Finite Group Databasebeta

← C2×#11742918 #14262171

Subgroups — C2×#11742918 #14262171

Order 1792.

7758 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×#41C211yesmaximal, characteristic, complemented
2C2×#90524C212yesmaximal, complemented
3#11742918C2132yesmaximal, direct product factor
4C2×#90270C212yesmaximal, complemented
5C2×#90275C212yesmaximal, complemented
6C2×#90242C212yesmaximal, complemented
7C2×#90254C212yesmaximal, complemented
8C2×#90256C214yesmaximal, complemented
9C2×#90243C214yesmaximal, complemented
10C2×#90225C214yesmaximal, complemented
11C2×#90214C212yesmaximal, complemented
12C2×#90168C212yesmaximal, complemented
13C2×#90168C211yesmaximal, characteristic, complemented
14C2×#90161C212yesmaximal, complemented
15C22×#6432C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C22×#1157C2212yes—
18C22×#1157C2214yes—
19C23×Dic14C2212yes—
20C4×C7×#41C22116yescomplemented
21C2×C4×C7×Q8C2211yescharacteristic
22C2×C4×C7×Q8C2211yescharacteristic
23C2×C4×C7×D4C2212yes—
24C2×C4×C7×D4C2212yes—
25C2×C4×C7×D4C2211yescharacteristic
26C2×C4×C7×D4C2211yescharacteristic
27C2×C7×#117C2211yescharacteristic
28C2×C7×#117C2212yes—
29C22×C42×C7C2211yescharacteristic
30C22×C42×C7C2212yes—
31#90524C22132yescomplemented
32C2×#6509C2214yes—
33C2×#6502C2218yes—
34C2×#6501C2214yes—
35C2×#6493C2214yes—
36C2×#6493C2212yes—
37C2×#6493C2212yes—
38C2×#6493C2214yes—
39C2×#6489C2214yes—
40C22×C4⋊Dic7C2212yes—
41C22×C4⋊Dic7C2212yes—
42C2×#6487C2214yes—
43C2×#6487C2214yes—
44#90275C22132yescomplemented
45#90270C22132yescomplemented
46#90256C22164yescomplemented
47#90254C22132yescomplemented
48#90243C22164yescomplemented
49#90242C22132yescomplemented
50#90225C22164yescomplemented
51#90214C22132yescomplemented
52C2×#6461C2218yes—
53C2×#6459C2218yes—
54C2×#6455C2214yes—
55C2×D7×C4⋊C4C2214yes—
56C2×#6448C2218yes—
57C2×#6446C2218yes—
58C2×(C22⋊D7)⋊C4C2218yes—
59#90168C22132yescomplemented
60#90168C22116yescomplemented
61C2×#6438C2212yes—
62C2×#6438C2214yes—
63C2×#6437C2211yescharacteristic
64C2×C4×D28C2214yes—
65C2×C4×D28C2214yes—
66C2×C4×D28C2212yes—
67C2×C4×D28C2212yes—
68#90161C22132yescomplemented
69C2×#6433C2214yes—
70C2×#6432C2212yes—
71C2×#6432C2212yes—
72C2×#6432C2212yes—
73C2×#6432C2212yes—
74C2×#6432C2211yescharacteristic
75C2×#6432C22116yescomplemented
76C2×C4×Dic14C2214yes—
77C2×C4×Dic14C2214yes—
78C2×#3511—71nomaximal, Sylow
79C2×C7×#41—28no—
80C2×C7×#41C2318yes—
81C22×C7×Q8C2311yescharacteristic
82C22×C7×D4C2311yescharacteristic
83C22×C7×D4C2312yes—
84C23×C4×C7C2312yes—
85C23×C4×C7C2312yes—
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2312yes—
88C23×C4×C7C2311yescharacteristic
89C23×C4×C7C2311yescharacteristic
90C22×C22⋊D7C2314yes—
91C22×C22⋊D7C2318yes—
