Finite Group Databasebeta

← C2×#11735589 #13521427

Subgroups — C2×#11735589 #13521427

Order 1792.

3114 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D7×C4⋊C4C211yesmaximal, characteristic, complemented
2C22×#6461C211yesmaximal, characteristic, complemented
3C2×C7×#400C211yesmaximal, characteristic, complemented
4C2×#89765C211yesmaximal, characteristic, complemented
5C2×#89761C211yesmaximal, characteristic, complemented
6#11735589C2116yesmaximal, direct product factor
7C2×#89448C211yesmaximal, characteristic, complemented
8C2×#89437C211yesmaximal, characteristic
9C2×#89437C211yesmaximal, characteristic
10C2×#89437C211yesmaximal, characteristic
11C2×#89439C211yesmaximal, characteristic, complemented
12C2×#89430C211yesmaximal, characteristic, complemented
13C2×#89441C211yesmaximal, characteristic, complemented
14C2×#89425C211yesmaximal, characteristic, complemented
15C2×#89424C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic, complemented
17C23×D28C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C23×C4×D7C2211yescharacteristic
20C23×C4×D7C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
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×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×C4×Dic7C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C2×#6461—28no—
41C2×#6461C2218yescomplemented
42C2×D7×C4⋊C4—28no—
43C2×D7×C4⋊C4C2218yescomplemented
44C7×#400C2218yescomplemented
45C2×C7×#95C2211yescharacteristic
46C2×C7×#95C2211yescharacteristic
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#89761C2218yescomplemented
59#89448C2218yescomplemented
60#89441C2218yescomplemented
61#89439C2218yescomplemented
62#89438C2218yescomplemented
63#89437C2218yes—
64#89437C2218yes—
65#89437C2218yes—
66#89430C2218yescomplemented
67#89425C2218yescomplemented
68#89424C2218yescomplemented
69C2×#2481—71nomaximal, Sylow
70C24×D7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C22×D28—24no—
86C22×D28—24no—
87C22×D28—24no—
88C22×D28C2314yes—
89C22×C4×D7—24no—
90C22×C4×D7—24no—
91C22×C4×D7—24no—
92C22×C4×D7—24no—
93C22×C4×D7—24no—
94C22×C4×D7—24no—
95C22×C4×D7—24no—
96C22×C4×D7—42no—
97C22×C4×D7—42no—
98C22×C4×D7C2314yes—
99C22×C4×D7C2314yes—
100C22×C4×D7C2314yes—
101C2×C7×C4⋊C4—24no—
102C2×C7×C4⋊C4—24no—
103C2×C7×C4⋊C4C2314yes—
104C2×C7×C4⋊C4C2314yes—
105C2×(C2×D7)⋊C4—24no—
106C2×(C2×D7)⋊C4—24no—
107C2×(C2×D7)⋊C4—24no—
108C2×(C2×D7)⋊C4—24no—
109C2×(C2×D7)⋊C4—24no—
110C2×(C2×D7)⋊C4—24no—
111C2×(C2×D7)⋊C4—24no—
112C2×(C2×D7)⋊C4—42no—
113C2×(C2×D7)⋊C4—42no—
114C2×(C2×D7)⋊C4C2314yes—
115C2×(C2×D7)⋊C4C2314yes—
116C2×(C2×D7)⋊C4C2314yes—
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⋊Dic7D418yescomplemented
124C2×C4⋊Dic7C2314yes—
125C2×Dic7⋊C4—24no—
126C2×Dic7⋊C4—24no—
127C2×Dic7⋊C4—24no—
128C2×Dic7⋊C4—24no—
129C2×Dic7⋊C4—42no—
130C2×Dic7⋊C4C2314yes—
