Finite Group Databasebeta

← C2×#11734238 #13523013

Subgroups — C2×#11734238 #13523013

Order 1792.

2854 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×#6507C211yesmaximal, characteristic, complemented
2C22×#6441C211yesmaximal, characteristic
3C2×C7×#393C211yesmaximal, characteristic
4C2×#90002C211yesmaximal, characteristic, complemented
5C2×#89719C211yesmaximal, characteristic
6C2×#89717C211yesmaximal, characteristic
7C2×#89716C211yesmaximal, characteristic
8C2×#89714C211yesmaximal, characteristic
9C2×C22⋊C4×Dic7C211yesmaximal, characteristic
10#11734238C2116yesmaximal, direct product factor
11C2×#89431C211yesmaximal, characteristic, complemented
12C2×#89430C211yesmaximal, characteristic, complemented
13C2×#89418C211yesmaximal, characteristic, complemented
14C2×#89418C211yesmaximal, characteristic, complemented
15C2×#89418C211yesmaximal, characteristic, complemented
16C2×#89421C211yesmaximal, characteristic, complemented
17C23×C7×Q8C2211yescharacteristic
18C24×Dic7C2211yescharacteristic
19C23×Dic14C2211yescharacteristic
20C23×Dic14C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C2×#6507—28no—
28C2×#6507C2218yescomplemented
29C22×C4⋊Dic7C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×C4×Dic7C2211yescharacteristic
37C22×C4×Dic7C2211yescharacteristic
38C22×C4×Dic7C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C2×#6441—28no—
41C2×#6441C2218yes—
42C7×#393C2218yes—
43C2×C7×#95C2211yescharacteristic
44C2×C7×#95C2211yescharacteristic
45C2×C7×#95C2211yescharacteristic
46#90002C2218yescomplemented
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
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
58#89719C2218yes—
59#89717C2218yes—
60#89716C2218yes—
61#89714C2218yes—
62C22⋊C4×Dic7C2218yes—
63#89431C2218yescomplemented
64#89430C2218yescomplemented
65#89421C2218yescomplemented
66#89418C2218yescomplemented
67#89418C2218yescomplemented
68#89418C2218yescomplemented
69C2×#2492—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C22×C7×Q8—24no—
72C22×C7×Q8—24no—
73C22×C7×Q8—42no—
74C22×C7×Q8C2314yes—
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×Dic7—24no—
82C23×Dic7—24no—
83C23×Dic7—24no—
84C23×Dic7C2314yes—
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C22×Dic14—24no—
94C22×Dic14—24no—
95C22×Dic14—24no—
96C22×Dic14—24no—
97C22×Dic14—24no—
98C22×Dic14—42no—
99C22×Dic14C2314yes—
100C22×Dic14C2314yes—
101C2×C7×C22⋊C4—24no—
102C2×C7×C22⋊C4—24no—
103C2×C7×C22⋊C4—42no—
104C2×C7×C22⋊C4C2314yes—
105C2×C7×C22⋊C4C2314yes—
106C2×C7×C22⋊C4C2314yes—
107C2×C22⋊Dic7—24no—
108C2×C22⋊Dic7—42no—
109C2×C22⋊Dic7Q818yescomplemented
110C2×C22⋊Dic7C2314yes—
111C2×C22⋊Dic7C2314yes—
112C2×C22⋊Dic7C2314yes—
113#6507—232no—
114C2×C4⋊Dic7—24no—
115C2×C4⋊Dic7C2314yes—
116C2×Dic7⋊C4—24no—
117C2×Dic7⋊C4—24no—
118C2×Dic7⋊C4—24no—
119C2×Dic7⋊C4—24no—
120C2×Dic7⋊C4—24no—
121C2×Dic7⋊C4D418yes—
122C2×Dic7⋊C4C2314yes—
123C2×Dic7⋊C4C2314yes—
124C2×Dic7⋊C4C2314yes—
125C2×Dic7⋊C4C2314yes—
126C2×Dic7⋊C4C2314yes—
127C2×Dic7⋊C4C2314yes—
128C2×C4×Dic7—24no—
129C2×C4×Dic7—24no—
130C2×C4×Dic7—42no—
131C2×C4×Dic7—42no—
132C2×C4×Dic7C2314yes—
133C2×C4×Dic7C2314yes—
134C2×C4×Dic7C2314yes—
135C2×C4×Dic7C2314yes—
136#6441—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×C4⋊Q8—71no—
152C22×C22⋊Q8—71no—
153#2492—716no—
154C2×#400—71no—
