Finite Group Databasebeta

← C2×#11743689 #14261682

Subgroups — C2×#11743689 #14261682

Order 1792.

12378 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6548C212yesmaximal, complemented
2C2×C7×D42C211yesmaximal, characteristic, complemented
3C2×D4×C22⋊D7C212yesmaximal, complemented
4C22×#6501C212yesmaximal, complemented
5C2×#90497C212yesmaximal, complemented
6#11743689C2132yesmaximal, direct product factor
7C2×#90408C211yesmaximal, characteristic, complemented
8C2×#90407C211yesmaximal, characteristic, complemented
9C2×#90303C212yesmaximal, complemented
10C2×#90299C212yesmaximal, complemented
11C2×D7×#121C212yesmaximal, complemented
12C2×#90302C212yesmaximal, complemented
13C2×#90282C214yesmaximal, complemented
14C2×#90280C214yesmaximal, complemented
15C2×#90242C211yesmaximal, characteristic, complemented
16C2×#90239C211yesmaximal, characteristic, complemented
17C2×C4×D4×D7C211yesmaximal, characteristic, complemented
18C2×#90246C211yesmaximal, characteristic, complemented
19C23×C7×D4C2212yescomplemented
20C23×C7×D4C2212yescomplemented
21C23×C22⋊D7C2214yescomplemented
22C23×C22⋊D7C2214yescomplemented
23C2×#6548—232no—
24C2×#6548C22132yescomplemented
25C22×#1159C2214yescomplemented
26C22×#1159C2212yescomplemented
27C22×#1159C2212yescomplemented
28C22×D4×D7C2211yescharacteristic
29C22×D4×D7C2214yescomplemented
30C22×D4×D7C2212yescomplemented
31C22×D4×D7C2212yescomplemented
32C22×#1157C2212yescomplemented
33C22×#1157C2212yescomplemented
34C23×C4×D7C2212yescomplemented
35C7×D42C22116yescomplemented
36C2×C7×#127C2211yescharacteristic, complemented
37C2×C7×#121C2212yescomplemented
38C2×C7×#121C2212yescomplemented
39C2×C7×#120C2214yescomplemented
40C2×C4×C7×D4C2211yescharacteristic, complemented
41C2×C4×C7×D4C2211yescharacteristic, complemented
42C2×#6516C2214yescomplemented
43C22×C22⋊Dic7C2214yescomplemented
44#90497C22132yescomplemented
45C2×#6503C2211yescharacteristic, complemented
46C2×#6502C2214yescomplemented
47C2×#6502C2214yescomplemented
48D4×C22⋊D7C22132yescomplemented
49C2×#6501C2212yescomplemented
50C2×#6501C2214yescomplemented
51C2×#6501C2214yescomplemented
52C2×#6501C2212yescomplemented
53C2×#6501C2212yescomplemented
54C2×#6501C2212yescomplemented
55C2×#6501C2211yescharacteristic, complemented
56C2×#6501C2212yescomplemented
57C2×#6501C22132yescomplemented
58C2×#6500C2214yescomplemented
59C2×#6500C2214yescomplemented
60C2×#6499C2212yescomplemented
61C2×#6498C2214yescomplemented
62C2×D4×Dic7C2212yescomplemented
63C2×D4×Dic7C2212yescomplemented
64C2×D4×Dic7C2211yescharacteristic, complemented
65C2×#6493C2212yescomplemented
66C2×C4×C22⋊D7C2212yescomplemented
67C2×C4×C22⋊D7C2212yescomplemented