131C2×Dic7⋊C4C2314yes—
132C2×Dic7⋊C4C2314yes—
133C2×Dic7⋊C4C2314yes—
134C2×Dic7⋊C4C2314yes—
135C2×C4×Dic7—24no—
136C2×C4×Dic7—42no—
137C2×C4×Dic7C2314yes—
138C2×C4×Dic7C2314yes—
139#6461—232no—
140D7×C4⋊C4—232no—
141C7×#95C2314yes—
142C7×#95C2314yes—
143C7×#95C2314yes—
144C7×#95C2314yes—
145C7×#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×#126—71no—
154C23×C4⋊C4—71no—
155#2481—716no—
156C2×#400—71no—
157C2×#400D711yescharacteristic, complemented
158C2×#397—71no—
159C2×#396—71no—
160C2×#388—71no—
161C2×#387—71no—
162C2×#387—71no—
163C2×#386—71no—
164C2×#386—71no—
165C2×#386—71no—
166C2×#385—71no—
167C2×#380—71no—
168C2×C4×C22⋊C4—71no—
169C24×C7C2411yescharacteristic
170C23×D7—22no—
171C23×D7—22no—
172C23×D7—22no—
173C23×D7—22no—
174C23×D7—22no—
175C23×D7—22no—
176C23×D7—22no—
177C23×D7—22no—
178C23×D7—22no—
179C23×D7—22no—
180C23×D7—22no—
181C23×D7#4114yes—
182C23×D7#4114yes—
183C23×D7#4114yes—
184C23×D7C2412yes—
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×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7C2×D414yes—
207C22×C4×C7C2412yes—
208C22×C4×C7C2412yes—
209C22×C4×C7C2412yes—
210C22×C4×C7C2412yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
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×Dic7C2×D414yes—
230C22×Dic7C2×D414yes—
231C22×Dic7#4114yes—
232C22×Dic7C2412yes—
233C22×Dic7C2412yes—
234C22×Dic7C2412yes—
235C22×Dic7C2412yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C2×D28—28no—
239C2×D28—28no—
240C2×D28—28no—
241C2×D28—416no—
242C2×C4×D7—232no—
243C2×C4×D7—28no—
244C2×C4×D7—28no—
245C2×C4×D7—28no—
246C2×C4×D7—28no—
247C2×C4×D7—28no—
248C2×C4×D7—28no—
249C2×C4×D7—28no—
250C2×C4×D7—44no—
251C2×C4×D7—44no—
252C2×C4×D7—416no—
253C2×C4×D7—416no—
254C7×C4⋊C4—28no—
255C7×C4⋊C4—28no—
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—
261(C2×D7)⋊C4—28no—
262(C2×D7)⋊C4—28no—
263(C2×D7)⋊C4—44no—
264(C2×D7)⋊C4—44no—
265C4⋊Dic7C2×D4116yescomplemented
266Dic7⋊C4—28no—
267Dic7⋊C4—28no—
268Dic7⋊C4—28no—
269Dic7⋊C4—28no—
270Dic7⋊C4—44no—
271C4×Dic7—28no—
272C4×Dic7—44no—
273C23×D4—71no—
274C24×C4—71no—
275C24×C4—71no—
276C24×C4—71no—
277C2×#126—78no—
278C2×#126—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—78no—
286C22×C4⋊C4—148no—
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×C42—71no—
299C22×C42—71no—
300#400—78no—
301#400C2×D718yescomplemented
302#397—78no—
303#396—78no—
304#388—78no—
305#387—78no—
306#387—78no—
307#386—78no—
308#386—78no—
309#386—78no—
310#385—78no—
311#380—78no—
312C4×C22⋊C4—78no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95C2×D711yescharacteristic
321C2×#95C2×D711yescharacteristic
322C2×#95C2×D711yescharacteristic
323C2×#95C2×D711yescharacteristic
324C2×#95C2×D711yescharacteristic
325C23×C7C22×D412yes—
326C23×C7C2×#4112yes—
327C23×C7C2×#4112yes—
328C23×C7C2×#4112yes—
329C23×C7C2×#4112yes—
