Finite Group Databasebeta

← C2×#11733805 #13523960

Subgroups — C2×#11733805 #13523960

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×#6442C211yesmaximal, characteristic, complemented
2C22×#6441C211yesmaximal, characteristic, complemented
3C2×C7×#390C211yesmaximal, characteristic
4C2×#89994C211yesmaximal, characteristic
5C2×#89992C211yesmaximal, characteristic
6C2×#89752C211yesmaximal, characteristic, complemented
7C2×#89753C211yesmaximal, characteristic, complemented
8C2×#89725C211yesmaximal, characteristic, complemented
9C2×#89719C211yesmaximal, characteristic, complemented
10C2×#89716C211yesmaximal, characteristic, complemented
11C2×#89716C211yesmaximal, characteristic, complemented
12C2×#89723C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
14C2×#89701C211yesmaximal, characteristic, complemented
15C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
16#11733805C2116yesmaximal, direct product factor
17C23×C7×D4C2211yescharacteristic
18C24×Dic7C2211yescharacteristic
19C23×Dic14C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C42×C7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C4⋊Dic7C2211yescharacteristic
34C22×C4⋊Dic7C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C22×C4×Dic7C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C2×#6442—28no—
43C2×#6442C2218yescomplemented
44C2×#6441—28no—
45C2×#6441C2218yescomplemented
46C7×#390C2218yes—
47#89994C2218yes—
48#89992C2218yes—
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59#89753C2218yescomplemented
60#89752C2218yescomplemented
61#89725C2218yescomplemented
62#89723C2218yescomplemented
63#89719C2218yescomplemented
64#89716C2218yescomplemented
65#89716C2218yescomplemented
66C22⋊C4×Dic7C2218yescomplemented
67C4×Dic7⋊C4C2218yescomplemented
68#89701C2218yescomplemented
69C2×#2560—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C25×C7C2311yescharacteristic
72C22×C7×D4—24no—
73C22×C7×D4—24no—
74C22×C7×D4—42no—
75C22×C7×D4C2314yes—
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×Dic7—24no—
82C23×Dic7—24no—
83C23×Dic7—42no—
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2314yes—
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C22×Dic14—24no—
94C22×Dic14—24no—
95C22×Dic14—42no—
96C22×Dic14C2314yes—
97C2×C7×C4⋊C4—24no—
98C2×C7×C4⋊C4C2314yes—
99C2×C7×C22⋊C4—24no—
100C2×C7×C22⋊C4—24no—
101C2×C7×C22⋊C4—24no—
102C2×C7×C22⋊C4—24no—
103C2×C7×C22⋊C4C2314yes—
104C2×C7×C22⋊C4C2314yes—
105C2×C7×C22⋊C4C2314yes—
106C2×C7×C22⋊C4C2314yes—
107C2×C42×C7—42no—
108C2×C42×C7C2314yes—
109C2×C22⋊Dic7—24no—
110C2×C22⋊Dic7—24no—
111C2×C22⋊Dic7—24no—
112C2×C22⋊Dic7—24no—
113C2×C22⋊Dic7—24no—
114C2×C22⋊Dic7—24no—
115C2×C22⋊Dic7—42no—
116C2×C22⋊Dic7C2314yes—
117C2×C22⋊Dic7C2314yes—
118C2×C22⋊Dic7C2314yes—
119C2×C22⋊Dic7C2314yes—
120C2×C22⋊Dic7C2314yes—
121C2×C22⋊Dic7C2314yes—
122C2×C22⋊Dic7C2314yes—
123C2×C4⋊Dic7—24no—
124C2×C4⋊Dic7—24no—
125C2×C4⋊Dic7C2314yes—
126C2×C4⋊Dic7C2314yes—
127C2×Dic7⋊C4—24no—
128C2×Dic7⋊C4—24no—
129C2×Dic7⋊C4—24no—
130C2×Dic7⋊C4D418yescomplemented
131C2×Dic7⋊C4C2314yes—
132C2×Dic7⋊C4C2314yes—
133C2×Dic7⋊C4C2314yes—
134C2×Dic7⋊C4C2314yes—
135C2×C4×Dic7—24no—
