Finite Group Databasebeta

← C2×#11730911 #13513314

Subgroups — C2×#11730911 #13513314

Order 1792.

3614 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
1C23×Dic7⋊C4C211yesmaximal, characteristic
2C22×#6441C211yesmaximal, characteristic
3C22×C4×Dic14C211yesmaximal, characteristic, complemented
4C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
5C2×#89982C211yesmaximal, characteristic
6C2×#89722C211yesmaximal, characteristic
7C2×C22⋊C4×Dic7C211yesmaximal, characteristic
8C2×C22⋊C4×Dic7C211yesmaximal, characteristic
9C2×#89700C211yesmaximal, characteristic, complemented
10C2×#89705C211yesmaximal, characteristic, complemented
11C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
12#11730911C2116yesmaximal, direct product factor
13C2×#89418C211yesmaximal, characteristic, complemented
14C2×#89419C211yesmaximal, characteristic, complemented
15C2×#89419C211yesmaximal, characteristic, complemented
16C2×#89426C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C24×Dic7C2211yescharacteristic
19C24×Dic7C2211yescharacteristic
20C23×Dic14C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C22×C42×C7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×Dic7⋊C4—28no—
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2218yes—
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×#6441C4116yescomplemented
45C2×#6441C2218yes—
46C2×C4×Dic14—28no—
47C2×C4×Dic14C2218yescomplemented
48C4×C7×C22⋊C4C2218yes—
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51#89982C2218yes—
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60#89722C2218yes—
61C22⋊C4×Dic7C2218yes—
62C22⋊C4×Dic7C2218yes—
63#89705C2218yescomplemented
64C4×Dic7⋊C4C2218yescomplemented
65#89700C2218yescomplemented
66#89426C2218yescomplemented
67#89419C2218yescomplemented
68#89419C2218yescomplemented
69#89418C2218yescomplemented
70C2×#2360—71nomaximal, Sylow
71C25×C7C2311yescharacteristic
72C23×C4×C7—24no—
73C23×C4×C7—24no—
74C23×C4×C7—42no—
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2314yes—
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×Dic7—24no—
83C23×Dic7—24no—
84C23×Dic7—24no—
85C23×Dic7—24no—
86C23×Dic7—42no—
87C23×Dic7C2×C418yes—
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2314yes—
92C23×Dic7C2314yes—
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2311yescharacteristic
98C22×Dic14—24no—
99C22×Dic14—24no—
100C22×Dic14C2×C418yescomplemented
101C22×Dic14C2314yes—
102C2×C7×C22⋊C4C2×C418yes—
103C2×C7×C22⋊C4Q818yescomplemented
104C2×C7×C22⋊C4C2314yes—
105C2×C7×C22⋊C4C2314yes—
106C2×C42×C7—24no—
107C2×C42×C7—42no—
108C2×C42×C7C2314yes—
109C2×C42×C7C2314yes—
110C2×C22⋊Dic7—24no—
111C2×C22⋊Dic7C2×C418yes—
112C2×C22⋊Dic7C2314yes—
113C2×C22⋊Dic7C2314yes—
114C2×C4⋊Dic7—24no—
115C2×C4⋊Dic7—42no—
116C2×C4⋊Dic7C2×C418yescomplemented
117C2×C4⋊Dic7C2314yes—
118C2×C4⋊Dic7C2314yes—
119C2×C4⋊Dic7C2314yes—
120C2×Dic7⋊C4—24no—
121C2×Dic7⋊C4—24no—
122C2×Dic7⋊C4—24no—
123C2×Dic7⋊C4—24no—
124C2×Dic7⋊C4—232no—
125C2×Dic7⋊C4—42no—
126C2×Dic7⋊C4C2×C418yescomplemented
127C2×Dic7⋊C4C2×C418yescomplemented
128C2×Dic7⋊C4D418yes—
129C2×Dic7⋊C4C2314yes—
