Finite Group Databasebeta

← C2×#11731861 #13521625

Subgroups — C2×#11731861 #13521625

Order 1792.

3550 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×#6487C211yesmaximal, characteristic
2C23×Dic7⋊C4C211yesmaximal, characteristic
3C22×#6451C211yesmaximal, characteristic, complemented
4C22×#6441C211yesmaximal, characteristic
5C2×C7×#385C211yesmaximal, characteristic
6C2×#89756C211yesmaximal, characteristic, complemented
7C2×#89751C211yesmaximal, characteristic, complemented
8C2×#89748C211yesmaximal, characteristic, complemented
9C2×#89722C211yesmaximal, characteristic
10C2×#89714C211yesmaximal, characteristic
11C2×C22⋊C4×Dic7C211yesmaximal, characteristic
12#11731861C2116yesmaximal, direct product factor
13C2×#89429C211yesmaximal, characteristic, complemented
14C2×#89428C211yesmaximal, characteristic, complemented
15C2×#89419C211yesmaximal, characteristic, complemented
16C2×#89419C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C24×Dic7C2211yescharacteristic
19C24×Dic7C2211yescharacteristic
20C23×Dic14C2211yescharacteristic
21C23×Dic14C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×C4⋊Dic7C2211yescharacteristic
31C22×C4⋊Dic7C2211yescharacteristic
32C2×#6487—28no—
33C2×#6487C2218yes—
34C22×Dic7⋊C4—28no—
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2218yes—
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×Dic7⋊C4C2211yescharacteristic
45C22×Dic7⋊C4C2211yescharacteristic
46C22×C4×Dic7C2211yescharacteristic
47C22×C4×Dic7C2211yescharacteristic
48C2×#6451—28no—
49C2×#6451C2218yescomplemented
50C2×#6441—28no—
51C2×#6441C2218yes—
52C7×#385C2218yes—
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#89756C2218yescomplemented
62#89751C2218yescomplemented
63#89748C2218yescomplemented
64#89722C2218yes—
65#89714C2218yes—
66C22⋊C4×Dic7C2218yes—
67#89429C2218yescomplemented
68#89428C2218yescomplemented
69#89419C2218yescomplemented
70#89419C2218yescomplemented
71C2×#2440—71nomaximal, Sylow
72C25×C7C2311yescharacteristic
73C23×C4×C7—24no—
74C23×C4×C7—24no—
75C23×C4×C7—42no—
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2314yes—
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×Dic7—24no—
84C23×Dic7—24no—
85C23×Dic7—24no—
86C23×Dic7—24no—
87C23×Dic7—42no—
88C23×Dic7Q818yescomplemented
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2314yes—
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2314yes—
98C23×Dic7C2311yescharacteristic
99C22×Dic14—24no—
100C22×Dic14—24no—
101C22×Dic14—24no—
102C22×Dic14—24no—
103C22×Dic14—42no—
104C22×Dic14—42no—
105C22×Dic14C2314yes—
106C22×Dic14C2314yes—
107C2×C7×C4⋊C4—24no—
108C2×C7×C4⋊C4—42no—
109C2×C7×C4⋊C4C2314yes—
110C2×C7×C4⋊C4C2314yes—
111C2×C7×C22⋊C4—24no—
112C2×C7×C22⋊C4Q818yescomplemented
113C2×C7×C22⋊C4C2314yes—
114C2×C7×C22⋊C4C2314yes—
115C2×C22⋊Dic7—24no—
116C2×C22⋊Dic7D418yes—
117C2×C22⋊Dic7C2314yes—
118C2×C22⋊Dic7C2314yes—
119C2×C4⋊Dic7—24no—
120C2×C4⋊Dic7—24no—
121C2×C4⋊Dic7—24no—
122C2×C4⋊Dic7—42no—
123C2×C4⋊Dic7C2314yes—
124C2×C4⋊Dic7C2314yes—
125C2×C4⋊Dic7C2314yes—
126C2×C4⋊Dic7C2314yes—
127#6487—232no—
128C2×Dic7⋊C4—24no—
129C2×Dic7⋊C4—24no—
130C2×Dic7⋊C4—24no—
