Finite Group Databasebeta

← C2×#11737965 #14233542

Subgroups — C2×#11737965 #14233542

Order 1792.

1950 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
1C2×#90372C211yesmaximal, characteristic, complemented
2C2×#90234C211yesmaximal, characteristic, complemented
3C2×C7×#463C211yesmaximal, characteristic, complemented
4C2×#89937C211yesmaximal, characteristic, complemented
5C2×#89936C211yesmaximal, characteristic, complemented
6C2×#89922C211yesmaximal, characteristic
7C2×D8×Dic7C211yesmaximal, characteristic, complemented
8C2×#89827C211yesmaximal, characteristic, complemented
9C2×#89786C211yesmaximal, characteristic, complemented
10#11737965C2116yesmaximal, direct product factor
11C2×#89618C211yesmaximal, characteristic, complemented
12C2×#89600C211yesmaximal, characteristic, complemented
13C2×#89572C211yesmaximal, characteristic, complemented
14C2×#89568C211yesmaximal, characteristic, complemented
15C2×#89536C211yesmaximal, characteristic, complemented
16C2×#89538C211yesmaximal, characteristic, complemented
17C22×C7×SD16C2211yescharacteristic
18C22×C7×D8C2211yescharacteristic
19C2×C7×#124C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C2×#6510C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C2×#6503C2211yescharacteristic
24C2×D4×Dic7C2211yescharacteristic
25C2×D4×Dic7C2211yescharacteristic
26C2×D4×Dic7C2211yescharacteristic
27C22×#1141C2211yescharacteristic
28C22×C4⋊Dic7—21no—
29C2×#6487—21no—
30#90372—24no—
31#90372C2218yescomplemented
32#90234—24no—
33#90234C2218yescomplemented
34C2×#6453C2211yescharacteristic
35C2×#6453C2211yescharacteristic
36C2×#6449—21no—
37C2×#6448—21no—
38C2×#6446—21no—
39C2×(C22⋊D7)⋊C4—21no—
40C2×#6441—21no—
41C2×#6441—21no—
42C2×C4×D28C2211yescharacteristic
43C2×#6432C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C7×#463C2218yescomplemented
46C2×C7×C4⋊C8C2211yescharacteristic
47C2×C7×#103C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×#6409C2211yescharacteristic
50C2×#6409C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×#6406C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54#89937C2218yescomplemented
55#89936C2218yescomplemented
56#89922C2218yes—
57D8×Dic7C2218yescomplemented
58C2×#6395C2211yescharacteristic
59C2×#6395C2211yescharacteristic
60C2×#6392C2211yescharacteristic
61C2×#6392C2211yescharacteristic
62C2×#6389C2211yescharacteristic
63C2×Dic7⋊C8C2211yescharacteristic
64C2×Dic7⋊C8C2211yescharacteristic
65C2×C8×Dic7C2211yescharacteristic
66#89827C2218yescomplemented
67#89786C2218yescomplemented
68C2×#6383C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6377C2211yescharacteristic
71#89618C2218yescomplemented
72#89600C2218yescomplemented
73#89572C2218yescomplemented
74#89568C2218yescomplemented
75#89538C2218yescomplemented
76#89536C2218yescomplemented
77C2×#3370—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4C2311yescharacteristic
80C22×C7×D4C2311yescharacteristic
81C23×C4×C7—21no—
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C23×Dic7—21no—
85C23×Dic7—21no—
86C23×Dic7—21no—
87C22×D28C2311yescharacteristic
88C22×C4×D7—21no—
89C22×Dic14—21no—
90C22×Dic14D411yescharacteristic
91C2×C7×SD16—24no—
92C2×C7×SD16C2314yes—
93C2×C7×D8—24no—
94C2×C7×D8C2314yes—
95C22×C7×C8C2311yescharacteristic
96C22×C7×C8C2311yescharacteristic