130C2×Dic7⋊C4C2314yes—
131C2×Dic7⋊C4C2314yes—
132C2×Dic7⋊C4C2314yes—
133C2×Dic7⋊C4C2314yes—
134C2×Dic7⋊C4C2314yes—
135C2×Dic7⋊C4C2314yes—
136C2×Dic7⋊C4C2314yes—
137C2×C4×Dic7—24no—
138C2×C4×Dic7—24no—
139C2×C4×Dic7—24no—
140C2×C4×Dic7—42no—
141C2×C4×Dic7C2314yes—
142C2×C4×Dic7C2314yes—
143C2×C4×Dic7C2314yes—
144C2×C4×Dic7C2314yes—
145#6441C2×C4164yescomplemented
146C4×Dic14—232no—
147C7×#95C2314yes—
148C7×#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C22×C22⋊Q8—71no—
158C22×C4×Q8—71no—
159C23×C4⋊C4—71no—
160#2360—716no—
161C2×#391—71no—
162C2×#389—71no—
163C2×#389—71no—
164C2×#389—71no—
165C2×#387—71no—
166C2×#387—71no—
167C2×#385—71no—
168C2×#385—71no—
169C2×C4×C4⋊C4—71no—
170C2×C4×C22⋊C4—71no—
171C2×C4×C22⋊C4—71no—
172C2×C4×C22⋊C4D711yescharacteristic
173C24×C7—22no—
174C24×C7—22no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7C22×C414yes—
178C24×C7C2×Q814yes—
179C24×C7#4114yes—
180C24×C7C2412yes—
181C24×C7C2411yescharacteristic
182C22×C4×C7—22no—
183C22×C4×C7—22no—
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—28no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—28no—
197C22×C4×C7—44no—
198C22×C4×C7—416no—
199C22×C4×C7C22×C414yes—
200C22×C4×C7C22×C414yes—
201C22×C4×C7C2×D414yes—
202C22×C4×C7C2×Q814yes—
203C22×C4×C7C2×Q814yes—
204C22×C4×C7C2412yes—
205C22×C4×C7C2412yes—
206C22×C4×C7C2412yes—
207C22×C4×C7C2412yes—
208C22×C4×C7C2412yes—
209C22×C4×C7C2412yes—
210C22×Dic7—22no—
211C22×Dic7—22no—
212C22×Dic7—22no—
213C22×Dic7—22no—
214C22×Dic7—22no—
215C22×Dic7—22no—
216C22×Dic7—22no—
217C22×Dic7—22no—
218C22×Dic7—232no—
219C22×Dic7—28no—
220C22×Dic7—28no—
221C22×Dic7—22no—
222C22×Dic7—22no—
223C22×Dic7—22no—
224C22×Dic7—22no—
225C22×Dic7—22no—
226C22×Dic7—28no—
227C22×Dic7—22no—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7—22no—
231C22×Dic7—28no—
232C22×Dic7—44no—
233C22×Dic7—416no—
234C22×Dic7C22×C4116yes—
235C22×Dic7C22×C414yes—
236C22×Dic7C22×C414yes—
237C22×Dic7C22×C414yes—
238C22×Dic7C22×C414yes—
239C22×Dic7C2×D414yes—
240C22×Dic7C2×D414yes—
241C22×Dic7#4114yes—
242C22×Dic7C2412yes—
243C22×Dic7C2412yes—
244C22×Dic7C2412yes—
245C22×Dic7C2412yes—
246C22×Dic7C2412yes—
247C22×Dic7C2412yes—
248C22×Dic7C2412yes—
249C22×Dic7C2412yes—
250C2×Dic14—232no—
251C2×Dic14—28no—
252C2×Dic14—28no—
253C2×Dic14C22×C4116yescomplemented
254C7×C22⋊C4C22×C4116yes—
255C7×C22⋊C4C2×Q8116yescomplemented
256C42×C7—28no—
257C42×C7—44no—
258C22⋊Dic7—28no—
259C22⋊Dic7C22×C4116yes—
260C4⋊Dic7—28no—
261C4⋊Dic7—44no—
262C4⋊Dic7C22×C4116yescomplemented
263Dic7⋊C4—28no—
264Dic7⋊C4—28no—
265Dic7⋊C4—28no—
266Dic7⋊C4—28no—
267Dic7⋊C4—44no—
268Dic7⋊C4C22×C4116yescomplemented
269Dic7⋊C4C22×C4116yescomplemented
270Dic7⋊C4C2×D4116yes—
271C4×Dic7—28no—
272C4×Dic7—28no—
273C4×Dic7—28no—
274C4×Dic7—44no—
275C23×Q8—71no—
276C24×C4—71no—
277C24×C4—71no—
278C24×C4C2×D711yescharacteristic
279C2×C22⋊Q8—716no—
280C2×C22⋊Q8—78no—
281C2×C4×Q8—78no—
282C2×C4×Q8—148no—
283C22×C4⋊C4—71no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C4⋊C4—71no—
287C22×C4⋊C4—78no—
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—148no—
