Finite Group Databasebeta

← C2×#11734847 #13560321

Subgroups — C2×#11734847 #13560321

Order 1792.

2566 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×#6452C211yesmaximal, characteristic, complemented
2C22×#6448C211yesmaximal, characteristic
3C2×C7×#396C211yesmaximal, characteristic, complemented
4C2×#89764C211yesmaximal, characteristic, complemented
5C2×#89766C211yesmaximal, characteristic, complemented
6C2×#89766C211yesmaximal, characteristic, complemented
7C2×#89751C211yesmaximal, characteristic, complemented
8C2×#89749C211yesmaximal, characteristic, complemented
9C2×#89731C211yesmaximal, characteristic
10C2×#89721C211yesmaximal, characteristic, complemented
11C2×#89724C211yesmaximal, characteristic, complemented
12C2×#89720C211yesmaximal, characteristic, complemented
13C2×#89733C211yesmaximal, characteristic
14#11734847C2116yesmaximal, direct product factor
15C2×#89447C211yesmaximal, characteristic, complemented
16C2×#89428C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C23×Dic14C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×C4⋊Dic7C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×C4⋊Dic7C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6452—28no—
45C2×#6452C2218yescomplemented
46C2×#6448—28no—
47C2×#6448C2218yes—
48C7×#396C2218yescomplemented
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#89766C2218yescomplemented
59#89764C2218yescomplemented
60#89751C2218yescomplemented
61#89749C2218yescomplemented
62#89733C2218yes—
63#89731C2218yes—
64#89724C2218yescomplemented
65#89721C2218yescomplemented
66#89720C2218yescomplemented
67#89447C2218yescomplemented
68#89428C2218yescomplemented
69C2×#2820—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—42no—
80C22×C22⋊D7—42no—
81C22×C22⋊D7C2314yes—
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C22×Dic14—24no—
90C22×Dic14—42no—
91C22×Dic14—42no—
92C22×Dic14C2314yes—
93C2×C7×C4⋊C4—24no—
94C2×C7×C4⋊C4—42no—
95C2×C7×C4⋊C4—42no—
96C2×C7×C4⋊C4C2314yes—
97C2×C7×C4⋊C4C2314yes—
98C2×C7×C4⋊C4C2314yes—
99C2×C7×C22⋊C4—24no—
100C2×C7×C22⋊C4—42no—
101C2×C7×C22⋊C4—42no—
102C2×C7×C22⋊C4C2314yes—
103C2×C7×C22⋊C4C2314yes—
104C2×C7×C22⋊C4C2314yes—
105C2×C22⋊Dic7—24no—
106C2×C22⋊Dic7—42no—
107C2×C22⋊Dic7—42no—
108C2×C22⋊Dic7C2314yes—
109C2×C22⋊Dic7C2314yes—
110C2×C22⋊Dic7C2314yes—
111C2×(C2×D7)⋊C4—24no—
112C2×(C2×D7)⋊C4—24no—
113C2×(C2×D7)⋊C4—42no—
114C2×(C2×D7)⋊C4—42no—
115C2×(C2×D7)⋊C4—42no—
116C2×(C2×D7)⋊C4—42no—
117C2×(C2×D7)⋊C4C2314yes—
118C2×(C2×D7)⋊C4C2314yes—
119C2×(C2×D7)⋊C4C2314yes—
120C2×(C2×D7)⋊C4C2314yes—
121C2×(C2×D7)⋊C4C2314yes—
122C2×(C2×D7)⋊C4C2314yes—
123C2×C4⋊Dic7—24no—
124C2×C4⋊Dic7—42no—
125C2×C4⋊Dic7—42no—
126C2×C4⋊Dic7C2314yes—
127C2×C4⋊Dic7C2314yes—
128C2×C4⋊Dic7C2314yes—
129C2×Dic7⋊C4—24no—
130C2×Dic7⋊C4—24no—
131C2×Dic7⋊C4—24no—
132C2×Dic7⋊C4—24no—
133C2×Dic7⋊C4—42no—
134C2×Dic7⋊C4—42no—
135C2×Dic7⋊C4C2314yes—
136C2×Dic7⋊C4C2314yes—
137C2×Dic7⋊C4C2314yes—
138C2×Dic7⋊C4C2314yes—
139C2×Dic7⋊C4C2314yes—
140C2×Dic7⋊C4C2314yes—
141C2×C4×Dic7D418yes—
142C2×C4×Dic7C2314yes—
143#6452—232no—
144#6448—232no—
145C7×#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×#125—71no—
154C22×#124—71no—
155#2820—716no—
156C2×#399—71no—
