Finite Group Databasebeta

← C2×#11731859 #13522445

Subgroups — C2×#11731859 #13522445

Order 1792.

3006 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6487C211yesmaximal, characteristic
2C22×#6440C211yesmaximal, characteristic
3C2×C7×#385C211yesmaximal, characteristic
4C22×C7⋊#95C211yesmaximal, characteristic
5C2×#89752C211yesmaximal, characteristic, complemented
6C2×#89751C211yesmaximal, characteristic, complemented
7C2×#89744C211yesmaximal, characteristic, complemented
8C2×#89753C211yesmaximal, characteristic, complemented
9C2×#89718C211yesmaximal, characteristic
10C2×#89715C211yesmaximal, characteristic
11C2×#89714C211yesmaximal, characteristic
12#11731859C2116yesmaximal, direct product factor
13C2×#89430C211yesmaximal, characteristic, complemented
14C2×#89429C211yesmaximal, characteristic, complemented
15C2×#89418C211yesmaximal, characteristic, complemented
16C2×#89424C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C24×Dic7C2211yescharacteristic
19C24×Dic7C2211yescharacteristic
20C23×Dic14C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C2×#6487—28no—
29C2×#6487C2218yes—
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×C4×Dic7C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C2×#6440—28no—
41C2×#6440C2218yes—
42C7×#385C2218yes—
43C2×C7×#95C2211yescharacteristic
44C2×C7×#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2218yes—
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58#89753C2218yescomplemented
59#89752C2218yescomplemented
60#89751C2218yescomplemented
61#89744C2218yescomplemented
62#89718C2218yes—
63#89715C2218yes—
64#89714C2218yes—
65#89430C2218yescomplemented
66#89429C2218yescomplemented
67#89424C2218yescomplemented
68#89418C2218yescomplemented
69C2×#2438—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C23×C4×C7—24no—
72C23×C4×C7—24no—
73C23×C4×C7—42no—
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2314yes—
80C23×C4×C7C2311yescharacteristic
81C23×Dic7—24no—
82C23×Dic7—24no—
83C23×Dic7—24no—
84C23×Dic7—24no—
85C23×Dic7—42no—
86C23×Dic7Q818yescomplemented
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2314yes—
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2314yes—
96C23×Dic7C2311yescharacteristic
97C22×Dic14—24no—
98C22×Dic14—24no—
99C22×Dic14—42no—
100C22×Dic14C2314yes—
101C2×C7×C4⋊C4—24no—
102C2×C7×C4⋊C4—42no—
103C2×C7×C4⋊C4C2314yes—
104C2×C7×C4⋊C4C2314yes—
105C2×C7×C22⋊C4—24no—
106C2×C7×C22⋊C4—24no—
107C2×C7×C22⋊C4C2314yes—
108C2×C7×C22⋊C4C2314yes—
109C2×C22⋊Dic7—24no—
110C2×C22⋊Dic7D418yes—
111C2×C22⋊Dic7C2314yes—
112C2×C22⋊Dic7C2314yes—
113C2×C4⋊Dic7—24no—
114C2×C4⋊Dic7C2314yes—
115#6487—232no—
116C2×Dic7⋊C4—24no—
117C2×Dic7⋊C4—24no—
118C2×Dic7⋊C4—24no—
119C2×Dic7⋊C4—24no—
120C2×Dic7⋊C4—24no—
121C2×Dic7⋊C4—24no—
122C2×Dic7⋊C4—42no—
