Finite Group Databasebeta

← C2×#11732923 #13513334

Subgroups — C2×#11732923 #13513334

Order 1792.

3310 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6450C211yesmaximal, characteristic, complemented
2C22×#6441C211yesmaximal, characteristic
3C22×#6440C211yesmaximal, characteristic
4C2×C7×#388C211yesmaximal, characteristic
5C2×#89750C211yesmaximal, characteristic, complemented
6C2×#89716C211yesmaximal, characteristic
7C2×#89716C211yesmaximal, characteristic
8C2×#89723C211yesmaximal, characteristic
9C2×C22⋊C4×Dic7C211yesmaximal, characteristic
10C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
11C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
12#11732923C2116yesmaximal, direct product factor
13C2×#89418C211yesmaximal, characteristic, complemented
14C2×#89419C211yesmaximal, characteristic, complemented
15C2×#89426C211yesmaximal, characteristic, complemented
16C2×#89421C211yesmaximal, characteristic, complemented
17C24×Dic7C2211yescharacteristic
18C23×Dic14C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×C4×Dic7C2211yescharacteristic
36C22×C4×Dic7C2211yescharacteristic
37C22×C4×Dic7C2211yescharacteristic
38C22×C4×Dic7C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C22×C4×Dic7C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C2×#6450—28no—
43C2×#6450C2218yescomplemented
44C2×#6441C4116yescomplemented
45C2×#6441C2218yes—
46C2×#6440—28no—
47C2×#6440C2218yes—
48C7×#388C2218yes—
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59#89750C2218yescomplemented
60#89723C2218yes—
61#89716C2218yes—
62#89716C2218yes—
63C22⋊C4×Dic7C2218yes—
64C4×C4⋊Dic7C2218yescomplemented
65C4×Dic7⋊C4C2218yescomplemented
66#89426C2218yescomplemented
67#89421C2218yescomplemented
68#89419C2218yescomplemented
69#89418C2218yescomplemented
70C2×#2362—71nomaximal, Sylow
71C25×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×Dic7—24no—
79C23×Dic7—24no—
80C23×Dic7C2×C418yes—
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2314yes—
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C22×Dic14—24no—
91C22×Dic14—24no—
92C22×Dic14C2×C418yes—
93C22×Dic14C2314yes—
94C2×C7×C4⋊C4—24no—
95C2×C7×C4⋊C4C2314yes—
96C2×C7×C22⋊C4—24no—
97C2×C7×C22⋊C4—24no—
98C2×C7×C22⋊C4C2×C418yes—
99C2×C7×C22⋊C4C2314yes—
100C2×C7×C22⋊C4C2314yes—
101C2×C7×C22⋊C4C2314yes—
102C2×C42×C7—24no—
103C2×C42×C7C2314yes—
104C2×C22⋊Dic7—24no—
105C2×C22⋊Dic7—24no—
106C2×C22⋊Dic7C2×C418yes—
107C2×C22⋊Dic7C2314yes—
108C2×C22⋊Dic7C2314yes—
109C2×C22⋊Dic7C2314yes—
110C2×C4⋊Dic7—24no—
111C2×C4⋊Dic7C2×C418yes—
112C2×C4⋊Dic7C2314yes—
113C2×C4⋊Dic7C2314yes—
114C2×Dic7⋊C4—24no—
115C2×Dic7⋊C4—24no—
116C2×Dic7⋊C4—24no—
117C2×Dic7⋊C4C2×C418yes—
118C2×Dic7⋊C4C2×C418yes—
119C2×Dic7⋊C4D418yes—
120C2×Dic7⋊C4C2314yes—
121C2×Dic7⋊C4C2314yes—
122C2×Dic7⋊C4C2314yes—
123C2×Dic7⋊C4C2314yes—
124C2×Dic7⋊C4C2314yes—
125C2×Dic7⋊C4C2314yes—
126C2×C4×Dic7—24no—
127C2×C4×Dic7—24no—
128C2×C4×Dic7—24no—
