C4×Dic7⋊C4C2218yescomplemented
63#89447C2218yescomplemented
64#89442C2218yescomplemented
65#89429C2218yescomplemented
66#89427C2218yescomplemented
67C2×#2651—71nomaximal, Sylow
68C25×C7C2311yescharacteristic
69C24×D7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C22×C22⋊D7—24no—
77C22×C22⋊D7—42no—
78C22×C22⋊D7—42no—
79C22×C22⋊D7C2314yes—
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C2×C7×C4⋊C4—42no—
88C2×C7×C4⋊C4C2314yes—
89C2×C7×C22⋊C4—24no—
90C2×C7×C22⋊C4—42no—
91C2×C7×C22⋊C4—42no—
92C2×C7×C22⋊C4C2314yes—
93C2×C7×C22⋊C4C2314yes—
94C2×C7×C22⋊C4C2314yes—
95C2×C42×C7—42no—
96C2×C42×C7C2314yes—
97C2×C22⋊Dic7—24no—
98C2×C22⋊Dic7—42no—
99C2×C22⋊Dic7—42no—
100C2×C22⋊Dic7C2314yes—
101C2×C22⋊Dic7C2314yes—
102C2×C22⋊Dic7C2314yes—
103C2×(C2×D7)⋊C4—24no—
104C2×(C2×D7)⋊C4—24no—
105C2×(C2×D7)⋊C4—42no—
106C2×(C2×D7)⋊C4—42no—
107C2×(C2×D7)⋊C4—42no—
108C2×(C2×D7)⋊C4—42no—
109C2×(C2×D7)⋊C4C2314yes—
110C2×(C2×D7)⋊C4C2314yes—
111C2×(C2×D7)⋊C4C2314yes—
112C2×(C2×D7)⋊C4C2314yes—
113C2×(C2×D7)⋊C4C2314yes—
114C2×(C2×D7)⋊C4C2314yes—
115C2×C4⋊Dic7—42no—
116C2×C4⋊Dic7—42no—
117C2×C4⋊Dic7C2314yes—
118C2×C4⋊Dic7C2314yes—
119C2×Dic7⋊C4—24no—
120C2×Dic7⋊C4—24no—
121C2×Dic7⋊C4—24no—
122C2×Dic7⋊C4—42no—
123C2×Dic7⋊C4—42no—
124C2×Dic7⋊C4—42no—
125C2×Dic7⋊C4C2314yes—
126C2×Dic7⋊C4C2314yes—
127C2×Dic7⋊C4C2314yes—
128C2×Dic7⋊C4C2314yes—
129C2×Dic7⋊C4C2314yes—
130C2×Dic7⋊C4C2314yes—
131C2×C4×Dic7—24no—
132C2×C4×Dic7—42no—
133C2×C4×Dic7C2314yes—
134C2×C4×Dic7C2314yes—
135C7×#95C2314yes—
136C7×#95C2314yes—
137C7⋊#95C2314yes—
138C7⋊#95C2314yes—
139C7⋊#95C2314yes—
140C7⋊#95C2314yes—
141C7⋊#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145#2651—716no—
146C2×#399—71no—
147C2×#398—71no—
148C2×#398—71no—
149C2×#397—71no—
150C2×#397—71no—
151C2×#396—71no—
152C2×#394—71no—
153C2×#394—71no—
154C2×#390—71no—
155C2×#388—71no—
156C2×#388—71no—
157C2×#388—71no—
158C2×#388D711yescharacteristic, complemented
159C2×#387—71no—
160C2×C4×C4⋊C4—71no—
161C24×C7—22no—
162C24×C7—22no—
163C24×C7—22no—
164C24×C7—22no—
165C24×C7—22no—
166C24×C7—22no—
167C24×C7—22no—
168C24×C7C2412yes—
169C24×C7C2411yescharacteristic
170C23×D7—22no—
171C23×D7—22no—
172C23×D7—22no—
173C23×D7—22no—
174C23×D7—22no—
175C23×D7—22no—
176C23×D7—22no—
177C23×D7C2412yes—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
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#4114yes—
196C22×C4×C7C2412yes—
197C22×C4×C7C2412yes—
198C22×C4×C7C2412yes—
199C22×C4×C7C2412yes—
200C22×C4×C7C2412yes—
201C22×C4×C7C2412yes—
202C2×C22⋊D7—28no—
203C2×C22⋊D7—44no—
204C2×C22⋊D7—44no—
205C2×C22⋊D7—416no—
206C22×Dic7—22no—
207C22×Dic7—22no—
208C22×Dic7—22no—
209C22×Dic7—22no—
210C22×Dic7—22no—
211C22×Dic7—22no—
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#4114yes—
226C22×Dic7#4114yes—
227C22×Dic7C2412yes—
228C22×Dic7C2412yes—
229C22×Dic7C2412yes—
230C22×Dic7C2412yes—
231C22×Dic7C2412yes—
232C22×Dic7C2412yes—
233C22×Dic7C2412yes—
234C7×C4⋊C4—44no—
235C7×C22⋊C4—28no—
236C7×C22⋊C4—44no—
237C7×C22⋊C4—44no—
238C42×C7—44no—
239C22⋊Dic7—28no—
240C22⋊Dic7—44no—
241C22⋊Dic7—44no—
242(C2×D7)⋊C4—28no—
243(C2×D7)⋊C4—28no—
