Finite Group Databasebeta

← C2×#11733514 #13523944

Subgroups — C2×#11733514 #13523944

Order 1792.

2834 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×#6457C211yesmaximal, characteristic
2C22×#6453C211yesmaximal, characteristic, complemented
3C2×C7×#389C211yesmaximal, characteristic, complemented
4C2×#89766C211yesmaximal, characteristic, complemented
5C2×#89766C211yesmaximal, characteristic, complemented
6C2×#89763C211yesmaximal, characteristic
7C2×#89761C211yesmaximal, characteristic, complemented
8C2×#89758C211yesmaximal, characteristic, complemented
9C2×#89762C211yesmaximal, characteristic, complemented
10C2×#89711C211yesmaximal, characteristic
11C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
12#11733514C2116yesmaximal, direct product factor
13C2×#89442C211yesmaximal, characteristic, complemented
14C2×#89442C211yesmaximal, characteristic, complemented
15C2×#89441C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic, complemented
17C23×D28C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
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×#6457—28no—
45C2×#6457C2218yes—
46C2×#6453—28no—
47C2×#6453C2218yescomplemented
48C7×#389C2218yescomplemented
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#89763C2218yes—
60#89762C2218yescomplemented
61#89761C2218yescomplemented
62#89758C2218yescomplemented
63#89711C2218yes—
64C4×Dic7⋊C4C2218yescomplemented
65#89442C2218yescomplemented
66#89442C2218yescomplemented
67#89441C2218yescomplemented
68#89438C2218yescomplemented
69C2×#2558—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—42no—
88C22×D28C2314yes—
89C22×C4×D7—24no—
90C22×C4×D7—24no—
91C22×C4×D7—42no—
92C22×C4×D7C2314yes—
93C2×C7×C4⋊C4—24no—
94C2×C7×C4⋊C4—24no—
95C2×C7×C4⋊C4—24no—
96C2×C7×C4⋊C4—42no—
97C2×C7×C4⋊C4C2314yes—
98C2×C7×C4⋊C4C2314yes—
99C2×C7×C4⋊C4C2314yes—
100C2×C7×C4⋊C4C2314yes—
101C2×C42×C7—42no—
102C2×C42×C7C2314yes—
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—24no—
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×(C2×D7)⋊C4C2314yes—
124C2×(C2×D7)⋊C4C2314yes—
125C2×C4⋊Dic7—24no—
126C2×C4⋊Dic7—24no—
127C2×C4⋊Dic7—24no—
128C2×C4⋊Dic7C2314yes—
129C2×C4⋊Dic7C2314yes—
130C2×C4⋊Dic7C2314yes—
131C2×Dic7⋊C4—24no—
132C2×Dic7⋊C4—24no—
133C2×Dic7⋊C4D418yes—
134C2×Dic7⋊C4C2314yes—
135C2×Dic7⋊C4C2314yes—
136C2×Dic7⋊C4C2314yes—
137C2×C4×Dic7—24no—
138C2×C4×Dic7—24no—
139C2×C4×Dic7—42no—
140C2×C4×Dic7C2314yes—
141C2×C4×Dic7C2314yes—
142C2×C4×Dic7C2314yes—
143#6457—232no—
144#6453—232no—
145C7×#95C2314yes—
146C7×#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×#125—71no—
154C22×#123—71no—
155#2558—716no—
156C2×#400—71no—
157C2×#396—71no—
158C2×#396—71no—
159C2×#394—71no—
160C2×#390—71no—
161C2×#389D711yescharacteristic, complemented
162C2×#388—71no—
163C2×#388—71no—
164C2×#388—71no—
165C2×#388—71no—
166C2×#385—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—
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×C7#4114yes—
205C22×C4×C7#4114yes—
206C22×C4×C7#4114yes—
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×Dic7—22no—
230C22×Dic7C2×D414yes—
231C22×Dic7C2×D414yes—
232C22×Dic7C2412yes—
233C22×Dic7C2412yes—
234C22×Dic7C2412yes—
235C22×Dic7C2412yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C2×D28—28no—
239C2×D28—28no—
240C2×D28—44no—
241C2×D28—416no—
242C2×C4×D7—28no—
243C2×C4×D7—28no—
244C2×C4×D7—44no—
245C2×C4×D7—416no—
246C7×C4⋊C4—28no—
247C7×C4⋊C4—28no—
248C7×C4⋊C4—28no—
249C7×C4⋊C4—44no—
250C42×C7—44no—
251(C2×D7)⋊C4—28no—
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—44no—
262C4⋊Dic7—28no—
263C4⋊Dic7—28no—
264C4⋊Dic7—28no—
265Dic7⋊C4—28no—
266Dic7⋊C4—28no—
267Dic7⋊C4C2×D4116yes—
268C4×Dic7—28no—
269C4×Dic7—28no—
270C4×Dic7—44no—
271C23×D4—71no—
272C24×C4—71no—
273C2×#125—78no—
274C2×#125—148no—
275C2×#123—78no—
276C2×#123—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⋊C4C2×D711yescharacteristic
