Finite Group Databasebeta

← C2×#11737887 #14226718

Subgroups — C2×#11737887 #14226718

Order 1792.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90422C211yesmaximal, characteristic, complemented
2C2×#90252C211yesmaximal, characteristic
3C2×C7×#461C211yesmaximal, characteristic, complemented
4C2×#89946C211yesmaximal, characteristic
5C2×#89943C211yesmaximal, characteristic
6C2×#89938C211yesmaximal, characteristic, complemented
7C2×#89938C211yesmaximal, characteristic, complemented
8C2×#89862C211yesmaximal, characteristic, complemented
9C2×#89781C211yesmaximal, characteristic, complemented
10#11737887C2116yesmaximal, direct product factor
11C2×#89601C211yesmaximal, characteristic, complemented
12C2×#89611C211yesmaximal, characteristic, complemented
13C2×#89588C211yesmaximal, characteristic, complemented
14C2×#89585C211yesmaximal, characteristic, complemented
15C2×#89566C211yesmaximal, characteristic, complemented
16C2×#89563C211yesmaximal, characteristic, complemented
17C22×C7×SD16C2211yescharacteristic
18C22×C7×SD16C2211yescharacteristic
19C2×C7×C4⋊Q8C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C2×#6509C2211yescharacteristic
22C2×#6509C2211yescharacteristic
23C2×Q8×Dic7C2211yescharacteristic
24C2×Q8×Dic7C2211yescharacteristic
25C22×#1144C2211yescharacteristic
26C22×#1144C2211yescharacteristic
27C2×#6501C2211yescharacteristic
28C2×#6499C2211yescharacteristic
29C2×#6492—21no—
30C2×#6487—21no—
31C22×#1131C2211yescharacteristic
32C22×C8×D7C2211yescharacteristic
33#90422—24no—
34#90422C2218yescomplemented
35#90252—24no—
36#90252C2218yes—
37C2×#6461—21no—
38C2×#6461—21no—
39C2×#6460C2211yescharacteristic
40C2×#6452—21no—
41C2×#6452—21no—
42C2×#6451C2211yescharacteristic
43C2×#6448—21no—
44C2×#6442—21no—
45C2×#6435C2211yescharacteristic
46C2×#6433C2211yescharacteristic
47C2×C4×Dic14C2211yescharacteristic
48C7×#461C2218yescomplemented
49C2×C7×C4⋊C8C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×C7×#103C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6406C2211yescharacteristic
55C2×#6406C2211yescharacteristic
56#89946C2218yes—
57#89943C2218yes—
58#89938C2218yescomplemented
59#89938C2218yescomplemented
60C2×#6392C2211yescharacteristic
61C2×#6391C2211yescharacteristic
62C2×#6390C2211yescharacteristic
63C2×#6390C2211yescharacteristic
64C2×Dic7⋊C8C2211yescharacteristic
65C2×Dic7⋊C8C2211yescharacteristic
66#89862C2218yescomplemented
67#89781C2218yescomplemented
68C2×#6382C2211yescharacteristic
69C2×#6381C2211yescharacteristic
70C2×C4⋊(C7⋊C8)C2211yescharacteristic
71#89611C2218yescomplemented
72#89601C2218yescomplemented
73#89588C2218yescomplemented
74#89585C2218yescomplemented
75#89566C2218yescomplemented
76#89563C2218yescomplemented
77C2×#3258—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C22×C7×D4C2311yescharacteristic
81C23×C4×C7—21no—
82C22×C22⋊D7—21no—
83C22×C4×D7C2311yescharacteristic
84C22×Dic14—21no—
85C22×Dic14C2311yescharacteristic
86C2×C7×SD16—42no—
87C2×C7×SD16—42no—
88C2×C7×SD16C2314yes—
89C2×C7×SD16C2314yes—
90C22×C7×C8C2311yescharacteristic
91C22×C7×C8C2311yescharacteristic
92C7×C4⋊Q8—22no—
93C7×C4⋊Q8C2314yes—