131C2×Dic7⋊C4—24no—
132C2×Dic7⋊C4—24no—
133C2×Dic7⋊C4—24no—
134C2×Dic7⋊C4—24no—
135C2×Dic7⋊C4—24no—
136C2×Dic7⋊C4—24no—
137C2×Dic7⋊C4—232no—
138C2×Dic7⋊C4D418yes—
139C2×Dic7⋊C4C2314yes—
140C2×Dic7⋊C4C2314yes—
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C2×Dic7⋊C4C2314yes—
144C2×Dic7⋊C4C2314yes—
145C2×Dic7⋊C4C2314yes—
146C2×Dic7⋊C4C2314yes—
147C2×Dic7⋊C4C2314yes—
148C2×Dic7⋊C4C2314yes—
149C2×C4×Dic7—24no—
150C2×C4×Dic7—24no—
151C2×C4×Dic7C2314yes—
152C2×C4×Dic7C2314yes—
153#6451—232no—
154#6441—232no—
155C7×#95C2314yes—
156C7×#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C7⋊#95C2314yes—
160C7⋊#95C2314yes—
161C7⋊#95C2314yes—
162C7⋊#95C2314yes—
163C22×C4⋊Q8—71no—
164C22×C22⋊Q8—71no—
165C22×C22⋊Q8—71no—
166C23×C4⋊C4—71no—
167#2440—716no—
168C2×#398—71no—
169C2×#398—71no—
170C2×#395—71no—
171C2×#395—71no—
172C2×#389—71no—
173C2×#389—71no—
174C2×#385—71no—
175C2×#385D711yescharacteristic
176C2×#384—71no—
177C2×#380—71no—
178C2×C4×C22⋊C4—71no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7—22no—
182C24×C7—22no—
183C24×C7C2×D414yes—
184C24×C7C2×Q814yes—
185C24×C7C2×Q814yes—
186C24×C7C2412yes—
187C24×C7C2411yescharacteristic
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—28no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—28no—
205C22×C4×C7—44no—
206C22×C4×C7—416no—
207C22×C4×C7C2×D414yes—
208C22×C4×C7C2×Q814yes—
209C22×C4×C7C2×Q814yes—
210C22×C4×C7C2412yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2412yes—
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—232no—
225C22×Dic7—28no—
226C22×Dic7—28no—
227C22×Dic7—28no—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7—22no—
231C22×Dic7—22no—
232C22×Dic7—22no—
233C22×Dic7—22no—
234C22×Dic7—22no—
235C22×Dic7—22no—
236C22×Dic7—22no—
237C22×Dic7—28no—
238C22×Dic7—44no—
239C22×Dic7—416no—
240C22×Dic7C2×D414yes—
241C22×Dic7C2×D414yes—
242C22×Dic7C2×D414yes—
243C22×Dic7C2×D414yes—
244C22×Dic7C2×Q814yes—
245C22×Dic7C2×Q814yes—
246C22×Dic7C2×Q8116yescomplemented
247C22×Dic7#4114yes—
248C22×Dic7C2412yes—
249C22×Dic7C2412yes—
250C22×Dic7C2412yes—
251C22×Dic7C2412yes—
252C22×Dic7C2412yes—
253C22×Dic7C2412yes—
254C22×Dic7C2412yes—
255C22×Dic7C2412yes—
256C2×Dic14—28no—
257C2×Dic14—28no—
258C2×Dic14—28no—
259C2×Dic14—28no—
260C2×Dic14—44no—
261C2×Dic14—44no—
262C2×Dic14—416no—
263C2×Dic14—416no—
264C7×C4⋊C4—28no—
265C7×C4⋊C4—44no—
266C7×C22⋊C4—28no—
267C7×C22⋊C4C2×Q8116yescomplemented
268C22⋊Dic7—28no—
269C22⋊Dic7C2×D4116yes—
270C4⋊Dic7—28no—
271C4⋊Dic7—28no—
272C4⋊Dic7—28no—
273C4⋊Dic7—44no—
274Dic7⋊C4—28no—
275Dic7⋊C4—28no—
276Dic7⋊C4—28no—
277Dic7⋊C4—28no—
278Dic7⋊C4—28no—
279Dic7⋊C4—28no—
280Dic7⋊C4—28no—
281Dic7⋊C4—28no—
282Dic7⋊C4—28no—
283Dic7⋊C4C2×D4116yes—
284C4×Dic7—28no—
285C4×Dic7—28no—
286C23×Q8—71no—
287C23×Q8—71no—
288C24×C4—71no—
289C24×C4—71no—
290C24×C4C2×D711yescharacteristic
291C2×C4⋊Q8—78no—
292C2×C4⋊Q8—148no—
293C2×C22⋊Q8—78no—
294C2×C22⋊Q8—78no—
295C2×C22⋊Q8—148no—
296C2×C22⋊Q8—148no—
297C22×C4⋊C4—71no—
298C22×C4⋊C4—71no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C4⋊C4—71no—
305C22×C4⋊C4—71no—
306C22×C4⋊C4—71no—
307C22×C4⋊C4—78no—
308C22×C4⋊C4—71no—