136C2×C4×Dic7—24no—
137C2×C4×Dic7—42no—
138C2×C4×Dic7C2314yes—
139C2×C4×Dic7C2314yes—
140C2×C4×Dic7C2314yes—
141#6442—232no—
142#6441—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×C22⋊Q8—71no—
155#2560—716no—
156C2×#398—71no—
157C2×#397—71no—
158C2×#394—71no—
159C2×#393—71no—
160C2×#391—71no—
161C2×#390D711yescharacteristic
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×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7—22no—
182C24×C7#4114yes—
183C24×C7C2412yes—
184C24×C7C2412yes—
185C24×C7C2411yescharacteristic
186C2×C7×D4—28no—
187C2×C7×D4—28no—
188C2×C7×D4—44no—
189C2×C7×D4—416no—
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×C7C2×D414yes—
203C22×C4×C7#4114yes—
204C22×C4×C7#4114yes—
205C22×C4×C7C2412yes—
206C22×C4×C7C2412yes—
207C22×C4×C7C2412yes—
208C22×C4×C7C2412yes—
209C22×C4×C7C2412yes—
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—22no—
226C22×Dic7—22no—
227C22×Dic7—22no—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7—22no—
231C22×Dic7—28no—
232C22×Dic7—28no—
233C22×Dic7—44no—
234C22×Dic7—416no—
235C22×Dic7C2×D414yes—
236C22×Dic7C2×D414yes—
237C22×Dic7#4114yes—
238C22×Dic7C2412yes—
239C22×Dic7C2412yes—
240C22×Dic7C2412yes—
241C22×Dic7C2412yes—
242C22×Dic7C2412yes—
243C22×Dic7C2412yes—
244C22×Dic7C2412yes—
245C22×Dic7C2412yes—
246C2×Dic14—28no—
247C2×Dic14—28no—
248C2×Dic14—44no—
249C2×Dic14—416no—
250C7×C4⋊C4—28no—
251C7×C22⋊C4—28no—
252C7×C22⋊C4—28no—
253C7×C22⋊C4—28no—
254C7×C22⋊C4—28no—
255C42×C7—44no—
256C22⋊Dic7—28no—
257C22⋊Dic7—28no—
258C22⋊Dic7—28no—
259C22⋊Dic7—28no—
260C22⋊Dic7—28no—
261C22⋊Dic7—28no—
262C22⋊Dic7—44no—
263C4⋊Dic7—28no—
264C4⋊Dic7—28no—
265Dic7⋊C4—28no—
266Dic7⋊C4—28no—
267Dic7⋊C4—28no—
268Dic7⋊C4C2×D4116yescomplemented
269C4×Dic7—28no—
270C4×Dic7—28no—
271C4×Dic7—44no—
272C23×Q8—71no—
273C23×D4C2×D711yescharacteristic
274C24×C4—71no—
275C2×#126—78no—
276C2×#126—148no—
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⋊C4—71no—
284C22×C4⋊C4—71no—
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⋊C4C2×D711yescharacteristic
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#390C2×D718yes—
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—28no—
325C23×C7—28no—
326C23×C7—28no—
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—44no—
341C23×C7—44no—
342C23×C7—44no—
343C23×C7—44no—
344C23×C7—44no—
345C23×C7—44no—
346C23×C7—44no—
347C23×C7—44no—
348C23×C7—44no—
349C23×C7—44no—
350C23×C7—44no—
351C23×C7C22×D412yes—
352C23×C7C2×#4114yes—
353C23×C7C2×#4112yes—
354C23×C7C2×#4112yes—
355C23×C7C2×#4112yes—
356C23×C7C2×#4112yes—
357C23×C7H(5,𝔽2)12yes—
358C23×C72−1+412yes—
359C23×C7C2511yescharacteristic
360C7×D4—416no—
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—44no—
377C2×C4×C7—44no—
378C2×C4×C7C22×D414yes—
379C2×C4×C7C2×#4114yes—
380C2×C4×C7C2×#4114yes—
381C2×Dic7—28no—
382C2×Dic7—28no—
383C2×Dic7—28no—
384C2×Dic7—22no—
385C2×Dic7—22no—
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—416no—
406C2×Dic7—44no—
407C2×Dic7—44no—
408C2×Dic7—44no—
409C2×Dic7—44no—
410C2×Dic7—44no—
411C2×Dic7C22×D414yes—
412C2×Dic7C22×D414yes—
413C2×Dic7C2×#4114yes—
414Dic14—416no—
415C25C22×D711yescharacteristic