129C2×C4×Dic7—24no—
130C2×C4×Dic7—24no—
131C2×C4×Dic7—24no—
132C2×C4×Dic7—24no—
133C2×C4×Dic7C2314yes—
134C2×C4×Dic7C2314yes—
135C2×C4×Dic7C2314yes—
136C2×C4×Dic7C2314yes—
137C2×C4×Dic7C2314yes—
138C2×C4×Dic7C2314yes—
139C2×C4×Dic7C2314yes—
140#6450—232no—
141#6441C2×C4164yescomplemented
142#6440—232no—
143C7×#95C2314yes—
144C7×#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×C22⋊Q8—71no—
154C22×C4×Q8—71no—
155C22×#117—71no—
156#2362—716no—
157C2×#391—71no—
158C2×#389—71no—
159C2×#388—71no—
160C2×#388—71no—
161C2×#388—71no—
162C2×#388D711yescharacteristic
163C2×#387—71no—
164C2×#387—71no—
165C2×C4×C4⋊C4—71no—
166C2×C4×C4⋊C4—71no—
167C2×C4×C4⋊C4—71no—
168C2×C4×C22⋊C4—71no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7—22no—
174C24×C7—22no—
175C24×C7C22×C414yes—
176C24×C7C2412yes—
177C24×C7C2411yescharacteristic
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
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×C7C22×C414yes—
193C22×C4×C7C22×C414yes—
194C22×C4×C7C2×D414yes—
195C22×C4×C7#4114yes—
196C22×C4×C7C2412yes—
197C22×C4×C7C2412yes—
198C22×C4×C7C2412yes—
199C22×C4×C7C2412yes—
200C22×C4×C7C2412yes—
201C22×C4×C7C2412yes—
202C22×Dic7—22no—
203C22×Dic7—22no—
204C22×Dic7—22no—
205C22×Dic7—22no—
206C22×Dic7—22no—
207C22×Dic7—22no—
208C22×Dic7—22no—
209C22×Dic7—22no—
210C22×Dic7—22no—
211C22×Dic7—22no—
212C22×Dic7—232no—
213C22×Dic7—28no—
214C22×Dic7—28no—
215C22×Dic7—22no—
216C22×Dic7—22no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7C22×C4116yes—
222C22×Dic7C22×C414yes—
223C22×Dic7C22×C414yes—
224C22×Dic7C22×C414yes—
225C22×Dic7C22×C414yes—
226C22×Dic7C2×D414yes—
227C22×Dic7C2×D414yes—
228C22×Dic7#4114yes—
229C22×Dic7#4114yes—
230C22×Dic7C2412yes—
231C22×Dic7C2412yes—
232C22×Dic7C2412yes—
233C22×Dic7C2412yes—
234C22×Dic7C2412yes—
235C22×Dic7C2412yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C2×Dic14—232no—
239C2×Dic14—28no—
240C2×Dic14—28no—
241C2×Dic14C22×C4116yes—
242C7×C4⋊C4—28no—
243C7×C22⋊C4—28no—
244C7×C22⋊C4—28no—
245C7×C22⋊C4C22×C4116yes—
246C42×C7—28no—
247C22⋊Dic7—28no—
248C22⋊Dic7—28no—
249C22⋊Dic7C22×C4116yes—
250C4⋊Dic7—28no—
251C4⋊Dic7C22×C4116yes—
252Dic7⋊C4—28no—
253Dic7⋊C4—28no—
254Dic7⋊C4—28no—
255Dic7⋊C4C22×C4116yes—
256Dic7⋊C4C22×C4116yes—
257Dic7⋊C4C2×D4116yes—
258C4×Dic7—28no—
259C4×Dic7—28no—
260C4×Dic7—28no—
261C4×Dic7—28no—
262C4×Dic7—28no—
263C4×Dic7—28no—
264C4×Dic7—28no—
265C23×Q8—71no—
266C24×C4—71no—
267C2×C22⋊Q8—716no—
268C2×C22⋊Q8—78no—
269C2×C4×Q8—78no—
270C2×C4×Q8—148no—
271C2×#117—78no—
272C2×#117—148no—
273C22×C4⋊C4—71no—
274C22×C4⋊C4—71no—
275C22×C4⋊C4—71no—
276C22×C4⋊C4—71no—
277C22×C4⋊C4—71no—
278C22×C4⋊C4—71no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4C2×D711yescharacteristic
282C22×C22⋊C4—71no—
283C22×C22⋊C4—71no—
284C22×C22⋊C4—71no—
285C22×C22⋊C4C2×D711yescharacteristic
286C22×C22⋊C4C2×D711yescharacteristic
287C22×C22⋊C4C2×D711yescharacteristic
