Finite Group Databasebeta

← C2×#11732780 #13523611

Subgroups — C2×#11732780 #13523611

Order 1792.

2918 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D7×C4⋊C4C211yesmaximal, characteristic
2C22×#6435C211yesmaximal, characteristic
3C2×C7×#387C211yesmaximal, characteristic, complemented
4C2×#89761C211yesmaximal, characteristic
5C2×#89756C211yesmaximal, characteristic, complemented
6C2×#89750C211yesmaximal, characteristic, complemented
7C2×#89705C211yesmaximal, characteristic, complemented
8#11732780C2116yesmaximal, direct product factor
9C2×#89440C211yesmaximal, characteristic
10C2×#89436C211yesmaximal, characteristic
11C2×#89436C211yesmaximal, characteristic
12C2×#89436C211yesmaximal, characteristic
13C2×#89432C211yesmaximal, characteristic, complemented
14C2×#89430C211yesmaximal, characteristic, complemented
15C2×#89429C211yesmaximal, characteristic, complemented
16C2×#89425C211yesmaximal, characteristic, complemented
17C23×C4×D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C23×C4×D7C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C42×C7C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
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
36C2×D7×C4⋊C4—28no—
37C2×D7×C4⋊C4C2218yes—
38C2×#6435—28no—
39C2×#6435C2218yes—
40C7×#387C2218yescomplemented
41C2×C7×#95C2211yescharacteristic
42C2×C7×#95C2211yescharacteristic
43C2×C7×#95C2211yescharacteristic
44C2×C7×#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
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
57#89761C2218yes—
58#89756C2218yescomplemented
59#89750C2218yescomplemented
60#89705C2218yescomplemented
61#89440C2218yes—
62#89436C2218yes—
63#89436C2218yes—
64#89436C2218yes—
65#89432C2218yescomplemented
66#89430C2218yescomplemented
67#89429C2218yescomplemented
68#89425C2218yescomplemented
69C2×#2484—71nomaximal, Sylow
70C24×D7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C22×C4×D7—24no—
86C22×C4×D7—24no—
87C22×C4×D7—24no—
88C22×C4×D7—24no—
89C22×C4×D7—24no—
90C22×C4×D7—24no—
91C22×C4×D7—24no—
92C22×C4×D7—24no—
93C22×C4×D7D418yes—
94C22×C4×D7C2314yes—
95C22×C4×D7C2314yes—
96C22×C4×D7C2314yes—
97C2×C7×C4⋊C4—24no—
98C2×C7×C4⋊C4—24no—
99C2×C7×C4⋊C4C2314yes—
100C2×C7×C4⋊C4C2314yes—
101C2×C42×C7—24no—
102C2×C42×C7C2314yes—
103C2×(C2×D7)⋊C4—24no—
104C2×(C2×D7)⋊C4—24no—
105C2×(C2×D7)⋊C4—24no—
106C2×(C2×D7)⋊C4—24no—
107C2×(C2×D7)⋊C4C2314yes—
108C2×(C2×D7)⋊C4C2314yes—
109C2×(C2×D7)⋊C4C2314yes—
110C2×(C2×D7)⋊C4C2314yes—
111C2×C4⋊Dic7—24no—
112C2×C4⋊Dic7—24no—
113C2×C4⋊Dic7C2314yes—
114C2×C4⋊Dic7C2314yes—
115C2×Dic7⋊C4—24no—
116C2×Dic7⋊C4—24no—
117C2×Dic7⋊C4—24no—
118C2×Dic7⋊C4—24no—
119C2×Dic7⋊C4—24no—
120C2×Dic7⋊C4—24no—
121C2×Dic7⋊C4C2314yes—
122C2×Dic7⋊C4C2314yes—
123C2×Dic7⋊C4C2314yes—