97C7×#124—22no—
98C7×#124C2314yes—
99C4×C7×D4—22no—
100C4×C7×D4C2314yes—
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C22⋊C4—21no—
103C2×C7×C22⋊C4—21no—
104C2×C7×C22⋊C4—21no—
105C2×C42×C7C2311yescharacteristic
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7—21no—
109#6510—22no—
110#6510C2314yes—
111Q8×Dic7—22no—
112Q8×Dic7C2314yes—
113#6503—22no—
114#6503C2314yes—
115D4×Dic7—22no—
116D4×Dic7—22no—
117D4×Dic7—22no—
118D4×Dic7C2314yes—
119D4×Dic7C2314yes—
120D4×Dic7C2314yes—
121C2×#1141—24no—
122C2×#1141C2314yes—
123C2×(C2×D7)⋊C4—21no—
124C2×(C2×D7)⋊C4—21no—
125C2×(C2×D7)⋊C4—21no—
126C2×C4⋊Dic7—21no—
127C2×C4⋊Dic7—21no—
128C2×C4⋊Dic7—21no—
129C2×C4⋊Dic7—21no—
130C2×C4⋊Dic7—28no—
131C2×C4⋊Dic7D411yescharacteristic
132C2×C4⋊Dic7C2311yescharacteristic
133C2×C4⋊Dic7C2311yescharacteristic
134C2×C4⋊Dic7C2311yescharacteristic
135#6487—28no—
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4—21no—
138C2×Dic7⋊C4D411yescharacteristic
139C2×Dic7⋊C4D411yescharacteristic
140C2×C4×Dic7—21no—
141C2×C4×Dic7C2311yescharacteristic
142C2×C4×Dic7C2311yescharacteristic
143C22×C7⋊C8C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145#6453—22no—
146#6453—22no—
147#6453C2314yes—
148#6453C2314yes—
149#6449—28no—
150#6448—28no—
151#6446—28no—
152(C22⋊D7)⋊C4—28no—
153#6441—28no—
154#6441—28no—
155C4×D28—22no—
156C4×D28C2314yes—
157#6432—22no—
158#6432C2314yes—
159C4×Dic14D414yes—
160C4×Dic14C2314yes—
161C7×C4⋊C8C2314yes—
162C7×#103C2314yes—
163C7×#102C2314yes—
164#6409C2314yes—
165#6409C2314yes—
166#6406C2314yes—
167#6406C2314yes—
168#6406C2314yes—
169#6395C2314yes—
170#6395C2314yes—
171#6392C2314yes—
172#6392C2314yes—
173#6389C2314yes—
174Dic7⋊C8C2314yes—
175Dic7⋊C8C2314yes—
176C8×Dic7C2314yes—
177#6383C2314yes—
178#6382C2314yes—
179#6377C2314yes—
180C2×#559—71no—
181C2×#554—71no—
182#3370—716no—
183C2×#490—71no—
184C2×#489—71no—
185C2×#488—71no—
186C2×#479—71no—
187C2×#478—71no—
188C2×#474—71no—
189C2×#463—71no—
190C2×#463D711yescharacteristic, complemented
191C2×#459—71no—
192C2×#446—71no—
193C2×#442—71no—
194C2×#440—71no—
195C2×C4×D8—71no—
196C24×C7—21no—
197C24×C7—21no—
198C23×D7—21no—
199C2×C7×Q8—21no—
200C2×C7×Q8—22no—
201C2×C7×Q8—22no—
202C2×C7×Q8C2412yes—
203C2×C7×D4—21no—
204C2×C7×D4—21no—
205C2×C7×D4—22no—
206C2×C7×D4—22no—
207C2×C7×D4—22no—
208C2×C7×D4#4114yes—
209C2×C7×D4C2412yes—
210C2×C7×D4C2412yes—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—24no—
214C22×C4×C7—44no—
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2411yescharacteristic
218C2×C22⋊D7—24no—
219C2×C22⋊D7—24no—
220C2×C22⋊D7—44no—
221C2×C22⋊D7—82no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—24no—
226C22×Dic7—24no—
227C22×Dic7—24no—
228C22×Dic7—82no—
229C22×Dic7—82no—
230C22×Dic7—82no—
231C22×Dic7C2×D411yescharacteristic
232C22×Dic7C2×D411yescharacteristic
233C22×Dic7C2×D411yescharacteristic
234C22×Dic7C2×D411yescharacteristic
235C2×D28—22no—
236C2×D28—22no—
237C2×D28—21no—
238C2×D28C2412yes—
239C2×C4×D7—24no—
240C2×C4×D7—82no—
241C2×Dic14—24no—
242C2×Dic14—42no—
243C2×Dic14—82no—
244C2×Dic14C2×D414yes—
245C7×SD16—28no—
246C7×D8—28no—
247C2×C7×C8—22no—
248C2×C7×C8—22no—
249C2×C7×C8C2412yes—
250C2×C7×C8C2412yes—
251C7×C4⋊C4—21no—
252C7×C4⋊C4C2412yes—
253C7×C22⋊C4—24no—
254C7×C22⋊C4—24no—
