Finite Group Databasebeta

← C2×#11733038 #13525132

Subgroups — C2×#11733038 #13525132

Order 1792.

3310 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6451C211yesmaximal, characteristic, complemented
2C22×#6448C211yesmaximal, characteristic
3C22×#6448C211yesmaximal, characteristic
4C22×C4×Dic14C211yesmaximal, characteristic, complemented
5C2×C7×#388C211yesmaximal, characteristic, complemented
6C2×#89766C211yesmaximal, characteristic, complemented
7C2×#89720C211yesmaximal, characteristic, complemented
8C2×#89720C211yesmaximal, characteristic, complemented
9C2×#89729C211yesmaximal, characteristic
10C2×#89716C211yesmaximal, characteristic, complemented
11C2×#89712C211yesmaximal, characteristic, complemented
12#11733038C2116yesmaximal, direct product factor
13C2×#89448C211yesmaximal, characteristic, complemented
14C2×#89418C211yesmaximal, characteristic, complemented
15C2×#89442C211yesmaximal, characteristic, complemented
16C2×#89421C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C23×Dic14C2211yescharacteristic
19C23×Dic14C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C42×C7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
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×C4⋊Dic7C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C2×#6451—28no—
47C2×#6451C2218yescomplemented
48C2×#6448—28no—
49C2×#6448—28no—
50C2×#6448C2218yes—
51C2×#6448C2218yes—
52C2×C4×Dic14—28no—
53C2×C4×Dic14C2218yescomplemented
54C7×#388C2218yescomplemented
55C2×C7×#95C2211yescharacteristic
56C2×C7×#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61#89766C2218yescomplemented
62#89729C2218yes—
63#89720C2218yescomplemented
64#89720C2218yescomplemented
65#89716C2218yescomplemented
66#89712C2218yescomplemented
67#89448C2218yescomplemented
68#89442C2218yescomplemented
69#89421C2218yescomplemented
70#89418C2218yescomplemented
71C2×#2545—71nomaximal, Sylow
72C25×C7C2311yescharacteristic
73C24×D7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C22×C22⋊D7—24no—
81C22×C22⋊D7—24no—
82C22×C22⋊D7—24no—
83C22×C22⋊D7C2314yes—
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
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⋊C4C2314yes—
101C2×C7×C22⋊C4—24no—
102C2×C7×C22⋊C4—24no—
103C2×C7×C22⋊C4—24no—
104C2×C7×C22⋊C4C2314yes—
105C2×C7×C22⋊C4C2314yes—
106C2×C7×C22⋊C4C2314yes—
107C2×C42×C7—24no—
108C2×C42×C7C2314yes—
109C2×C22⋊Dic7—24no—
110C2×C22⋊Dic7—24no—
111C2×C22⋊Dic7—24no—
112C2×C22⋊Dic7C2314yes—
113C2×C22⋊Dic7C2314yes—
114C2×C22⋊Dic7C2314yes—
115C2×(C2×D7)⋊C4—24no—
116C2×(C2×D7)⋊C4—24no—
117C2×(C2×D7)⋊C4—24no—
118C2×(C2×D7)⋊C4—24no—
119C2×(C2×D7)⋊C4—24no—
120C2×(C2×D7)⋊C4—24no—
121C2×(C2×D7)⋊C4C2314yes—
122C2×(C2×D7)⋊C4C2314yes—
123C2×(C2×D7)⋊C4C2314yes—
124C2×(C2×D7)⋊C4C2314yes—
125C2×(C2×D7)⋊C4C2314yes—
126C2×(C2×D7)⋊C4C2314yes—
127C2×C4⋊Dic7—24no—
128C2×C4⋊Dic7—24no—
129C2×C4⋊Dic7C2314yes—
130C2×C4⋊Dic7C2314yes—
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⋊C4C2314yes—
138C2×Dic7⋊C4C2314yes—
139C2×Dic7⋊C4C2314yes—