94C4×C7×D4—22no—
95C4×C7×D4C2314yes—
96C2×C7×C4⋊C4—21no—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C22⋊C4—21no—
100C2×C42×C7C2311yescharacteristic
101C2×C22⋊Dic7—21no—
102C2×C22⋊Dic7—21no—
103C2×C22⋊Dic7—21no—
104#6509—22no—
105#6509—22no—
106#6509C2314yes—
107#6509C2314yes—
108Q8×Dic7—22no—
109Q8×Dic7—22no—
110Q8×Dic7C2314yes—
111Q8×Dic7C2314yes—
112C2×#1144—42no—
113C2×#1144—42no—
114C2×#1144C2314yes—
115C2×#1144C2314yes—
116#6501—22no—
117#6501C2314yes—
118#6499—22no—
119#6499C2314yes—
120#6492—28no—
121C2×(C2×D7)⋊C4—21no—
122C2×(C2×D7)⋊C4—21no—
123C2×(C2×D7)⋊C4—21no—
124C2×(C2×D7)⋊C4D411yescharacteristic
125C2×(C2×D7)⋊C4D411yescharacteristic
126C2×C4⋊Dic7—21no—
127C2×C4⋊Dic7—21no—
128C2×C4⋊Dic7—21no—
129C2×C4⋊Dic7C2311yescharacteristic
130C2×C4⋊Dic7C2311yescharacteristic
131C2×C4⋊Dic7C2311yescharacteristic
132#6487—28no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4—21no—
138C2×Dic7⋊C4—21no—
139C2×Dic7⋊C4D411yescharacteristic
140C2×Dic7⋊C4D411yescharacteristic
141C2×C4×Dic7—21no—
142C2×C4×Dic7—21no—
143C2×C4×Dic7—21no—
144C2×C4×Dic7C2311yescharacteristic
145C22×C7⋊C8C2311yescharacteristic
146C22×C7⋊C8C2311yescharacteristic
147C2×#1131—42no—
148C2×#1131C2314yes—
149C2×C8×D7—42no—
150C2×C8×D7C2314yes—
151#6461—28no—
152#6461—28no—
153#6460—22no—
154#6460C2314yes—
155#6452—28no—
156#6452—28no—
157#6451—22no—
158#6451C2314yes—
159#6448—28no—
160#6442—28no—
161#6435D414yes—
162#6435C2314yes—
163#6433—22no—
164#6433C2314yes—
165C4×Dic14—22no—
166C4×Dic14C2314yes—
167C7×C4⋊C8C2314yes—
168C7×#103C2314yes—
169C7×#103C2314yes—
170#6409C2314yes—
171#6409C2314yes—
172#6406C2314yes—
173#6406C2314yes—
174#6392C2314yes—
175#6391C2314yes—
176#6390C2314yes—
177#6390C2314yes—
178Dic7⋊C8C2314yes—
179Dic7⋊C8C2314yes—
180#6382C2314yes—
181#6381C2314yes—
182C4⋊(C7⋊C8)C2314yes—
183C2×#542—71no—
184C2×#541—71no—
185#3258—716no—
186C2×#479—71no—
187C2×#477—71no—
188C2×#475—71no—
189C2×#478—71no—
190C2×#470—71no—
191C2×#468—71no—
192C2×#467—71no—
193C2×#465—71no—
194C2×#464—71no—
195C2×#464—71no—
196C2×#462—71no—
197C2×#461D711yescharacteristic, complemented
198C2×#424—71no—
199C24×C7—21no—
200C23×D7C2×D411yescharacteristic
201C2×C7×Q8—21no—
202C2×C7×Q8—21no—
203C2×C7×Q8—22no—
204C2×C7×Q8—22no—
205C2×C7×Q8—22no—
206C2×C7×Q8—22no—
207C2×C7×Q8C2412yes—
208C2×C7×Q8C2412yes—
209C2×C7×D4—21no—
210C2×C7×D4—22no—
211C2×C7×D4—22no—
212C2×C7×D4C2412yes—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—24no—
217C22×C4×C7—82no—
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7C2411yescharacteristic
221C2×C22⋊D7—24no—
222C2×C22⋊D7—82no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7C2×D411yescharacteristic
228C22×Dic7C2×D411yescharacteristic
229C22×Dic7C2×D411yescharacteristic
230C2×C4×D7—22no—
231C2×C4×D7—22no—
232C2×C4×D7C2×D412yes—
233C2×C4×D7C2412yes—
234C2×Dic14—22no—
235C2×Dic14—22no—
236C2×Dic14—21no—
237C2×Dic14—24no—
238C2×Dic14—82no—
239C2×Dic14C2412yes—
240C7×SD16—44no—
241C7×SD16—44no—
242C2×C7×C8—22no—
243C2×C7×C8—22no—
244C2×C7×C8C2412yes—
245C2×C7×C8C2412yes—
246C7×C4⋊C4—21no—
247C7×C4⋊C4—24no—
248C7×C4⋊C4—24no—
249C7×C4⋊C4C2412yes—