255C7×C22⋊C4—24no—
256C42×C7C2×D412yes—
257C42×C7C2412yes—
258C22⋊Dic7—24no—
259C22⋊Dic7—24no—
260C22⋊Dic7—24no—
261#1141—28no—
262(C2×D7)⋊C4—24no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265C4⋊Dic7—21no—
266C4⋊Dic7—21no—
267C4⋊Dic7—24no—
268C4⋊Dic7—21no—
269C4⋊Dic7—24no—
270C4⋊Dic7—24no—
271C4⋊Dic7—24no—
272C4⋊Dic7C2×D414yes—
273C4⋊Dic7C2412yes—
274C4⋊Dic7C2412yes—
275C4⋊Dic7C2412yes—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4C2×D414yes—
279Dic7⋊C4C2×D414yes—
280C4×Dic7—24no—
281C4×Dic7C2×D412yes—
282C4×Dic7C2×D412yes—
283C4×Dic7C2412yes—
284C4×Dic7C2412yes—
285C2×C7⋊C8—22no—
286C2×C7⋊C8—22no—
287C2×C7⋊C8C2412yes—
288C2×C7⋊C8C2412yes—
289C22×SD16C2×D711yescharacteristic
290C22×D8—71no—
291C22×D8C2×D711yescharacteristic
292#559—78no—
293#559—144no—
294#554—78no—
295#554—144no—
296C2×C4⋊Q8—71no—
297C2×#127—71no—
298C2×#125—71no—
299C2×#125—71no—
300C2×#124—71no—
301C2×#124—141no—
302C2×#124C2×D711yescharacteristic
303C2×#123—141no—
304C2×#123—141no—
305C2×C22⋊Q8—141no—
306C2×C22⋊Q8—141no—
307C2×C22⋊Q8—141no—
308C2×C4×Q8—71no—
309C2×C4×Q8—71no—
310C2×C4×D4—71no—
311C2×C4×D4—71no—
312C2×C4×D4—71no—
313C2×C4×D4—71no—
314C2×C4×D4—141no—
315C2×C4×D4C2×D711yescharacteristic
316C22×C4⋊C4—141no—
317#490—78no—
318#489—78no—
319#488—78no—
320#479—78no—
321#478—78no—
322#474—78no—
323#463—78no—
324#463C2×D718yescomplemented
325#459—78no—
326#446—78no—
327#442—78no—
328#440—78no—
329C4×D8—78no—
330C2×#107—71no—
331C2×#107—71no—
332C2×#106—71no—
333C2×C4⋊C8—71no—
334C2×C4⋊C8—71no—
335C2×C4⋊C8C2×D711yescharacteristic
336C2×#103—71no—
337C2×#103—71no—
338C2×#103C2×D711yescharacteristic
339C2×#102—71no—
340C2×#102—71no—
341C2×#102—71no—
342C2×#102—71no—
343C2×#102—71no—
344C2×#102—71no—
345C2×#102C2×D711yescharacteristic
346C2×#97—71no—
347C2×#97—71no—
348C2×C4×C8—71no—
349C23×C7—24no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—42no—
353C23×C7—42no—
354C23×C7—42no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7C22×D411yescharacteristic
358C22×D7—22no—
359C22×D7—42no—
360C22×D7—42no—
361C22×D7—42no—
362C7×Q8—22no—
363C7×Q8—22no—
364C7×Q8—42no—
365C7×D4—24no—
366C7×D4—22no—
367C7×D4—22no—
368C7×D4—22no—
369C7×D4—42no—
370C7×D4C2×#4114yes—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—48no—
376C2×C4×C7—42no—
377C2×C4×C7—42no—
378C2×C4×C7C22×D412yes—
379C2×C4×C7C22×D412yes—
380C2×C4×C7C22×D411yescharacteristic
381C2×C4×C7C2×#4112yes—
382C2×C4×C72−1+412yes—
383C2×C4×C7C2511yescharacteristic
384C22⋊D7—48no—
385C22⋊D7—84no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7—42no—
396C2×Dic7—84no—
397C2×Dic7—84no—
398C2×Dic7—84no—
399C2×Dic7C22×D412yes—
400C2×Dic7C22×D412yes—
401C2×Dic7C22×D412yes—
402C2×Dic7C22×D412yes—
403D28—22no—
404D28—22no—
405D28—42no—
406C4×D7—84no—
407Dic14—44no—
408Dic14—84no—
409C7×C8—22no—
410C7×C8—22no—
411C7⋊C8—22no—
412C7⋊C8—22no—
413C22×Q8—71no—
414C22×Q8—141no—
415C22×Q8C22×D711yescharacteristic
416C22×D4—71no—
417C22×D4—141no—
418C22×D4—141no—
419C22×D4C22×D711yescharacteristic
420C22×D4C22×D711yescharacteristic
421C23×C4—21no—
422C23×C4—141no—
423C23×C4—141no—
424C23×C4—141no—
425C23×C4—141no—
426C2×SD16—24no—
427C2×SD16C22×D714yes—
428C2×D8—24no—
429C2×D8—74no—
430C2×D8—144no—
431C2×D8C22×D714yes—
432C22×C8—71no—
433C22×C8—71no—