309C22×C4⋊C4—71no—
310C22×C4⋊C4—71no—
311C22×C4⋊C4—71no—
312C22×C4⋊C4—148no—
313C22×C4⋊C4C2×D711yescharacteristic
314C22×C4⋊C4C2×D711yescharacteristic
315C22×C22⋊C4—71no—
316C22×C22⋊C4—71no—
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C22⋊C4C2×D711yescharacteristic
319C22×C42—71no—
320C22×C42—71no—
321#398—78no—
322#398—78no—
323#395—78no—
324#395—78no—
325#389—78no—
326#389—78no—
327#385—78no—
328#385C2×D718yes—
329#384—78no—
330#380—78no—
331C4×C22⋊C4—78no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95C2×D711yescharacteristic
339C2×#95C2×D711yescharacteristic
340C23×C7—28no—
341C23×C7—28no—
342C23×C7—28no—
343C23×C7—28no—
344C23×C7—28no—
345C23×C7—28no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7C4⋊Q8116yescomplemented
351C23×C7C22×D414yes—
352C23×C7C22×D412yes—
353C23×C7C22×D412yes—
354C23×C7C22×Q814yes—
355C23×C7C22×Q812yes—
356C23×C7C22×Q814yes—
357C23×C7C22×Q812yes—
358C23×C7C2×#4112yes—
359C23×C7H(5,𝔽2)12yes—
360C23×C72−1+412yes—
361C23×C7C2511yescharacteristic
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—416no—
381C2×C4×C7—44no—
382C2×C4×C7—44no—
383C2×C4×C7—44no—
384C2×C4×C7C22×D414yes—
385C2×C4×C7C22×Q814yes—
386C2×C4×C7C22×Q814yes—
387C2×Dic7—28no—
388C2×Dic7—28no—
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—232no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—416no—
410C2×Dic7—44no—
411C2×Dic7—44no—
412C2×Dic7—44no—
413C2×Dic7C22⋊Q8116yescomplemented
414C2×Dic7C22×D414yes—
415C2×Dic7C22×D414yes—
416C2×Dic7C22×D414yes—
417C2×Dic7C22×D414yes—
418C2×Dic7C22×Q814yes—
419C2×Dic7C22×Q814yes—
420C2×Dic7C2×#4114yes—
421Dic14—416no—
422Dic14—416no—
423C25C22×D711yescharacteristic
424C22×Q8—74no—
425C22×Q8—74no—
426C22×Q8—144no—
427C22×Q8—144no—
428C22×Q8—144no—
429C22×Q8—144no—
430C22×Q8—282no—
431C22×Q8—282no—
432C23×C4—24no—
433C23×C4—24no—
434C23×C4—42no—
435C23×C4—71no—
436C23×C4—78no—
437C23×C4—74no—
438C23×C4—71no—
439C23×C4—71no—
440C23×C4—71no—
441C23×C4—71no—
442C23×C4—71no—
443C23×C4—71no—
444C23×C4—71no—
445C23×C4—74no—
446C23×C4—144no—
447C23×C4—144no—
448C23×C4—144no—
449C23×C4—144no—
450C23×C4—282no—
451C23×C4C22×D711yescharacteristic
452C23×C4C22×D711yescharacteristic
453C23×C4C22×D711yescharacteristic
454C23×C4C22×D714yes—
455C23×C4C22×D711yescharacteristic
456C23×C4C22×D711yescharacteristic
457C23×C4C22×D711yescharacteristic
458C4⋊Q8—1432no—
459C22⋊Q8—1432no—
460C22⋊Q8—1432no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—78no—
464C2×C4⋊C4—74no—
465C2×C4⋊C4—74no—
466C2×C4⋊C4—74no—
467C2×C4⋊C4—74no—
468C2×C4⋊C4—74no—
469C2×C4⋊C4—74no—
470C2×C4⋊C4—74no—
471C2×C4⋊C4—74no—
472C2×C4⋊C4—74no—
473C2×C4⋊C4—74no—
474C2×C4⋊C4—74no—
475C2×C4⋊C4—74no—
476C2×C4⋊C4—74no—
477C2×C4⋊C4—74no—
478C2×C4⋊C4—1432no—
479C2×C4⋊C4—144no—
480C2×C4⋊C4—144no—
481C2×C4⋊C4—144no—
482C2×C4⋊C4—144no—
483C2×C4⋊C4—144no—
484C2×C4⋊C4—144no—
485C2×C4⋊C4—144no—
486C2×C4⋊C4—144no—
487C2×C4⋊C4—144no—
488C2×C4⋊C4—144no—
489C2×C4⋊C4—144no—
490C2×C4⋊C4—144no—
491C2×C4⋊C4—282no—
492C2×C4⋊C4C22×D714yes—
493C2×C4⋊C4C22×D714yes—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—78no—
496C2×C22⋊C4—74no—