284C22×C4⋊C4C2×D711yescharacteristic
285C22×C4⋊C4C2×D711yescharacteristic
286C22×C4⋊C4C2×D711yescharacteristic
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×C22⋊C4—71no—
298C22×C42—71no—
299C22×C42—71no—
300C22×C42—71no—
301C22×C42C2×D711yescharacteristic
302#400—78no—
303#396—78no—
304#396—78no—
305#394—78no—
306#390—78no—
307#389C2×D718yescomplemented
308#388—78no—
309#388—78no—
310#388—78no—
311#388—78no—
312#385—78no—
313C4×C4⋊C4—78no—
314C4×C22⋊C4—78no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95C2×D711yescharacteristic
322C2×#95C2×D711yescharacteristic
323C23×C7C22×D412yes—
324C23×C7C2×#4112yes—
325C23×C7C2×#4112yes—
326C23×C7C2×#4112yes—
327C23×C7C2×#4112yes—
328C23×C7H(5,𝔽2)12yes—
329C23×C72−1+412yes—
330C23×C7C2511yescharacteristic
331C22×D7—28no—
332C22×D7—28no—
333C22×D7—28no—
334C22×D7—22no—
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—44no—
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×D7C2×#4114yes—
359C2×C4×C7—28no—
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—22no—
379C2×C4×C7—22no—
380C2×C4×C7—44no—
381C2×C4×C7—44no—
382C2×C4×C7—44no—
383C2×C4×C7C22×D414yes—
384C2×C4×C7C2×#4114yes—
385C2×C4×C7C2×#4114yes—
386C2×C4×C7C2×#4114yes—
387C2×Dic7—28no—
388C2×Dic7—28no—
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×Dic7C22×D414yes—
410C2×Dic7C22×D414yes—
411D28—416no—
412C4×D7—416no—
413C25—71no—
414C25—71no—
415C22×D4—74no—
416C22×D4—144no—
417C22×D4—144no—
418C22×D4—282no—
419C23×C4—71no—
420C23×C4—71no—
421C23×C4—71no—
422C23×C4—71no—
423C23×C4—71no—
424C23×C4—71no—
425C23×C4—74no—
426C23×C4—144no—
427C23×C4—144no—
428C23×C4—282no—
429C23×C4C22×D711yescharacteristic
430C23×C4C22×D711yescharacteristic
431C23×C4C22×D711yescharacteristic
432C23×C4C22×D711yescharacteristic
433C23×C4C22×D711yescharacteristic
434C23×C4C22×D711yescharacteristic
435C23×C4C22×D711yescharacteristic
436#125—1432no—
437#123—1432no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4—78no—
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—144no—
450C2×C4⋊C4—144no—
451C2×C4⋊C4—144no—
452C2×C4⋊C4—144no—
453C2×C4⋊C4—144no—
454C2×C4⋊C4C22×D714yes—
455C2×C4⋊C4C22×D714yes—
456C2×C4⋊C4C22×D714yes—
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—
496C22×C7#52914yes—
497C22×C7#53214yes—
498C22×C7#53914yes—
499C22×C7#54614yes—
500C22×C7#54814yes—
501C22×C7#55214yes—
502C22×C7#55314yes—
503C22×C7C23×D411yescharacteristic
504C22×C7C22×#4111yescharacteristic
505C22×C7C22×#4111yescharacteristic
506C22×C7C22×#4111yescharacteristic
507C22×C7C22×#4111yescharacteristic
508C22×C7C2×H(5,𝔽2)11yescharacteristic
509C22×C7C2×2−1+411yescharacteristic
510C2×D7—24no—
511C2×D7—24no—
512C2×D7—24no—
513C2×D7—42no—
514C2×D7—42no—
515C2×D7—42no—
516C2×D7—42no—
517C2×D7—416no—
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—24no—
528C4×C7—24no—
529C4×C7—24no—
530C4×C7—42no—
531C4×C7—42no—
532C4×C7—42no—
533Dic7—24no—
534Dic7—24no—
535Dic7—42no—
536Dic7—42no—
537Dic7—42no—
538Dic7—42no—
539C24—74no—
540C24—72no—
541C24—72no—
542C24—142no—
543C24—142no—
544C24—142no—
545C24—142no—
546C24—142no—
547C24—142no—
548C24—142no—
549C24—142no—
550C24—142no—
551C24—142no—
552C24—142no—
553C24—142no—
554C24—142no—
555C24C23×D711yescharacteristic
556C2×D4—148no—
557C2×D4—148no—
558C2×D4—284no—
559C2×D4—2816no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
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—74no—
578C22×C4—74no—
579C22×C4—72no—
580C22×C4—72no—
581C22×C4—72no—
582C22×C4—72no—
583C22×C4—72no—
584C22×C4—72no—
585C22×C4—148no—
586C22×C4—148no—
587C22×C4—142no—
588C22×C4—142no—
589C22×C4—142no—
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—284no—
604C22×C4—2816no—
605C22×C4#115714yes—
606C22×C4D4×D714yes—
607C22×C4#116114yes—
608C22×C4#116114yes—
609C22×C4C23×D712yes—
610C22×C4C23×D712yes—
611C22×C4C23×D712yes—
612C22×C4C23×D712yes—