330C23×C7H(5,𝔽2)12yes—
331C23×C72−1+412yes—
332C23×C7C2511yescharacteristic
333C22×D7—28no—
334C22×D7—28no—
335C22×D7—28no—
336C22×D7—28no—
337C22×D7—28no—
338C22×D7—28no—
339C22×D7—22no—
340C22×D7—22no—
341C22×D7—22no—
342C22×D7—22no—
343C22×D7—22no—
344C22×D7—22no—
345C22×D7—22no—
346C22×D7—22no—
347C22×D7—22no—
348C22×D7—22no—
349C22×D7—22no—
350C22×D7—44no—
351C22×D7—44no—
352C22×D7—44no—
353C22×D7—44no—
354C22×D7—44no—
355C22×D7—44no—
356C22×D7—44no—
357C22×D7#126116yescomplemented
358C22×D7C2×#4114yes—
359C22×D7C2×#4114yes—
360C22×D7C2×#4114yes—
361C2×C4×C7—28no—
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—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—44no—
383C2×C4×C7—44no—
384C2×C4×C7—44no—
385C2×C4×C7—44no—
386C2×C4×C7—44no—
387C2×C4×C7—44no—
388C2×C4×C7C22×D414yes—
389C2×Dic7—28no—
390C2×Dic7—28no—
391C2×Dic7—28no—
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×Dic7C22×D414yes—
411C2×Dic7C22×D414yes—
412C2×Dic7C2×#4114yes—
413D28—416no—
414C4×D7—232no—
415C4×D7—416no—
416C4×D7—416no—
417C25—71no—
418C25—71no—
419C22×D4—74no—
420C22×D4—144no—
421C22×D4—144no—
422C22×D4—144no—
423C23×C4—71no—
424C23×C4—71no—
425C23×C4—71no—
426C23×C4—71no—
427C23×C4—71no—
428C23×C4—71no—
429C23×C4—74no—
430C23×C4—74no—
431C23×C4—74no—
432C23×C4—144no—
433C23×C4—144no—
434C23×C4—144no—
435C23×C4—144no—
436C23×C4—144no—
437C23×C4—144no—
438C23×C4—144no—
439C23×C4—282no—
440C23×C4—282no—
441C23×C4C22×D711yescharacteristic
442C23×C4C22×D711yescharacteristic
443C23×C4C22×D711yescharacteristic
444C23×C4C22×D711yescharacteristic
445C23×C4C22×D711yescharacteristic
446C23×C4C22×D711yescharacteristic
447C23×C4C22×D711yescharacteristic
448#126—1432no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—78no—
452C2×C4⋊C4—74no—
453C2×C4⋊C4—74no—
454C2×C4⋊C4—74no—
455C2×C4⋊C4—74no—
456C2×C4⋊C4—74no—
457C2×C4⋊C4—74no—
458C2×C4⋊C4—1432no—
459C2×C4⋊C4—144no—
460C2×C4⋊C4—144no—
461C2×C4⋊C4—144no—
462C2×C4⋊C4—144no—
463C2×C4⋊C4—282no—
464C2×C4⋊C4C22×D714yes—
465C2×C4⋊C4C22×D714yes—
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—74no—
475C2×C22⋊C4—144no—
476C2×C22⋊C4—144no—
477C2×C22⋊C4—144no—
478C2×C22⋊C4—144no—
479C2×C22⋊C4—144no—
480C2×C22⋊C4—144no—
481C2×C22⋊C4—144no—
482C2×C22⋊C4—282no—
483C2×C22⋊C4—282no—
484C2×C42—74no—
485C2×C42—74no—
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—
498#95C22×D714yes—
499#95C22×D714yes—
500C22×C7#52514yes—
501C22×C7C2×#12614yes—
502C22×C7#53914yes—
503C22×C7#54614yes—
504C22×C7#54814yes—
505C22×C7#55214yes—
506C22×C7#55314yes—
507C22×C7C23×D411yescharacteristic
508C22×C7C22×#4111yescharacteristic
509C22×C7C22×#4111yescharacteristic
510C22×C7C22×#4111yescharacteristic
511C22×C7C22×#4111yescharacteristic
512C22×C7C2×H(5,𝔽2)11yescharacteristic
513C22×C7C2×2−1+411yescharacteristic
514C2×D7—24no—
515C2×D7—24no—
516C2×D7—24no—
517C2×D7—24no—