68C22×C4⋊Dic7C2212yescomplemented
69C2×#6487C2212yescomplemented
70#90408C22116yescomplemented
71#90407C22116yescomplemented
72#90303C22132yescomplemented
73#90302C22132yescomplemented
74#90299C22132yescomplemented
75D7×#121C22132yescomplemented
76#90282C22164yescomplemented
77#90280C22164yescomplemented
78#90246C22116yescomplemented
79#90242C22116yescomplemented
80#90239C22116yescomplemented
81C4×D4×D7C22116yescomplemented
82C2×#6460C2212yescomplemented
83C2×#6458C2211yescharacteristic, complemented
84C2×#6456C2211yescharacteristic, complemented
85C2×D7×C4⋊C4C2212yescomplemented
86C2×D7×C4⋊C4C2211yescharacteristic, complemented
87C2×#6451C2211yescharacteristic, complemented
88C2×#6449C2214yescomplemented
89C2×#6448C2212yescomplemented
90C2×#6447C2212yescomplemented
91C2×#6447C2214yescomplemented
92C2×#6446C2214yescomplemented
93C2×#6446C2214yescomplemented
94C2×(C22⋊D7)⋊C4C2212yescomplemented
95C2×D7×C22⋊C4C2212yescomplemented
96C2×D7×C22⋊C4C2214yescomplemented
97C2×#6441C2214yescomplemented
98C2×C4×D28C2211yescharacteristic, complemented
99C2×C4×D28C2211yescharacteristic, complemented
100C2×C42×D7C2211yescharacteristic, complemented
101C2×#6432C2211yescharacteristic, complemented
102C2×#3496—71nomaximal, Sylow
103C25×C7C2314yes—
104C24×D7C2314yes—
105C24×D7C2312yes—
106C22×C7×D4—216no—
107C22×C7×D4—48no—
108C22×C7×D4C2311yescharacteristic
109C22×C7×D4C2312yes—
110C22×C7×D4C2314yes—
111C22×C7×D4C2312yes—
112C22×C7×D4C2314yes—
113C22×C7×D4C2312yes—
114C22×C7×D4C2311yescharacteristic
115C22×C7×D4C23116yescomplemented
116C22×C7×D4C23116yescomplemented
117C23×C4×C7C2312yes—
118C23×C4×C7C2312yes—
119C22×C22⋊D7—232no—
120C22×C22⋊D7—232no—
121C22×C22⋊D7C2314yes—
122C22×C22⋊D7C2314yes—
123C22×C22⋊D7C2312yes—
124C22×C22⋊D7C2314yes—
125C22×C22⋊D7C2312yes—
126C22×C22⋊D7C2314yes—
127C22×C22⋊D7C2312yes—
128C22×C22⋊D7C2314yes—
129C22×C22⋊D7C2312yes—
130C22×C22⋊D7C23132yescomplemented
131C22×C22⋊D7C23132yescomplemented
132C23×Dic7C2314yes—
133C23×Dic7C2314yes—
134C23×Dic7C2312yes—
135#6548—2256no—
136C2×#1159—216no—
137C2×#1159—232no—
138C2×#1159—216no—
139C2×#1159C23116yescomplemented
140C2×#1159C23116yescomplemented
141C2×#1159C23132yescomplemented
142C2×D4×D7—232no—
143C2×D4×D7—216no—
144C2×D4×D7—48no—
145C2×D4×D7D4116yescomplemented
146C2×D4×D7C2318yes—
147C2×D4×D7C23116yescomplemented
148C2×D4×D7C23132yescomplemented
149C2×D4×D7C23116yescomplemented
150C2×#1157—216no—
151C2×#1157—216no—
152C2×#1157C23116yescomplemented
153C2×#1157C23116yescomplemented
154C22×D28C2311yescharacteristic
155C22×D28C2312yes—
156C22×D28C2311yescharacteristic
157C22×C4×D7—48no—
158C22×C4×D7C2311yescharacteristic
159C22×C4×D7C2312yes—
160C22×C4×D7C2312yes—