92C23×Dic7C2314yes—
93C2×#1157—216no—
94C2×#1157—416no—
95C2×#1157C23116yes—
96C2×#1157C23132yes—
97C22×D28C2312yes—
98C22×D28C2312yes—
99C22×D28C2312yes—
100C22×C4×D7C2314yes—
101C22×C4×D7C2318yes—
102C22×Dic14—48no—
103C22×Dic14C2312yes—
104C22×Dic14C2314yes—
105C22×Dic14C2314yes—
106C22×Dic14C23116yes—
107C4×C7×Q8C2318yes—
108C4×C7×Q8C2318yes—
109C4×C7×D4C2318yes—
110C4×C7×D4C23116yes—
111C4×C7×D4C2318yes—
112C4×C7×D4C23116yes—
113C7×#117C2318yes—
114C7×#117C23116yes—
115C2×C7×C4⋊C4C2311yescharacteristic
116C2×C7×C4⋊C4C2311yescharacteristic
117C2×C7×C4⋊C4C2312yes—
118C2×C7×C4⋊C4C2312yes—
119C2×C7×C22⋊C4C2312yes—
120C2×C7×C22⋊C4C2312yes—
121C2×C7×C22⋊C4C2312yes—
122C2×C42×C7C2312yes—
123C2×C42×C7C2312yes—
124C2×C42×C7C2311yescharacteristic
125C2×C42×C7C2311yescharacteristic
126C2×C42×C7C2311yescharacteristic
127C2×C42×C7C2311yescharacteristic
128C2×C42×C7C2318yes—
129C2×C42×C7C2312yes—
130C2×C42×C7C23116yes—
131C2×C22⋊Dic7C2318yes—
132#6509C23132yes—
133#6502C23164yes—
134#6501C23132yes—
135#6493C23132yes—
136#6493C23116yes—
137#6493C23132yes—
138#6493C23116yes—
139C2×(C2×D7)⋊C4C2318yes—
140C2×(C2×D7)⋊C4C2314yes—
141C2×(C2×D7)⋊C4C2314yes—
142C2×(C2×D7)⋊C4C2318yes—
143#6489C23132yes—
144C2×C4⋊Dic7C2312yes—
145C2×C4⋊Dic7C2314yes—
146C2×C4⋊Dic7C2314yes—
147C2×C4⋊Dic7C2314yes—
148C2×C4⋊Dic7C2314yes—
149C2×C4⋊Dic7C2312yes—
150C2×C4⋊Dic7C23116yes—
151C2×C4⋊Dic7C23116yes—
152#6487C23132yes—
153#6487C23132yes—
154C2×Dic7⋊C4C2318yes—
155C2×Dic7⋊C4C2318yes—
156C2×C4×Dic7C2318yes—
157#6461C23164yes—
158#6459C23164yes—
159#6455C23132yes—
160D7×C4⋊C4C23132yes—
161#6448C23164yes—
162#6446C23164yes—
163(C22⋊D7)⋊C4C23164yes—
164#6438C23116yes—
165#6438C23132yes—
166#6437C2318yes—
167C4×D28C23132yes—
168C4×D28C23116yes—
169C4×D28C23116yes—
170C4×D28C23132yes—
171#6433C23132yes—
172#6432C23116yes—
173#6432C23116yes—
174#6432C23116yes—
175#6432C23116yes—
176#6432C2318yes—
177C4×Dic14C23132yes—
178C4×Dic14C23132yes—
179#3511—732no—
180C2×#556—72no—
181C2×#555—72no—
182C2×#554—72no—
183C2×#553—74no—
184C2×#548—74no—
185C2×#547—72no—
186C2×#542—74no—
187C2×#537—72no—
188C2×#533—72no—
189C2×#532—72no—
190C2×#532—71no—
191C22×C4⋊Q8—71no—
192C2×#520—72no—
193C2×C4×#41D711yescharacteristic, complemented
194C24×C7C2412yes—
195C24×C7C2411yescharacteristic
196C23×D7C2414yes—
197C7×#41—232no—
198C2×C7×Q8—24no—
199C2×C7×Q8C2414yes—
200C2×C7×D4—28no—
201C2×C7×D4—24no—
202C2×C7×D4C2414yes—
203C2×C7×D4C2418yes—
204C22×C4×C7—28no—
205C22×C4×C7—24no—
206C22×C4×C7—28no—
207C22×C4×C7—24no—
208C22×C4×C7—28no—
209C22×C4×C7#4118yescomplemented
210C22×C4×C7C2412yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2418yes—
214C22×C4×C7C2418yes—
215C22×C4×C7C2411yescharacteristic
216C22×C4×C7C2414yes—