434C22×C8C22×D711yescharacteristic
435C22×C8C22×D711yescharacteristic
436C4⋊Q8—74no—
437C4⋊Q8—142no—
438#127—74no—
439#127—142no—
440#125—74no—
441#125—74no—
442#125—142no—
443#125—142no—
444#124—22no—
445#124—74no—
446#124—142no—
447#124—148no—
448#124C22×D714yes—
449#123—148no—
450#123—148no—
451C22⋊Q8—148no—
452C22⋊Q8—148no—
453C22⋊Q8—148no—
454C4×Q8—74no—
455C4×Q8—74no—
456C4×Q8—74no—
457C4×Q8—142no—
458C4×D4—22no—
459C4×D4—74no—
460C4×D4—74no—
461C4×D4—74no—
462C4×D4—74no—
463C4×D4—142no—
464C4×D4—142no—
465C4×D4—142no—
466C4×D4—148no—
467C4×D4—142no—
468C4×D4C22×D714yes—
469C2×C4⋊C4—71no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—71no—
472C2×C4⋊C4—71no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—71no—
475C2×C4⋊C4—148no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4—141no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—141no—
482C2×C4⋊C4C22×D711yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—141no—
487C2×C22⋊C4—141no—
488C2×C22⋊C4—141no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C42—71no—
493C2×C42—71no—
494C2×C42—141no—
495C2×C42C22×D711yescharacteristic
496#107—74no—
497#107—74no—
498#106—74no—
499C4⋊C8—74no—
500C4⋊C8—74no—
501C4⋊C8C22×D714yes—
502#103—74no—
503#103—74no—
504#103C22×D714yes—
505#102—74no—
506#102—74no—
507#102—74no—
508#102—74no—
509#102—74no—
510#102—74no—
511#102C22×D714yes—
512#97—74no—
513#97—74no—
514C4×C8—74no—
515C22×C7—24no—
516C22×C7—48no—
517C22×C7—42no—
518C22×C7—42no—
519C22×C7—42no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—84no—
523C22×C7#54812yes—
524C22×C7#57512yes—
525C22×C7#57612yes—
526C22×C7C23×D411yescharacteristic
527C2×D7—42no—
528C2×D7—42no—
529C2×D7—42no—
530C2×D7—84no—
531C4×C7—22no—
532C4×C7—22no—
533C4×C7—42no—
534C4×C7—42no—
535C4×C7#54812yes—
536C4×C7C22×#4111yescharacteristic
537C4×C7C2×2−1+411yescharacteristic
538Dic7—22no—
539Dic7—22no—
540Dic7—22no—
541Dic7—22no—
542Dic7—42no—
543Dic7—42no—
544Dic7—42no—
545C24—21no—
546C24—21no—
547C24—141no—
548C2×Q8—21no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—74no—
552C2×Q8—144no—
553C2×Q8—282no—
554C2×Q8—562no—
555C2×Q8C23×D712yes—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—72no—
562C2×D4—144no—
563C2×D4—144no—
564C2×D4—141no—
565C2×D4—142no—
566C2×D4—142no—
567C2×D4—284no—
568C2×D4—562no—
569C2×D4#115914yes—
570C2×D4C23×D712yes—
571C2×D4C23×D712yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—24no—
575C22×C4—44no—
576C22×C4—71no—
577C22×C4—71no—
578C22×C4—71no—
579C22×C4—71no—
580C22×C4—144no—
581C22×C4—144no—
582C22×C4—144no—
583C22×C4—141no—
584C22×C4—141no—
585C22×C4—141no—
586C22×C4—144no—
587C22×C4—562no—
588C22×C4—562no—
589C22×C4—562no—
590C22×C4—562no—
591C22×C4D4×D711yescharacteristic
592C22×C4D4×D711yescharacteristic
593C22×C4C23×D711yescharacteristic
594SD16—28no—
595D8—28no—
596D8—148no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—72no—
600C2×C8—72no—
601C2×C8—142no—
602C2×C8—142no—
603C2×C8C23×D712yes—
604C2×C8C23×D712yes—
605C4⋊C4—21no—
606C4⋊C4—74no—
607C4⋊C4—74no—
608C4⋊C4—74no—
609C4⋊C4—72no—
610C4⋊C4—72no—
611C4⋊C4—72no—
612C4⋊C4—144no—
613C4⋊C4—144no—
614C4⋊C4—144no—
615C4⋊C4—144no—
616C4⋊C4—144no—
617C4⋊C4—141no—
618C4⋊C4—141no—
619C4⋊C4—141no—
620C4⋊C4—144no—