123C2×Dic7⋊C4—42no—
124C2×Dic7⋊C4C2314yes—
125C2×Dic7⋊C4C2314yes—
126C2×Dic7⋊C4C2314yes—
127C2×Dic7⋊C4C2314yes—
128C2×Dic7⋊C4C2314yes—
129C2×Dic7⋊C4C2314yes—
130C2×Dic7⋊C4C2314yes—
131C2×Dic7⋊C4C2314yes—
132C2×C4×Dic7—24no—
133C2×C4×Dic7—24no—
134C2×C4×Dic7C2314yes—
135C2×C4×Dic7C2314yes—
136#6440—232no—
137C7×#95C2314yes—
138C7×#95C2314yes—
139C7⋊#95C2314yes—
140C7⋊#95C2314yes—
141C7⋊#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C22×C22⋊Q8—71no—
152C22×#117—71no—
153#2438—716no—
154C2×#400—71no—
155C2×#398—71no—
156C2×#398—71no—
157C2×#395—71no—
158C2×#391—71no—
159C2×#389—71no—
160C2×#387—71no—
161C2×#387—71no—
162C2×#385—71no—
163C2×#385D711yescharacteristic
164C2×#381—71no—
165C2×#380—71no—
166C22×#95—71no—
167C24×C7—22no—
168C24×C7—22no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7C2×D414yes—
172C24×C7C2×Q814yes—
173C24×C7#4114yes—
174C24×C7C2412yes—
175C24×C7C2411yescharacteristic
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—28no—
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—22no—
194C22×C4×C7—28no—
195C22×C4×C7—44no—
196C22×C4×C7—416no—
197C22×C4×C7#4114yes—
198C22×C4×C7C2412yes—
199C22×C4×C7C2412yes—
200C22×C4×C7C2412yes—
201C22×C4×C7C2412yes—
202C22×C4×C7C2412yes—
203C22×C4×C7C2412yes—
204C22×Dic7—232no—
205C22×Dic7—28no—
206C22×Dic7—22no—
207C22×Dic7—22no—
208C22×Dic7—22no—
209C22×Dic7—22no—
210C22×Dic7—22no—
211C22×Dic7—22no—
212C22×Dic7—28no—
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—28no—
222C22×Dic7—22no—
223C22×Dic7—22no—
224C22×Dic7—22no—
225C22×Dic7—22no—
226C22×Dic7—22no—
227C22×Dic7—28no—
228C22×Dic7—44no—
229C22×Dic7—416no—
230C22×Dic7C2×D414yes—
231C22×Dic7C2×D414yes—
232C22×Dic7C2×Q814yes—
233C22×Dic7C2×Q814yes—
234C22×Dic7C2×Q8116yescomplemented
235C22×Dic7#4114yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C22×Dic7C2412yes—
239C22×Dic7C2412yes—
240C22×Dic7C2412yes—
241C22×Dic7C2412yes—
242C22×Dic7C2412yes—
243C22×Dic7C2412yes—
244C2×Dic14—28no—
245C2×Dic14—28no—
246C2×Dic14—44no—
247C2×Dic14—416no—
248C7×C4⋊C4—28no—
249C7×C4⋊C4—44no—
250C7×C22⋊C4—28no—
251C7×C22⋊C4—28no—
252C22⋊Dic7—28no—
253C22⋊Dic7C2×D4116yes—
254C4⋊Dic7—28no—
255Dic7⋊C4—28no—
256Dic7⋊C4—28no—
257Dic7⋊C4—28no—
258Dic7⋊C4—28no—
259Dic7⋊C4—28no—
260Dic7⋊C4—28no—
261Dic7⋊C4—44no—
262Dic7⋊C4—44no—
263C4×Dic7—28no—
264C4×Dic7—28no—
265C23×Q8—71no—
266C24×C4—71no—
267C24×C4—71no—
268C24×C4C2×D711yescharacteristic
269C2×C22⋊Q8—78no—
270C2×C22⋊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⋊C4—71no—
282C22×C4⋊C4C2×D711yescharacteristic
283C22×C4⋊C4C2×D711yescharacteristic
284C22×C22⋊C4—71no—
285C22×C22⋊C4—71no—
286C22×C22⋊C4C2×D711yescharacteristic
287C22×C22⋊C4C2×D711yescharacteristic
288C22×C42—71no—
289C22×C42—71no—
290#400—78no—
291#398—78no—
292#398—78no—
293#395—78no—