217C22×C4×C7C2418yes—
218C22×C4×C7C2411yescharacteristic
219C22×C4×C7C2414yes—
220C22×C4×C7C2411yescharacteristic
221C22×C4×C7C2411yescharacteristic
222C22×C4×C7C2414yes—
223C22×C4×C7C2411yescharacteristic
224C22×C4×C7C2411yescharacteristic
225C2×C22⋊D7—216no—
226C2×C22⋊D7—416no—
227C2×C22⋊D7C24116yes—
228C2×C22⋊D7C24132yes—
229C22×Dic7—48no—
230C22×Dic7C2414yes—
231C22×Dic7C2418yes—
232C22×Dic7C24116yes—
233#1157—264no—
234#1157—464no—
235C2×D28—28no—
236C2×D28—28no—
237C2×D28—28no—
238C2×D28C2418yes—
239C2×D28C2418yes—
240C2×D28C2418yes—
241C2×C4×D7—216no—
242C2×C4×D7—416no—
243C2×C4×D7C24116yes—
244C2×C4×D7C24132yes—
245C2×Dic14—28no—
246C2×Dic14—216no—
247C2×Dic14—432no—
248C2×Dic14—48no—
249C2×Dic14C2418yes—
250C2×Dic14C24116yes—
251C2×Dic14C24116yes—
252C7×C4⋊C4C2414yes—
253C7×C4⋊C4C2414yes—
254C7×C4⋊C4C2418yes—
255C7×C4⋊C4C2418yes—
256C7×C22⋊C4C2418yes—
257C7×C22⋊C4C2418yes—
258C7×C22⋊C4C2418yes—
259C42×C7C2418yes—
260C42×C7C2418yes—
261C42×C7C2414yes—
262C42×C7C2414yes—
263C42×C7C2414yes—
264C42×C7C2414yes—
265C42×C7C2418yes—
266C22⋊Dic7C24132yes—
267(C2×D7)⋊C4C24132yes—
268(C2×D7)⋊C4C24116yes—
269(C2×D7)⋊C4C24116yes—
270(C2×D7)⋊C4C24132yes—
271C4⋊Dic7C2418yes—
272C4⋊Dic7C24116yes—
273C4⋊Dic7C24116yes—
274C4⋊Dic7C24116yes—
275C4⋊Dic7C24116yes—
276C4⋊Dic7C2418yes—
277Dic7⋊C4C24132yes—
278Dic7⋊C4C24132yes—
279C4×Dic7C24132yes—
280C22×#41—72no—
281C22×#41—74no—
282C22×#41C2×D711yescharacteristic
283C23×Q8—72no—
284#556—732no—
285#555—732no—
286#554—732no—
287#553—764no—
288#548—764no—
289#547—732no—
290#542—764no—
291#537—732no—
292#533—732no—
293#532—716no—
294#532—732no—
295C2×C4⋊Q8—72no—
296C2×C4⋊Q8—72no—
297C2×C4⋊Q8—72no—
298C2×C4⋊Q8—72no—
299C2×C4⋊Q8—71no—
300C2×C4⋊Q8—716no—
301C2×#127—71no—
302C2×#126—78no—
303C2×#125—74no—
304C2×#124—78no—
305C2×#124—72no—
306C2×#124—74no—
307C2×#123—78no—
308C2×C22⋊Q8—74no—
309C2×C22⋊Q8—74no—
310C2×C22⋊Q8—74no—
311C2×C22⋊Q8—78no—
312C2×#121—74no—
313C2×#121—78no—
314C2×#121—74no—
315C2×#121—72no—
316C2×#121—72no—
317C2×#121—74no—
318#520—732no—
319C4×#41C2×D7116yescomplemented
320C2×C4×Q8—74no—
321C2×C4×Q8—74no—
322C2×C4×Q8C2×D711yescharacteristic
323C2×C4×Q8C2×D711yescharacteristic
324C2×C4×D4—78no—
325C2×C4×D4—74no—
326C2×C4×D4—72no—
327C2×C4×D4—74no—
328C2×C4×D4—72no—
329C2×C4×D4C2×D711yescharacteristic
330C2×C4×D4C2×D712yes—
331C2×C4×D4C2×D712yes—
332C2×C4×D4C2×D711yescharacteristic
333C2×#117—74no—
334C2×#117—74no—
335C2×#117C2×D711yescharacteristic
336C2×#117C2×D712yes—
337C22×C4⋊C4—72no—
338C22×C4⋊C4—72no—
339C22×C4⋊C4—74no—
340C22×C42C2×D711yescharacteristic
341C22×C42C2×D712yes—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—24no—
345C23×C7—24no—
346C23×C7—24no—
347C23×C7C2×#4114yes—
348C23×C7C2514yes—