161C22×C4×D7C2314yes—
162C22×C4×D7C2311yescharacteristic
163C22×C4×D7C2312yes—
164C22×C4×D7C2312yes—
165C22×C4×D7C2311yescharacteristic
166C22×C4×D7C23116yescomplemented
167C22×Dic14C2312yes—
168C22×Dic14C2312yes—
169C7×#127C2318yescomplemented
170C7×#121C23116yescomplemented
171C7×#121C23116yescomplemented
172C7×#120C23132yescomplemented
173C4×C7×D4C2318yescomplemented
174C4×C7×D4C2318yescomplemented
175C2×C7×C4⋊C4C2311yescharacteristic
176C2×C7×C4⋊C4C2311yescharacteristic
177C2×C7×C22⋊C4C2314yes—
178C2×C7×C22⋊C4C2312yes—
179C2×C7×C22⋊C4C2312yes—
180C2×C42×C7C2311yescharacteristic
181#6516C23132yescomplemented
182C2×C22⋊Dic7C2314yes—
183C2×C22⋊Dic7C2312yes—
184C2×C22⋊Dic7C2314yes—
185C2×C22⋊Dic7C2314yes—
186C2×C22⋊Dic7C2314yes—
187C2×C22⋊Dic7C2312yes—
188C2×C22⋊Dic7C23132yescomplemented
189#6503C2318yescomplemented
190#6502C23132yescomplemented
191#6502C23132yescomplemented
192#6501C23116yescomplemented
193#6501C23116yescomplemented
194#6501C23116yescomplemented
195#6501C23116yescomplemented
196#6501C2318yescomplemented
197#6501C23116yescomplemented
198#6501C23132yescomplemented
199#6501C23132yescomplemented
200#6500C23132yescomplemented
201#6500C23132yescomplemented
202#6499C23116yescomplemented
203#6498C23132yescomplemented
204D4×Dic7C23116yescomplemented
205D4×Dic7C23116yescomplemented
206D4×Dic7C2318yescomplemented
207#6493C23116yescomplemented
208C4×C22⋊D7C23116yescomplemented
209C4×C22⋊D7C23116yescomplemented
210C2×(C2×D7)⋊C4C2312yes—
211C2×(C2×D7)⋊C4C2312yes—
212C2×(C2×D7)⋊C4C2312yes—
213C2×(C2×D7)⋊C4C2312yes—
214C2×(C2×D7)⋊C4C2314yes—
215C2×C4⋊Dic7C2312yes—
216C2×C4⋊Dic7C2312yes—
217C2×C4⋊Dic7C2311yescharacteristic
218C2×C4⋊Dic7C2311yescharacteristic
219C2×C4⋊Dic7C2314yes—
220C2×C4⋊Dic7C23116yescomplemented
221#6487C23116yescomplemented
222C2×Dic7⋊C4C2312yes—
223C2×Dic7⋊C4C2314yes—
224C2×Dic7⋊C4C2312yes—
225C2×C4×Dic7C2311yescharacteristic
226C2×C4×Dic7C2311yescharacteristic
227C2×C4×Dic7C2311yescharacteristic
228#6460C23116yescomplemented
229#6458C2318yescomplemented
230#6456C2318yescomplemented
231D7×C4⋊C4C2318yescomplemented
232D7×C4⋊C4C23116yescomplemented
233#6451C2318yescomplemented
234#6449C23132yescomplemented
235#6448C23116yescomplemented
236#6447C23116yescomplemented
237#6447C23132yescomplemented
238#6446C23132yescomplemented
239#6446C23132yescomplemented
240(C22⋊D7)⋊C4C23116yescomplemented
241D7×C22⋊C4C23116yescomplemented
242D7×C22⋊C4C23132yescomplemented
243#6441C23132yescomplemented
244C4×D28C2318yescomplemented
245C4×D28C2318yescomplemented
246C42×D7C2318yescomplemented
247#6432C2318yescomplemented
248C22×H(5,𝔽2)—72no—
249#3496—732no—
250C2×#547—72no—
251C2×#547—71no—
252C2×#547—71no—