294#391—78no—
295#389—78no—
296#387—78no—
297#387—78no—
298#385—78no—
299#385C2×D718yes—
300#381—78no—
301#380—78no—
302C2×#95—71no—
303C2×#95—71no—
304C2×#95—71no—
305C2×#95—71no—
306C2×#95—71no—
307C2×#95—71no—
308C2×#95—71no—
309C2×#95—71no—
310C2×#95—78no—
311C2×#95—71no—
312C2×#95—71no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95C2×D711yescharacteristic
316C2×#95C2×D711yescharacteristic
317C23×C7—28no—
318C23×C7—28no—
319C23×C7—28no—
320C23×C7—28no—
321C23×C7—28no—
322C23×C7—28no—
323C23×C7—22no—
324C23×C7—22no—
325C23×C7—22no—
326C23×C7—22no—
327C23×C7C22⋊Q8116yes—
328C23×C7C22×D414yes—
329C23×C7C22×D412yes—
330C23×C7C22×Q814yes—
331C23×C7C22×Q812yes—
332C23×C7C2×#4114yes—
333C23×C7C2×#4112yes—
334C23×C7C2×#4112yes—
335C23×C7C2×#4112yes—
336C23×C7H(5,𝔽2)12yes—
337C23×C72−1+412yes—
338C23×C7C2511yescharacteristic
339C2×C4×C7—28no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
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—416no—
358C2×C4×C7—44no—
359C2×C4×C7—44no—
360C2×C4×C7—44no—
361C2×C4×C7—44no—
362C2×C4×C7—44no—
363C2×C4×C7C2×#4114yes—
364C2×Dic7—28no—
365C2×Dic7—28no—
366C2×Dic7—232no—
367C2×Dic7—28no—
368C2×Dic7—28no—
369C2×Dic7—28no—
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—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—416no—
390C2×Dic7—44no—
391C2×Dic7—44no—
392C2×Dic7—44no—
393C2×Dic7C22×D414yes—
394C2×Dic7C22×D414yes—
395C2×Dic7C22×Q814yes—
396C2×Dic7C22×Q814yes—
397C2×Dic7C2×#4114yes—
398Dic14—416no—
399C25C22×D711yescharacteristic
400C22×Q8—74no—
401C22×Q8—144no—
402C22×Q8—144no—
403C22×Q8—282no—
404C23×C4—24no—
405C23×C4—24no—
406C23×C4—42no—
407C23×C4—78no—
408C23×C4—74no—
409C23×C4—71no—
410C23×C4—71no—
411C23×C4—71no—
412C23×C4—71no—
413C23×C4—71no—
414C23×C4—71no—
415C23×C4—71no—
416C23×C4—71no—
417C23×C4—74no—
418C23×C4—144no—
419C23×C4—144no—
420C23×C4—144no—
421C23×C4—144no—
422C23×C4—282no—
423C23×C4C22×D711yescharacteristic
424C23×C4C22×D711yescharacteristic
425C23×C4C22×D711yescharacteristic
426C23×C4C22×D711yescharacteristic
427C23×C4C22×D711yescharacteristic
428C23×C4C22×D714yes—
429C23×C4C22×D711yescharacteristic
430C22⋊Q8—1432no—
431#117—1432no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—74no—
435C2×C4⋊C4—74no—
436C2×C4⋊C4—74no—
437C2×C4⋊C4—74no—
438C2×C4⋊C4—74no—
439C2×C4⋊C4—74no—
440C2×C4⋊C4—74no—
441C2×C4⋊C4—74no—
442C2×C4⋊C4—74no—
443C2×C4⋊C4—144no—
444C2×C4⋊C4—144no—
445C2×C4⋊C4—144no—
446C2×C4⋊C4—144no—
447C2×C4⋊C4—144no—
448C2×C4⋊C4—144no—
449C2×C4⋊C4—144no—
450C2×C4⋊C4—282no—
451C2×C4⋊C4—282no—
452C2×C4⋊C4C22×D714yes—
453C2×C4⋊C4C22×D714yes—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—78no—
457C2×C22⋊C4—74no—
458C2×C22⋊C4—74no—
459C2×C22⋊C4—144no—
460C2×C22⋊C4C22×D714yes—
461C2×C22⋊C4C22×D714yes—
462C2×C42—74no—
