Finite Group Databasebeta

← C2×#11735189 #13521813

Subgroups — C2×#11735189 #13521813

Order 1792.

3246 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6459C211yesmaximal, characteristic
2C22×#6459C211yesmaximal, characteristic
3C22×#6451C211yesmaximal, characteristic, complemented
4C22×#6450C211yesmaximal, characteristic, complemented
5C2×C7×#398C211yesmaximal, characteristic, complemented
6C2×#89766C211yesmaximal, characteristic
7C2×#89744C211yesmaximal, characteristic, complemented
8C2×#89745C211yesmaximal, characteristic, complemented
9C2×#89762C211yesmaximal, characteristic
10#11735189C2116yesmaximal, direct product factor
11C2×#89448C211yesmaximal, characteristic
12C2×#89429C211yesmaximal, characteristic, complemented
13C2×#89418C211yesmaximal, characteristic, complemented
14C2×#89419C211yesmaximal, characteristic, complemented
15C2×#89442C211yesmaximal, characteristic
16C2×#89438C211yesmaximal, characteristic
17C23×C4×D7C2211yescharacteristic
18C23×Dic14C2211yescharacteristic
19C23×Dic14C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊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×C4⋊Dic7C2211yescharacteristic
31C22×C4⋊Dic7C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×C4×Dic7C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6459—28no—
45C2×#6459—28no—
46C2×#6459C2218yes—
47C2×#6459C2218yes—
48C2×#6451—28no—
49C2×#6451C2218yescomplemented
50C2×#6450—28no—
51C2×#6450C2218yescomplemented
52C7×#398C2218yescomplemented
53C2×C7×#95C2211yescharacteristic
54C2×C7×#95C2211yescharacteristic
55C2×C7×#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61#89766C2218yes—
62#89762C2218yes—
63#89745C2218yescomplemented
64#89744C2218yescomplemented
65#89448C2218yes—
66#89442C2218yes—
67#89438C2218yes—
68#89429C2218yescomplemented
69#89419C2218yescomplemented
70#89418C2218yescomplemented
71C2×#2429—71nomaximal, Sylow
72C24×D7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C22×C4×D7—24no—
88C22×C4×D7—24no—
89C22×C4×D7—24no—
90C22×C4×D7C2314yes—
91C22×Dic14—24no—
92C22×Dic14—24no—
93C22×Dic14—24no—
94C22×Dic14—24no—
95C22×Dic14—24no—
96C22×Dic14D418yes—
97C22×Dic14C2314yes—
98C22×Dic14C2314yes—
99C2×C7×C4⋊C4—24no—
100C2×C7×C4⋊C4—24no—
101C2×C7×C4⋊C4—24no—
102C2×C7×C4⋊C4—24no—
103C2×C7×C4⋊C4C2314yes—
104C2×C7×C4⋊C4C2314yes—
105C2×C7×C4⋊C4C2314yes—
106C2×C7×C4⋊C4C2314yes—
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)⋊C4Q818yescomplemented
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×C4⋊Dic7—24no—
120C2×C4⋊Dic7—24no—
121C2×C4⋊Dic7C2314yes—
122C2×C4⋊Dic7C2314yes—
123C2×Dic7⋊C4—24no—
124C2×Dic7⋊C4—24no—
125C2×Dic7⋊C4—24no—
126C2×Dic7⋊C4—24no—
127C2×Dic7⋊C4—24no—
128C2×Dic7⋊C4—24no—
129C2×Dic7⋊C4—24no—
130C2×Dic7⋊C4D418yes—
131C2×Dic7⋊C4C2314yes—
132C2×Dic7⋊C4C2314yes—
133C2×Dic7⋊C4C2314yes—