155C2×#400—71no—
156C2×#393—71no—
157C2×#393D711yescharacteristic
158C2×#391—71no—
159C2×#391—71no—
160C2×#391—71no—
161C2×#391—71no—
162C2×#388—71no—
163C2×#388—71no—
164C2×#380—71no—
165C2×C4×C4⋊C4—71no—
166C2×C4×C22⋊C4—71no—
167C24×C7—22no—
168C24×C7—22no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7C2×Q814yes—
174C24×C7C2412yes—
175C24×C7C2411yescharacteristic
176C2×C7×Q8—28no—
177C2×C7×Q8—28no—
178C2×C7×Q8—44no—
179C2×C7×Q8—416no—
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×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7C2×D414yes—
197C22×C4×C7#4114yes—
198C22×C4×C7C2412yes—
199C22×C4×C7C2412yes—
200C22×C4×C7C2412yes—
201C22×C4×C7C2412yes—
202C22×C4×C7C2412yes—
203C22×C4×C7C2412yes—
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—22no—
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—22no—
222C22×Dic7—28no—
223C22×Dic7—28no—
224C22×Dic7—28no—
225C22×Dic7—416no—
226C22×Dic7C2×D414yes—
227C22×Dic7C2×D414yes—
228C22×Dic7C2×Q814yes—
229C22×Dic7C2×Q814yes—
230C22×Dic7#4114yes—
231C22×Dic7#4114yes—
232C22×Dic7C2412yes—
233C22×Dic7C2412yes—
234C22×Dic7C2412yes—
235C22×Dic7C2412yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C22×Dic7C2412yes—
239C22×Dic7C2412yes—
240C2×Dic14—28no—
241C2×Dic14—28no—
242C2×Dic14—28no—
243C2×Dic14—28no—
244C2×Dic14—28no—
245C2×Dic14—44no—
246C2×Dic14—416no—
247C2×Dic14—416no—
248C7×C22⋊C4—28no—
249C7×C22⋊C4—28no—
250C7×C22⋊C4—44no—
251C22⋊Dic7—28no—
252C22⋊Dic7—44no—
253C22⋊Dic7C2×Q8116yescomplemented
254C4⋊Dic7—28no—
255Dic7⋊C4—28no—
256Dic7⋊C4—28no—
257Dic7⋊C4—28no—
258Dic7⋊C4—28no—
259Dic7⋊C4—28no—
260Dic7⋊C4C2×D4116yes—
261C4×Dic7—28no—
262C4×Dic7—28no—
263C4×Dic7—44no—
264C4×Dic7—44no—
265C23×Q8—71no—
266C23×Q8—71no—
267C23×Q8C2×D711yescharacteristic
268C24×C4—71no—
269C2×C4⋊Q8—78no—
270C2×C4⋊Q8—148no—
271C2×C22⋊Q8—78no—
272C2×C22⋊Q8—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×C22⋊C4—71no—
281C22×C22⋊C4—71no—
282C22×C22⋊C4—71no—
283C22×C22⋊C4C2×D711yescharacteristic
284C22×C22⋊C4C2×D711yescharacteristic
285C22×C22⋊C4C2×D711yescharacteristic
286C22×C42—71no—
287C22×C42—71no—
288C22×C42—71no—
289C22×C42—71no—
290#400—78no—
291#400—78no—
292#393—78no—
293#393C2×D718yes—
294#391—78no—
295#391—78no—
296#391—78no—
297#391—78no—
298#388—78no—
299#388—78no—
300#380—78no—
301C4×C4⋊C4—78no—
302C4×C22⋊C4—78no—
303C2×#95—71no—
304C2×#95—71no—
305C2×#95—71no—
306C2×#95—71no—
307C2×#95—71no—
308C2×#95—71no—
309C2×#95—71no—
310C2×#95—71no—
311C2×#95—71no—
312C2×#95—71no—
313C2×#95—71no—
314C2×#95C2×D711yescharacteristic
315C2×#95C2×D711yescharacteristic
316C2×#95C2×D711yescharacteristic
317C23×C7—28no—
318C23×C7—28no—
319C23×C7—28no—
320C23×C7—22no—
321C23×C7—22no—
322C23×C7—22no—
323C23×C7—22no—
324C23×C7—22no—
325C23×C7—22no—
326C23×C7—44no—
327C23×C7—44no—
328C23×C7—44no—
329C23×C7—44no—
330C23×C7C22×D412yes—
331C23×C7C22×Q814yes—
332C23×C7C22×Q812yes—
333C23×C7C2×#4112yes—
334C23×C7C2×#4112yes—
335C23×C7C2×#4112yes—
336C23×C7H(5,𝔽2)12yes—
337C23×C72−1+412yes—
338C23×C7C2511yescharacteristic
339C7×Q8—416no—
340C2×C4×C7—28no—
341C2×C4×C7—28no—
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—22no—
358C2×C4×C7—44no—
359C2×C4×C7—44no—
360C2×C4×C7—44no—
361C2×C4×C7—44no—
362C2×C4×C7C22×D414yes—
363C2×C4×C7C2×#4114yes—
364C2×Dic7—28no—
365C2×Dic7—28no—
366C2×Dic7—28no—