288C22×C42—71no—
289C22×C42—71no—
290C22×C42—71no—
291C22×C42—71no—
292C22×C42—71no—
293C22×C42—71no—
294C22×C42—71no—
295C22×C42C2×D711yescharacteristic
296#391—78no—
297#389—78no—
298#388—78no—
299#388—78no—
300#388—78no—
301#388C2×D718yes—
302#387—78no—
303#387—78no—
304C4×C4⋊C4—78no—
305C4×C4⋊C4—78no—
306C4×C4⋊C4—78no—
307C4×C22⋊C4—78no—
308C2×#95—71no—
309C2×#95—71no—
310C2×#95—71no—
311C2×#95—71no—
312C2×#95—71no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95—71no—
316C2×#95C2×D711yescharacteristic
317C2×#95C2×D711yescharacteristic
318C23×C7—28no—
319C23×C7—28no—
320C23×C7—28no—
321C23×C7—22no—
322C23×C7—22no—
323C23×C7—22no—
324C23×C7—22no—
325C23×C7—22no—
326C23×C7—22no—
327C23×C7—44no—
328C23×C7—44no—
329C23×C7—44no—
330C23×C7—44no—
331C23×C7C23×C414yes—
332C23×C7C23×C412yes—
333C23×C7C22×D412yes—
334C23×C7C2×#4112yes—
335C23×C7C2×#4112yes—
336C23×C7C2×#4112yes—
337C23×C72−1+412yes—
338C23×C72−1+412yes—
339C23×C7C2511yescharacteristic
340C2×C4×C7—28no—
341C2×C4×C7—28no—
342C2×C4×C7—28no—
343C2×C4×C7—28no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—44no—
359C2×C4×C7—44no—
360C2×C4×C7C23×C414yes—
361C2×C4×C7C23×C414yes—
362C2×C4×C7C22×D414yes—
363C2×C4×C7C2×#4114yes—
364C2×Dic7—28no—
365C2×Dic7—28no—
366C2×Dic7—28no—
367C2×Dic7—28no—
368C2×Dic7—28no—
369C2×Dic7—22no—
370C2×Dic7—22no—
371C2×Dic7—22no—
372C2×Dic7—22no—
373C2×Dic7—22no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—22no—
378C2×Dic7—22no—
379C2×Dic7—232no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—44no—
387C2×Dic7—44no—
388C2×Dic7C4×D4116yes—
389C2×Dic7C23×C414yes—
390C2×Dic7C23×C414yes—
391C2×Dic7C23×C414yes—
392C2×Dic7C23×C414yes—
393C2×Dic7C22×D414yes—
394C2×Dic7C22×D414yes—
395C2×Dic7C2×#4114yes—
396C2×Dic7C2×#4114yes—
397Dic14—232no—
398C25C22×D711yescharacteristic
399C22×Q8—78no—
400C22×Q8—74no—
401C22×Q8—144no—
402C22×Q8—144no—
403C23×C4—71no—
404C23×C4—78no—
405C23×C4—74no—
406C23×C4—71no—
407C23×C4—71no—
408C23×C4—71no—
409C23×C4—71no—
410C23×C4—71no—
411C23×C4—71no—
412C23×C4—71no—
413C23×C4—144no—
414C23×C4—144no—
415C23×C4C22×D711yescharacteristic
416C23×C4C22×D711yescharacteristic
417C23×C4C22×D711yescharacteristic
418C23×C4C22×D711yescharacteristic
419C23×C4C22×D711yescharacteristic
420C23×C4C22×D711yescharacteristic
421C22⋊Q8—764no—
422C4×Q8—1432no—
423#117—1432no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—78no—
426C2×C4⋊C4—78no—
427C2×C4⋊C4—78no—
428C2×C4⋊C4—78no—
429C2×C4⋊C4—74no—
430C2×C4⋊C4—74no—
431C2×C4⋊C4—74no—
432C2×C4⋊C4—74no—
433C2×C4⋊C4—74no—
434C2×C4⋊C4—74no—
435C2×C4⋊C4—74no—
436C2×C4⋊C4—74no—
437C2×C4⋊C4—144no—
438C2×C4⋊C4—144no—
439C2×C4⋊C4—144no—
440C2×C4⋊C4—144no—
441C2×C4⋊C4C22×D714yes—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—78no—
445C2×C22⋊C4—74no—
446C2×C22⋊C4—74no—
447C2×C22⋊C4—74no—
448C2×C22⋊C4—144no—
449C2×C22⋊C4—144no—
450C2×C22⋊C4C4×D718yes—
451C2×C22⋊C4C22×D714yes—
452C2×C22⋊C4C22×D714yes—