140C2×Dic7⋊C4C2314yes—
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C2×C4×Dic7—24no—
144C2×C4×Dic7—24no—
145C2×C4×Dic7—24no—
146C2×C4×Dic7D418yes—
147C2×C4×Dic7C2314yes—
148C2×C4×Dic7C2314yes—
149C2×C4×Dic7C2314yes—
150C2×C4×Dic7C2314yes—
151#6451—232no—
152#6448—232no—
153#6448—232no—
154C4×Dic14—232no—
155C7×#95C2314yes—
156C7×#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C7⋊#95C2314yes—
160C7⋊#95C2314yes—
161C22×C4⋊Q8—71no—
162C22×#124—71no—
163C22×#124—71no—
164C22×C4×Q8—71no—
165#2545—716no—
166C2×#396—71no—
167C2×#396—71no—
168C2×#396—71no—
169C2×#396—71no—
170C2×#391—71no—
171C2×#390—71no—
172C2×#388—71no—
173C2×#388—71no—
174C2×#388—71no—
175C2×#388D711yescharacteristic, complemented
176C2×C4×C4⋊C4—71no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7—22no—
182C24×C7—22no—
183C24×C7—22no—
184C24×C7C2412yes—
185C24×C7C2411yescharacteristic
186C23×D7—22no—
187C23×D7—22no—
188C23×D7—22no—
189C23×D7—22no—
190C23×D7—22no—
191C23×D7—22no—
192C23×D7—22no—
193C23×D7C2412yes—
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×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7C2×D414yes—
210C22×C4×C7C2×D414yes—
211C22×C4×C7#4114yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2412yes—
216C22×C4×C7C2412yes—
217C22×C4×C7C2412yes—
218C2×C22⋊D7—28no—
219C2×C22⋊D7—28no—
220C2×C22⋊D7—28no—
221C2×C22⋊D7—416no—
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×Dic7—22no—
235C22×Dic7—22no—
236C22×Dic7—22no—
237C22×Dic7C2×D414yes—
238C22×Dic7C2×D414yes—
239C22×Dic7C2×D414yes—
240C22×Dic7C2×D414yes—
241C22×Dic7#4114yes—
242C22×Dic7#4114yes—
243C22×Dic7C2412yes—
244C22×Dic7C2412yes—
245C22×Dic7C2412yes—
246C22×Dic7C2412yes—
247C22×Dic7C2412yes—
248C22×Dic7C2412yes—
249C22×Dic7C2412yes—
250C2×Dic14—232no—
251C2×Dic14—28no—
252C2×Dic14—28no—
253C2×Dic14—28no—
254C2×Dic14—28no—
255C2×Dic14—28no—
256C2×Dic14—416no—
257C2×Dic14C2×D4116yes—
258C7×C4⋊C4—28no—
259C7×C22⋊C4—28no—
260C7×C22⋊C4—28no—
261C7×C22⋊C4—28no—
262C42×C7—28no—
263C22⋊Dic7—28no—
264C22⋊Dic7—28no—
265C22⋊Dic7—28no—
266(C2×D7)⋊C4—28no—
267(C2×D7)⋊C4—28no—
268(C2×D7)⋊C4—28no—
269(C2×D7)⋊C4—28no—
270(C2×D7)⋊C4—28no—
271(C2×D7)⋊C4—28no—
272C4⋊Dic7—28no—
273C4⋊Dic7—28no—
274Dic7⋊C4—28no—
275Dic7⋊C4—28no—
276Dic7⋊C4—28no—
277Dic7⋊C4—28no—
278Dic7⋊C4—28no—
279Dic7⋊C4—28no—
280C4×Dic7—28no—
281C4×Dic7—28no—
282C4×Dic7—28no—
283C4×Dic7C2×D4116yes—
284C23×Q8—71no—
285C23×Q8—71no—
286C23×D4—71no—
287C2×C4⋊Q8—78no—
288C2×C4⋊Q8—148no—
289C2×#124—78no—
290C2×#124—78no—
291C2×#124—148no—
292C2×#124—148no—
293C2×C4×Q8—78no—
294C2×C4×Q8—148no—
295C22×C4⋊C4—71no—
296C22×C4⋊C4—71no—
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⋊C4C2×D711yescharacteristic
304C22×C22⋊C4—71no—
305C22×C22⋊C4—71no—
306C22×C22⋊C4—71no—
307C22×C22⋊C4—71no—
308C22×C22⋊C4—71no—
309C22×C22⋊C4—71no—
310C22×C22⋊C4—71no—
311C22×C22⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4C2×D711yescharacteristic
314C22×C22⋊C4C2×D711yescharacteristic
315C22×C22⋊C4C2×D711yescharacteristic
316C22×C42—71no—