349C23×C7C2512yes—
350C23×C7C2511yescharacteristic
351C22×D7—28no—
352C22×D7—28no—
353C22×D7—28no—
354C22×D7C2518yes—
355C7×Q8—28no—
356C7×D4—216no—
357C7×D4—28no—
358C2×C4×C7—24no—
359C2×C4×C7—22no—
360C2×C4×C7—24no—
361C2×C4×C7—24no—
362C2×C4×C7—22no—
363C2×C4×C7—216no—
364C2×C4×C7—28no—
365C2×C4×C7—216no—
366C2×C4×C7—28no—
367C2×C4×C7—216no—
368C2×C4×C7C2×#4114yes—
369C2×C4×C7C2×#4114yes—
370C2×C4×C7C2×#41116yescomplemented
371C2×C4×C7H(5,𝔽2)14yes—
372C2×C4×C72−1+414yes—
373C2×C4×C7C2514yes—
374C2×C4×C7C2514yes—
375C2×C4×C7C2514yes—
376C2×C4×C7C2512yes—
377C2×C4×C7C2512yes—
378C2×C4×C7C2512yes—
379C2×C4×C7C2512yes—
380C2×C4×C7C2512yes—
381C2×C4×C7C2512yes—
382C22⋊D7—232no—
383C22⋊D7—432no—
384C2×Dic7—28no—
385C2×Dic7—216no—
386C2×Dic7—416no—
387C2×Dic7C2518yes—
388C2×Dic7C25116yes—
389D28—216no—
390D28—216no—
391D28—216no—
392C4×D7—232no—
393C4×D7—432no—
394Dic14—216no—
395Dic14—232no—
396Dic14—416no—
397C2×#41—28no—
398C2×#41—716no—
399C2×#41—732no—
400C2×#41—1416no—
401C2×#41—2816no—
402C2×#41C22×D718yes—
403C22×Q8—72no—
404C22×Q8—74no—
405C22×Q8—74no—
406C22×Q8—716no—
407C22×Q8—288no—
408C22×Q8C22×D711yescharacteristic
409C22×D4—74no—
410C22×D4—78no—
411C22×D4—72no—
412C22×D4—72no—
413C22×D4—72no—
414C22×D4C22×D712yes—
415C22×D4C22×D711yescharacteristic
416C23×C4—74no—
417C23×C4—74no—
418C23×C4—78no—
419C23×C4C22×D711yescharacteristic
420C23×C4C22×D712yes—
421C23×C4C22×D712yes—
422C23×C4C22×D711yescharacteristic
423C23×C4C22×D712yes—
424C23×C4C22×D711yescharacteristic
425C4⋊Q8—716no—
426C4⋊Q8—716no—
427C4⋊Q8—716no—
428C4⋊Q8—716no—
429C4⋊Q8—78no—
430#127—78no—
431#126—764no—
432#125—732no—
433#124—764no—
434#124—716no—
435#124—732no—
436#123—764no—
437C22⋊Q8—732no—
438C22⋊Q8—732no—
439C22⋊Q8—732no—
440C22⋊Q8—764no—
441#121—732no—
442#121—764no—
443#121—732no—
444#121—716no—
445#121—716no—
446#121—732no—
447C4×Q8—732no—
448C4×Q8—732no—
449C4×Q8C22×D718yes—
450C4×Q8C22×D718yes—
451C4×D4—764no—
452C4×D4—732no—
453C4×D4—716no—
454C4×D4—732no—
455C4×D4—716no—
456C4×D4C22×D718yes—
457C4×D4C22×D7116yes—
458C4×D4C22×D7116yes—
459C4×D4C22×D718yes—
460#117—732no—
461#117—732no—
462#117C22×D718yes—
463#117C22×D7116yes—
464C2×C4⋊C4—74no—
465C2×C4⋊C4—74no—
466C2×C4⋊C4—74no—
467C2×C4⋊C4—78no—
468C2×C4⋊C4—716no—
469C2×C4⋊C4—74no—
470C2×C4⋊C4—716no—
471C2×C4⋊C4—72no—
472C2×C4⋊C4—72no—
473C2×C4⋊C4—78no—
474C2×C4⋊C4—732no—
475C2×C4⋊C4C22×D711yescharacteristic
476C2×C4⋊C4C22×D711yescharacteristic
477C2×C4⋊C4C22×D712yes—
478C2×C4⋊C4C22×D712yes—
479C2×C22⋊C4—78no—
480C2×C22⋊C4—78no—
481C2×C22⋊C4—78no—
482C2×C22⋊C4—74no—
483C2×C22⋊C4—74no—
484C2×C22⋊C4C22×D712yes—
485C2×C22⋊C4C22×D712yes—
486C2×C22⋊C4C22×D712yes—
487C2×C42—78no—
488C2×C42C22×D712yes—
489C2×C42C22×D711yescharacteristic