453C2×C22⋊C4C22×D714yes—
454C2×C42—24no—
455C2×C42—74no—
456C2×C42—74no—
457C2×C42—74no—
458C2×C42—74no—
459C2×C42—74no—
460C2×C42—74no—
461C2×C42—74no—
462C2×C42—144no—
463C2×C42—144no—
464C2×C42—144no—
465C2×C42—144no—
466C2×C42—144no—
467C2×C42—144no—
468C2×C42—144no—
469C2×C42C22×D714yes—
470#95—74no—
471#95—74no—
472#95—74no—
473#95—74no—
474#95—74no—
475#95—74no—
476#95—74no—
477#95—74no—
478#95C22×D714yes—
479#95C22×D714yes—
480C22×C7—24no—
481C22×C7—24no—
482C22×C7—24no—
483C22×C7—416no—
484C22×C7—42no—
485C22×C7—42no—
486C22×C7—42no—
487C22×C7—42no—
488C22×C7C2×C4×D414yes—
489C22×C7C4×#4114yes—
490C22×C7#51914yes—
491C22×C7#54714yes—
492C22×C7#54814yes—
493C22×C7#55214yes—
494C22×C7#55614yes—
495C22×C7C24×C411yescharacteristic
496C22×C7C23×D411yescharacteristic
497C22×C7C22×#4111yescharacteristic
498C22×C7C22×#4111yescharacteristic
499C22×C7C22×#4111yescharacteristic
500C22×C7C2×2−1+411yescharacteristic
501C22×C7C2×2−1+411yescharacteristic
502C4×C7—24no—
503C4×C7—24no—
504C4×C7—24no—
505C4×C7—24no—
506C4×C7—42no—
507C4×C7—42no—
508Dic7—24no—
509Dic7—24no—
510Dic7—24no—
511Dic7—24no—
512Dic7—24no—
513Dic7—42no—
514Dic7—42no—
515Dic7C2×C4×D418yes—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24C2×C4×D714yes—
523C24C23×D712yes—
524C24C23×D711yescharacteristic
525C2×Q8—716no—
526C2×Q8—148no—
527C2×Q8—1432no—
528C2×Q8—148no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—74no—
544C22×C4—74no—
545C22×C4—74no—
546C22×C4—72no—
547C22×C4—74no—
548C22×C4—74no—
549C22×C4—74no—
550C22×C4—716no—
551C22×C4—74no—
552C22×C4—74no—
553C22×C4—72no—
554C22×C4—72no—
555C22×C4—72no—
556C22×C4—72no—
557C22×C4—72no—
558C22×C4—72no—
559C22×C4—72no—
560C22×C4—148no—
561C22×C4—1432no—
562C22×C4—148no—
563C22×C4—142no—
564C22×C4—142no—
565C22×C4—142no—
566C22×C4—142no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—142no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—142no—
575C22×C4—142no—
576C22×C4—142no—
577C22×C4—142no—
578C22×C4—142no—
579C22×C4C2×C4×D714yes—
580C22×C4C2×C4×D714yes—
581C22×C4D4×D714yes—
582C22×C4#115914yes—
583C22×C4C23×D712yes—
584C22×C4C23×D712yes—
585C22×C4C23×D712yes—
586C22×C4C23×D712yes—
587C22×C4C23×D712yes—
588C22×C4C23×D712yes—
589C4⋊C4—28no—
590C4⋊C4—716no—
591C4⋊C4—716no—
592C4⋊C4—716no—
593C4⋊C4—716no—
594C4⋊C4—148no—
595C4⋊C4—148no—
596C4⋊C4—148no—
597C4⋊C4—148no—
598C22⋊C4—28no—
599C22⋊C4—28no—
600C22⋊C4—716no—
601C22⋊C4—148no—
602C22⋊C4—148no—
603C22⋊C4C2×C4×D7116yes—
604C42—28no—
605C42—148no—
606C42—148no—
607C42—148no—
608C42—148no—
609C42—148no—
610C42—148no—
611C42—148no—
612C2×C7—44no—
613C2×C7#236218yescomplemented
614C2×C7C22×C4×D411yescharacteristic
615C2×C7C2×C4×#4111yescharacteristic
616C2×C7C2×#51911yescharacteristic
617C2×C7C2×#54711yescharacteristic
618C2×C7C2×#54811yescharacteristic
619C2×C7C2×#55211yescharacteristic
620C2×C7C2×#55611yescharacteristic
621C23—28no—
622C23—28no—