157C2×#399—71no—
158C2×#397—71no—
159C2×#397—71no—
160C2×#396—71no—
161C2×#396—71no—
162C2×#396—71no—
163C2×#396D711yescharacteristic, complemented
164C2×#395—71no—
165C2×#395—71no—
166C2×#394—71no—
167C2×#394—71no—
168C2×#382—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—22no—
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×C7—22no—
202C22×C4×C7—22no—
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—44no—
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—22no—
233C22×Dic7C2×D414yes—
234C22×Dic7C2×D414yes—
235C22×Dic7C2412yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C22×Dic7C2412yes—
239C22×Dic7C2412yes—
240C22×Dic7C2412yes—
241C22×Dic7C2412yes—
242C2×Dic14—28no—
243C2×Dic14—44no—
244C2×Dic14—44no—
245C2×Dic14—416no—
246C7×C4⋊C4—28no—
247C7×C4⋊C4—44no—
248C7×C4⋊C4—44no—
249C7×C22⋊C4—28no—
250C7×C22⋊C4—44no—
251C7×C22⋊C4—44no—
252C22⋊Dic7—28no—
253C22⋊Dic7—44no—
254C22⋊Dic7—44no—
255(C2×D7)⋊C4—28no—
256(C2×D7)⋊C4—28no—
257(C2×D7)⋊C4—44no—
258(C2×D7)⋊C4—44no—
259(C2×D7)⋊C4—44no—
260(C2×D7)⋊C4—44no—
261C4⋊Dic7—28no—
262C4⋊Dic7—44no—
263C4⋊Dic7—44no—
264Dic7⋊C4—28no—
265Dic7⋊C4—28no—
266Dic7⋊C4—28no—
267Dic7⋊C4—28no—
268Dic7⋊C4—44no—
269Dic7⋊C4—44no—
270C4×Dic7C2×D4116yes—
271C23×Q8—71no—
272C23×D4—71no—
273C2×#125—78no—
274C2×#125—148no—
275C2×#124—78no—
276C2×#124—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×C4⋊C4C2×D711yescharacteristic
288C22×C4⋊C4C2×D711yescharacteristic
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⋊C4—71no—
296C22×C22⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C22⋊C4C2×D711yescharacteristic
299C22×C22⋊C4C2×D711yescharacteristic
300C22×C22⋊C4C2×D711yescharacteristic
301C22×C42—71no—
302#399—78no—
303#399—78no—
304#397—78no—
305#397—78no—
306#396—78no—
307#396—78no—
308#396—78no—
309#396C2×D718yescomplemented
310#395—78no—
311#395—78no—
312#394—78no—
313#394—78no—
314#382—78no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
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×C7H(5,𝔽2)12yes—
339C23×C7H(5,𝔽2)12yes—
340C23×C7H(5,𝔽2)12yes—
341C23×C72−1+412yes—
342C23×C72−1+412yes—
343C23×C72−1+412yes—
344C23×C7C2511yescharacteristic
345C22×D7—22no—
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×D7—44no—
357C22×D7—44no—
358C22×D7—44no—
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—22no—
376C2×C4×C7—22no—
377C2×C4×C7—44no—
378C2×C4×C7—44no—
379C2×C4×C7—44no—
380C2×C4×C7—44no—
381C2×C4×C7—44no—
382C2×C4×C7C22×D414yes—
383C22⋊D7—416no—
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—22no—
404C2×Dic7—22no—
405C2×Dic7—44no—
406C2×Dic7—44no—
407C2×Dic7—44no—
408C2×Dic7—44no—
409C2×Dic7—44no—
410C2×Dic7C22×D414yes—
411C2×Dic7C22×D414yes—
412Dic14—416no—
413C25—71no—
414C25C22×D711yescharacteristic
415C22×Q8—74no—
416C22×Q8—144no—
417C22×Q8—282no—
418C22×Q8—282no—
419C22×D4—74no—
420C22×D4—144no—
421C22×D4—282no—
422C22×D4—282no—
423C23×C4—71no—
424C23×C4—71no—
425C23×C4—71no—
426C23×C4—71no—
427C23×C4—71no—
428C23×C4—71no—
429C23×C4—71no—
430C23×C4C22×D711yescharacteristic
431C23×C4C22×D711yescharacteristic
432C23×C4C22×D711yescharacteristic
433C23×C4C22×D711yescharacteristic
434C23×C4C22×D711yescharacteristic
435C23×C4C22×D711yescharacteristic