463C2×C42—74no—
464C2×C42—144no—
465C2×C42—144no—
466#95—74no—
467#95—74no—
468#95—74no—
469#95—74no—
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—232no—
483C22×C7—24no—
484C22×C7—24no—
485C22×C7—24no—
486C22×C7—24no—
487C22×C7C2×C22⋊Q818yes—
488C22×C7C2×C22⋊Q814yes—
489C22×C7#53314yes—
490C22×C7#54414yes—
491C22×C7#54614yes—
492C22×C7#54714yes—
493C22×C7#55114yes—
494C22×C7#55214yes—
495C22×C7C23×D411yescharacteristic
496C22×C7C23×Q811yescharacteristic
497C22×C7C22×#4111yescharacteristic
498C22×C7C22×#4111yescharacteristic
499C22×C7C22×#4111yescharacteristic
500C22×C7C2×H(5,𝔽2)11yescharacteristic
501C22×C7C2×2−1+411yescharacteristic
502C4×C7—24no—
503C4×C7—42no—
504C4×C7—42no—
505C4×C7—42no—
506C4×C7—42no—
507C4×C7—42no—
508Dic7—24no—
509Dic7—24no—
510Dic7—24no—
511Dic7—24no—
512Dic7—24no—
513Dic7—42no—
514Dic7—42no—
515Dic7—42no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24#115714yes—
521C24D4×D714yes—
522C24Q8×D714yes—
523C24C23×D712yes—
524C24C23×D711yescharacteristic
525C2×Q8—148no—
526C2×Q8—148no—
527C2×Q8—284no—
528C2×Q8—2816no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—28no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—28no—
548C22×C4—44no—
549C22×C4—416no—
550C22×C4—74no—
551C22×C4—74no—
552C22×C4—74no—
553C22×C4—74no—
554C22×C4—716no—
555C22×C4—74no—
556C22×C4—72no—
557C22×C4—72no—
558C22×C4—72no—
559C22×C4—72no—
560C22×C4—72no—
561C22×C4—72no—
562C22×C4—72no—
563C22×C4—72no—
564C22×C4—148no—
565C22×C4—1432no—
566C22×C4—148no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—142no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—148no—
573C22×C4—142no—
574C22×C4—142no—
575C22×C4—142no—
576C22×C4—142no—
577C22×C4—142no—
578C22×C4—148no—
579C22×C4—142no—
580C22×C4—142no—
581C22×C4—142no—
582C22×C4—142no—
583C22×C4—142no—
584C22×C4—142no—
585C22×C4—142no—
586C22×C4—142no—
587C22×C4—142no—
588C22×C4—284no—
589C22×C4—2816no—
590C22×C4#115914yes—
591C22×C4C23×D712yes—
592C22×C4C23×D712yes—
593C22×C4C23×D712yes—
594C22×C4C23×D712yes—
595C22×C4C23×D712yes—
596C22×C4C23×D712yes—
597C4⋊C4—28no—
598C4⋊C4—44no—
599C4⋊C4—148no—
600C4⋊C4—148no—
601C4⋊C4—148no—
602C4⋊C4—148no—
603C4⋊C4—148no—
604C4⋊C4—148no—
605C4⋊C4—148no—
606C4⋊C4—284no—
607C4⋊C4—284no—
608C22⋊C4—28no—
609C22⋊C4—28no—
610C22⋊C4—716no—
611C22⋊C4—148no—
612C42—148no—
613C42—148no—
614C2×C7—28no—
615C2×C7#243818yescomplemented
616C2×C7C22×C22⋊Q811yescharacteristic
617C2×C7C2×#53311yescharacteristic
618C2×C7C2×#54411yescharacteristic
619C2×C7C2×#54611yescharacteristic
620C2×C7C2×#54711yescharacteristic
621C2×C7C2×#55111yescharacteristic
622C2×C7C2×#55211yescharacteristic
623C23—28no—
624C23—28no—
625C23—28no—
626C23—28no—
627C23—28no—
628C23—28no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#6459116yes—