134C2×Dic7⋊C4C2314yes—
135C2×Dic7⋊C4C2314yes—
136C2×Dic7⋊C4C2314yes—
137C2×Dic7⋊C4C2314yes—
138C2×Dic7⋊C4C2314yes—
139C2×C4×Dic7—24no—
140C2×C4×Dic7—24no—
141C2×C4×Dic7—24no—
142C2×C4×Dic7—24no—
143C2×C4×Dic7C2314yes—
144C2×C4×Dic7C2314yes—
145C2×C4×Dic7C2314yes—
146C2×C4×Dic7C2314yes—
147#6459—232no—
148#6459—232no—
149#6451—232no—
150#6450—232no—
151C7×#95C2314yes—
152C7×#95C2314yes—
153C7×#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×C4⋊Q8—71no—
160C22×C22⋊Q8—71no—
161C22×C22⋊Q8—71no—
162C22×C4×Q8—71no—
163#2429—716no—
164C2×#398—71no—
165C2×#398D711yescharacteristic, complemented
166C2×#396—71no—
167C2×#396—71no—
168C2×#391—71no—
169C2×#389—71no—
170C2×#389—71no—
171C2×#389—71no—
172C2×#388—71no—
173C2×#388—71no—
174C2×C4×C22⋊C4—71no—
175C24×C7C2411yescharacteristic
176C23×D7—22no—
177C23×D7—22no—
178C23×D7—22no—
179C23×D7—22no—
180C23×D7—22no—
181C23×D7—22no—
182C23×D7C2×Q814yes—
183C23×D7C2412yes—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
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×C7C2×D414yes—
203C22×C4×C7C2×D414yes—
204C22×C4×C7C2×Q814yes—
205C22×C4×C7C2412yes—
206C22×C4×C7C2412yes—
207C22×C4×C7C2412yes—
208C22×C4×C7C2412yes—
209C22×C4×C7C2412yes—
210C22×C4×C7C2412yes—
211C22×C4×C7C2412yes—
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×Dic7C2×D414yes—
227C22×Dic7C2×D414yes—
228C22×Dic7C2×D414yes—
229C22×Dic7C2×D414yes—
230C22×Dic7C2×Q814yes—
231C22×Dic7#4114yes—
232C22×Dic7#4114yes—
233C22×Dic7C2412yes—
234C22×Dic7C2412yes—
235C22×Dic7C2412yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C22×Dic7C2412yes—
239C22×Dic7C2412yes—
240C2×C4×D7—28no—
241C2×C4×D7—28no—
242C2×C4×D7—28no—
243C2×C4×D7—416no—
244C2×Dic14—232no—
245C2×Dic14—28no—
246C2×Dic14—28no—
247C2×Dic14—28no—
248C2×Dic14—28no—
249C2×Dic14—28no—
250C2×Dic14—416no—
251C2×Dic14C2×D4116yes—
252C7×C4⋊C4—28no—
253C7×C4⋊C4—28no—
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)⋊C4C2×Q8116yescomplemented
262C4⋊Dic7—28no—
263C4⋊Dic7—28no—
264Dic7⋊C4—28no—
265Dic7⋊C4—28no—
266Dic7⋊C4—28no—
267Dic7⋊C4—28no—
268Dic7⋊C4—28no—
269Dic7⋊C4—28no—
270Dic7⋊C4—28no—
271Dic7⋊C4C2×D4116yes—
272C4×Dic7—28no—
273C4×Dic7—28no—
274C4×Dic7—28no—
275C4×Dic7—28no—
276C23×Q8—71no—
277C23×Q8—71no—
278C24×C4—71no—
279C2×C4⋊Q8—78no—
280C2×C4⋊Q8—148no—
281C2×C22⋊Q8—78no—
282C2×C22⋊Q8—78no—
283C2×C22⋊Q8—148no—
284C2×C22⋊Q8—148no—
285C2×C4×Q8—78no—
286C2×C4×Q8—148no—
287C22×C4⋊C4—71no—
288C22×C4⋊C4—71no—
289C22×C4⋊C4—71no—
290C22×C4⋊C4—71no—
291C22×C4⋊C4—71no—
292C22×C4⋊C4—71no—
293C22×C4⋊C4—71no—
294C22×C4⋊C4—71no—
295C22×C4⋊C4—71no—
296C22×C4⋊C4—71no—
297C22×C4⋊C4C2×D711yescharacteristic
298C22×C4⋊C4C2×D711yescharacteristic
299C22×C4⋊C4C2×D711yescharacteristic
300C22×C4⋊C4C2×D711yescharacteristic
301C22×C22⋊C4—71no—
302C22×C22⋊C4—71no—
303C22×C22⋊C4—71no—