250C7×C22⋊C4—24no—
251C42×C7C2×D412yes—
252C42×C7C2412yes—
253C22⋊Dic7—24no—
254C22⋊Dic7—24no—
255C22⋊Dic7—24no—
256#1144—44no—
257#1144—44no—
258(C2×D7)⋊C4—24no—
259(C2×D7)⋊C4—24no—
260(C2×D7)⋊C4—24no—
261(C2×D7)⋊C4C2×D414yes—
262(C2×D7)⋊C4C2×D414yes—
263C4⋊Dic7—21no—
264C4⋊Dic7—21no—
265C4⋊Dic7—21no—
266C4⋊Dic7—24no—
267C4⋊Dic7—24no—
268C4⋊Dic7—24no—
269C4⋊Dic7C2412yes—
270C4⋊Dic7C2412yes—
271C4⋊Dic7C2412yes—
272Dic7⋊C4—24no—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4C2×D414yes—
279Dic7⋊C4C2×D414yes—
280C4×Dic7—24no—
281C4×Dic7—24no—
282C4×Dic7—24no—
283C4×Dic7C2×D412yes—
284C4×Dic7C2412yes—
285C2×C7⋊C8—22no—
286C2×C7⋊C8—22no—
287C2×C7⋊C8C2412yes—
288C2×C7⋊C8C2412yes—
289#1131—44no—
290C8×D7—44no—
291C22×Q16—71no—
292C22×Q16—71no—
293C22×SD16C2×D711yescharacteristic
294C22×SD16C2×D711yescharacteristic
295C22×M16—71no—
296C23×C8—71no—
297#542—78no—
298#542—144no—
299#541—78no—
300#541—144no—
301C2×C4⋊Q8—71no—
302C2×C4⋊Q8C2×D711yescharacteristic
303C2×#126—141no—
304C2×#126—141no—
305C2×#126—141no—
306C2×#125—71no—
307C2×#125—141no—
308C2×#125—141no—
309C2×#124—71no—
310C2×#124—141no—
311C2×#123—141no—
312C2×C22⋊Q8—71no—
313C2×C22⋊Q8—71no—
314C2×C22⋊Q8—71no—
315C2×C22⋊Q8—141no—
316C2×#121—71no—
317C2×C4×Q8—71no—
318C2×C4×Q8—71no—
319C2×C4×Q8—71no—
320C2×C4×D4C2×D711yescharacteristic
321C2×#117—71no—
322#479—78no—
323#478—78no—
324#477—78no—
325#475—78no—
326#470—78no—
327#468—78no—
328#467—78no—
329#465—78no—
330#464—78no—
331#464—78no—
332#462—78no—
333#461C2×D718yescomplemented
334C2×#107—71no—
335C2×#107—71no—
336C2×#106—71no—
337C2×#106—71no—
338#424—78no—
339C2×C4⋊C8—71no—
340C2×C4⋊C8—71no—
341C2×C4⋊C8—71no—
342C2×C4⋊C8C2×D711yescharacteristic
343C2×#103—71no—
344C2×#103—71no—
345C2×#103—71no—
346C2×#103—71no—
347C2×#103C2×D711yescharacteristic
348C2×#103C2×D711yescharacteristic
349C2×#102—71no—
350C2×#102—71no—
351C23×C7—22no—
352C23×C7—42no—
353C23×C7—42no—
354C23×C7—42no—
355C23×C7C22×D411yescharacteristic
356C22×D7—22no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7C22×D412yes—
360C7×Q8—22no—
361C7×Q8—22no—
362C7×Q8—22no—
363C7×Q8—22no—
364C7×Q8—42no—
365C7×Q8—42no—
366C7×D4—22no—
367C7×D4—22no—
368C7×D4—42no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—42no—
375C2×C4×C7—42no—
376C2×C4×C7—42no—
377C2×C4×C7—84no—
378C2×C4×C7C22×D412yes—
379C2×C4×C7C22×D412yes—
380C2×C4×C7C22×D411yescharacteristic
381C2×C4×C7H(5,𝔽2)12yes—
382C2×C4×C72−1+412yes—
383C2×C4×C7C2511yescharacteristic
384C22⋊D7—84no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7—42no—
396C2×Dic7C22×D412yes—
397C2×Dic7C22×D412yes—
398C2×Dic7C22×D412yes—
399C4×D7—24no—
400C4×D7—22no—
401C4×D7—22no—
402Dic14—22no—
403Dic14—22no—
404Dic14—42no—
405Dic14—84no—
406C7×C8—22no—
407C7×C8—22no—
408C7⋊C8—22no—
409C7⋊C8—22no—
410C22×Q8—71no—
411C22×Q8—141no—
412C22×Q8C22×D711yescharacteristic
413C22×Q8C22×D711yescharacteristic
414C22×D4—141no—
415C22×D4C22×D711yescharacteristic
416C23×C4—21no—
417C23×C4—71no—
418C2×Q16—74no—
419C2×Q16—74no—
420C2×Q16—282no—
421C2×Q16—282no—
422C2×SD16—42no—
423C2×SD16—42no—
424C2×SD16C22×D714yes—
425C2×SD16C22×D714yes—
426C2×M16—74no—