623C23—28no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—44no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23C22×C4×D714yes—
635C23C22×C4×D712yes—
636C23C2×D4×D712yes—
637C23C2×#115912yes—
638C23D7×#4112yes—
639C23D7×#4112yes—
640C23#655412yes—
641C23#655412yes—
642C23C24×D711yescharacteristic
643Q8—1432no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—716no—
665C2×C4—74no—
666C2×C4—74no—
667C2×C4—74no—
668C2×C4—74no—
669C2×C4—74no—
670C2×C4—74no—
671C2×C4—74no—
672C2×C4—74no—
673C2×C4—1432no—
674C2×C4—148no—
675C2×C4—148no—
676C2×C4—148no—
677C2×C4—148no—
678C2×C4—148no—
679C2×C4—142no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—142no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—142no—
694C2×C4—142no—
695C2×C4—284no—
696C2×C4—284no—
697C2×C4C22×C4×D714yes—
698C2×C4C22×C4×D714yes—
699C2×C4C2×D4×D714yes—
700C2×C4C2×#115914yes—
701C7C2×#236211yescharacteristic, complemented, Sylow
702C22—24no—
703C22—24no—
704C22—24no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—416no—
709C22—42no—
710C22#9020714yes—
711C22C4×#115914yes—
712C22C4×D4×D714yes—
713C22#9030214yes—
714C22#9034114yes—
715C22#9036814yes—
716C22#9039314yes—
717C22C23×C4×D711yescharacteristic
718C22C22×D4×D711yescharacteristic
719C22C22×#115911yescharacteristic
720C22C2×D7×#4111yescharacteristic
721C22C2×D7×#4111yescharacteristic
722C22C2×#655411yescharacteristic
723C22C2×#655411yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—78no—
731C4—144no—
732C4—144no—
733C4—144no—
734C4—144no—
735C4—144no—
736C4—282no—
737C4—282no—
738C2—44no—
739C2#1173292318yesdirect product factor
740C2C2×#9020711yescharacteristic
741C2C2×C4×#115911yescharacteristic
742C2C2×C4×D4×D711yescharacteristic
743C2C2×#9030211yescharacteristic
744C2C2×#9034111yescharacteristic
745C2C2×#9036811yescharacteristic
746C2C2×#9039311yescharacteristic
subgroupG/H
centerC24C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC2×C7×#388C2
socleC24×C7C24
prime radicalC25×C7C23
cosocleC23×C7C25
hypercenterC2×#388D7
hypocenterC7C2×#2362
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#6450C2semidirect
5. C2×#89750C2semidirect
10. C2×C4×C4⋊Dic7C2semidirect
11. C2×C4×Dic7⋊C4C2semidirect
12. #11732923C2direct (N × H)
13. C2×#89418C2semidirect
14. C2×#89419C2semidirect
15. C2×#89426C2semidirect
16. C2×#89421C2semidirect
43. C2×#6450C22semidirect
44. C2×#6441C4semidirect
59. #89750C22semidirect
64. C4×C4⋊Dic7C22semidirect
65. C4×Dic7⋊C4C22semidirect
66. #89426C22semidirect
67. #89421C22semidirect
68. #89419C22semidirect
69. #89418C22semidirect
141. #6441C2×C4semidirect
613. C2×C7#2362semidirect
701. C7C2×#2362semidirect
739. C2#11732923direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64502
C22×#64412
C22×#64402
C2×C7×#3882
C2×#897502
C2×#897162
C2×#897232
C2×C22⋊C4×Dic72
C2×C4×C4⋊Dic72
C2×C4×Dic7⋊C42
#117329232
C2×#894182
C2×#894192
C2×#894262
C2×#894212
C2×#23627