367C2×Dic7—22no—
368C2×Dic7—22no—
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—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—44no—
386C2×Dic7—44no—
387C2×Dic7—44no—
388C2×Dic7—44no—
389C2×Dic7—416no—
390C2×Dic7#124116yes—
391C2×Dic7C22×D414yes—
392C2×Dic7C22×D414yes—
393C2×Dic7C22×Q814yes—
394C2×Dic7C22×Q814yes—
395C2×Dic7C2×#4114yes—
396C2×Dic7C2×#4114yes—
397Dic14—416no—
398Dic14—416no—
399C25C22×D711yescharacteristic
400C22×Q8—24no—
401C22×Q8—24no—
402C22×Q8—42no—
403C22×Q8—74no—
404C22×Q8—74no—
405C22×Q8—144no—
406C22×Q8—144no—
407C22×Q8—144no—
408C22×Q8—144no—
409C22×Q8—144no—
410C22×Q8—282no—
411C22×Q8C22×D714yes—
412C23×C4—71no—
413C23×C4—71no—
414C23×C4—71no—
415C23×C4—71no—
416C23×C4—74no—
417C23×C4—71no—
418C23×C4—71no—
419C23×C4—71no—
420C23×C4—71no—
421C23×C4—144no—
422C23×C4—144no—
423C23×C4—144no—
424C23×C4C22×D711yescharacteristic
425C23×C4C22×D711yescharacteristic
426C23×C4C22×D711yescharacteristic
427C23×C4C22×D711yescharacteristic
428C23×C4C22×D711yescharacteristic
429C23×C4C22×D711yescharacteristic
430C4⋊Q8—1432no—
431C22⋊Q8—1432no—
432C2×C4⋊C4—78no—
433C2×C4⋊C4—74no—
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—144no—
441C2×C4⋊C4—144no—
442C2×C4⋊C4—144no—
443C2×C4⋊C4—144no—
444C2×C4⋊C4—144no—
445C2×C4⋊C4—144no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4—78no—
450C2×C22⋊C4—74no—
451C2×C22⋊C4—74no—
452C2×C22⋊C4—74no—
453C2×C22⋊C4—144no—
454C2×C22⋊C4—282no—
455C2×C22⋊C4C22×D714yes—
456C2×C22⋊C4C22×D714yes—
457C2×C22⋊C4C22×D714yes—
458C2×C42—74no—
459C2×C42—74no—
460C2×C42—74no—
461C2×C42—74no—
462C2×C42—144no—
463C2×C42—144no—
464C2×C42—282no—
465C2×C42—282no—
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#95C22×D714yes—
478#95C22×D714yes—
479#95C22×D714yes—
480C22×C7—24no—
481C22×C7—24no—
482C22×C7—24no—
483C22×C7—42no—
484C22×C7—42no—
485C22×C7—42no—
486C22×C7—42no—
487C22×C7—416no—
488C22×C7C2×#12414yes—
489C22×C7#53314yes—
490C22×C7#54214yes—
491C22×C7#54614yes—
492C22×C7D4×Q814yes—
493C22×C7#55414yes—
494C22×C7#55614yes—
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—24no—
504C4×C7—42no—
505C4×C7—42no—
506C4×C7—42no—
507C4×C7—42no—
508Dic7—24no—
509Dic7—24no—
510Dic7—24no—
511Dic7—42no—
512Dic7—42no—
513Dic7—42no—
514Dic7—42no—
515Dic7C2×#12418yes—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24Q8×D714yes—
523C24C23×D712yes—
524C24C23×D711yescharacteristic
525C2×Q8—28no—
526C2×Q8—28no—
527C2×Q8—44no—
528C2×Q8—416no—
529C2×Q8—148no—
530C2×Q8—148no—
531C2×Q8—148no—
532C2×Q8—148no—
533C2×Q8—148no—
534C2×Q8—284no—
535C2×Q8—2816no—
536C2×Q8—2816no—
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—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—74no—
554C22×C4—74no—
555C22×C4—74no—
556C22×C4—72no—
557C22×C4—74no—
558C22×C4—74no—
559C22×C4—74no—
560C22×C4—72no—
561C22×C4—72no—
562C22×C4—72no—
563C22×C4—72no—
564C22×C4—72no—
565C22×C4—72no—
566C22×C4—72no—
567C22×C4—148no—
568C22×C4—148no—
569C22×C4—148no—
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×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—2816no—
589C22×C4D4×D714yes—
590C22×C4#115914yes—
591C22×C4C23×D712yes—
592C22×C4C23×D712yes—
593C22×C4C23×D712yes—
594C22×C4C23×D712yes—
595C22×C4C23×D712yes—
596C22×C4C23×D712yes—
597C4⋊C4—716no—
598C4⋊C4—148no—
599C4⋊C4—148no—
600C4⋊C4—148no—