427C2×M16—282no—
428C22×C8—71no—
429C22×C8—71no—
430C22×C8—74no—
431C22×C8—282no—
432C22×C8C22×D711yescharacteristic
433C22×C8C22×D711yescharacteristic
434C4⋊Q8—22no—
435C4⋊Q8—74no—
436C4⋊Q8—142no—
437C4⋊Q8C22×D714yes—
438#126—148no—
439#126—148no—
440#126—148no—
441#125—74no—
442#125—148no—
443#125—148no—
444#125—142no—
445#124—74no—
446#124—142no—
447#124—148no—
448#123—148no—
449C22⋊Q8—74no—
450C22⋊Q8—74no—
451C22⋊Q8—74no—
452C22⋊Q8—142no—
453C22⋊Q8—148no—
454C22⋊Q8—142no—
455C22⋊Q8—142no—
456#121—74no—
457#121—142no—
458C4×Q8—74no—
459C4×Q8—74no—
460C4×Q8—74no—
461C4×Q8—142no—
462C4×Q8—142no—
463C4×Q8—142no—
464C4×D4—22no—
465C4×D4C22×D714yes—
466#117—74no—
467#117—74no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—71no—
472C2×C4⋊C4—71no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—71no—
475C2×C4⋊C4—141no—
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⋊C4—141no—
483C2×C4⋊C4—141no—
484C2×C4⋊C4C22×D711yescharacteristic
485C2×C22⋊C4—21no—
486C2×C22⋊C4—71no—
487C2×C22⋊C4—71no—
488C2×C22⋊C4—141no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4—141no—
493C2×C22⋊C4—141no—
494C2×C42—71no—
495C2×C42—141no—
496C2×C42—141no—
497C2×C42—141no—
498C2×C42C22×D711yescharacteristic
499#107—74no—
500#107—74no—
501#106—74no—
502#106—74no—
503C4⋊C8—74no—
504C4⋊C8—74no—
505C4⋊C8—74no—
506C4⋊C8C22×D714yes—
507#103—74no—
508#103—74no—
509#103—74no—
510#103—74no—
511#103C22×D714yes—
512#103C22×D714yes—
513#102—74no—
514#102—74no—
515C22×C7—42no—
516C22×C7—42no—
517C22×C7—42no—
518C22×C7—84no—
519C22×C7#53712yes—
520C22×C7#57712yes—
521C22×C7#57812yes—
522C22×C7C23×D411yescharacteristic
523C2×D7—22no—
524C2×D7—22no—
525C2×D7—22no—
526C2×D7—44no—
527C4×C7—22no—
528C4×C7—22no—
529C4×C7—42no—
530C4×C7—42no—
531C4×C7—42no—
532C4×C7#53712yes—
533C4×C7C2×H(5,𝔽2)11yescharacteristic
534C4×C7C2×2−1+411yescharacteristic
535Dic7—22no—
536Dic7—22no—
537Dic7—22no—
538Dic7—42no—
539Dic7—42no—
540Dic7—42no—
541Dic7—42no—
542C24—21no—
543C24—71no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—72no—
551C2×Q8—144no—
552C2×Q8—141no—
553C2×Q8—142no—
554C2×Q8—142no—
555C2×Q8—562no—
556C2×Q8C23×D712yes—
557C2×Q8C23×D712yes—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—144no—
562C2×D4—562no—
563C2×D4C23×D712yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—71no—
569C22×C4—71no—
570C22×C4—71no—
571C22×C4—72no—
572C22×C4—72no—
573C22×C4—82no—
574C22×C4—142no—
575C22×C4—142no—
576C22×C4—141no—
577C22×C4—141no—
578C22×C4—141no—
579C22×C4—141no—
580C22×C4D4×D711yescharacteristic
581C22×C4D4×D711yescharacteristic
582C22×C4C23×D711yescharacteristic
583Q16—284no—
584Q16—284no—
585SD16—44no—
586SD16—44no—
587M16—284no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—72no—
591C2×C8—72no—
592C2×C8—142no—
593C2×C8—142no—
594C2×C8—284no—
595C2×C8C23×D712yes—
596C2×C8C23×D712yes—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—21no—
600C4⋊C4—74no—
601C4⋊C4—74no—
602C4⋊C4—72no—
603C4⋊C4—72no—
604C4⋊C4—72no—
605C4⋊C4—144no—
606C4⋊C4—144no—
607C4⋊C4—144no—
608C4⋊C4—144no—
609C4⋊C4—144no—
610C4⋊C4—144no—
611C4⋊C4—144no—
612C4⋊C4—144no—
613C4⋊C4—144no—