518C2×D7—24no—
519C2×D7—24no—
520C2×D7—232no—
521C2×D7—42no—
522C2×D7—42no—
523C2×D7—42no—
524C2×D7—42no—
525C2×D7—42no—
526C2×D7—42no—
527C2×D7—42no—
528C2×D7—88no—
529C2×D7C2×#12618yescomplemented
530C4×C7—24no—
531C4×C7—42no—
532C4×C7—42no—
533C4×C7—42no—
534C4×C7—42no—
535C4×C7—42no—
536C4×C7—42no—
537Dic7—24no—
538Dic7—24no—
539Dic7—24no—
540Dic7—42no—
541Dic7—42no—
542Dic7—42no—
543C24—74no—
544C24—74no—
545C24—74no—
546C24—72no—
547C24—72no—
548C24—142no—
549C24—142no—
550C24—142no—
551C24—142no—
552C24—142no—
553C24—142no—
554C24—142no—
555C24—142no—
556C24—142no—
557C24—142no—
558C24—142no—
559C24C23×D711yescharacteristic
560C2×D4—148no—
561C2×D4—148no—
562C2×D4—148no—
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—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—74no—
585C22×C4—74no—
586C22×C4—74no—
587C22×C4—72no—
588C22×C4—72no—
589C22×C4—72no—
590C22×C4—72no—
591C22×C4—72no—
592C22×C4—72no—
593C22×C4—148no—
594C22×C4—148no—
595C22×C4—148no—
596C22×C4—148no—
597C22×C4—1432no—
598C22×C4—148no—
599C22×C4—148no—
600C22×C4—142no—
601C22×C4—142no—
602C22×C4—142no—
603C22×C4—142no—
604C22×C4—142no—
605C22×C4—142no—
606C22×C4—148no—
607C22×C4—142no—
608C22×C4—142no—
609C22×C4—142no—
610C22×C4—142no—
611C22×C4—142no—
612C22×C4—142no—
613C22×C4—142no—
614C22×C4—142no—
615C22×C4—142no—
616C22×C4—284no—
617C22×C4—284no—
618C22×C4—2816no—
619C22×C4—2816no—
620C22×C4D4×D714yes—
621C22×C4C23×D712yes—
622C22×C4C23×D712yes—
623C22×C4C23×D712yes—
624C22×C4C23×D712yes—
625C22×C4C23×D712yes—
626C22×C4C23×D712yes—
627C22×C4C23×D712yes—
628C4⋊C4—28no—
629C4⋊C4—28no—
630C4⋊C4—716no—
631C4⋊C4—148no—
632C4⋊C4—148no—
633C4⋊C4—148no—
634C4⋊C4—148no—
635C4⋊C4—284no—
636C22⋊C4—148no—
637C22⋊C4—148no—
638C22⋊C4—148no—
639C22⋊C4—148no—
640C22⋊C4—148no—
641C22⋊C4—148no—
642C22⋊C4—148no—
643C22⋊C4—284no—
644C22⋊C4—284no—
645C42—148no—
646C42—284no—
647C2×C7#248118yescomplemented
648C2×C7C2×#52511yescharacteristic
649C2×C7C22×#12611yescharacteristic
650C2×C7C2×#53911yescharacteristic
651C2×C7C2×#54611yescharacteristic
652C2×C7C2×#54811yescharacteristic
653C2×C7C2×#55211yescharacteristic
654C2×C7C2×#55311yescharacteristic
655D7—28no—
656D7—82no—
657C23—716no—
658C23—74no—
659C23—74no—
660C23—74no—
661C23—148no—
662C23—148no—
663C23—148no—
664C23—148no—
665C23—148no—
666C23—142no—
667C23—142no—
668C23—142no—
669C23—142no—
670C23—148no—
671C23—142no—
672C23—142no—
673C23—142no—
674C23—142no—
675C23—142no—
676C23—142no—
677C23—142no—
678C23—284no—
679C23—284no—
680C23—284no—
681C23—284no—
682C23—284no—
683C23—284no—
684C23—284no—
685C23C2×D4×D712yes—
686C23#655112yes—
687C23D7×#4112yes—
688C23D7×#4112yes—
689C23D7×#4112yes—
690C23D7×#4112yes—
691C23#655312yes—
692C23C24×D711yescharacteristic
693D4—2816no—
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—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—74no—