497C2×C22⋊C4—74no—
498C2×C22⋊C4—144no—
499C2×C22⋊C4Dic1418yescomplemented
500C2×C22⋊C4C22×D714yes—
501C2×C22⋊C4C22×D714yes—
502C2×C42—74no—
503C2×C42—74no—
504C2×C42—144no—
505C2×C42—144no—
506#95—74no—
507#95—74no—
508#95—74no—
509#95—74no—
510#95—74no—
511#95—74no—
512#95C22×D714yes—
513#95C22×D714yes—
514C22×C7—24no—
515C22×C7—24no—
516C22×C7—24no—
517C22×C7—232no—
518C22×C7—24no—
519C22×C7—24no—
520C22×C7—24no—
521C22×C7C2×C22⋊Q814yes—
522C22×C7C2×C4⋊Q814yes—
523C22×C7C2×C4⋊Q818yescomplemented
524C22×C7#54414yes—
525C22×C7D4214yes—
526C22×C7#54714yes—
527C22×C7D4×Q814yes—
528C22×C7#55414yes—
529C22×C7C23×D411yescharacteristic
530C22×C7C23×D411yescharacteristic
531C22×C7C23×Q811yescharacteristic
532C22×C7C23×Q811yescharacteristic
533C22×C7C22×#4111yescharacteristic
534C22×C7C2×H(5,𝔽2)11yescharacteristic
535C22×C7C2×2−1+411yescharacteristic
536C4×C7—24no—
537C4×C7—24no—
538C4×C7—24no—
539C4×C7—42no—
540C4×C7—42no—
541C4×C7—42no—
542Dic7—24no—
543Dic7—24no—
544Dic7—24no—
545Dic7—24no—
546Dic7—42no—
547Dic7—42no—
548Dic7—42no—
549Dic7C2×C22⋊Q818yescomplemented
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24C2×Dic1414yes—
555C24D4×D714yes—
556C24Q8×D714yes—
557C24C23×D712yes—
558C24C23×D711yescharacteristic
559C2×Q8—148no—
560C2×Q8—148no—
561C2×Q8—148no—
562C2×Q8—148no—
563C2×Q8—284no—
564C2×Q8—284no—
565C2×Q8—2816no—
566C2×Q8—2816no—
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—28no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—28no—
584C22×C4—44no—
585C22×C4—416no—
586C22×C4—74no—
587C22×C4—74no—
588C22×C4—74no—
589C22×C4—72no—
590C22×C4—74no—
591C22×C4—74no—
592C22×C4—74no—
593C22×C4—74no—
594C22×C4—716no—
595C22×C4—72no—
596C22×C4—72no—
597C22×C4—72no—
598C22×C4—72no—
599C22×C4—72no—
600C22×C4—72no—
601C22×C4—72no—
602C22×C4—148no—
603C22×C4—1432no—
604C22×C4—148no—
605C22×C4—148no—
606C22×C4—142no—
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—142no—
617C22×C4—142no—
618C22×C4—142no—
619C22×C4—148no—
620C22×C4—142no—
621C22×C4—142no—
622C22×C4—142no—
623C22×C4—142no—
624C22×C4—284no—
625C22×C4—2816no—
626C22×C4C2×Dic1414yes—
627C22×C4C2×Dic1414yes—
628C22×C4D4×D714yes—
629C22×C4C23×D712yes—
630C22×C4C23×D712yes—
631C22×C4C23×D712yes—
632C22×C4C23×D712yes—
633C22×C4C23×D712yes—
634C22×C4C23×D712yes—
635C4⋊C4—28no—
636C4⋊C4—44no—
637C4⋊C4—716no—
638C4⋊C4—148no—
639C4⋊C4—148no—
640C4⋊C4—148no—
641C4⋊C4—148no—
642C4⋊C4—148no—
643C4⋊C4—148no—
644C4⋊C4—148no—
645C4⋊C4—148no—
646C4⋊C4—148no—
647C4⋊C4—148no—
648C4⋊C4—148no—
649C4⋊C4—148no—
650C4⋊C4—284no—
651C22⋊C4—28no—
652C22⋊C4—716no—
653C22⋊C4—148no—
654C22⋊C4C2×Dic14116yescomplemented
655C42—148no—
656C42—148no—
657C2×C7—28no—
658C2×C7#244018yescomplemented
659C2×C7C22×C22⋊Q811yescharacteristic
660C2×C7C22×C4⋊Q811yescharacteristic
661C2×C7C2×#54411yescharacteristic
662C2×C7C2×D4211yescharacteristic
663C2×C7C2×#54711yescharacteristic
664C2×C7C2×D4×Q811yescharacteristic
665C2×C7C2×#55411yescharacteristic
666C23—28no—
667C23—28no—
668C23—28no—
669C23—28no—
670C23—28no—
671C23—28no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23#6451116yescomplemented
677C23C22×Dic1414yes—