296C22×C22⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C22⋊C4C2×D711yescharacteristic
299C22×C22⋊C4C2×D711yescharacteristic
300C22×C42—71no—
301C22×C42—71no—
302C22×C42—71no—
303C22×C42—71no—
304C22×C42C2×D711yescharacteristic
305C22×C42C2×D711yescharacteristic
306#391—78no—
307#389—78no—
308#389—78no—
309#389—78no—
310#387—78no—
311#387—78no—
312#385—78no—
313#385—78no—
314C4×C4⋊C4—78no—
315C4×C22⋊C4—78no—
316C4×C22⋊C4—78no—
317C4×C22⋊C4C2×D718yes—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95—71no—
326C2×#95C2×D711yescharacteristic
327C2×#95C2×D711yescharacteristic
328C23×C7—28no—
329C23×C7—28no—
330C23×C7—28no—
331C23×C7—28no—
332C23×C7—28no—
333C23×C7—28no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7C4×Q8116yescomplemented
339C23×C7C23×C414yes—
340C23×C7C23×C412yes—
341C23×C7C22×D412yes—
342C23×C7C22×Q814yes—
343C23×C7C22×Q812yes—
344C23×C7C2×#4114yes—
345C23×C7C2×#4112yes—
346C23×C7C2×#4112yes—
347C23×C7H(5,𝔽2)12yes—
348C23×C72−1+412yes—
349C23×C7C2511yescharacteristic
350C2×C4×C7—28no—
351C2×C4×C7—28no—
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—416no—
369C2×C4×C7—44no—
370C2×C4×C7C23×C414yes—
371C2×C4×C7C23×C414yes—
372C2×C4×C7C22×D414yes—
373C2×C4×C7C22×Q814yes—
374C2×C4×C7C22×Q814yes—
375C2×Dic7—28no—
376C2×Dic7—28no—
377C2×Dic7—28no—
378C2×Dic7—28no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—232no—
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—416no—
398C2×Dic7—44no—
399C2×Dic7—44no—
400C2×Dic7—44no—
401C2×Dic7C4×D4116yes—
402C2×Dic7C23×C414yes—
403C2×Dic7C23×C414yes—
404C2×Dic7C23×C414yes—
405C2×Dic7C23×C414yes—
406C2×Dic7C22×D414yes—
407C2×Dic7C22×D414yes—
408C2×Dic7C2×#4114yes—
409Dic14—232no—
410C25C22×D711yescharacteristic
411C22×Q8—78no—
412C22×Q8—74no—
413C22×Q8—144no—
414C22×Q8—144no—
415C23×C4—24no—
416C23×C4—24no—
417C23×C4—42no—
418C23×C4—71no—
419C23×C4—78no—
420C23×C4—74no—
421C23×C4—71no—
422C23×C4—71no—
423C23×C4—71no—
424C23×C4—71no—
425C23×C4—71no—
426C23×C4—71no—
427C23×C4—71no—
428C23×C4—74no—
429C23×C4—144no—
430C23×C4—144no—
431C23×C4—144no—
432C23×C4—144no—
433C23×C4—282no—
434C23×C4C22×D711yescharacteristic
435C23×C4C22×D714yes—
436C23×C4C22×D711yescharacteristic
437C23×C4C22×D711yescharacteristic
438C23×C4C22×D711yescharacteristic
439C23×C4C22×D711yescharacteristic
440C23×C4C22×D711yescharacteristic
441C22⋊Q8—764no—
442C4×Q8—1432no—
443C2×C4⋊C4—78no—
444C2×C4⋊C4—78no—
445C2×C4⋊C4—78no—
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—74no—
458C2×C4⋊C4—1432no—
459C2×C4⋊C4—144no—
460C2×C4⋊C4—144no—
461C2×C4⋊C4—144no—
462C2×C4⋊C4—144no—
463C2×C4⋊C4—144no—
464C2×C4⋊C4—282no—
465C2×C4⋊C4—282no—
466C2×C22⋊C4—78no—
467C2×C22⋊C4—74no—
468C2×C22⋊C4—74no—
469C2×C22⋊C4—144no—
470C2×C22⋊C4Dic1418yescomplemented
471C2×C22⋊C4C4×D718yes—
472C2×C22⋊C4C22×D714yes—
473C2×C22⋊C4C22×D714yes—
474C2×C42—24no—
475C2×C42—42no—
476C2×C42—74no—
477C2×C42—74no—
478C2×C42—74no—
479C2×C42—74no—
480C2×C42—144no—
481C2×C42—144no—
482C2×C42—144no—
483C2×C42—282no—
484C2×C42C22×D714yes—
485C2×C42C22×D714yes—
486#95—74no—
487#95—74no—
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—232no—
497C22×C7—24no—
