Finite Group Databasebeta

← C2×#11735479 #13522864

Subgroups — C2×#11735479 #13522864

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×#6461C211yesmaximal, characteristic, complemented
2C22×#6448C211yesmaximal, characteristic
3C2×C7×#399C211yesmaximal, characteristic, complemented
4C2×#89765C211yesmaximal, characteristic, complemented
5C2×#89759C211yesmaximal, characteristic, complemented
6C2×#89746C211yesmaximal, characteristic, complemented
7C2×#89753C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
9C2×#89728C211yesmaximal, characteristic
10C2×#89733C211yesmaximal, characteristic
11C2×#89717C211yesmaximal, characteristic, complemented
12C2×#89723C211yesmaximal, characteristic, complemented
13C2×#89723C211yesmaximal, characteristic, complemented
14#11735479C2116yesmaximal, direct product factor
15C2×#89428C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C23×Dic14C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
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×C4×Dic7C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C22×C4×Dic7C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C2×#6461—28no—
43C2×#6461C2218yescomplemented
44C2×#6448—28no—
45C2×#6448C2218yes—
46C7×#399C2218yescomplemented
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
56C2×C7⋊#95C2211yescharacteristic
57#89765C2218yescomplemented
58#89759C2218yescomplemented
59#89753C2218yescomplemented
60C4⋊C4×Dic7C2218yescomplemented
61#89746C2218yescomplemented
62#89733C2218yes—
63#89728C2218yes—
64#89723C2218yescomplemented
65#89723C2218yescomplemented
66#89717C2218yescomplemented
67#89438C2218yescomplemented
68#89428C2218yescomplemented
69C2×#2521—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—
97C2×C7×C4⋊C4—24no—
98C2×C7×C4⋊C4—24no—
99C2×C7×C4⋊C4—24no—
100C2×C7×C4⋊C4C2314yes—
101C2×C7×C4⋊C4C2314yes—
102C2×C7×C4⋊C4C2314yes—
103C2×C7×C22⋊C4—24no—
104C2×C7×C22⋊C4—24no—
105C2×C7×C22⋊C4—24no—
106C2×C7×C22⋊C4C2314yes—
107C2×C7×C22⋊C4C2314yes—
108C2×C7×C22⋊C4C2314yes—
109C2×C22⋊Dic7—24no—
110C2×C22⋊Dic7—24no—
111C2×C22⋊Dic7—42no—
112C2×C22⋊Dic7C2314yes—
113C2×C22⋊Dic7C2314yes—
114C2×C22⋊Dic7C2314yes—
115C2×(C2×D7)⋊C4—24no—
116C2×(C2×D7)⋊C4—24no—
117C2×(C2×D7)⋊C4—24no—
118C2×(C2×D7)⋊C4—24no—
119C2×(C2×D7)⋊C4D418yes—
120C2×(C2×D7)⋊C4C2314yes—
121C2×(C2×D7)⋊C4C2314yes—
122C2×(C2×D7)⋊C4C2314yes—
123C2×(C2×D7)⋊C4C2314yes—
124C2×(C2×D7)⋊C4C2314yes—
125C2×C4⋊Dic7—24no—
126C2×C4⋊Dic7—24no—
127C2×C4⋊Dic7—42no—
128C2×C4⋊Dic7C2314yes—
129C2×C4⋊Dic7C2314yes—
130C2×C4⋊Dic7C2314yes—
131C2×Dic7⋊C4—24no—
132C2×Dic7⋊C4C2314yes—
133C2×C4×Dic7—24no—
134C2×C4×Dic7—24no—
135C2×C4×Dic7—24no—
136C2×C4×Dic7—42no—
137C2×C4×Dic7C2314yes—
138C2×C4×Dic7C2314yes—
139C2×C4×Dic7C2314yes—
140C2×C4×Dic7C2314yes—
141#6461—232no—
142#6448—232no—
143C7×#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×#126—71no—
154C22×#124—71no—
155#2521—716no—
156C2×#399D711yescharacteristic, complemented
157C2×#397—71no—
158C2×#395—71no—
159C2×#394—71no—
160C2×#391—71no—
161C2×#388—71no—
162C2×#388—71no—
163C2×#388—71no—
164C2×#387—71no—
165C2×#386—71no—
166C2×#380—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×D7C2×D414yes—
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×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⋊C4—28no—
253C7×C22⋊C4—28no—
254C7×C22⋊C4—28no—
255C7×C22⋊C4—28no—
256C22⋊Dic7—28no—
257C22⋊Dic7—28no—
258C22⋊Dic7—44no—
259(C2×D7)⋊C4—28no—
260(C2×D7)⋊C4—28no—
261(C2×D7)⋊C4—28no—
262(C2×D7)⋊C4—28no—
263(C2×D7)⋊C4C2×D4116yes—
264C4⋊Dic7—28no—
265C4⋊Dic7—28no—
266C4⋊Dic7—44no—
267Dic7⋊C4—28no—
268C4×Dic7—28no—
269C4×Dic7—28no—
270C4×Dic7—28no—
271C4×Dic7—44no—
272C23×Q8—71no—
273C23×D4—71no—
274C24×C4—71no—
275C2×#126—78no—
276C2×#126—148no—
277C2×#124—78no—