416C25C22×D711yescharacteristic
417C22×Q8—74no—
418C22×Q8—144no—
419C22×Q8—144no—
420C22×Q8—282no—
421C22×D4—24no—
422C22×D4—24no—
423C22×D4—42no—
424C22×D4C22×D714yes—
425C23×C4—71no—
426C23×C4—71no—
427C23×C4—71no—
428C23×C4—71no—
429C23×C4—71no—
430C23×C4—71no—
431C23×C4—71no—
432C23×C4—71no—
433C23×C4—74no—
434C23×C4—144no—
435C23×C4—144no—
436C23×C4—282no—
437C23×C4C22×D711yescharacteristic
438C23×C4C22×D711yescharacteristic
439C23×C4C22×D711yescharacteristic
440C23×C4C22×D711yescharacteristic
441C23×C4C22×D711yescharacteristic
442#126—1432no—
443C22⋊Q8—1432no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—78no—
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—144no—
457C2×C4⋊C4C22×D714yes—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
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—282no—
476C2×C22⋊C4C22×D714yes—
477C2×C22⋊C4C22×D714yes—
478C2×C22⋊C4C22×D714yes—
479C2×C22⋊C4C22×D714yes—
480C2×C42—42no—
481C2×C42—74no—
482C2×C42—74no—
483C2×C42—74no—
484C2×C42—144no—
485C2×C42—144no—
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—24no—
499C22×C7—24no—
500C22×C7—24no—
501C22×C7—416no—
502C22×C7—42no—
503C22×C7—42no—
504C22×C7—42no—
505C22×C7—42no—
506C22×C7—42no—
507C22×C7—42no—
508C22×C7—42no—
509C22×C7—42no—
510C22×C7—42no—
511C22×C7—42no—
512C22×C7—42no—
513C22×C7—88no—
514C22×C7#52914yes—
515C22×C7#53214yes—
516C22×C7#53914yes—
517C22×C7#54614yes—
518C22×C7#54814yes—
519C22×C7#55114yes—
520C22×C7#55614yes—
521C22×C7C23×D411yescharacteristic
522C22×C7C22×#4111yescharacteristic
523C22×C7C22×#4111yescharacteristic
524C22×C7C22×#4111yescharacteristic
525C22×C7C22×#4111yescharacteristic
526C22×C7C2×H(5,𝔽2)11yescharacteristic
527C22×C7C2×2−1+411yescharacteristic
528C4×C7—24no—
529C4×C7—24no—
530C4×C7—24no—
531C4×C7—42no—
532C4×C7—42no—
533Dic7—24no—
534Dic7—24no—
535Dic7—24no—
536Dic7—42no—
537Dic7—42no—
538Dic7—42no—
539Dic7—42no—
540Dic7—42no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24#115714yes—
555C24C23×D712yes—
556C24C23×D712yes—
557C24C23×D711yescharacteristic
558C2×Q8—148no—
559C2×Q8—148no—
560C2×Q8—284no—
561C2×Q8—2816no—
562C2×D4—28no—
563C2×D4—28no—
564C2×D4—44no—
565C2×D4—416no—
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—74no—
579C22×C4—74no—
580C22×C4—74no—
581C22×C4—72no—
582C22×C4—72no—
583C22×C4—72no—
584C22×C4—72no—
585C22×C4—72no—
586C22×C4—72no—
587C22×C4—72no—
588C22×C4—72no—
589C22×C4—148no—
590C22×C4—148no—
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×C4—142no—
610C22×C4—142no—
611C22×C4—142no—
612C22×C4—284no—
613C22×C4—2816no—
614C22×C4D4×D714yes—
615C22×C4#115914yes—
616C22×C4#115914yes—
617C22×C4C23×D712yes—
618C22×C4C23×D712yes—
619C22×C4C23×D712yes—
620C22×C4C23×D712yes—
621C22×C4C23×D712yes—
622C4⋊C4—28no—
623C4⋊C4—716no—
624C4⋊C4—148no—
625C4⋊C4—148no—
626C4⋊C4—148no—
627C4⋊C4—148no—
628C4⋊C4—148no—
629C22⋊C4—28no—
630C22⋊C4—28no—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—148no—
634C22⋊C4—148no—
635C22⋊C4—148no—
636C22⋊C4—148no—
637C22⋊C4—148no—
638C22⋊C4—148no—
639C22⋊C4—284no—
640C42—44no—
641C42—148no—
642C42—148no—
643C42—284no—
644C2×C7—44no—
645C2×C7—82no—