498C22×C7—24no—
499C22×C7—24no—
500C22×C7—24no—
501C22×C7—24no—
502C22×C7—24no—
503C22×C7C2×C4×D414yes—
504C22×C7C2×C4×Q814yes—
505C22×C7C2×C4×Q818yescomplemented
506C22×C7#52014yes—
507C22×C7#54614yes—
508C22×C7D4×Q814yes—
509C22×C7#55214yes—
510C22×C7#55414yes—
511C22×C7C24×C411yescharacteristic
512C22×C7C23×D411yescharacteristic
513C22×C7C23×Q811yescharacteristic
514C22×C7C22×#4111yescharacteristic
515C22×C7C22×#4111yescharacteristic
516C22×C7C2×H(5,𝔽2)11yescharacteristic
517C22×C7C2×2−1+411yescharacteristic
518C4×C7—24no—
519C4×C7—24no—
520C4×C7—24no—
521C4×C7—24no—
522C4×C7—24no—
523C4×C7—42no—
524Dic7—24no—
525Dic7—24no—
526Dic7—24no—
527Dic7—24no—
528Dic7—42no—
529Dic7—42no—
530Dic7—42no—
531Dic7C2×C4×D418yes—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24C2×Dic1414yes—
537C24C2×C4×D714yes—
538C24#115714yes—
539C24C23×D712yes—
540C24C23×D711yescharacteristic
541C2×Q8—716no—
542C2×Q8—148no—
543C2×Q8—1432no—
544C2×Q8—148no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—28no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—28no—
560C22×C4—44no—
561C22×C4—416no—
562C22×C4—74no—
563C22×C4—74no—
564C22×C4—74no—
565C22×C4—72no—
566C22×C4—74no—
567C22×C4—74no—
568C22×C4—74no—
569C22×C4—716no—
570C22×C4—74no—
571C22×C4—72no—
572C22×C4—72no—
573C22×C4—72no—
574C22×C4—72no—
575C22×C4—72no—
576C22×C4—72no—
577C22×C4—72no—
578C22×C4—148no—
579C22×C4—1432no—
580C22×C4—148no—
581C22×C4—148no—
582C22×C4—142no—
583C22×C4—142no—
584C22×C4—142no—
585C22×C4—142no—
586C22×C4—142no—
587C22×C4—142no—
588C22×C4—142no—
589C22×C4—142no—
590C22×C4—142no—
591C22×C4—142no—
592C22×C4—148no—
593C22×C4—142no—
594C22×C4—142no—
595C22×C4—142no—
596C22×C4—142no—
597C22×C4—142no—
598C22×C4—142no—
599C22×C4—142no—
600C22×C4—284no—
601C22×C4—2816no—
602C22×C4C2×Dic1414yes—
603C22×C4C2×Dic1414yes—
604C22×C4C2×C4×D714yes—
605C22×C4C2×C4×D714yes—
606C22×C4D4×D714yes—
607C22×C4C23×D712yes—
608C22×C4C23×D712yes—
609C22×C4C23×D712yes—
610C22×C4C23×D712yes—
611C22×C4C23×D712yes—
612C22×C4C23×D712yes—
613C4⋊C4—716no—
614C4⋊C4—716no—
615C4⋊C4—716no—
616C4⋊C4—716no—
617C4⋊C4—148no—
618C4⋊C4—148no—
619C4⋊C4—148no—
620C4⋊C4—148no—
621C4⋊C4—148no—
622C4⋊C4—284no—
623C4⋊C4—284no—
624C22⋊C4—716no—
625C22⋊C4—148no—
626C22⋊C4C2×Dic14116yescomplemented
627C22⋊C4C2×C4×D7116yes—
628C42—28no—
629C42—44no—
630C42—148no—
631C42—148no—
632C42—148no—
633C42—284no—
634C2×C7—28no—
635C2×C7#236018yescomplemented
636C2×C7C22×C4×D411yescharacteristic
637C2×C7C22×C4×Q811yescharacteristic
638C2×C7C2×#52011yescharacteristic
639C2×C7C2×#54611yescharacteristic
640C2×C7C2×D4×Q811yescharacteristic
641C2×C7C2×#55211yescharacteristic
642C2×C7C2×#55411yescharacteristic
643C23—28no—
644C23—28no—
645C23—28no—
646C23—28no—
647C23—28no—
648C23—28no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23C4×Dic14116yescomplemented
654C23C22×Dic1414yes—
655C23C22×Dic1412yes—
656C23C22×C4×D714yes—
657C23C22×C4×D712yes—
658C23C2×#115714yes—
659C23C2×#115712yes—
660C23C2×D4×D712yes—
661C23#654812yes—
662C23D7×#4112yes—
663C23#655412yes—
664C23C24×D711yescharacteristic
665Q8—1432no—
666C2×C4—28no—