436#125—1432no—
437#124—1432no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—42no—
440C2×C4⋊C4—42no—
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—74no—
450C2×C4⋊C4—144no—
451C2×C4⋊C4—144no—
452C2×C4⋊C4—144no—
453C2×C4⋊C4—144no—
454C2×C4⋊C4—144no—
455C2×C4⋊C4—282no—
456C2×C4⋊C4—282no—
457C2×C4⋊C4—282no—
458C2×C4⋊C4—282no—
459C2×C4⋊C4C22×D714yes—
460C2×C4⋊C4C22×D714yes—
461C2×C4⋊C4C22×D714yes—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—74no—
466C2×C22⋊C4—74no—
467C2×C22⋊C4—74no—
468C2×C22⋊C4—74no—
469C2×C22⋊C4—74no—
470C2×C22⋊C4—74no—
471C2×C22⋊C4—74no—
472C2×C22⋊C4—74no—
473C2×C22⋊C4—74no—
474C2×C22⋊C4—144no—
475C2×C22⋊C4—144no—
476C2×C22⋊C4—144no—
477C2×C22⋊C4—282no—
478C2×C22⋊C4—282no—
479C2×C22⋊C4—282no—
480C2×C22⋊C4—282no—
481C2×C22⋊C4—282no—
482C2×C22⋊C4—282no—
483C2×C22⋊C4C22×D714yes—
484C2×C22⋊C4C22×D714yes—
485C2×C22⋊C4C22×D714yes—
486C2×C42—78no—
487C2×C42—74no—
488#95—74no—
489#95—74no—
490#95—74no—
491#95—74no—
492#95—74no—
493#95—74no—
494#95—74no—
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#53514yes—
505C22×C7#53614yes—
506C22×C7#53714yes—
507C22×C7#56214yes—
508C22×C7#56214yes—
509C22×C7#56314yes—
510C22×C7#56314yes—
511C22×C7C23×D411yescharacteristic
512C22×C7C2×H(5,𝔽2)11yescharacteristic
513C22×C7C2×H(5,𝔽2)11yescharacteristic
514C22×C7C2×H(5,𝔽2)11yescharacteristic
515C22×C7C2×2−1+411yescharacteristic
516C22×C7C2×2−1+411yescharacteristic
517C22×C7C2×2−1+411yescharacteristic
518C2×D7—42no—
519C2×D7—42no—
520C2×D7—42no—
521C2×D7—42no—
522C2×D7—42no—
523C2×D7—42no—
524C2×D7—42no—
525C2×D7—88no—
526C4×C7—24no—
527C4×C7—42no—
528C4×C7—42no—
529C4×C7—42no—
530C4×C7—42no—
531C4×C7—42no—
532Dic7—24no—
533Dic7—24no—
534Dic7—42no—
535Dic7—42no—
536Dic7—42no—
537Dic7—42no—
538Dic7—42no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—72no—
547C24—142no—
548C24—142no—
549C24—142no—
550C24—142no—
551C24—142no—
552C24—142no—
553C24—142no—
554C24C23×D712yes—
555C24C23×D711yescharacteristic
556C2×Q8—148no—
557C2×Q8—284no—
558C2×Q8—284no—
559C2×Q8—2816no—
560C2×D4—148no—
561C2×D4—284no—
562C2×D4—284no—
563C2×D4—2816no—
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—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—74no—
582C22×C4—74no—
583C22×C4—72no—
584C22×C4—72no—
585C22×C4—72no—
586C22×C4—72no—
587C22×C4—72no—
588C22×C4—72no—
589C22×C4—72no—
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—142no—
606C22×C4—142no—
607C22×C4—142no—
608C22×C4—142no—
609C22×C4D4×D714yes—
610C22×C4C23×D712yes—
611C22×C4C23×D712yes—
612C22×C4C23×D712yes—
613C22×C4C23×D712yes—
614C22×C4C23×D712yes—
615C22×C4C23×D712yes—
616C4⋊C4—28no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—148no—
620C4⋊C4—148no—
621C4⋊C4—148no—
622C4⋊C4—148no—
623C4⋊C4—148no—
624C4⋊C4—284no—
625C4⋊C4—284no—
626C4⋊C4—284no—
627C4⋊C4—284no—
628C22⋊C4—28no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—148no—
632C22⋊C4—148no—
633C22⋊C4—148no—
634C22⋊C4—284no—
635C22⋊C4—284no—
636C22⋊C4—284no—
637C22⋊C4—284no—
638C22⋊C4—284no—
639C22⋊C4—284no—
640C42—716no—
641C2×C7—82no—
642C2×C7#282018yescomplemented
643C2×C7C2×#53511yescharacteristic
644C2×C7C2×#53611yescharacteristic
645C2×C7C2×#53711yescharacteristic