124C2×Dic7⋊C4C2314yes—
125C2×Dic7⋊C4C2314yes—
126C2×Dic7⋊C4C2314yes—
127C2×C4×Dic7—24no—
128C2×C4×Dic7C2314yes—
129D7×C4⋊C4—232no—
130#6435—232no—
131C7×#95C2314yes—
132C7×#95C2314yes—
133C7×#95C2314yes—
134C7×#95C2314yes—
135C7⋊#95C2314yes—
136C7⋊#95C2314yes—
137C7⋊#95C2314yes—
138C7⋊#95C2314yes—
139C7⋊#95C2314yes—
140C7⋊#95C2314yes—
141C7⋊#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C22×#117—71no—
148C23×C4⋊C4—71no—
149#2484—716no—
150C2×#400—71no—
151C2×#400—71no—
152C2×#398—71no—
153C2×#398—71no—
154C2×#387—71no—
155C2×#387—71no—
156C2×#387—71no—
157C2×#387D711yescharacteristic, complemented
158C2×#385—71no—
159C2×#385—71no—
160C2×#381—71no—
161C2×#381—71no—
162C2×#381—71no—
163C24×C7C2411yescharacteristic
164C23×D7—22no—
165C23×D7—22no—
166C23×D7—22no—
167C23×D7—22no—
168C23×D7C2×D414yes—
169C23×D7#4114yes—
170C23×D7#4114yes—
171C23×D7C2412yes—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
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×C7C2×D414yes—
192C22×C4×C7#4114yes—
193C22×C4×C7C2412yes—
194C22×C4×C7C2412yes—
195C22×C4×C7C2412yes—
196C22×C4×C7C2412yes—
197C22×C4×C7C2412yes—
198C22×C4×C7C2412yes—
199C22×C4×C7C2412yes—
200C22×Dic7—22no—
201C22×Dic7—22no—
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—22no—
213C22×Dic7—22no—
214C22×Dic7—22no—
215C22×Dic7—22no—
216C22×Dic7—22no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7C2×D414yes—
220C22×Dic7#4114yes—
221C22×Dic7C2412yes—
222C22×Dic7C2412yes—
223C22×Dic7C2412yes—
224C22×Dic7C2412yes—
225C22×Dic7C2412yes—
226C22×Dic7C2412yes—
227C22×Dic7C2412yes—
228C2×C4×D7—232no—
229C2×C4×D7—232no—
230C2×C4×D7—28no—
231C2×C4×D7—28no—
232C2×C4×D7—28no—
233C2×C4×D7—28no—
234C2×C4×D7—28no—
235C2×C4×D7—28no—
236C2×C4×D7—28no—
237C2×C4×D7—28no—
238C2×C4×D7—416no—
239C2×C4×D7C2×D4116yes—
240C7×C4⋊C4—28no—
241C7×C4⋊C4—28no—
242C42×C7—28no—
243(C2×D7)⋊C4—28no—
244(C2×D7)⋊C4—28no—
245(C2×D7)⋊C4—28no—
246(C2×D7)⋊C4—28no—
247C4⋊Dic7—28no—
248C4⋊Dic7—28no—
249Dic7⋊C4—28no—
250Dic7⋊C4—28no—
251Dic7⋊C4—28no—
252Dic7⋊C4—28no—
253Dic7⋊C4—28no—
254Dic7⋊C4—28no—
255C4×Dic7—28no—
256C24×C4—71no—
257C24×C4—71no—
258C24×C4—71no—
259C2×#117—78no—
260C2×#117—148no—
261C22×C4⋊C4—71no—
262C22×C4⋊C4—71no—
263C22×C4⋊C4—71no—
264C22×C4⋊C4—71no—
265C22×C4⋊C4—71no—
266C22×C4⋊C4—71no—
267C22×C4⋊C4—71no—
268C22×C4⋊C4—71no—
269C22×C4⋊C4—78no—
270C22×C4⋊C4—148no—
271C22×C4⋊C4C2×D711yescharacteristic
272C22×C4⋊C4C2×D711yescharacteristic
273C22×C22⋊C4—71no—
274C22×C22⋊C4—71no—
275C22×C22⋊C4—71no—
276C22×C22⋊C4—71no—
277C22×C42—71no—
278C22×C42C2×D711yescharacteristic
279#400—78no—
280#400—78no—
281#398—78no—
282#398—78no—
283#387—78no—
284#387—78no—
285#387—78no—
286#387C2×D718yescomplemented
287#385—78no—
288#385—78no—
289#381—78no—
290#381—78no—