304C22×C22⋊C4—71no—
305C22×C22⋊C4—71no—
306C22×C22⋊C4—71no—
307C22×C42—71no—
308C22×C42—71no—
309C22×C42—71no—
310C22×C42—71no—
311#398—78no—
312#398C2×D718yescomplemented
313#396—78no—
314#396—78no—
315#391—78no—
316#389—78no—
317#389—78no—
318#389—78no—
319#388—78no—
320#388—78no—
321C4×C22⋊C4—78no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95—71no—
326C2×#95—71no—
327C2×#95C2×D711yescharacteristic
328C2×#95C2×D711yescharacteristic
329C2×#95C2×D711yescharacteristic
330C23×C7C22×D412yes—
331C23×C7C22×D412yes—
332C23×C7C22×Q812yes—
333C23×C7C2×#4112yes—
334C23×C7C2×#4112yes—
335C23×C72−1+412yes—
336C23×C72−1+412yes—
337C23×C7C2511yescharacteristic
338C22×D7—28no—
339C22×D7—28no—
340C22×D7—28no—
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×D7C22×Q814yes—
352C2×C4×C7—28no—
353C2×C4×C7—28no—
354C2×C4×C7—28no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
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—44no—
374C2×C4×C7—44no—
375C2×C4×C7—44no—
376C2×C4×C7—44no—
377C2×C4×C7C22×D414yes—
378C2×C4×C7C22×D414yes—
379C2×C4×C7C22×Q814yes—
380C2×Dic7—28no—
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—44no—
399C2×Dic7—44no—
400C2×Dic7#121116yes—
401C2×Dic7C22×D414yes—
402C2×Dic7C22×D414yes—
403C2×Dic7C22×D414yes—
404C2×Dic7C22×D414yes—
405C2×Dic7C22×Q814yes—
406C2×Dic7C2×#4114yes—
407C2×Dic7C2×#4114yes—
408C4×D7—416no—
409Dic14—232no—
410Dic14—416no—
411C25—71no—
412C22×Q8—78no—
413C22×Q8—74no—
414C22×Q8—74no—
415C22×Q8—144no—
416C22×Q8—144no—
417C22×Q8—144no—
418C22×Q8—144no—
419C22×Q8—144no—
420C23×C4—71no—
421C23×C4—71no—
422C23×C4—71no—
423C23×C4—71no—
424C23×C4—71no—
425C23×C4—71no—
426C23×C4—71no—
427C23×C4—74no—
428C23×C4—144no—
429C23×C4—144no—
430C23×C4—144no—
431C23×C4C22×D711yescharacteristic
432C23×C4C22×D711yescharacteristic
433C23×C4C22×D711yescharacteristic
434C23×C4C22×D711yescharacteristic
435C23×C4C22×D711yescharacteristic
436C23×C4C22×D711yescharacteristic
437C23×C4C22×D711yescharacteristic
438C4⋊Q8—1432no—
439C22⋊Q8—1432no—
440C22⋊Q8—1432no—
441C4×Q8—1432no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—78no—
447C2×C4⋊C4—74no—
448C2×C4⋊C4—74no—
449C2×C4⋊C4—74no—
450C2×C4⋊C4—74no—
451C2×C4⋊C4—74no—
452C2×C4⋊C4—74no—
453C2×C4⋊C4—74no—
454C2×C4⋊C4—74no—
455C2×C4⋊C4—74no—
456C2×C4⋊C4—74no—
457C2×C4⋊C4—144no—
458C2×C4⋊C4—144no—
459C2×C4⋊C4—144no—
460C2×C4⋊C4—144no—
461C2×C4⋊C4—144no—
462C2×C4⋊C4—144no—
463C2×C4⋊C4—144no—
464C2×C4⋊C4—144no—
465C2×C4⋊C4—144no—
466C2×C4⋊C4C22×D714yes—
467C2×C4⋊C4C22×D714yes—
468C2×C4⋊C4C22×D714yes—
469C2×C4⋊C4C22×D714yes—
470C2×C22⋊C4—78no—
471C2×C22⋊C4—74no—
472C2×C22⋊C4—74no—
473C2×C22⋊C4—74no—
474C2×C22⋊C4—74no—
475C2×C22⋊C4—74no—
476C2×C22⋊C4—74no—
477C2×C22⋊C4—144no—
478C2×C22⋊C4—144no—
479C2×C22⋊C4—144no—
480C2×C22⋊C4—144no—
481C2×C22⋊C4—144no—
482C2×C42—74no—