722C2×C4—74no—
723C2×C4—74no—
724C2×C4—1432no—
725C2×C4—148no—
726C2×C4—142no—
727C2×C4—142no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—148no—
733C2×C4—148no—
734C2×C4—142no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—142no—
738C2×C4—142no—
739C2×C4—142no—
740C2×C4—142no—
741C2×C4—142no—
742C2×C4—142no—
743C2×C4—2816no—
744C2×C4—2816no—
745C2×C4—284no—
746C2×C4—284no—
747C2×C4—284no—
748C2×C4C2×D4×D714yes—
749C7C2×#248111yescharacteristic, complemented, Sylow
750C22—78no—
751C22—1432no—
752C22—144no—
753C22—144no—
754C22—144no—
755C22—144no—
756C22—144no—
757C22—144no—
758C22—282no—
759C22—282no—
760C22—282no—
761C22—282no—
762C22—282no—
763C22—282no—
764C22—282no—
765C22—568no—
766C22#9032414yes—
767C22#9034714yes—
768C22#9036714yes—
769C22#9038314yes—
770C22#9038414yes—
771C22D7×#12614yes—
772C22#9040014yes—
773C22C22×D4×D711yescharacteristic
774C22C2×#655111yescharacteristic
775C22C2×D7×#4111yescharacteristic
776C22C2×D7×#4111yescharacteristic
777C22C2×D7×#4111yescharacteristic
778C22C2×D7×#4111yescharacteristic
779C22C2×#655311yescharacteristic
780C4—24no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—144no—
788C4—144no—
789C4—144no—
790C4—282no—
791C4—282no—
792C4—282no—
793C2—148no—
794C2—562no—
795C2#1173558918yesdirect product factor
796C2C2×#9032411yescharacteristic
797C2C2×#9034711yescharacteristic
798C2C2×#9036711yescharacteristic
799C2C2×#9038311yescharacteristic
800C2C2×#9038411yescharacteristic
801C2C2×#9040011yescharacteristic
802C2C2×D7×#12611yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#400C2
socleC24×C7C24
prime radicalC23×D28C22
hypercenterC2×#400D7
hypocenterC7C2×#2481
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. C22×D7×C4⋊C4C2semidirect
2. C22×#6461C2semidirect
3. C2×C7×#400C2semidirect
4. C2×#89765C2semidirect
5. C2×#89761C2semidirect
6. #11735589C2direct (N × H)
7. C2×#89448C2semidirect
11. C2×#89439C2semidirect
12. C2×#89430C2semidirect
13. C2×#89441C2semidirect
14. C2×#89425C2semidirect
15. C2×#89424C2semidirect
16. C2×#89438C2semidirect
41. C2×#6461C22semidirect
43. C2×D7×C4⋊C4C22semidirect
44. C7×#400C22semidirect
57. #89765C22semidirect
58. #89761C22semidirect
59. #89448C22semidirect
60. #89441C22semidirect
61. #89439C22semidirect
62. #89438C22semidirect
66. #89430C22semidirect
67. #89425C22semidirect
68. #89424C22semidirect
123. C2×C4⋊Dic7D4semidirect
157. C2×#400D7semidirect
265. C4⋊Dic7C2×D4semidirect
301. #400C2×D7semidirect
357. C22×D7#126semidirect
529. C2×D7C2×#126semidirect
647. C2×C7#2481semidirect
749. C7C2×#2481semidirect
795. C2#11735589direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D7×C4⋊C42
C22×#64612
C2×C7×#4002
C2×#897652
C2×#897612
#117355892
C2×#894482
C2×#894372
C2×#894392
C2×#894302
C2×#894412
C2×#894252
C2×#894242
C2×#894382
C2×#24817