291#381—78no—
292C2×#95—71no—
293C2×#95—71no—
294C2×#95—71no—
295C2×#95—71no—
296C2×#95—71no—
297C2×#95—71no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95—71no—
302C2×#95—71no—
303C2×#95—71no—
304C2×#95C2×D711yescharacteristic
305C2×#95C2×D711yescharacteristic
306C2×#95C2×D711yescharacteristic
307C2×#95C2×D711yescharacteristic
308C23×C7C22×D412yes—
309C23×C7C2×#4112yes—
310C23×C7C2×#4112yes—
311C23×C7C2×#4112yes—
312C23×C7C2×#4112yes—
313C23×C72−1+412yes—
314C23×C72−1+412yes—
315C23×C7C2511yescharacteristic
316C22×D7—28no—
317C22×D7—28no—
318C22×D7—28no—
319C22×D7—28no—
320C22×D7—28no—
321C22×D7—28no—
322C22×D7—22no—
323C22×D7—22no—
324C22×D7—22no—
325C22×D7—22no—
326C22×D7#123116yes—
327C22×D7C22×D414yes—
328C22×D7C2×#4114yes—
329C22×D7C2×#4114yes—
330C2×C4×C7—28no—
331C2×C4×C7—28no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
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—44no—
352C2×C4×C7—44no—
353C2×C4×C7—44no—
354C2×C4×C7—44no—
355C2×C4×C7—44no—
356C2×C4×C7C22×D414yes—
357C2×C4×C7C2×#4114yes—
358C2×Dic7—28no—
359C2×Dic7—28no—
360C2×Dic7—22no—
361C2×Dic7—22no—
362C2×Dic7—22no—
363C2×Dic7—22no—
364C2×Dic7—22no—
365C2×Dic7—22no—
366C2×Dic7—22no—
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—44no—
380C2×Dic7—44no—
381C2×Dic7—44no—
382C2×Dic7—44no—
383C2×Dic7—44no—
384C2×Dic7C22×D414yes—
385C2×Dic7C2×#4114yes—
386C4×D7—232no—
387C4×D7—232no—
388C4×D7—416no—
389C25—71no—
390C23×C4—71no—
391C23×C4—71no—
392C23×C4—78no—
393C23×C4—74no—
394C23×C4—71no—
395C23×C4—71no—
396C23×C4—71no—
397C23×C4—71no—
398C23×C4—71no—
399C23×C4—74no—
400C23×C4—74no—
401C23×C4—144no—
402C23×C4—144no—
403C23×C4—144no—
404C23×C4—144no—
405C23×C4—144no—
406C23×C4—144no—
407C23×C4—144no—
408C23×C4—144no—
409C23×C4C22×D711yescharacteristic
410C23×C4C22×D711yescharacteristic
411C23×C4C22×D711yescharacteristic
412C23×C4C22×D711yescharacteristic
413C23×C4C22×D711yescharacteristic
414C23×C4C22×D711yescharacteristic
415C23×C4C22×D711yescharacteristic
416#117—1432no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—74no—
420C2×C4⋊C4—74no—
421C2×C4⋊C4—74no—
422C2×C4⋊C4—74no—
423C2×C4⋊C4—74no—
424C2×C4⋊C4—74no—
425C2×C4⋊C4—74no—
426C2×C4⋊C4—74no—
427C2×C4⋊C4—1432no—
428C2×C4⋊C4—144no—
429C2×C4⋊C4—144no—
430C2×C4⋊C4—144no—
431C2×C4⋊C4—144no—
432C2×C4⋊C4—144no—
433C2×C4⋊C4—144no—
434C2×C4⋊C4—144no—
435C2×C4⋊C4—144no—
436C2×C4⋊C4C22×D714yes—
437C2×C4⋊C4C22×D714yes—
438C2×C22⋊C4—74no—
439C2×C22⋊C4—74no—
440C2×C22⋊C4—74no—
441C2×C22⋊C4—74no—
442C2×C22⋊C4—144no—
443C2×C22⋊C4—144no—
444C2×C22⋊C4—144no—
445C2×C22⋊C4—144no—
446C2×C42—24no—
447C2×C42—74no—
448C2×C42—144no—
449C2×C42C22×D714yes—
450#95—74no—
451#95—74no—
452#95—74no—
453#95—74no—
454#95—74no—
455#95—74no—
456#95—74no—