490C2×C42C22×D712yes—
491C2×C42C22×D711yescharacteristic
492C2×C42C22×D711yescharacteristic
493C2×C42C22×D712yes—
494C2×C42C22×D718yes—
495C2×C42C22×D7116yes—
496C2×C42C22×D711yescharacteristic
497C22×C7—22no—
498C22×C7—22no—
499C22×C7—28no—
500C22×C7—24no—
501C22×C7—24no—
502C22×C7—24no—
503C22×C7—48no—
504C22×C7C22×#4114yes—
505C22×C7C22×#4112yes—
506C22×C7C2×H(5,𝔽2)12yes—
507C22×C7C2×2−1+412yes—
508C22×C7C2611yescharacteristic
509C2×D7—28no—
510C2×D7—28no—
511C2×D7—28no—
512C2×D7—416no—
513C4×C7—24no—
514C4×C7—22no—
515C4×C7—24no—
516C4×C7—24no—
517C4×C7—22no—
518C4×C7C22×#4114yes—
519C4×C7C22×#4114yes—
520C4×C7C2×H(5,𝔽2)14yes—
521C4×C7C2×2−1+414yes—
522Dic7—28no—
523Dic7—216no—
524C24—74no—
525C24C23×D712yes—
526C24C23×D711yescharacteristic
527#41—232no—
528#41—1464no—
529#41—2864no—
530C2×Q8—24no—
531C2×Q8—78no—
532C2×Q8—716no—
533C2×Q8—716no—
534C2×Q8—148no—
535C2×Q8—1416no—
536C2×Q8—288no—
537C2×Q8—2832no—
538C2×Q8C23×D714yes—
539C2×D4—28no—
540C2×D4—24no—
541C2×D4—716no—
542C2×D4—732no—
543C2×D4—78no—
544C2×D4—78no—
545C2×D4—78no—
546C2×D4—1416no—
547C2×D4—148no—
548C2×D4—148no—
549C2×D4—148no—
550C2×D4—2816no—
551C2×D4C23×D718yes—
552C2×D4C23×D714yes—
553C22×C4—28no—
554C22×C4—24no—
555C22×C4—28no—
556C22×C4—24no—
557C22×C4—28no—
558C22×C4—74no—
559C22×C4—78no—
560C22×C4—716no—
561C22×C4—716no—
562C22×C4—732no—
563C22×C4—1416no—
564C22×C4—2816no—
565C22×C4—288no—
566C22×C4#115718yescomplemented
567C22×C4C23×D714yes—
568C22×C4C23×D718yes—
569C22×C4C23×D718yes—
570C22×C4C23×D714yes—
571C22×C4C23×D718yes—
572C22×C4C23×D712yes—
573C22×C4C23×D711yescharacteristic
574C22×C4C23×D711yescharacteristic
575C22×C4C23×D712yes—
576C22×C4C23×D712yes—
577C22×C4C23×D711yescharacteristic
578C22×C4C23×D711yescharacteristic
579C22×C4C23×D714yes—
580C22×C4C23×D711yescharacteristic
581C22×C4C23×D711yescharacteristic
582C4⋊C4—732no—
583C4⋊C4—732no—
584C4⋊C4—716no—
585C4⋊C4—716no—
586C4⋊C4—716no—
587C4⋊C4—716no—
588C4⋊C4—78no—
589C4⋊C4—78no—
590C4⋊C4C23×D714yes—
591C4⋊C4C23×D714yes—
592C4⋊C4C23×D718yes—
593C4⋊C4C23×D718yes—
594C22⋊C4—732no—
595C22⋊C4—732no—
596C22⋊C4—732no—
597C22⋊C4—716no—
598C22⋊C4—716no—
599C22⋊C4C23×D718yes—
600C22⋊C4C23×D718yes—
601C22⋊C4C23×D718yes—
602C42—732no—
603C42C23×D714yes—
604C42C23×D718yes—
605C42C23×D714yes—
606C42C23×D718yes—
607C42C23×D714yes—
608C42C23×D714yes—
609C42C23×D718yes—
610C2×C7—24no—
611C2×C7—44no—
612C2×C7#351114yescomplemented
613C2×C7C23×#4111yescharacteristic
614C2×C7C22×H(5,𝔽2)11yescharacteristic
615C2×C7C22×2−1+411yescharacteristic
616D7—48no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—78no—
623C23—148no—
624C23—148no—
625C23—148no—
626C23C2×#115714yes—
627C23C24×D714yes—
628C23C24×D712yes—
629C23C24×D711yescharacteristic