253C2×#546—72no—
254C2×#546—72no—
255C2×#546—74no—
256C2×D42—72no—
257C2×D42—71no—
258C2×D42D711yescharacteristic, complemented
259C2×#537—72no—
260C2×#534—74no—
261C2×#532—71no—
262C2×#532—71no—
263C22×#121—72no—
264C22×#121—72no—
265C22×C4×D4—71no—
266C24×C7—216no—
267C24×C7—48no—
268C24×C7—48no—
269C24×C7C2414yes—
270C24×C7C2412yes—
271C24×C7C2412yes—
272C24×C7C24116yes—
273C23×D7—216no—
274C23×D7—44no—
275C23×D7—44no—
276C23×D7—48no—
277C23×D7—48no—
278C23×D7C2×D4116yescomplemented
279C23×D7C2412yes—
280C23×D7C2412yes—
281C23×D7C2411yescharacteristic
282C23×D7C24116yes—
283C23×D7C2418yes—
284C2×C7×D4—216no—
285C2×C7×D4—264no—
286C2×C7×D4—28no—
287C2×C7×D4—28no—
288C2×C7×D4—24no—
289C2×C7×D4—432no—
290C2×C7×D4—48no—
291C2×C7×D4—44no—
292C2×C7×D4C2×D418yescomplemented
293C2×C7×D4C2418yes—
294C2×C7×D4C24116yes—
295C2×C7×D4C2418yes—
296C2×C7×D4C2414yes—
297C2×C7×D4C2418yes—
298C2×C7×D4C24116yes—
299C2×C7×D4C2414yes—
300C22×C4×C7—28no—
301C22×C4×C7—28no—
302C22×C4×C7C2411yescharacteristic
303C22×C4×C7C2412yes—
304C22×C4×C7C2412yes—
305C22×C4×C7C2418yes—
306C22×C4×C7C2418yes—
307C22×C4×C7C2411yescharacteristic
308C22×C4×C7C2411yescharacteristic
309C2×C22⋊D7—216no—
310C2×C22⋊D7—216no—
311C2×C22⋊D7—28no—
312C2×C22⋊D7—216no—
313C2×C22⋊D7—216no—
314C2×C22⋊D7—2128no—
315C2×C22⋊D7—2128no—
316C2×C22⋊D7—28no—
317C2×C22⋊D7—48no—
318C2×C22⋊D7—44no—
319C2×C22⋊D7C2×D4116yescomplemented
320C2×C22⋊D7C24116yes—
321C2×C22⋊D7C24116yes—
322C2×C22⋊D7C2418yes—
323C2×C22⋊D7C24116yes—
324C2×C22⋊D7C2418yes—
325C2×C22⋊D7C24116yes—
326C2×C22⋊D7C2418yes—
327C2×C22⋊D7C24116yes—
328C2×C22⋊D7C2418yes—
329C22×Dic7—216no—
330C22×Dic7—216no—
331C22×Dic7—44no—
332C22×Dic7C24116yes—
333C22×Dic7C24116yes—
334C22×Dic7C2411yescharacteristic
335C22×Dic7C2411yescharacteristic
336C22×Dic7C2412yes—
337C22×Dic7C2414yes—
338C22×Dic7C2412yes—
339C22×Dic7C2418yes—
340C22×Dic7C2411yescharacteristic
341#1159—264no—
342#1159—2128no—
343#1159—264no—
344D4×D7—2128no—
345D4×D7—264no—
346D4×D7—432no—
347D4×D7C2×D4164yescomplemented
348#1157—264no—
349#1157—264no—
350C2×D28—28no—
351C2×D28—24no—
352C2×D28C2×D418yescomplemented
353C2×D28C2414yes—
354C2×D28C2418yes—
355C2×D28C2414yes—
356C2×C4×D7—216no—
357C2×C4×D7—28no—
358C2×C4×D7—24no—
359C2×C4×D7—28no—
360C2×C4×D7—432no—
361C2×C4×D7—44no—
362C2×C4×D7—44no—
363C2×C4×D7—42no—
364C2×C4×D7C2×D418yescomplemented
365C2×C4×D7C2414yes—
366C2×C4×D7C2418yes—
367C2×C4×D7C2418yes—
368C2×C4×D7C24116yes—
369C2×C4×D7C2414yes—
370C2×C4×D7C2418yes—
371C2×C4×D7C2418yes—
372C2×C4×D7C2414yes—
373C2×Dic14—28no—
374C2×Dic14—28no—
375C2×Dic14C2418yes—
376C2×Dic14C2418yes—
377C7×C4⋊C4C2414yes—
378C7×C4⋊C4C2414yes—