457#95—74no—
458#95—74no—
459#95—74no—
460#95—74no—
461#95—74no—
462#95C22×D714yes—
463#95C22×D714yes—
464#95C22×D714yes—
465#95C22×D714yes—
466C22×C7C2×#12314yes—
467C22×C7#52514yes—
468C22×C7#53614yes—
469C22×C7#55214yes—
470C22×C7#55214yes—
471C22×C7#55214yes—
472C22×C7#55214yes—
473C22×C7C23×D411yescharacteristic
474C22×C7C22×#4111yescharacteristic
475C22×C7C22×#4111yescharacteristic
476C22×C7C22×#4111yescharacteristic
477C22×C7C22×#4111yescharacteristic
478C22×C7C2×2−1+411yescharacteristic
479C22×C7C2×2−1+411yescharacteristic
480C2×D7—24no—
481C2×D7—24no—
482C2×D7—24no—
483C2×D7—24no—
484C2×D7—24no—
485C2×D7—24no—
486C2×D7—232no—
487C2×D7C2×#12318yes—
488C4×C7—24no—
489C4×C7—24no—
490C4×C7—42no—
491C4×C7—42no—
492C4×C7—42no—
493C4×C7—42no—
494C4×C7—42no—
495Dic7—24no—
496Dic7—24no—
497Dic7—42no—
498Dic7—42no—
499Dic7—42no—
500Dic7—42no—
501Dic7—42no—
502C24—74no—
503C24—74no—
504C24—74no—
505C24—72no—
506C24—142no—
507C24—142no—
508C24—142no—
509C24—142no—
510C24C23×D711yescharacteristic
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—74no—
531C22×C4—74no—
532C22×C4—72no—
533C22×C4—72no—
534C22×C4—716no—
535C22×C4—72no—
536C22×C4—72no—
537C22×C4—72no—
538C22×C4—72no—
539C22×C4—72no—
540C22×C4—148no—
541C22×C4—148no—
542C22×C4—1432no—
543C22×C4—148no—
544C22×C4—148no—
545C22×C4—1432no—
546C22×C4—148no—
547C22×C4—148no—
548C22×C4—148no—
549C22×C4—142no—
550C22×C4—142no—
551C22×C4—142no—
552C22×C4—142no—
553C22×C4—148no—
554C22×C4—142no—
555C22×C4—142no—
556C22×C4—142no—
557C22×C4—142no—
558C22×C4—142no—
559C22×C4—142no—
560C22×C4—142no—
561C22×C4—142no—
562C22×C4—142no—
563C22×C4—142no—
564C22×C4—142no—
565C22×C4—142no—
566C22×C4—142no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—2816no—
570C22×C4#115714yes—
571C22×C4D4×D714yes—
572C22×C4C23×D712yes—
573C22×C4C23×D712yes—
574C22×C4C23×D712yes—
575C22×C4C23×D712yes—
576C22×C4C23×D712yes—
577C22×C4C23×D712yes—
578C22×C4C23×D712yes—
579C4⋊C4—28no—
580C4⋊C4—28no—
581C4⋊C4—148no—
582C4⋊C4—148no—
583C4⋊C4—148no—
584C4⋊C4—148no—
585C4⋊C4—148no—
586C4⋊C4—148no—
587C4⋊C4—148no—
588C4⋊C4—148no—
589C22⋊C4—148no—
590C22⋊C4—148no—
591C22⋊C4—148no—
592C22⋊C4—148no—
593C42—28no—
594C42—148no—
595C2×C7#248418yescomplemented
596C2×C7C22×#12311yescharacteristic
597C2×C7C2×#52511yescharacteristic
598C2×C7C2×#53611yescharacteristic
599C2×C7C2×#55211yescharacteristic
600C2×C7C2×#55211yescharacteristic
601C2×C7C2×#55211yescharacteristic
602C2×C7C2×#55211yescharacteristic
603D7—28no—
604C23—716no—
605C23—74no—
606C23—74no—
607C23—74no—
608C23—148no—
609C23—148no—
610C23—148no—
611C23—148no—
612C23—148no—
613C23—148no—
614C23—142no—
615C23—142no—
616C23—142no—
617C23—142no—
618C23C2×#115712yes—
619C23C2×D4×D712yes—
620C23#655112yes—