317C22×C42—71no—
318C22×C42—71no—
319C22×C42—71no—
320C22×C42C2×D711yescharacteristic
321#396—78no—
322#396—78no—
323#396—78no—
324#396—78no—
325#391—78no—
326#390—78no—
327#388—78no—
328#388—78no—
329#388—78no—
330#388C2×D718yescomplemented
331C4×C4⋊C4—78no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95C2×D711yescharacteristic
337C2×#95C2×D711yescharacteristic
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—44no—
346C23×C7—44no—
347C23×C7—44no—
348C23×C7—44no—
349C23×C7—44no—
350C23×C7—44no—
351C23×C7—44no—
352C23×C7C22×D412yes—
353C23×C7C22×D412yes—
354C23×C7C2×#4112yes—
355C23×C7C2×#4112yes—
356C23×C7C2×#4112yes—
357C23×C72−1+412yes—
358C23×C72−1+412yes—
359C23×C7C2511yescharacteristic
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—44no—
368C22×D7—44no—
369C22×D7—44no—
370C22×D7—44no—
371C22×D7—44no—
372C22×D7—44no—
373C22×D7—44no—
374C2×C4×C7—28no—
375C2×C4×C7—28no—
376C2×C4×C7—28no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—44no—
393C2×C4×C7—44no—
394C2×C4×C7—44no—
395C2×C4×C7C22×D414yes—
396C2×C4×C7C22×D414yes—
397C2×C4×C7C2×#4114yes—
398C22⋊D7—416no—
399C2×Dic7—28no—
400C2×Dic7—28no—
401C2×Dic7—28no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—44no—
418C2×Dic7—44no—
419C2×Dic7—44no—
420C2×Dic7#121116yes—
421C2×Dic7C22×D414yes—
422C2×Dic7C22×D414yes—
423C2×Dic7C22×D414yes—
424C2×Dic7C22×D414yes—
425C2×Dic7C2×#4114yes—
426C2×Dic7C2×#4114yes—
427Dic14—232no—
428Dic14—416no—
429C25—71no—
430C25C22×D711yescharacteristic
431C22×Q8—78no—
432C22×Q8—74no—
433C22×Q8—74no—
434C22×Q8—144no—
435C22×Q8—144no—
436C22×Q8—144no—
437C22×Q8—144no—
438C22×Q8—144no—
439C22×D4—74no—
440C22×D4—144no—
441C22×D4—144no—
442C22×D4—144no—
443C23×C4—71no—
444C23×C4—71no—
445C23×C4—71no—
446C23×C4—71no—
447C23×C4—71no—
448C23×C4—71no—
449C23×C4—71no—
450C23×C4C22×D711yescharacteristic
451C23×C4C22×D711yescharacteristic
452C23×C4C22×D711yescharacteristic
453C23×C4C22×D711yescharacteristic
454C23×C4C22×D711yescharacteristic
455C23×C4C22×D711yescharacteristic
456C4⋊Q8—1432no—
457#124—1432no—
458#124—1432no—
459C4×Q8—1432no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—74no—
462C2×C4⋊C4—74no—
463C2×C4⋊C4—74no—
464C2×C4⋊C4—74no—
465C2×C4⋊C4—74no—
466C2×C4⋊C4—74no—
467C2×C4⋊C4—74no—
468C2×C4⋊C4—74no—
469C2×C4⋊C4—144no—
470C2×C4⋊C4—144no—
471C2×C4⋊C4—144no—
472C2×C4⋊C4—144no—
473C2×C4⋊C4—144no—
474C2×C4⋊C4—144no—
475C2×C4⋊C4—144no—
476C2×C4⋊C4—144no—
477C2×C4⋊C4C22×D714yes—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—74no—
482C2×C22⋊C4—74no—
483C2×C22⋊C4—74no—
484C2×C22⋊C4—74no—
485C2×C22⋊C4—74no—
486C2×C22⋊C4—74no—
487C2×C22⋊C4—74no—
488C2×C22⋊C4—74no—
489C2×C22⋊C4—74no—
490C2×C22⋊C4—144no—
491C2×C22⋊C4—144no—
492C2×C22⋊C4—144no—
493C2×C22⋊C4—144no—
494C2×C22⋊C4—144no—
495C2×C22⋊C4—144no—
496C2×C22⋊C4—144no—
497C2×C22⋊C4—144no—
498C2×C22⋊C4—144no—
499C2×C22⋊C4C22×D714yes—
500C2×C22⋊C4C22×D714yes—
501C2×C22⋊C4C22×D714yes—
502C2×C42—24no—
503C2×C42—78no—
504C2×C42—74no—
505C2×C42—74no—
506C2×C42—74no—