483C2×C42—74no—
484C2×C42—74no—
485C2×C42—74no—
486C2×C42—144no—
487C2×C42—144no—
488C2×C42—144no—
489C2×C42—144no—
490#95—74no—
491#95—74no—
492#95—74no—
493#95—74no—
494#95—74no—
495#95C22×D714yes—
496#95C22×D714yes—
497#95C22×D714yes—
498C22×C7C2×#12114yes—
499C22×C7#53314yes—
500C22×C7#54114yes—
501C22×C7#54714yes—
502C22×C7#54814yes—
503C22×C7D4×Q814yes—
504C22×C7D4×Q814yes—
505C22×C7C23×D411yescharacteristic
506C22×C7C23×D411yescharacteristic
507C22×C7C23×Q811yescharacteristic
508C22×C7C22×#4111yescharacteristic
509C22×C7C22×#4111yescharacteristic
510C22×C7C2×2−1+411yescharacteristic
511C22×C7C2×2−1+411yescharacteristic
512C2×D7—24no—
513C2×D7—24no—
514C2×D7—24no—
515C2×D7—42no—
516C2×D7—416no—
517C2×D7—42no—
518C2×D7—42no—
519C2×D7—42no—
520C4×C7—24no—
521C4×C7—24no—
522C4×C7—24no—
523C4×C7—42no—
524C4×C7—42no—
525C4×C7—42no—
526C4×C7—42no—
527Dic7—24no—
528Dic7—24no—
529Dic7—24no—
530Dic7—24no—
531Dic7—42no—
532Dic7—42no—
533Dic7C2×#12118yes—
534C24—74no—
535C24—72no—
536C24—142no—
537C24—142no—
538C24—142no—
539C24—142no—
540C24—142no—
541C24—142no—
542C24C23×D711yescharacteristic
543C2×Q8—716no—
544C2×Q8—148no—
545C2×Q8—1432no—
546C2×Q8—148no—
547C2×Q8—148no—
548C2×Q8—148no—
549C2×Q8—148no—
550C2×Q8—2816no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
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—74no—
570C22×C4—74no—
571C22×C4—74no—
572C22×C4—72no—
573C22×C4—74no—
574C22×C4—74no—
575C22×C4—74no—
576C22×C4—74no—
577C22×C4—72no—
578C22×C4—72no—
579C22×C4—72no—
580C22×C4—72no—
581C22×C4—72no—
582C22×C4—72no—
583C22×C4—148no—
584C22×C4—148no—
585C22×C4—148no—
586C22×C4—142no—
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—2816no—
601C22×C4D4×D714yes—
602C22×C4D4×D714yes—
603C22×C4Q8×D714yes—
604C22×C4C23×D712yes—
605C22×C4C23×D712yes—
606C22×C4C23×D712yes—
607C22×C4C23×D712yes—
608C22×C4C23×D712yes—
609C22×C4C23×D712yes—
610C22×C4C23×D712yes—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—28no—
614C4⋊C4—28no—
615C4⋊C4—716no—
616C4⋊C4—148no—
617C4⋊C4—148no—
618C4⋊C4—148no—
619C4⋊C4—148no—
620C4⋊C4—148no—
621C4⋊C4—148no—
622C4⋊C4—148no—
623C4⋊C4—148no—
624C4⋊C4—148no—
625C22⋊C4—716no—
626C22⋊C4—148no—
627C22⋊C4—148no—
628C22⋊C4—148no—
629C22⋊C4—148no—
630C22⋊C4—148no—
631C42—148no—
632C42—148no—
633C42—148no—
634C42—148no—
635C2×C7#242918yescomplemented
636C2×C7C22×#12111yescharacteristic
637C2×C7C2×#53311yescharacteristic
638C2×C7C2×#54111yescharacteristic
639C2×C7C2×#54711yescharacteristic
640C2×C7C2×#54811yescharacteristic
641C2×C7C2×D4×Q811yescharacteristic
642C2×C7C2×D4×Q811yescharacteristic
643D7—44no—
644C23—74no—
645C23—148no—
646C23—148no—
647C23—148no—
648C23—142no—
649C23—142no—
650C23—142no—
651C23—142no—
652C23—142no—
653C23—142no—
654C23—284no—
655C23—284no—
656C23—284no—
657C23—284no—