621C23D7×#4112yes—
622C23D7×#4112yes—
623C23D7×#4112yes—
624C23#655412yes—
625C23C24×D711yescharacteristic
626C2×C4—28no—
627C2×C4—28no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—44no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—74no—
653C2×C4—74no—
654C2×C4—1432no—
655C2×C4—1432no—
656C2×C4—148no—
657C2×C4—148no—
658C2×C4—142no—
659C2×C4—142no—
660C2×C4—142no—
661C2×C4—142no—
662C2×C4—142no—
663C2×C4—142no—
664C2×C4—142no—
665C2×C4—142no—
666C2×C4—142no—
667C2×C4—142no—
668C2×C4—142no—
669C2×C4—142no—
670C2×C4—142no—
671C2×C4—142no—
672C2×C4—142no—
673C2×C4—142no—
674C2×C4—142no—
675C2×C4—142no—
676C2×C4—142no—
677C2×C4—2816no—
678C2×C4—284no—
679C2×C4—284no—
680C2×C4—284no—
681C2×C4—284no—
682C2×C4—284no—
683C2×C4C2×#115714yes—
684C2×C4C2×D4×D714yes—
685C7C2×#248411yescharacteristic, complemented, Sylow
686C22—78no—
687C22—1432no—
688C22—144no—
689C22—144no—
690C22—144no—
691C22—144no—
692C22—144no—
693C22—144no—
694C22#9022014yes—
695C22#9023814yes—
696C22#9027214yes—
697C22#9031914yes—
698C22D7×#12314yes—
699C22#9038414yes—
700C22#9039914yes—
701C22C22×#115711yescharacteristic
702C22C22×D4×D711yescharacteristic
703C22C2×#655111yescharacteristic
704C22C2×D7×#4111yescharacteristic
705C22C2×D7×#4111yescharacteristic
706C22C2×D7×#4111yescharacteristic
707C22C2×#655411yescharacteristic
708C4—24no—
709C4—24no—
710C4—42no—
711C4—42no—
712C4—42no—
713C4—42no—
714C4—42no—
715C4—144no—
716C4—144no—
717C4—282no—
718C4—282no—
719C4—282no—
720C4—282no—
721C4—282no—
722C2—148no—
723C2#1173278018yesdirect product factor
724C2C2×#9022011yescharacteristic
725C2C2×#9023811yescharacteristic
726C2C2×#9027211yescharacteristic
727C2C2×#9031911yescharacteristic
728C2C2×D7×#12311yescharacteristic
729C2C2×#9038411yescharacteristic
730C2C2×#9039911yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#387C2
socleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#387D7
hypocenterC7C2×#2484
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. C2×C7×#387C2semidirect
5. C2×#89756C2semidirect
6. C2×#89750C2semidirect
7. C2×#89705C2semidirect
8. #11732780C2direct (N × H)
13. C2×#89432C2semidirect
14. C2×#89430C2semidirect
15. C2×#89429C2semidirect
16. C2×#89425C2semidirect
40. C7×#387C22semidirect
58. #89756C22semidirect
59. #89750C22semidirect
60. #89705C22semidirect
65. #89432C22semidirect
66. #89430C22semidirect
67. #89429C22semidirect
68. #89425C22semidirect
157. C2×#387D7semidirect
286. #387C2×D7semidirect
595. C2×C7#2484semidirect
685. C7C2×#2484semidirect
723. C2#11732780direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D7×C4⋊C42
C22×#64352
C2×C7×#3872
C2×#897612
C2×#897562
C2×#897502
C2×#897052
#117327802
C2×#894402
C2×#894362
C2×#894322
C2×#894302
C2×#894292
C2×#894252
C2×#24847