244(C2×D7)⋊C4—44no—
245(C2×D7)⋊C4—44no—
246(C2×D7)⋊C4—44no—
247(C2×D7)⋊C4—44no—
248C4⋊Dic7—44no—
249C4⋊Dic7—44no—
250Dic7⋊C4—28no—
251Dic7⋊C4—28no—
252Dic7⋊C4—28no—
253Dic7⋊C4—44no—
254Dic7⋊C4—44no—
255Dic7⋊C4—44no—
256C4×Dic7—28no—
257C4×Dic7—44no—
258C23×D4—71no—
259C22×C4⋊C4—71no—
260C22×C4⋊C4—71no—
261C22×C4⋊C4—71no—
262C22×C4⋊C4—71no—
263C22×C4⋊C4—71no—
264C22×C4⋊C4—71no—
265C22×C4⋊C4—71no—
266C22×C4⋊C4—71no—
267C22×C4⋊C4C2×D711yescharacteristic
268C22×C22⋊C4—71no—
269C22×C22⋊C4—71no—
270C22×C22⋊C4—71no—
271C22×C22⋊C4—71no—
272C22×C22⋊C4—71no—
273C22×C22⋊C4—71no—
274C22×C22⋊C4—71no—
275C22×C22⋊C4—71no—
276C22×C22⋊C4—71no—
277C22×C22⋊C4C2×D711yescharacteristic
278C22×C22⋊C4C2×D711yescharacteristic
279C22×C22⋊C4C2×D711yescharacteristic
280C22×C42—71no—
281C22×C42—71no—
282C22×C42C2×D711yescharacteristic
283#399—78no—
284#398—78no—
285#398—78no—
286#397—78no—
287#397—78no—
288#396—78no—
289#394—78no—
290#394—78no—
291#390—78no—
292#388—78no—
293#388—78no—
294#388—78no—
295#388C2×D718yescomplemented
296#387—78no—
297C4×C4⋊C4—78no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95—71no—
302C2×#95—71no—
303C2×#95—71no—
304C2×#95—71no—
305C2×#95—71no—
306C2×#95C2×D711yescharacteristic
307C2×#95C2×D711yescharacteristic
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—22no—
314C23×C7—22no—
315C23×C7—44no—
316C23×C7—44no—
317C23×C7—44no—
318C23×C7—44no—
319C23×C7—44no—
320C23×C7—44no—
321C23×C7—44no—
322C23×C7C2×#4112yes—
323C23×C7C2×#4112yes—
324C23×C7C2×#4112yes—
325C23×C7H(5,𝔽2)12yes—
326C23×C7H(5,𝔽2)12yes—
327C23×C7H(5,𝔽2)12yes—
328C23×C72−1+412yes—
329C23×C7C2511yescharacteristic
330C22×D7—22no—
331C22×D7—22no—
332C22×D7—22no—
333C22×D7—22no—
334C22×D7—22no—
335C22×D7—22no—
336C22×D7—22no—
337C22×D7—44no—
338C22×D7—44no—
339C22×D7—44no—
340C22×D7—44no—
341C22×D7—44no—
342C22×D7—44no—
343C22×D7—44no—
344C2×C4×C7—28no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—44no—
363C2×C4×C7—44no—
364C2×C4×C7—44no—
365C2×C4×C7—44no—
366C2×C4×C7—44no—
367C2×C4×C7C2×#4114yes—
368C22⋊D7—416no—
369C2×Dic7—28no—
370C2×Dic7—28no—
371C2×Dic7—22no—
372C2×Dic7—22no—
373C2×Dic7—22no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—22no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—44no—
391C2×Dic7—44no—
392C2×Dic7—44no—
393C2×Dic7—44no—
394C2×Dic7—44no—
395C2×Dic7C2×#4114yes—
396C2×Dic7C2×#4114yes—
397C25—71no—
398C25C22×D711yescharacteristic
399C22×D4—74no—
400C22×D4—144no—
401C22×D4—282no—
402C22×D4—282no—
403C23×C4—71no—
404C23×C4—71no—
405C23×C4—71no—
406C23×C4—71no—
407C23×C4—71no—
408C23×C4—71no—
409C23×C4—71no—
410C23×C4C22×D711yescharacteristic
411C23×C4C22×D711yescharacteristic
412C23×C4C22×D711yescharacteristic
413C23×C4C22×D711yescharacteristic
414C23×C4C22×D711yescharacteristic
415C23×C4C22×D711yescharacteristic
416C2×C4⋊C4—42no—
417C2×C4⋊C4—74no—
418C2×C4⋊C4—74no—
419C2×C4⋊C4—74no—
420C2×C4⋊C4—74no—
421C2×C4⋊C4—74no—
422C2×C4⋊C4—74no—
423C2×C4⋊C4—74no—
424C2×C4⋊C4—74no—
425C2×C4⋊C4—144no—
426C2×C4⋊C4—144no—
427C2×C4⋊C4—144no—
428C2×C4⋊C4—282no—
429C2×C4⋊C4—282no—
430C2×C4⋊C4—282no—
431C2×C4⋊C4—282no—
432C2×C4⋊C4—282no—