507C2×C42—74no—
508C2×C42—144no—
509C2×C42—144no—
510C2×C42—144no—
511C2×C42C22×D714yes—
512#95—74no—
513#95—74no—
514#95—74no—
515#95—74no—
516#95C22×D714yes—
517#95C22×D714yes—
518C22×C7—42no—
519C22×C7—42no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7—88no—
526C22×C7C2×#12114yes—
527C22×C7#53214yes—
528C22×C7#53614yes—
529C22×C7#54814yes—
530C22×C7#54814yes—
531C22×C7#55614yes—
532C22×C7#55614yes—
533C22×C7C23×D411yescharacteristic
534C22×C7C23×D411yescharacteristic
535C22×C7C22×#4111yescharacteristic
536C22×C7C22×#4111yescharacteristic
537C22×C7C22×#4111yescharacteristic
538C22×C7C2×2−1+411yescharacteristic
539C22×C7C2×2−1+411yescharacteristic
540C2×D7—42no—
541C2×D7—42no—
542C2×D7—42no—
543C2×D7—42no—
544C2×D7—42no—
545C2×D7—42no—
546C2×D7—42no—
547C2×D7—88no—
548C4×C7—24no—
549C4×C7—24no—
550C4×C7—24no—
551C4×C7—42no—
552C4×C7—42no—
553C4×C7—42no—
554Dic7—24no—
555Dic7—24no—
556Dic7—24no—
557Dic7—42no—
558Dic7—42no—
559Dic7—42no—
560Dic7C2×#12118yes—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—72no—
569C24—142no—
570C24—142no—
571C24—142no—
572C24—142no—
573C24—142no—
574C24—142no—
575C24—142no—
576C24C23×D712yes—
577C24C23×D711yescharacteristic
578C2×Q8—716no—
579C2×Q8—148no—
580C2×Q8—1432no—
581C2×Q8—148no—
582C2×Q8—148no—
583C2×Q8—148no—
584C2×Q8—148no—
585C2×Q8—2816no—
586C2×D4—148no—
587C2×D4—148no—
588C2×D4—148no—
589C2×D4—2816no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—74no—
606C22×C4—74no—
607C22×C4—74no—
608C22×C4—72no—
609C22×C4—74no—
610C22×C4—74no—
611C22×C4—74no—
612C22×C4—72no—
613C22×C4—72no—
614C22×C4—72no—
615C22×C4—72no—
616C22×C4—72no—
617C22×C4—72no—
618C22×C4—142no—
619C22×C4—142no—
620C22×C4—142no—
621C22×C4—142no—
622C22×C4—142no—
623C22×C4—142no—
624C22×C4—142no—
625C22×C4—142no—
626C22×C4—142no—
627C22×C4—142no—
628C22×C4—142no—
629C22×C4—142no—
630C22×C4—142no—
631C22×C4—142no—
632C22×C4—142no—
633C22×C4#115714yes—
634C22×C4D4×D714yes—
635C22×C4D4×D714yes—
636C22×C4C23×D712yes—
637C22×C4C23×D712yes—
638C22×C4C23×D712yes—
639C22×C4C23×D712yes—
640C22×C4C23×D712yes—
641C22×C4C23×D712yes—
642C4⋊C4—28no—
643C4⋊C4—148no—
644C4⋊C4—148no—
645C4⋊C4—148no—
646C4⋊C4—148no—
647C4⋊C4—148no—
648C4⋊C4—148no—
649C4⋊C4—148no—
650C4⋊C4—148no—
651C22⋊C4—28no—
652C22⋊C4—28no—
653C22⋊C4—28no—
654C22⋊C4—148no—
655C22⋊C4—148no—
656C22⋊C4—148no—
657C22⋊C4—148no—
658C22⋊C4—148no—
659C22⋊C4—148no—
660C22⋊C4—148no—
661C22⋊C4—148no—
662C22⋊C4—148no—
663C42—28no—
664C42—716no—
665C42—148no—
666C42—148no—
667C42—148no—
668C2×C7—82no—
669C2×C7#254518yescomplemented
670C2×C7C22×#12111yescharacteristic
671C2×C7C2×#53211yescharacteristic
672C2×C7C2×#53611yescharacteristic
673C2×C7C2×#54811yescharacteristic
674C2×C7C2×#54811yescharacteristic
675C2×C7C2×#55611yescharacteristic
676C2×C7C2×#55611yescharacteristic
677D7—82no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—142no—
693C23—142no—
694C23—142no—
695C23—142no—
696C23—142no—
697C23—142no—
698C23—142no—
699C23—284no—
700C23—284no—
701C23—284no—