613C22×C4C23×D712yes—
614C22×C4C23×D712yes—
615C22×C4C23×D712yes—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—28no—
619C4⋊C4—44no—
620C4⋊C4—716no—
621C4⋊C4—148no—
622C4⋊C4—148no—
623C4⋊C4—148no—
624C4⋊C4—148no—
625C4⋊C4—148no—
626C22⋊C4—148no—
627C22⋊C4—148no—
628C22⋊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—284no—
637C42—44no—
638C42—148no—
639C42—148no—
640C42—284no—
641C2×C7#255818yescomplemented
642C2×C7C2×#52911yescharacteristic
643C2×C7C2×#53211yescharacteristic
644C2×C7C2×#53911yescharacteristic
645C2×C7C2×#54611yescharacteristic
646C2×C7C2×#54811yescharacteristic
647C2×C7C2×#55211yescharacteristic
648C2×C7C2×#55311yescharacteristic
649D7—44no—
650D7—82no—
651C23—74no—
652C23—148no—
653C23—148no—
654C23—148no—
655C23—142no—
656C23—142no—
657C23—142no—
658C23—142no—
659C23—142no—
660C23—142no—
661C23—142no—
662C23—142no—
663C23—142no—
664C23—142no—
665C23—142no—
666C23—142no—
667C23—142no—
668C23—284no—
669C23—284no—
670C23—284no—
671C23—284no—
672C23—284no—
673C23—284no—
674C23—284no—
675C23—284no—
676C23—284no—
677C23—284no—
678C23—284no—
679C23C2×#115712yes—
680C23C2×D4×D712yes—
681C23#654812yes—
682C23C2×#116112yes—
683C23C2×#116112yes—
684C23D7×#4112yes—
685C23#655412yes—
686C23C24×D711yescharacteristic
687D4—2816no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—28no—
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—22no—
708C2×C4—22no—
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—2816no—
733C2×C4—284no—
734C2×C4—284no—
735C2×C4—284no—
736C2×C4—284no—
737C2×C4C2×#115714yes—
738C2×C4C2×D4×D714yes—
739C2×C4C2×#116114yes—
740C2×C4C2×#116114yes—
741C7C2×#255811yescharacteristic, complemented, Sylow
742C22—144no—
743C22—144no—
744C22—144no—
745C22—2816no—
746C22—282no—
747C22—282no—
748C22—282no—
749C22—282no—
750C22—282no—
751C22—282no—
752C22—282no—
753C22—282no—
754C22—282no—
755C22—282no—
756C22—282no—
757C22—568no—
758C22#9020514yes—
759C22#9024314yes—
760C22#9027114yes—
761C22#9030114yes—
762C22#9033614yes—
763C22#9038514yes—
764C22#9041614yes—
765C22C22×#115711yescharacteristic
766C22C22×D4×D711yescharacteristic
767C22C2×#654811yescharacteristic
768C22C22×#116111yescharacteristic
769C22C22×#116111yescharacteristic
770C22C2×D7×#4111yescharacteristic
771C22C2×#655411yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—144no—
780C4—144no—
781C4—282no—
782C4—282no—
783C4—282no—
784C4—282no—
785C2—284no—
786C2—562no—
787C2#1173351418yesdirect product factor
788C2C2×#9020511yescharacteristic
789C2C2×#9024311yescharacteristic
790C2C2×#9027111yescharacteristic
791C2C2×#9030111yescharacteristic
792C2C2×#9033611yescharacteristic
793C2C2×#9038511yescharacteristic
794C2C2×#9041611yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#389C2
socleC24×C7C24
prime radicalC23×D28C22
hypercenterC2×#389D7
hypocenterC7C2×#2558
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C22×#6453C2semidirect
3. C2×C7×#389C2semidirect
4. C2×#89766C2semidirect
5. C2×#89766C2semidirect
7. C2×#89761C2semidirect
8. C2×#89758C2semidirect
9. C2×#89762C2semidirect
11. C2×C4×Dic7⋊C4C2semidirect
12. #11733514C2direct (N × H)
13. C2×#89442C2semidirect
14. C2×#89442C2semidirect
15. C2×#89441C2semidirect
16. C2×#89438C2semidirect
47. C2×#6453C22semidirect
48. C7×#389C22semidirect
57. #89766C22semidirect
58. #89766C22semidirect
60. #89762C22semidirect
61. #89761C22semidirect
62. #89758C22semidirect
64. C4×Dic7⋊C4C22semidirect
65. #89442C22semidirect
66. #89442C22semidirect
67. #89441C22semidirect
68. #89438C22semidirect
161. C2×#389D7semidirect
307. #389C2×D7semidirect
641. C2×C7#2558semidirect
741. C7C2×#2558semidirect
787. C2#11733514direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64572
C22×#64532
C2×C7×#3892
C2×#897662
C2×#897632
C2×#897612
C2×#897582
C2×#897622
C2×#897112
C2×C4×Dic7⋊C42
#117335142
C2×#894422
C2×#894412
C2×#894382
C2×#25587