667C2×C4—28no—
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—416no—
685C2×C4—44no—
686C2×C4—716no—
687C2×C4—74no—
688C2×C4—74no—
689C2×C4—74no—
690C2×C4—74no—
691C2×C4—74no—
692C2×C4—74no—
693C2×C4—74no—
694C2×C4—1432no—
695C2×C4—148no—
696C2×C4—148no—
697C2×C4—148no—
698C2×C4—148no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—142no—
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—2816no—
717C2×C4—284no—
718C2×C4—284no—
719C2×C4—284no—
720C2×C4C22×Dic1414yes—
721C2×C4C22×Dic1414yes—
722C2×C4C22×C4×D714yes—
723C2×C4C22×C4×D714yes—
724C2×C4C2×D4×D714yes—
725C7C2×#236011yescharacteristic, complemented, Sylow
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—232no—
733C22C2×C4×Dic1414yes—
734C22C2×C4×Dic1418yescomplemented
735C22#9018114yes—
736C22#9022214yes—
737C22D4×Dic1414yes—
738C22#9023014yes—
739C22C4×D4×D714yes—
740C22#9023714yes—
741C22C23×Dic1411yescharacteristic
742C22C23×C4×D711yescharacteristic
743C22C22×#115711yescharacteristic
744C22C22×D4×D711yescharacteristic
745C22C2×#654811yescharacteristic
746C22C2×D7×#4111yescharacteristic
747C22C2×#655411yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—24no—
753C4—42no—
754C4—78no—
755C4—144no—
756C4—144no—
757C4—144no—
758C4—144no—
759C4—282no—
760C4—282no—
761C4—282no—
762C2—28no—
763C2#1173091118yesdirect product factor
764C2C22×C4×Dic1411yescharacteristic
765C2C2×#9018111yescharacteristic
766C2C2×#9022211yescharacteristic
767C2C2×#9023711yescharacteristic
768C2C2×D4×Dic1411yescharacteristic
769C2C2×#9023011yescharacteristic
770C2C2×C4×D4×D711yescharacteristic
subgroupG/H
centerC24C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC2×C4×C7×C22⋊C4C2
socleC24×C7C24
prime radicalC25×C7C23
cosocleC23×C7C25
hypercenterC2×C4×C22⋊C4D7
hypocenterC7C2×#2360
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C4×Dic14C2semidirect
9. C2×#89700C2semidirect
10. C2×#89705C2semidirect
11. C2×C4×Dic7⋊C4C2semidirect
12. #11730911C2direct (N × H)
13. C2×#89418C2semidirect
14. C2×#89419C2semidirect
15. C2×#89419C2semidirect
16. C2×#89426C2semidirect
44. C2×#6441C4semidirect
47. C2×C4×Dic14C22semidirect
63. #89705C22semidirect
64. C4×Dic7⋊C4C22semidirect
65. #89700C22semidirect
66. #89426C22semidirect
67. #89419C22semidirect
68. #89419C22semidirect
69. #89418C22semidirect
100. C22×Dic14C2×C4semidirect
103. C2×C7×C22⋊C4Q8semidirect
116. C2×C4⋊Dic7C2×C4semidirect
126. C2×Dic7⋊C4C2×C4semidirect
127. C2×Dic7⋊C4C2×C4semidirect
145. #6441C2×C4semidirect
253. C2×Dic14C22×C4semidirect
255. C7×C22⋊C4C2×Q8semidirect
262. C4⋊Dic7C22×C4semidirect
268. Dic7⋊C4C22×C4semidirect
269. Dic7⋊C4C22×C4semidirect
338. C23×C7C4×Q8semidirect
470. C2×C22⋊C4Dic14semidirect
505. C22×C7C2×C4×Q8semidirect
626. C22⋊C4C2×Dic14semidirect
635. C2×C7#2360semidirect
653. C23C4×Dic14semidirect
725. C7C2×#2360semidirect
734. C22C2×C4×Dic14semidirect
763. C2#11730911direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Dic7⋊C42
C22×#64412
C22×C4×Dic142
C2×C4×C7×C22⋊C42
C2×#899822
C2×#897222
C2×C22⋊C4×Dic72
C2×#897002
C2×#897052
C2×C4×Dic7⋊C42
#117309112
C2×#894182
C2×#894192
C2×#894262
C2×#23607