Finite Group Databasebeta

← C2×#11733985 #13523952

Subgroups — C2×#11733985 #13523952

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×#6509C211yesmaximal, characteristic, complemented
2C22×#6461C211yesmaximal, characteristic, complemented
3C2×C7×#391C211yesmaximal, characteristic, complemented
4C2×#90003C211yesmaximal, characteristic, complemented
5C2×#89765C211yesmaximal, characteristic, complemented
6C2×#89711C211yesmaximal, characteristic
7C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
8#11733985C2116yesmaximal, direct product factor
9C2×#89437C211yesmaximal, characteristic
10C2×#89433C211yesmaximal, characteristic, complemented
11C2×#89444C211yesmaximal, characteristic
12C2×#89442C211yesmaximal, characteristic, complemented
13C2×#89442C211yesmaximal, characteristic, complemented
14C2×#89441C211yesmaximal, characteristic, complemented
15C2×#89426C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic, complemented
17C23×C7×Q8C2211yescharacteristic
18C23×D28C2211yescharacteristic
19C23×C4×D7C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C42×C7C2211yescharacteristic
22C2×#6509—28no—
23C2×#6509C2218yescomplemented
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×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×C4⋊Dic7C2211yescharacteristic
37C22×C4⋊Dic7C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6461—28no—
45C2×#6461C2218yescomplemented
46C7×#391C2218yescomplemented
47C2×C7×#95C2211yescharacteristic
48C2×C7×#95C2211yescharacteristic
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51#90003C2218yescomplemented
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58#89765C2218yescomplemented
59#89711C2218yes—
60C4×Dic7⋊C4C2218yescomplemented
61#89444C2218yes—
62#89442C2218yescomplemented
63#89442C2218yescomplemented
64#89441C2218yescomplemented
65#89438C2218yescomplemented
66#89437C2218yes—
67#89433C2218yescomplemented
68#89426C2218yescomplemented
69C2×#2560—71nomaximal, Sylow
70C24×D7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C22×C7×Q8—24no—
73C22×C7×Q8—24no—
74C22×C7×Q8—42no—
75C22×C7×Q8C2314yes—
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C22×D28—24no—
90C22×D28—24no—
91C22×D28—42no—
92C22×D28C2314yes—
93C22×C4×D7—24no—
94C22×C4×D7—24no—
95C22×C4×D7—42no—
96C22×C4×D7C2314yes—
97C2×C7×C4⋊C4—24no—
98C2×C7×C4⋊C4C2314yes—
99C2×C42×C7—42no—
100C2×C42×C7C2314yes—
101#6509—232no—
102C2×(C2×D7)⋊C4—24no—
103C2×(C2×D7)⋊C4—24no—
104C2×(C2×D7)⋊C4—24no—
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)⋊C4C2314yes—
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×(C2×D7)⋊C4C2314yes—
124C2×C4⋊Dic7—24no—
125C2×C4⋊Dic7—24no—
126C2×C4⋊Dic7—24no—
127C2×C4⋊Dic7C2314yes—
128C2×C4⋊Dic7C2314yes—
129C2×C4⋊Dic7C2314yes—
130C2×Dic7⋊C4—24no—
131C2×Dic7⋊C4—24no—
132C2×Dic7⋊C4D418yescomplemented
133C2×Dic7⋊C4C2314yes—
134C2×Dic7⋊C4C2314yes—
135C2×Dic7⋊C4C2314yes—
136C2×C4×Dic7—24no—
137C2×C4×Dic7—24no—
138C2×C4×Dic7—42no—
139C2×C4×Dic7C2314yes—
140C2×C4×Dic7C2314yes—
141C2×C4×Dic7C2314yes—
142#6461—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×#391D711yescharacteristic, complemented
161C2×#390—71no—
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×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—22no—
182C23×D7—22no—
183C23×D7#4114yes—
184C23×D7C2412yes—
185C23×D7C2412yes—
186C2×C7×Q8—28no—
187C2×C7×Q8—28no—
188C2×C7×Q8—44no—
189C2×C7×Q8—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×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7C2×D414yes—
208C22×C4×C7#4114yes—
209C22×C4×C7#4114yes—
210C22×C4×C7#4114yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2412yes—
216C22×C4×C7C2412yes—
217C22×C4×C7C2412yes—
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×Dic7—22no—
234C22×Dic7C2×D414yes—
235C22×Dic7C2×D414yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C22×Dic7C2412yes—
239C22×Dic7C2412yes—
240C22×Dic7C2412yes—
241C22×Dic7C2412yes—
242C2×D28—28no—