433C2×C4⋊C4C22×D714yes—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4—74no—
438C2×C22⋊C4—74no—
439C2×C22⋊C4—74no—
440C2×C22⋊C4—74no—
441C2×C22⋊C4—74no—
442C2×C22⋊C4—74no—
443C2×C22⋊C4—74no—
444C2×C22⋊C4—74no—
445C2×C22⋊C4—74no—
446C2×C22⋊C4—144no—
447C2×C22⋊C4—144no—
448C2×C22⋊C4—144no—
449C2×C22⋊C4—282no—
450C2×C22⋊C4—282no—
451C2×C22⋊C4—282no—
452C2×C22⋊C4—282no—
453C2×C22⋊C4—282no—
454C2×C22⋊C4—282no—
455C2×C22⋊C4C22×D714yes—
456C2×C22⋊C4C22×D714yes—
457C2×C22⋊C4C22×D714yes—
458C2×C42—42no—
459C2×C42—74no—
460C2×C42—74no—
461C2×C42—144no—
462C2×C42—282no—
463C2×C42C22×D714yes—
464#95—74no—
465#95—74no—
466#95—74no—
467#95—74no—
468#95—74no—
469#95—74no—
470#95—74no—
471#95—74no—
472#95C22×D714yes—
473#95C22×D714yes—
474C22×C7—42no—
475C22×C7—42no—
476C22×C7—42no—
477C22×C7—42no—
478C22×C7—42no—
479C22×C7—42no—
480C22×C7—42no—
481C22×C7—88no—
482C22×C7#52914yes—
483C22×C7#53814yes—
484C22×C7#53914yes—
485C22×C7#54014yes—
486C22×C7#54014yes—
487C22×C7#54214yes—
488C22×C7#54214yes—
489C22×C7C22×#4111yescharacteristic
490C22×C7C22×#4111yescharacteristic
491C22×C7C22×#4111yescharacteristic
492C22×C7C2×H(5,𝔽2)11yescharacteristic
493C22×C7C2×H(5,𝔽2)11yescharacteristic
494C22×C7C2×H(5,𝔽2)11yescharacteristic
495C22×C7C2×2−1+411yescharacteristic
496C2×D7—42no—
497C2×D7—42no—
498C2×D7—42no—
499C2×D7—42no—
500C2×D7—42no—
501C2×D7—42no—
502C2×D7—42no—
503C2×D7—88no—
504C4×C7—24no—
505C4×C7—42no—
506C4×C7—42no—
507C4×C7—42no—
508C4×C7—42no—
509C4×C7—42no—
510Dic7—24no—
511Dic7—24no—
512Dic7—42no—
513Dic7—42no—
514Dic7—42no—
515Dic7—42no—
516Dic7—42no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—72no—
525C24—142no—
526C24—142no—
527C24—142no—
528C24—142no—
529C24—142no—
530C24—142no—
531C24—142no—
532C24C23×D712yes—
533C24C23×D711yescharacteristic
534C2×D4—148no—
535C2×D4—284no—
536C2×D4—284no—
537C2×D4—2816no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—74no—
556C22×C4—74no—
557C22×C4—72no—
558C22×C4—72no—
559C22×C4—72no—
560C22×C4—72no—
561C22×C4—72no—
562C22×C4—72no—
563C22×C4—72no—
564C22×C4—142no—
565C22×C4—142no—
566C22×C4—142no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—142no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—142no—
575C22×C4—142no—
576C22×C4—142no—
577C22×C4—142no—
578C22×C4—142no—
579C22×C4—142no—
580C22×C4—142no—
581C22×C4—142no—
582C22×C4—142no—
583C22×C4#115714yes—
584C22×C4C23×D712yes—
585C22×C4C23×D712yes—
586C22×C4C23×D712yes—
587C22×C4C23×D712yes—
588C22×C4C23×D712yes—
589C22×C4C23×D712yes—
590C4⋊C4—44no—
591C4⋊C4—148no—
592C4⋊C4—148no—
593C4⋊C4—148no—
594C4⋊C4—284no—
595C4⋊C4—284no—
596C4⋊C4—284no—
597C4⋊C4—284no—
598C4⋊C4—284no—
599C22⋊C4—28no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—148no—
603C22⋊C4—148no—
604C22⋊C4—148no—
605C22⋊C4—284no—
606C22⋊C4—284no—
607C22⋊C4—284no—
608C22⋊C4—284no—
609C22⋊C4—284no—
610C22⋊C4—284no—
611C42—44no—
612C42—148no—
613C42—284no—
614C2×C7—82no—
615C2×C7#265118yescomplemented
616C2×C7C2×#52911yescharacteristic
617C2×C7C2×#53811yescharacteristic
618C2×C7C2×#53911yescharacteristic
619C2×C7C2×#54011yescharacteristic
620C2×C7C2×#54011yescharacteristic