614C4⋊C4—141no—
615C4⋊C4—141no—
616C4⋊C4—141no—
617C4⋊C4C23×D712yes—
618C22⋊C4—24no—
619C22⋊C4—74no—
620C22⋊C4—74no—
621C22⋊C4—144no—
622C22⋊C4—144no—
623C22⋊C4—144no—
624C22⋊C4—144no—
625C22⋊C4—144no—
626C22⋊C4—144no—
627C42—72no—
628C42—72no—
629C42—144no—
630C42—144no—
631C42—144no—
632C42D4×D712yes—
633C42C23×D712yes—
634C2×C7—82no—
635C2×C7#325814yescomplemented
636C2×C7C2×#53711yescharacteristic
637C2×C7C2×#57711yescharacteristic
638C2×C7C2×#57811yescharacteristic
639D7—42no—
640C23—22no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—72no—
645C23—142no—
646C23—142no—
647C23—142no—
648C23C2×D4×D711yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—42no—
654Q8—42no—
655Q8—142no—
656Q8—142no—
657Q8—282no—
658Q8—564no—
659D4—22no—
660D4—22no—
661D4—42no—
662D4—564no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—72no—
672C2×C4—72no—
673C2×C4—72no—
674C2×C4—84no—
675C2×C4—142no—
676C2×C4—142no—
677C2×C4—142no—
678C2×C4—144no—
679C2×C4—142no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—142no—
685C2×C4—282no—
686C2×C4—282no—
687C2×C4—282no—
688C2×C4—282no—
689C2×C4C2×D4×D712yes—
690C2×C4C2×D4×D712yes—
691C2×C4C2×D4×D711yescharacteristic
692C2×C4#654812yes—
693C2×C4#655412yes—
694C2×C4C24×D711yescharacteristic
695C8—22no—
696C8—22no—
697C8—142no—
698C8—142no—
699C7C2×#325811yescharacteristic, complemented, Sylow
700C22—42no—
701C22—42no—
702C22—42no—
703C22—84no—
704C22—142no—
705C22—142no—
706C22—142no—
707C22—284no—
708C22#9029912yes—
709C22#9045312yes—
710C22#9047012yes—
711C22C22×D4×D711yescharacteristic
712C4—22no—
713C4—22no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—142no—
718C4—142no—
719C4—142no—
720C4—282no—
721C4—282no—
722C4—282no—
723C4—282no—
724C4#9029912yes—
725C4C2×#654811yescharacteristic
726C4C2×#655411yescharacteristic
727C2—82no—
728C2—282no—
729C2#1173788714yesdirect product factor
730C2C2×#9029911yescharacteristic
731C2C2×#9045311yescharacteristic
732C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#461C2
socleC23×C7C22×D4
prime radicalC2×#6501C22
hypercenterC2×#461D7
hypocenterC7C2×#3258
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#90422C2semidirect
3. C2×C7×#461C2semidirect
6. C2×#89938C2semidirect
7. C2×#89938C2semidirect
8. C2×#89862C2semidirect
9. C2×#89781C2semidirect
10. #11737887C2direct (N × H)
11. C2×#89601C2semidirect
12. C2×#89611C2semidirect
13. C2×#89588C2semidirect
14. C2×#89585C2semidirect
15. C2×#89566C2semidirect
16. C2×#89563C2semidirect
34. #90422C22semidirect
48. C7×#461C22semidirect
58. #89938C22semidirect
59. #89938C22semidirect
66. #89862C22semidirect
67. #89781C22semidirect
71. #89611C22semidirect
72. #89601C22semidirect
73. #89588C22semidirect
74. #89585C22semidirect
75. #89566C22semidirect
76. #89563C22semidirect
197. C2×#461D7semidirect
333. #461C2×D7semidirect
635. C2×C7#3258semidirect
699. C7C2×#3258semidirect
729. C2#11737887direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904222
C2×#902522
C2×C7×#4612
C2×#899462
C2×#899432
C2×#899382
C2×#898622
C2×#897812
#117378872
C2×#896012
C2×#896112
C2×#895882
C2×#895852
C2×#895662
C2×#895632
C2×#32587