243C2×D28—28no—
244C2×D28—44no—
245C2×D28—416no—
246C2×C4×D7—28no—
247C2×C4×D7—28no—
248C2×C4×D7—44no—
249C2×C4×D7—416no—
250C7×C4⋊C4—28no—
251C42×C7—44no—
252(C2×D7)⋊C4—28no—
253(C2×D7)⋊C4—28no—
254(C2×D7)⋊C4—28no—
255(C2×D7)⋊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—44no—
263C4⋊Dic7—28no—
264C4⋊Dic7—28no—
265C4⋊Dic7—28no—
266Dic7⋊C4—28no—
267Dic7⋊C4—28no—
268Dic7⋊C4C2×D4116yescomplemented
269C4×Dic7—28no—
270C4×Dic7—28no—
271C4×Dic7—44no—
272C23×Q8C2×D711yescharacteristic
273C23×D4—71no—
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⋊C4—71no—
294C22×C22⋊C4—71no—
295C22×C22⋊C4—71no—
296C22×C22⋊C4—71no—
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#391C2×D718yescomplemented
306#390—78no—
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×#95C2×D711yescharacteristic
321C2×#95C2×D711yescharacteristic
322C2×#95C2×D711yescharacteristic
323C2×#95C2×D711yescharacteristic
324C23×C7C22×D412yes—
325C23×C7C2×#4112yes—
326C23×C7C2×#4112yes—
327C23×C7C2×#4112yes—
328C23×C7C2×#4112yes—
329C23×C7H(5,𝔽2)12yes—
330C23×C72−1+412yes—
331C23×C7C2511yescharacteristic
332C22×D7—28no—
333C22×D7—28no—
334C22×D7—28no—
335C22×D7—22no—
336C22×D7—22no—
337C22×D7—22no—
338C22×D7—22no—
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—44no—
349C22×D7—44no—
350C22×D7—44no—
351C22×D7—44no—
352C22×D7—44no—
353C22×D7—44no—
354C22×D7—44no—
355C22×D7—44no—
356C22×D7—44no—
357C22×D7—44no—
358C22×D7—44no—
359C22×D7C2×#4114yes—
360C7×Q8—416no—
361C2×C4×C7—28no—
362C2×C4×C7—28no—
363C2×C4×C7—28no—
364C2×C4×C7—28no—
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×C7C22×D414yes—
386C2×C4×C7C2×#4114yes—
387C2×C4×C7C2×#4114yes—
388C2×C4×C7C2×#4114yes—
389C2×Dic7—28no—
390C2×Dic7—28no—
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—22no—
407C2×Dic7—44no—
408C2×Dic7—44no—
409C2×Dic7—44no—
410C2×Dic7—44no—
411C2×Dic7C22×D414yes—
412C2×Dic7C22×D414yes—
413D28—416no—
414C4×D7—416no—
415C25—71no—
416C25—71no—
417C22×Q8—24no—
418C22×Q8—24no—
419C22×Q8—42no—
420C22×Q8C22×D714yes—
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—74no—
432C23×C4—144no—
433C23×C4—144no—
434C23×C4—282no—
435C23×C4C22×D711yescharacteristic
436C23×C4C22×D711yescharacteristic
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—74no—
459C2×C22⋊C4—74no—
460C2×C22⋊C4—74no—
461C2×C22⋊C4—74no—
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—144no—
476C2×C22⋊C4—144no—
477C2×C22⋊C4—144no—
478C2×C22⋊C4—144no—
479C2×C22⋊C4—282no—
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#95C22×D714yes—
495#95C22×D714yes—
496#95C22×D714yes—
497#95C22×D714yes—
498C22×C7#52914yes—
499C22×C7#53214yes—
500C22×C7#53914yes—
501C22×C7#54614yes—
502C22×C7#54814yes—
503C22×C7#55114yes—
504C22×C7#55614yes—
505C22×C7C23×D411yescharacteristic
506C22×C7C22×#4111yescharacteristic
507C22×C7C22×#4111yescharacteristic
508C22×C7C22×#4111yescharacteristic
509C22×C7C22×#4111yescharacteristic
510C22×C7C2×H(5,𝔽2)11yescharacteristic
511C22×C7C2×2−1+411yescharacteristic
512C2×D7—24no—
513C2×D7—24no—
514C2×D7—24no—
515C2×D7—416no—
516C2×D7—42no—
517C2×D7—42no—
518C2×D7—42no—
519C2×D7—42no—
520C2×D7—42no—
521C2×D7—42no—
522C2×D7—42no—
523C2×D7—42no—
524C2×D7—42no—
525C2×D7—42no—
526C2×D7—42no—
527C2×D7—88no—
528C4×C7—24no—
529C4×C7—24no—
530C4×C7—24no—
531C4×C7—24no—
532C4×C7—42no—
533C4×C7—42no—
534C4×C7—42no—
535Dic7—24no—
536Dic7—24no—
537Dic7—42no—
538Dic7—42no—
539Dic7—42no—
540Dic7—42no—
541C24—74no—
542C24—72no—
543C24—72no—
544C24—142no—
545C24—142no—
546C24—142no—
547C24—142no—
548C24—142no—
549C24—142no—
550C24—142no—
551C24—142no—
552C24—142no—
553C24—142no—
554C24—142no—
555C24—142no—
556C24—142no—
557C24C23×D711yescharacteristic
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—44no—
561C2×Q8—416no—
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—22no—
582C22×C4—22no—
583C22×C4—74no—
584C22×C4—74no—
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—148no—