621C2×C7C2×#54211yescharacteristic
622C2×C7C2×#54211yescharacteristic
623D7—82no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—142no—
639C23—142no—
640C23—142no—
641C23—142no—
642C23—142no—
643C23—142no—
644C23—142no—
645C23—284no—
646C23—284no—
647C23—284no—
648C23—284no—
649C23—284no—
650C23—284no—
651C23—284no—
652C23C2×#115712yes—
653C23#654812yes—
654C23#654812yes—
655C23D7×#4112yes—
656C23D7×#4112yes—
657C23#655312yes—
658C23#655412yes—
659C23C24×D711yescharacteristic
660D4—2816no—
661C2×C4—28no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—74no—
685C2×C4—74no—
686C2×C4—148no—
687C2×C4—148no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—142no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—142no—
705C2×C4—142no—
706C2×C4—142no—
707C2×C4—284no—
708C2×C4—284no—
709C2×C4—284no—
710C2×C4—284no—
711C2×C4—284no—
712C2×C4C2×#115714yes—
713C7C2×#265111yescharacteristic, complemented, Sylow
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—88no—
722C22—282no—
723C22—282no—
724C22—282no—
725C22—282no—
726C22—282no—
727C22—282no—
728C22—282no—
729C22—568no—
730C22#9021914yes—
731C22#9025314yes—
732C22#9025514yes—
733C22#9030414yes—
734C22#9035414yes—
735C22#9036014yes—
736C22#9040114yes—
737C22C22×#115711yescharacteristic
738C22C2×#654811yescharacteristic
739C22C2×#654811yescharacteristic
740C22C2×D7×#4111yescharacteristic
741C22C2×D7×#4111yescharacteristic
742C22C2×#655311yescharacteristic
743C22C2×#655411yescharacteristic
744C4—24no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—144no—
751C4—144no—
752C4—282no—
753C4—282no—
754C4—282no—
755C4—282no—
756C4—282no—
757C2—82no—
758C2—562no—
759C2#1173310318yesdirect product factor
760C2C2×#9021911yescharacteristic
761C2C2×#9025511yescharacteristic
762C2C2×#9025311yescharacteristic
763C2C2×#9030411yescharacteristic
764C2C2×#9035411yescharacteristic
765C2C2×#9036011yescharacteristic
766C2C2×#9040111yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#388C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#388D7
hypocenterC7C2×#2651
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C2×C7×#388C2semidirect
2. C2×#89766C2semidirect
3. C2×#89752C2semidirect
6. C2×#89721C2semidirect
7. C2×#89725C2semidirect
9. C2×#89716C2semidirect
10. C2×#89712C2semidirect
11. C2×C4×Dic7⋊C4C2semidirect
12. #11733103C2direct (N × H)
13. C2×#89447C2semidirect
14. C2×#89429C2semidirect
15. C2×#89442C2semidirect
16. C2×#89427C2semidirect
42. C7×#388C22semidirect
53. #89766C22semidirect
54. #89752C22semidirect
58. #89725C22semidirect
59. #89721C22semidirect
60. #89716C22semidirect
61. #89712C22semidirect
62. C4×Dic7⋊C4C22semidirect
63. #89447C22semidirect
64. #89442C22semidirect
65. #89429C22semidirect
66. #89427C22semidirect
158. C2×#388D7semidirect
295. #388C2×D7semidirect
615. C2×C7#2651semidirect
713. C7C2×#2651semidirect
759. C2#11733103direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3882
C2×#897662
C2×#897522
C2×#897312
C2×#897212
C2×#897252
C2×#897292
C2×#897162
C2×#897122
C2×C4×Dic7⋊C42
#117331032
C2×#894472
C2×#894292
C2×#894422
C2×#894272
C2×#26517