630Q8—28no—
631Q8—1416no—
632Q8—1432no—
633Q8—2816no—
634D4—216no—
635D4—28no—
636D4—1432no—
637D4—1416no—
638D4—1416no—
639D4—1416no—
640D4—2832no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—216no—
647C2×C4—28no—
648C2×C4—216no—
649C2×C4—28no—
650C2×C4—216no—
651C2×C4—78no—
652C2×C4—716no—
653C2×C4—148no—
654C2×C4—1416no—
655C2×C4—1432no—
656C2×C4—2832no—
657C2×C4—2816no—
658C2×C4C2×#115714yes—
659C2×C4C2×#115714yes—
660C2×C4C2×#1157116yescomplemented
661C2×C4#655314yes—
662C2×C4#655414yes—
663C2×C4C24×D714yes—
664C2×C4C24×D712yes—
665C2×C4C24×D712yes—
666C2×C4C24×D714yes—
667C2×C4C24×D714yes—
668C2×C4C24×D712yes—
669C2×C4C24×D712yes—
670C2×C4C24×D712yes—
671C2×C4C24×D712yes—
672C7C2×#351111yescharacteristic, complemented, Sylow
673C22—22no—
674C22—22no—
675C22—28no—
676C22—24no—
677C22—24no—
678C22—24no—
679C22—48no—
680C22—148no—
681C22—148no—
682C22—148no—
683C22—2816no—
684C22C22×#115714yes—
685C22C22×#115712yes—
686C22C2×#655312yes—
687C22C2×#655412yes—
688C22C25×D711yescharacteristic
689C4—24no—
690C4—24no—
691C4—22no—
692C4—24no—
693C4—22no—
694C4—148no—
695C4—1416no—
696C4C22×#115714yes—
697C4C22×#115714yes—
698C4C2×#655314yes—
699C4C2×#655414yes—
700C2—24no—
701C2—44no—
702C2—288no—
703C2#1174291814yesdirect product factor
704C2C23×#115711yescharacteristic
705C2C22×#655411yescharacteristic
706C2C22×#655311yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C4×C7×#41C2
socleC23×C7C25
hypercenterC2×C4×#41D7
hypocenterC7C2×#3511
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×C4×C7×#41C2semidirect
2. C2×#90524C2semidirect
3. #11742918C2direct (N × H)
4. C2×#90270C2semidirect
5. C2×#90275C2semidirect
6. C2×#90242C2semidirect
7. C2×#90254C2semidirect
8. C2×#90256C2semidirect
9. C2×#90243C2semidirect
10. C2×#90225C2semidirect
11. C2×#90214C2semidirect
12. C2×#90168C2semidirect
13. C2×#90168C2semidirect
14. C2×#90161C2semidirect
15. C22×#6432C2semidirect
20. C4×C7×#41C22semidirect
31. #90524C22semidirect
44. #90275C22semidirect
45. #90270C22semidirect
46. #90256C22semidirect
47. #90254C22semidirect
48. #90243C22semidirect
49. #90242C22semidirect
50. #90225C22semidirect
51. #90214C22semidirect
59. #90168C22semidirect
60. #90168C22semidirect
68. #90161C22semidirect
75. C2×#6432C22semidirect
193. C2×C4×#41D7semidirect
209. C22×C4×C7#41semidirect
319. C4×#41C2×D7semidirect
370. C2×C4×C7C2×#41semidirect
566. C22×C4#1157semidirect
612. C2×C7#3511semidirect
660. C2×C4C2×#1157semidirect
672. C7C2×#3511semidirect
703. C2#11742918direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C7×#412
C2×#905242
#117429182
C2×#902702
C2×#902752
C2×#902422
C2×#902542
C2×#902562
C2×#902432
C2×#902252
C2×#902142
C2×#901682
C2×#901612
C22×#64322
C2×#35117