646C2×C7#256018yescomplemented
647C2×C7C2×#52911yescharacteristic
648C2×C7C2×#53211yescharacteristic
649C2×C7C2×#53911yescharacteristic
650C2×C7C2×#54611yescharacteristic
651C2×C7C2×#54811yescharacteristic
652C2×C7C2×#55111yescharacteristic
653C2×C7C2×#55611yescharacteristic
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23C2×#115714yes—
682C23C2×#115712yes—
683C23C2×D4×D712yes—
684C23C2×#115912yes—
685C23C2×#115912yes—
686C23#654812yes—
687C23D7×#4112yes—
688C23#655412yes—
689C23C24×D711yescharacteristic
690Q8—2816no—
691D4—416no—
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—44no—
708C2×C4—44no—
709C2×C4—74no—
710C2×C4—74no—
711C2×C4—74no—
712C2×C4—148no—
713C2×C4—148no—
714C2×C4—148no—
715C2×C4—142no—
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—142no—
736C2×C4—2816no—
737C2×C4—284no—
738C2×C4—284no—
739C2×C4—284no—
740C2×C4—284no—
741C2×C4—284no—
742C2×C4C2×D4×D714yes—
743C2×C4C2×#115914yes—
744C2×C4C2×#115914yes—
745C7C2×#256011yescharacteristic, complemented, Sylow
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—416no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—88no—
762C22#9018614yes—
763C22#9022914yes—
764C22#9024314yes—
765C22#9029314yes—
766C22#9030114yes—
767C22#9036214yes—
768C22#9040714yes—
769C22C22×#115711yescharacteristic
770C22C22×D4×D711yescharacteristic
771C22C22×#115911yescharacteristic
772C22C22×#115911yescharacteristic
773C22C2×#654811yescharacteristic
774C22C2×D7×#4111yescharacteristic
775C22C2×#655411yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—144no—
782C4—144no—
783C4—144no—
784C4—282no—
785C4—282no—
786C4—282no—
787C4—282no—
788C4—282no—
789C2—44no—
790C2—82no—
791C2#1173380518yesdirect product factor
792C2C2×#9018611yescharacteristic
793C2C2×#9022911yescharacteristic
794C2C2×#9024311yescharacteristic
795C2C2×#9029311yescharacteristic
796C2C2×#9030111yescharacteristic
797C2C2×#9036211yescharacteristic
798C2C2×#9040711yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#390C2
socleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC2×#390D7
hypocenterC7C2×#2560
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#6442C2semidirect
2. C22×#6441C2semidirect
6. C2×#89752C2semidirect
7. C2×#89753C2semidirect
8. C2×#89725C2semidirect
9. C2×#89719C2semidirect
10. C2×#89716C2semidirect
11. C2×#89716C2semidirect
12. C2×#89723C2semidirect
13. C2×C22⋊C4×Dic7C2semidirect
14. C2×#89701C2semidirect
15. C2×C4×Dic7⋊C4C2semidirect
16. #11733805C2direct (N × H)
43. C2×#6442C22semidirect
45. C2×#6441C22semidirect
59. #89753C22semidirect
60. #89752C22semidirect
61. #89725C22semidirect
62. #89723C22semidirect
63. #89719C22semidirect
64. #89716C22semidirect
65. #89716C22semidirect
66. C22⋊C4×Dic7C22semidirect
67. C4×Dic7⋊C4C22semidirect
68. #89701C22semidirect
130. C2×Dic7⋊C4D4semidirect
268. Dic7⋊C4C2×D4semidirect
646. C2×C7#2560semidirect
745. C7C2×#2560semidirect
791. C2#11733805direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64422
C22×#64412
C2×C7×#3902
C2×#899942
C2×#899922
C2×#897522
C2×#897532
C2×#897252
C2×#897192
C2×#897162
C2×#897232
C2×C22⋊C4×Dic72
C2×#897012
C2×C4×Dic7⋊C42
#117338052
C2×#25607