678C23C22×Dic1412yes—
679C23C2×D4×D714yes—
680C23C2×D4×D712yes—
681C23C2×D4×D712yes—
682C23#654812yes—
683C23C2×Q8×D714yes—
684C23C2×Q8×D712yes—
685C23D7×#4112yes—
686C23#655412yes—
687C23C24×D711yescharacteristic
688Q8—2816no—
689Q8—2816no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
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—416no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—716no—
713C2×C4—74no—
714C2×C4—74no—
715C2×C4—74no—
716C2×C4—74no—
717C2×C4—74no—
718C2×C4—74no—
719C2×C4—74no—
720C2×C4—1432no—
721C2×C4—148no—
722C2×C4—148no—
723C2×C4—148no—
724C2×C4—148no—
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—142no—
737C2×C4—142no—
738C2×C4—142no—
739C2×C4—142no—
740C2×C4—142no—
741C2×C4—142no—
742C2×C4—2816no—
743C2×C4—284no—
744C2×C4—284no—
745C2×C4—284no—
746C2×C4C22×Dic1414yes—
747C2×C4C22×Dic1414yes—
748C2×C4C2×D4×D714yes—
749C7C2×#244011yescharacteristic, complemented, Sylow
750C22—24no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—232no—
757C22C2×#645114yes—
758C22C2×#645118yescomplemented
759C22D4×Dic1414yes—
760C22#9023014yes—
761C22#9028114yes—
762C22#9031414yes—
763C22D7×C22⋊Q814yes—
764C22#9034614yes—
765C22C23×Dic1411yescharacteristic
766C22C22×D4×D711yescharacteristic
767C22C22×D4×D711yescharacteristic
768C22C2×#654811yescharacteristic
769C22C22×Q8×D711yescharacteristic
770C22C2×D7×#4111yescharacteristic
771C22C2×#655411yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—78no—
779C4—144no—
780C4—144no—
781C4—144no—
782C4—144no—
783C4—282no—
784C4—282no—
785C4—282no—
786C2—28no—
787C2#1173186118yesdirect product factor
788C2C22×#645111yescharacteristic
789C2C2×D4×Dic1411yescharacteristic
790C2C2×#9023011yescharacteristic
791C2C2×#9028111yescharacteristic
792C2C2×#9031411yescharacteristic
793C2C2×D7×C22⋊Q811yescharacteristic
794C2C2×#9034611yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#385C2
socleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#385D7
hypocenterC7C2×#2440
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C22×#6451C2semidirect
6. C2×#89756C2semidirect
7. C2×#89751C2semidirect
8. C2×#89748C2semidirect
12. #11731861C2direct (N × H)
13. C2×#89429C2semidirect
14. C2×#89428C2semidirect
15. C2×#89419C2semidirect
16. C2×#89419C2semidirect
49. C2×#6451C22semidirect
61. #89756C22semidirect
62. #89751C22semidirect
63. #89748C22semidirect
67. #89429C22semidirect
68. #89428C22semidirect
69. #89419C22semidirect
70. #89419C22semidirect
88. C23×Dic7Q8semidirect
112. C2×C7×C22⋊C4Q8semidirect
246. C22×Dic7C2×Q8semidirect
267. C7×C22⋊C4C2×Q8semidirect
350. C23×C7C4⋊Q8semidirect
413. C2×Dic7C22⋊Q8semidirect
499. C2×C22⋊C4Dic14semidirect
523. C22×C7C2×C4⋊Q8semidirect
549. Dic7C2×C22⋊Q8semidirect
654. C22⋊C4C2×Dic14semidirect
658. C2×C7#2440semidirect
676. C23#6451semidirect
749. C7C2×#2440semidirect
758. C22C2×#6451semidirect
787. C2#11731861direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64872
C23×Dic7⋊C42
C22×#64512
C22×#64412
C2×C7×#3852
C2×#897562
C2×#897512
C2×#897482
C2×#897222
C2×#897142
C2×C22⋊C4×Dic72
#117318612
C2×#894292
C2×#894282
C2×#894192
C2×#24407