658C23C2×D4×D712yes—
659C23C2×D4×D712yes—
660C23C2×Q8×D712yes—
661C23#655112yes—
662C23D7×#4112yes—
663C23D7×#4112yes—
664C23#655412yes—
665C23C24×D711yescharacteristic
666Q8—1432no—
667Q8—2816no—
668C2×C4—28no—
669C2×C4—28no—
670C2×C4—28no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—716no—
694C2×C4—74no—
695C2×C4—74no—
696C2×C4—74no—
697C2×C4—74no—
698C2×C4—74no—
699C2×C4—74no—
700C2×C4—74no—
701C2×C4—148no—
702C2×C4—148no—
703C2×C4—148no—
704C2×C4—148no—
705C2×C4—142no—
706C2×C4—142no—
707C2×C4—142no—
708C2×C4—142no—
709C2×C4—142no—
710C2×C4—142no—
711C2×C4—142no—
712C2×C4—142no—
713C2×C4—142no—
714C2×C4—142no—
715C2×C4—142no—
716C2×C4—142no—
717C2×C4—142no—
718C2×C4—142no—
719C2×C4—2816no—
720C2×C4—284no—
721C2×C4—284no—
722C2×C4C2×D4×D714yes—
723C2×C4C2×D4×D714yes—
724C2×C4C2×Q8×D714yes—
725C7C2×#242911yescharacteristic, complemented, Sylow
726C22—144no—
727C22—144no—
728C22—144no—
729C22—282no—
730C22—282no—
731C22—282no—
732C22—2816no—
733C22—282no—
734C22D7×#12114yes—
735C22#9032314yes—
736C22#9032414yes—
737C22#9034614yes—
738C22#9037914yes—
739C22#9038714yes—
740C22#9041814yes—
741C22C22×D4×D711yescharacteristic
742C22C22×D4×D711yescharacteristic
743C22C22×Q8×D711yescharacteristic
744C22C2×#655111yescharacteristic
745C22C2×D7×#4111yescharacteristic
746C22C2×D7×#4111yescharacteristic
747C22C2×#655411yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—78no—
756C4—144no—
757C4—144no—
758C4—144no—
759C4—144no—
760C4—282no—
761C4—282no—
762C2—284no—
763C2#1173518918yesdirect product factor
764C2C2×D7×#12111yescharacteristic
765C2C2×#9032311yescharacteristic
766C2C2×#9032411yescharacteristic
767C2C2×#9034611yescharacteristic
768C2C2×#9037911yescharacteristic
769C2C2×#9038711yescharacteristic
770C2C2×#9041811yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#398C2
socleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#398D7
hypocenterC7C2×#2429
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. C22×#6451C2semidirect
4. C22×#6450C2semidirect
5. C2×C7×#398C2semidirect
7. C2×#89744C2semidirect
8. C2×#89745C2semidirect
10. #11735189C2direct (N × H)
12. C2×#89429C2semidirect
13. C2×#89418C2semidirect
14. C2×#89419C2semidirect
49. C2×#6451C22semidirect
51. C2×#6450C22semidirect
52. C7×#398C22semidirect
63. #89745C22semidirect
64. #89744C22semidirect
68. #89429C22semidirect
69. #89419C22semidirect
70. #89418C22semidirect
112. C2×(C2×D7)⋊C4Q8semidirect
165. C2×#398D7semidirect
261. (C2×D7)⋊C4C2×Q8semidirect
312. #398C2×D7semidirect
635. C2×C7#2429semidirect
725. C7C2×#2429semidirect
763. C2#11735189direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64592
C22×#64512
C22×#64502
C2×C7×#3982
C2×#897662
C2×#897442
C2×#897452
C2×#897622
#117351892
C2×#894482
C2×#894292
C2×#894182
C2×#894192
C2×#894422
C2×#894382
C2×#24297