601C4⋊C4—148no—
602C4⋊C4—148no—
603C4⋊C4—148no—
604C22⋊C4—28no—
605C22⋊C4—28no—
606C22⋊C4—44no—
607C22⋊C4—716no—
608C22⋊C4—148no—
609C22⋊C4—284no—
610C42—148no—
611C42—148no—
612C42—284no—
613C42—284no—
614C2×C7—44no—
615C2×C7#249218yescomplemented
616C2×C7C22×#12411yescharacteristic
617C2×C7C2×#53311yescharacteristic
618C2×C7C2×#54211yescharacteristic
619C2×C7C2×#54611yescharacteristic
620C2×C7C2×D4×Q811yescharacteristic
621C2×C7C2×#55411yescharacteristic
622C2×C7C2×#55611yescharacteristic
623C23—28no—
624C23—28no—
625C23—28no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23C2×D4×D712yes—
637C23C2×#115912yes—
638C23#654812yes—
639C23C2×Q8×D714yes—
640C23C2×Q8×D712yes—
641C23D7×#4112yes—
642C23D7×#4112yes—
643C23#655412yes—
644C23C24×D711yescharacteristic
645Q8—416no—
646Q8—2816no—
647Q8—2816no—
648C2×C4—28no—
649C2×C4—28no—
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—22no—
665C2×C4—22no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—74no—
671C2×C4—74no—
672C2×C4—74no—
673C2×C4—716no—
674C2×C4—74no—
675C2×C4—74no—
676C2×C4—74no—
677C2×C4—148no—
678C2×C4—148no—
679C2×C4—148no—
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—142no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—2816no—
699C2×C4—284no—
700C2×C4—284no—
701C2×C4—284no—
702C2×C4—284no—
703C2×C4C2×D4×D714yes—
704C2×C4C2×#115914yes—
705C7C2×#249211yescharacteristic, complemented, Sylow
706C22—24no—
707C22—24no—
708C22—24no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—416no—
714C22#9028214yes—
715C22#9031314yes—
716C22#9032314yes—
717C22#9032714yes—
718C22#9036014yes—
719C22#9036214yes—
720C22D7×#12414yes—
721C22C22×D4×D711yescharacteristic
722C22C22×#115911yescharacteristic
723C22C2×#654811yescharacteristic
724C22C22×Q8×D711yescharacteristic
725C22C2×D7×#4111yescharacteristic
726C22C2×D7×#4111yescharacteristic
727C22C2×#655411yescharacteristic
728C4—24no—
729C4—24no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—78no—
735C4—144no—
736C4—144no—
737C4—144no—
738C4—282no—
739C4—282no—
740C4—282no—
741C4—282no—
742C2—44no—
743C2#1173423818yesdirect product factor
744C2C2×#9028211yescharacteristic
745C2C2×#9031311yescharacteristic
746C2C2×#9032311yescharacteristic
747C2C2×#9032711yescharacteristic
748C2C2×#9036011yescharacteristic
749C2C2×#9036211yescharacteristic
750C2C2×D7×#12411yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#393C2
socleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#393D7
hypocenterC7C2×#2492
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#6507C2semidirect
4. C2×#90002C2semidirect
10. #11734238C2direct (N × H)
11. C2×#89431C2semidirect
12. C2×#89430C2semidirect
13. C2×#89418C2semidirect
14. C2×#89418C2semidirect
15. C2×#89418C2semidirect
16. C2×#89421C2semidirect
28. C2×#6507C22semidirect
46. #90002C22semidirect
63. #89431C22semidirect
64. #89430C22semidirect
65. #89421C22semidirect
66. #89418C22semidirect
67. #89418C22semidirect
68. #89418C22semidirect
109. C2×C22⋊Dic7Q8semidirect
253. C22⋊Dic7C2×Q8semidirect
615. C2×C7#2492semidirect
705. C7C2×#2492semidirect
743. C2#11734238direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#65072
C22×#64412
C2×C7×#3932
C2×#900022
C2×#897192
C2×#897172
C2×#897162
C2×#897142
C2×C22⋊C4×Dic72
#117342382
C2×#894312
C2×#894302
C2×#894182
C2×#894212
C2×#24927