278C2×#124—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×C42—71no—
301#399C2×D718yescomplemented
302#397—78no—
303#395—78no—
304#394—78no—
305#391—78no—
306#388—78no—
307#388—78no—
308#388—78no—
309#387—78no—
310#386—78no—
311#380—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×#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×D7C22×D414yes—
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×C7C2×#4114yes—
383C2×C4×C7C2×#4114yes—
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×Dic7C22×D414yes—
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—1432no—
443#124—1432no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—74no—
448C2×C4⋊C4—74no—
449C2×C4⋊C4—74no—
450C2×C4⋊C4—74no—
451C2×C4⋊C4—144no—
452C2×C4⋊C4—144no—
453C2×C4⋊C4—144no—
454C2×C4⋊C4—282no—
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—78no—
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—74no—
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#95—74no—
496#95—74no—
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#52914yes—
507C22×C7#53214yes—
508C22×C7#54214yes—
509C22×C7#54614yes—
510C22×C7#54714yes—
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—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—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×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—28no—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—148no—
626C4⋊C4—148no—
627C4⋊C4—148no—
628C4⋊C4—284no—
629C22⋊C4—28no—
630C22⋊C4—28no—
631C22⋊C4—28no—
632C22⋊C4—716no—
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#252118yescomplemented
646C2×C7C2×#52911yescharacteristic
647C2×C7C2×#53211yescharacteristic
648C2×C7C2×#54211yescharacteristic
649C2×C7C2×#54611yescharacteristic
650C2×C7C2×#54711yescharacteristic
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—
682C23C2×D4×D712yes—
683C23C2×#115912yes—
684C23C2×#115912yes—
685C23#655112yes—
686C23D7×#4112yes—
687C23D7×#4112yes—
688C23#655312yes—
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×C4C2×D4×D714yes—
743C2×C4C2×#115914yes—
744C2×C4C2×#115914yes—
745C7C2×#252111yescharacteristic, 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#9032214yes—
763C22#9033214yes—
764C22#9033414yes—
765C22#9034014yes—
766C22#9034514yes—
767C22#9034914yes—
768C22#9040714yes—
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#1173547918yesdirect product factor
792C2C2×#9033411yescharacteristic
793C2C2×#9033211yescharacteristic
794C2C2×#9032211yescharacteristic
795C2C2×#9034011yescharacteristic
796C2C2×#9034511yescharacteristic
797C2C2×#9034911yescharacteristic
798C2C2×#9040711yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#399C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#399D7
hypocenterC7C2×#2521
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#6461C2semidirect
3. C2×C7×#399C2semidirect
4. C2×#89765C2semidirect
5. C2×#89759C2semidirect
6. C2×#89746C2semidirect
7. C2×#89753C2semidirect
8. C2×C4⋊C4×Dic7C2semidirect
11. C2×#89717C2semidirect
12. C2×#89723C2semidirect
13. C2×#89723C2semidirect
14. #11735479C2direct (N × H)
15. C2×#89428C2semidirect
16. C2×#89438C2semidirect
43. C2×#6461C22semidirect
46. C7×#399C22semidirect
57. #89765C22semidirect
58. #89759C22semidirect
59. #89753C22semidirect
60. C4⋊C4×Dic7C22semidirect
61. #89746C22semidirect
64. #89723C22semidirect
65. #89723C22semidirect
66. #89717C22semidirect
67. #89438C22semidirect
68. #89428C22semidirect
156. C2×#399D7semidirect
301. #399C2×D7semidirect
645. C2×C7#2521semidirect
745. C7C2×#2521semidirect
791. C2#11735479direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64612
C22×#64482
C2×C7×#3992
C2×#897652
C2×#897592
C2×#897462
C2×#897532
C2×C4⋊C4×Dic72
C2×#897282
C2×#897332
C2×#897172
C2×#897232
#117354792
C2×#894282
C2×#894382
C2×#25217