634C23C2×#115714yes—
635C23C2×#115712yes—
636C23C2×D4×D714yes—
637C23C2×D4×D712yes—
638C23C2×#115912yes—
639C23#654812yes—
640C23C2×Q8×D714yes—
641C23C2×Q8×D712yes—
642C23D7×#4112yes—
643C23#655412yes—
644C23C24×D711yescharacteristic
645Q8—2816no—
646C2×C4—28no—
647C2×C4—22no—
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—22no—
663C2×C4—22no—
664C2×C4—416no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—74no—
671C2×C4—74no—
672C2×C4—74no—
673C2×C4—74no—
674C2×C4—74no—
675C2×C4—1432no—
676C2×C4—148no—
677C2×C4—148no—
678C2×C4—148no—
679C2×C4—148no—
680C2×C4—148no—
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—142no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—2816no—
701C2×C4—284no—
702C2×C4—284no—
703C2×C4—284no—
704C2×C4C2×#115914yes—
705C7C2×#243811yescharacteristic, complemented, Sylow
706C22—24no—
707C22—24no—
708C22—24no—
709C22—24no—
710C22—24no—
711C22—24no—
712C22—232no—
713C22C2×#645918yes—
714C22C2×#645914yes—
715C22#9023214yes—
716C22#9024714yes—
717C22#9028214yes—
718C22#9031314yes—
719C22#9031414yes—
720C22#9034614yes—
721C22C22×#115711yescharacteristic
722C22C22×D4×D711yescharacteristic
723C22C22×#115911yescharacteristic
724C22C2×#654811yescharacteristic
725C22C22×Q8×D711yescharacteristic
726C22C2×D7×#4111yescharacteristic
727C22C2×#655411yescharacteristic
728C4—24no—
729C4—42no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—144no—
735C4—144no—
736C4—144no—
737C4—144no—
738C4—144no—
739C4—282no—
740C4—282no—
741C4—282no—
742C2—28no—
743C2#1173185918yesdirect product factor
744C2C22×#645911yescharacteristic
745C2C2×#9023211yescharacteristic
746C2C2×#9024711yescharacteristic
747C2C2×#9028211yescharacteristic
748C2C2×#9031311yescharacteristic
749C2C2×#9031411yescharacteristic
750C2C2×#9034611yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#385C2
socleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#385D7
hypocenterC7C2×#2438
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
5. C2×#89752C2semidirect
6. C2×#89751C2semidirect
7. C2×#89744C2semidirect
8. C2×#89753C2semidirect
12. #11731859C2direct (N × H)
13. C2×#89430C2semidirect
14. C2×#89429C2semidirect
15. C2×#89418C2semidirect
16. C2×#89424C2semidirect
58. #89753C22semidirect
59. #89752C22semidirect
60. #89751C22semidirect
61. #89744C22semidirect
65. #89430C22semidirect
66. #89429C22semidirect
67. #89424C22semidirect
68. #89418C22semidirect
86. C23×Dic7Q8semidirect
234. C22×Dic7C2×Q8semidirect
615. C2×C7#2438semidirect
705. C7C2×#2438semidirect
743. C2#11731859direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64872
C22×#64402
C2×C7×#3852
C22×C7⋊#952
C2×#897522
C2×#897512
C2×#897442
C2×#897532
C2×#897182
C2×#897152
C2×#897142
#117318592
C2×#894302
C2×#894292
C2×#894182
C2×#894242
C2×#24387