609C22×C4—284no—
610C22×C4—2816no—
611C22×C4#115714yes—
612C22×C4D4×D714yes—
613C22×C4#116114yes—
614C22×C4#116114yes—
615C22×C4C23×D712yes—
616C22×C4C23×D712yes—
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—148no—
630C22⋊C4—148no—
631C22⋊C4—148no—
632C22⋊C4—148no—
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#256018yescomplemented
645C2×C7C2×#52911yescharacteristic
646C2×C7C2×#53211yescharacteristic
647C2×C7C2×#53911yescharacteristic
648C2×C7C2×#54611yescharacteristic
649C2×C7C2×#54811yescharacteristic
650C2×C7C2×#55111yescharacteristic
651C2×C7C2×#55611yescharacteristic
652D7—44no—
653D7—82no—
654C23—74no—
655C23—148no—
656C23—148no—
657C23—148no—
658C23—142no—
659C23—142no—
660C23—142no—
661C23—142no—
662C23—142no—
663C23—142no—
664C23—142no—
665C23—142no—
666C23—142no—
667C23—142no—
668C23—142no—
669C23—142no—
670C23—142no—
671C23—284no—
672C23—284no—
673C23—284no—
674C23—284no—
675C23—284no—
676C23—284no—
677C23—284no—
678C23—284no—
679C23—284no—
680C23—284no—
681C23—284no—
682C23C2×#115712yes—
683C23C2×D4×D712yes—
684C23#654812yes—
685C23C2×#116112yes—
686C23C2×#116112yes—
687C23D7×#4112yes—
688C23#655412yes—
689C23C24×D711yescharacteristic
690Q8—416no—
691D4—2816no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—28no—
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—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—74no—
717C2×C4—74no—
718C2×C4—148no—
719C2×C4—148no—
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×C4C2×#115714yes—
742C2×C4C2×D4×D714yes—
743C2×C4C2×#116114yes—
744C2×C4C2×#116114yes—
745C7C2×#256011yescharacteristic, complemented, Sylow
746C22—144no—
747C22—144no—
748C22—144no—
749C22—282no—
750C22—282no—
751C22—282no—
752C22—282no—
753C22—2816no—
754C22—282no—
755C22—282no—
756C22—282no—
757C22—282no—
758C22—282no—
759C22—282no—
760C22—282no—
761C22—568no—
762C22#9018114yes—
763C22#9027114yes—
764C22#9027514yes—
765C22#9032814yes—
766C22#9033614yes—
767C22#9036814yes—
768C22#9041614yes—
769C22C22×#115711yescharacteristic
770C22C22×D4×D711yescharacteristic
771C22C2×#654811yescharacteristic
772C22C22×#116111yescharacteristic
773C22C22×#116111yescharacteristic
774C22C2×D7×#4111yescharacteristic
775C22C2×#655411yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—24no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—144no—
784C4—144no—
785C4—282no—
786C4—282no—
787C4—282no—
788C4—282no—
789C2—284no—
790C2—562no—
791C2#1173398518yesdirect product factor
792C2C2×#9018111yescharacteristic
793C2C2×#9027511yescharacteristic
794C2C2×#9027111yescharacteristic
795C2C2×#9033611yescharacteristic
796C2C2×#9032811yescharacteristic
797C2C2×#9036811yescharacteristic
798C2C2×#9041611yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#391C2
socleC24×C7C24
prime radicalC23×D28C22
hypercenterC2×#391D7
hypocenterC7C2×#2560
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
1. C22×#6509C2semidirect
2. C22×#6461C2semidirect
3. C2×C7×#391C2semidirect
4. C2×#90003C2semidirect
5. C2×#89765C2semidirect
7. C2×C4×Dic7⋊C4C2semidirect
8. #11733985C2direct (N × H)
10. C2×#89433C2semidirect
12. C2×#89442C2semidirect
13. C2×#89442C2semidirect
14. C2×#89441C2semidirect
15. C2×#89426C2semidirect
16. C2×#89438C2semidirect
23. C2×#6509C22semidirect
45. C2×#6461C22semidirect
46. C7×#391C22semidirect
51. #90003C22semidirect
58. #89765C22semidirect
60. C4×Dic7⋊C4C22semidirect
62. #89442C22semidirect
63. #89442C22semidirect
64. #89441C22semidirect
65. #89438C22semidirect
67. #89433C22semidirect
68. #89426C22semidirect
132. C2×Dic7⋊C4D4semidirect
160. C2×#391D7semidirect
268. Dic7⋊C4C2×D4semidirect
305. #391C2×D7semidirect
644. C2×C7#2560semidirect
745. C7C2×#2560semidirect
791. C2#11733985direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#65092
C22×#64612
C2×C7×#3912
C2×#900032
C2×#897652
C2×#897112
C2×C4×Dic7⋊C42
#117339852
C2×#894372
C2×#894332
C2×#894442
C2×#894422
C2×#894412
C2×#894262
C2×#894382
C2×#25607