702C23—284no—
703C23—284no—
704C23—284no—
705C23—284no—
706C23C2×#115712yes—
707C23C2×D4×D712yes—
708C23C2×D4×D712yes—
709C23D7×#4112yes—
710C23D7×#4112yes—
711C23#655412yes—
712C23#655412yes—
713C23C24×D711yescharacteristic
714Q8—1432no—
715Q8—2816no—
716D4—2816no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—716no—
739C2×C4—74no—
740C2×C4—74no—
741C2×C4—74no—
742C2×C4—74no—
743C2×C4—74no—
744C2×C4—74no—
745C2×C4—148no—
746C2×C4—148no—
747C2×C4—148no—
748C2×C4—142no—
749C2×C4—142no—
750C2×C4—142no—
751C2×C4—142no—
752C2×C4—142no—
753C2×C4—142no—
754C2×C4—142no—
755C2×C4—142no—
756C2×C4—142no—
757C2×C4—142no—
758C2×C4—142no—
759C2×C4—142no—
760C2×C4—142no—
761C2×C4—142no—
762C2×C4—142no—
763C2×C4—284no—
764C2×C4—284no—
765C2×C4—284no—
766C2×C4C2×#115714yes—
767C2×C4C2×D4×D714yes—
768C2×C4C2×D4×D714yes—
769C7C2×#254511yescharacteristic, complemented, Sylow
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—88no—
778C22—282no—
779C22—282no—
780C22—282no—
781C22—282no—
782C22—282no—
783C22—282no—
784C22—282no—
785C22—568no—
786C22#9022414yes—
787C22#9023914yes—
788C22#9024314yes—
789C22D7×#12114yes—
790C22#9033914yes—
791C22#9036814yes—
792C22#9039314yes—
793C22C22×#115711yescharacteristic
794C22C22×D4×D711yescharacteristic
795C22C22×D4×D711yescharacteristic
796C22C2×D7×#4111yescharacteristic
797C22C2×D7×#4111yescharacteristic
798C22C2×#655411yescharacteristic
799C22C2×#655411yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—78no—
807C4—144no—
808C4—144no—
809C4—144no—
810C4—282no—
811C4—282no—
812C4—282no—
813C2—82no—
814C2—562no—
815C2#1173303818yesdirect product factor
816C2C2×#9022411yescharacteristic
817C2C2×#9024311yescharacteristic
818C2C2×#9023911yescharacteristic
819C2C2×D7×#12111yescharacteristic
820C2C2×#9033911yescharacteristic
821C2C2×#9036811yescharacteristic
822C2C2×#9039311yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#388C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#388D7
hypocenterC7C2×#2545
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#6451C2semidirect
4. C22×C4×Dic14C2semidirect
5. C2×C7×#388C2semidirect
6. C2×#89766C2semidirect
7. C2×#89720C2semidirect
8. C2×#89720C2semidirect
10. C2×#89716C2semidirect
11. C2×#89712C2semidirect
12. #11733038C2direct (N × H)
13. C2×#89448C2semidirect
14. C2×#89418C2semidirect
15. C2×#89442C2semidirect
16. C2×#89421C2semidirect
47. C2×#6451C22semidirect
53. C2×C4×Dic14C22semidirect
54. C7×#388C22semidirect
61. #89766C22semidirect
63. #89720C22semidirect
64. #89720C22semidirect
65. #89716C22semidirect
66. #89712C22semidirect
67. #89448C22semidirect
68. #89442C22semidirect
69. #89421C22semidirect
70. #89418C22semidirect
175. C2×#388D7semidirect
330. #388C2×D7semidirect
669. C2×C7#2545semidirect
769. C7C2×#2545semidirect
815. C2#11733038direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64512
C22×#64482
C22×C4×Dic142
C2×C7×#3882
C2×#897662
C2×#897202
C2×#897292
C2×#897162
C2×#897122
#117330382
C2×#894482
C2×#894182
C2×#894422
C2×#894212
C2×#25457