621C4⋊C4C23×D712yes—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—144no—
626C22⋊C4—144no—
627C22⋊C4—144no—
628C22⋊C4—144no—
629C22⋊C4—144no—
630C22⋊C4—144no—
631C42—72no—
632C42—72no—
633C42—72no—
634C42—72no—
635C42—144no—
636C42D4×D712yes—
637C42C23×D712yes—
638C2×C7—44no—
639C2×C7—82no—
640C2×C7#337014yescomplemented
641C2×C7C2×#54811yescharacteristic
642C2×C7C2×#57511yescharacteristic
643C2×C7C2×#57611yescharacteristic
644D7—82no—
645C23—24no—
646C23—22no—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—142no—
654C23—282no—
655C23—282no—
656C23—282no—
657C23C2×D4×D711yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—284no—
662Q8—564no—
663D4—24no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—42no—
668D4—142no—
669D4—142no—
670D4—288no—
671D4—282no—
672D4—564no—
673D4C2×#115914yes—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—48no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—72no—
682C2×C4—72no—
683C2×C4—72no—
684C2×C4—72no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—282no—
693C2×C4—282no—
694C2×C4—282no—
695C2×C4—564no—
696C2×C4—564no—
697C2×C4—564no—
698C2×C4—564no—
699C2×C4C2×D4×D712yes—
700C2×C4C2×D4×D712yes—
701C2×C4C2×D4×D711yescharacteristic
702C2×C4C2×#115912yes—
703C2×C4#655412yes—
704C2×C4C24×D711yescharacteristic
705C8—22no—
706C8—22no—
707C8—142no—
708C8—142no—
709C7C2×#337011yescharacteristic, complemented, Sylow
710C22—24no—
711C22—42no—
712C22—48no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22—282no—
719C22—282no—
720C22—282no—
721C22—564no—
722C22#9028912yes—
723C22#9046012yes—
724C22#9046412yes—
725C22C22×D4×D711yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—142no—
731C4—142no—
732C4—142no—
733C4—142no—
734C4—282no—
735C4—282no—
736C4—282no—
737C4#9028912yes—
738C4C22×#115911yescharacteristic
739C4C2×#655411yescharacteristic
740C2—44no—
741C2—82no—
742C2—562no—
743C2#1173796514yesdirect product factor
744C2C2×#9028911yescharacteristic
745C2C2×#9046011yescharacteristic
746C2C2×#9046411yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#463C2
socleC23×C7C22×D4
prime radicalC2×#89922C2
hypercenterC2×#463D7
hypocenterC7C2×#3370
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#90372C2semidirect
2. C2×#90234C2semidirect
3. C2×C7×#463C2semidirect
4. C2×#89937C2semidirect
5. C2×#89936C2semidirect
7. C2×D8×Dic7C2semidirect
8. C2×#89827C2semidirect
9. C2×#89786C2semidirect
10. #11737965C2direct (N × H)
11. C2×#89618C2semidirect
12. C2×#89600C2semidirect
13. C2×#89572C2semidirect
14. C2×#89568C2semidirect
15. C2×#89536C2semidirect
16. C2×#89538C2semidirect
31. #90372C22semidirect
33. #90234C22semidirect
45. C7×#463C22semidirect
54. #89937C22semidirect
55. #89936C22semidirect
57. D8×Dic7C22semidirect
66. #89827C22semidirect
67. #89786C22semidirect
71. #89618C22semidirect
72. #89600C22semidirect
73. #89572C22semidirect
74. #89568C22semidirect
75. #89538C22semidirect
76. #89536C22semidirect
190. C2×#463D7semidirect
324. #463C2×D7semidirect
640. C2×C7#3370semidirect
709. C7C2×#3370semidirect
743. C2#11737965direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903722
C2×#902342
C2×C7×#4632
C2×#899372
C2×#899362
C2×#899222
C2×D8×Dic72
C2×#898272
C2×#897862
#117379652
C2×#896182
C2×#896002
C2×#895722
C2×#895682
C2×#895362
C2×#895382
C2×#33707