646C2×C7C2×#56211yescharacteristic
647C2×C7C2×#56211yescharacteristic
648C2×C7C2×#56311yescharacteristic
649C2×C7C2×#56311yescharacteristic
650D7—82no—
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—142no—
666C23—142no—
667C23—142no—
668C23—142no—
669C23—142no—
670C23—142no—
671C23—142no—
672C23—284no—
673C23—284no—
674C23—284no—
675C23—284no—
676C23—284no—
677C23—284no—
678C23—284no—
679C23C2×D4×D712yes—
680C23#654812yes—
681C23#654812yes—
682C23#655112yes—
683C23#655312yes—
684C23#655412yes—
685C23#655412yes—
686C23C24×D711yescharacteristic
687Q8—2816no—
688D4—2816no—
689C2×C4—28no—
690C2×C4—22no—
691C2×C4—22no—
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—22no—
706C2×C4—22no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—74no—
713C2×C4—74no—
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—142no—
734C2×C4—142no—
735C2×C4—284no—
736C2×C4—284no—
737C2×C4—284no—
738C2×C4—284no—
739C2×C4—284no—
740C2×C4C2×D4×D714yes—
741C7C2×#282011yescharacteristic, complemented, Sylow
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—88no—
750C22—282no—
751C22—282no—
752C22—282no—
753C22—282no—
754C22—282no—
755C22—282no—
756C22—282no—
757C22—568no—
758C22#9028814yes—
759C22#9029814yes—
760C22#9031214yes—
761C22#9031914yes—
762C22#9033714yes—
763C22#9033814yes—
764C22#9040314yes—
765C22C22×D4×D711yescharacteristic
766C22C2×#654811yescharacteristic
767C22C2×#654811yescharacteristic
768C22C2×#655111yescharacteristic
769C22C2×#655311yescharacteristic
770C22C2×#655411yescharacteristic
771C22C2×#655411yescharacteristic
772C4—24no—
773C4—42no—
774C4—42no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—144no—
779C4—144no—
780C4—282no—
781C4—282no—
782C4—282no—
783C4—282no—
784C4—282no—
785C2—82no—
786C2—562no—
787C2#1173484718yesdirect product factor
788C2C2×#9028811yescharacteristic
789C2C2×#9029811yescharacteristic
790C2C2×#9031211yescharacteristic
791C2C2×#9033711yescharacteristic
792C2C2×#9031911yescharacteristic
793C2C2×#9033811yescharacteristic
794C2C2×#9040311yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#396C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#396D7
hypocenterC7C2×#2820
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#6452C2semidirect
3. C2×C7×#396C2semidirect
4. C2×#89764C2semidirect
5. C2×#89766C2semidirect
6. C2×#89766C2semidirect
7. C2×#89751C2semidirect
8. C2×#89749C2semidirect
10. C2×#89721C2semidirect
11. C2×#89724C2semidirect
12. C2×#89720C2semidirect
14. #11734847C2direct (N × H)
15. C2×#89447C2semidirect
16. C2×#89428C2semidirect
45. C2×#6452C22semidirect
48. C7×#396C22semidirect
57. #89766C22semidirect
58. #89766C22semidirect
59. #89764C22semidirect
60. #89751C22semidirect
61. #89749C22semidirect
64. #89724C22semidirect
65. #89721C22semidirect
66. #89720C22semidirect
67. #89447C22semidirect
68. #89428C22semidirect
163. C2×#396D7semidirect
309. #396C2×D7semidirect
642. C2×C7#2820semidirect
741. C7C2×#2820semidirect
787. C2#11734847direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64522
C22×#64482
C2×C7×#3962
C2×#897642
C2×#897662
C2×#897512
C2×#897492
C2×#897312
C2×#897212
C2×#897242
C2×#897202
C2×#897332
#117348472
C2×#894472
C2×#894282
C2×#28207