379C7×C22⋊C4C24116yes—
380C7×C22⋊C4C2418yes—
381C7×C22⋊C4C2418yes—
382C42×C7C2414yes—
383C22⋊Dic7C24116yes—
384C22⋊Dic7C2418yes—
385C22⋊Dic7C24116yes—
386C22⋊Dic7C24116yes—
387C22⋊Dic7C24116yes—
388C22⋊Dic7C2418yes—
389(C2×D7)⋊C4C2418yes—
390(C2×D7)⋊C4C2418yes—
391(C2×D7)⋊C4C2418yes—
392(C2×D7)⋊C4C2418yes—
393(C2×D7)⋊C4C24116yes—
394C4⋊Dic7C2418yes—
395C4⋊Dic7C2418yes—
396C4⋊Dic7C2414yes—
397C4⋊Dic7C2414yes—
398C4⋊Dic7C24116yes—
399Dic7⋊C4C2418yes—
400Dic7⋊C4C24116yes—
401Dic7⋊C4C2418yes—
402C4×Dic7C2414yes—
403C4×Dic7C2414yes—
404C4×Dic7C2414yes—
405C2×H(5,𝔽2)—732no—
406C2×H(5,𝔽2)—1432no—
407C22×#41—72no—
408C22×#41—72no—
409C22×#41—74no—
410C22×#41—72no—
411C22×#41—72no—
412C23×D4—71no—
413C23×D4—74no—
414C23×D4—74no—
415C23×D4—74no—
416C23×D4—72no—
417C23×D4—72no—
418C23×D4C2×D712yescomplemented
419C23×D4C2×D712yescomplemented
420C24×C4—72no—
421#547—732no—
422#547—716no—
423#547—716no—
424#546—732no—
425#546—732no—
426#546—764no—
427D42—732no—
428D42—716no—
429D42C2×D7116yescomplemented
430#537—732no—
431#534—764no—
432#532—716no—
433#532—716no—
434C2×C4⋊Q8—71no—
435C2×C4⋊Q8—71no—
436C2×#127—71no—
437C2×#127C2×D711yescharacteristic, complemented
438C2×#124—72no—
439C2×#124—72no—
440C2×#123—74no—
441C2×#123—74no—
442C2×#123—74no—
443C2×#123—74no—
444C2×C22⋊Q8—72no—
445C2×C22⋊Q8—72no—
446C2×C22⋊Q8—74no—
447C2×#121—72no—
448C2×#121—71no—
449C2×#121—74no—
450C2×#121—72no—
451C2×#121—72no—
452C2×#121—74no—
453C2×#121—74no—
454C2×#121—72no—
455C2×#121—72no—
456C2×#121—74no—
457C2×#121—732no—
458C2×#121—72no—
459C2×#121—732no—
460C2×#121—71no—
461C2×#121—74no—
462C2×#121—72no—
463C2×#121C2×D712yescomplemented
464C2×#121C2×D712yescomplemented
465C2×#120—74no—
466C2×#120—74no—
467C2×#120—74no—
468C2×#120C2×D714yescomplemented
469C2×C4×D4—71no—
470C2×C4×D4—72no—
471C2×C4×D4—72no—
472C2×C4×D4—72no—
473C2×C4×D4—72no—
474C2×C4×D4—716no—
475C2×C4×D4—71no—
476C2×C4×D4—72no—
477C2×C4×D4—71no—
478C2×C4×D4—71no—
479C2×C4×D4C2×D711yescharacteristic, complemented
480C2×C4×D4C2×D711yescharacteristic, complemented
481C22×C4⋊C4—72no—
482C22×C4⋊C4—71no—
483C22×C4⋊C4—72no—
484C22×C22⋊C4—74no—
485C22×C22⋊C4—72no—
486C22×C22⋊C4—74no—
487C22×C42—71no—
488C23×C7—24no—
489C23×C7—24no—
490C23×C7—28no—
491C23×C7—24no—
492C23×C7—28no—
493C23×C7—24no—
494C23×C7—24no—
495C23×C7—28no—
496C23×C7—232no—
497C23×C7—416no—
498C23×C7—416no—
499C23×C7—832no—
500C23×C7C22×D418yes—
501C23×C7C2518yes—
502C23×C7C2514yes—
503C23×C7C2514yes—
504C23×C7C2511yescharacteristic
505C22×D7—22no—
506C22×D7—24no—
507C22×D7—22no—
508C22×D7—24no—
509C22×D7—24no—
510C22×D7—24no—
511C22×D7—24no—
512C22×D7—232no—
513C22×D7—48no—
514C22×D7—432no—
515C22×D7—48no—
516C22×D7—416no—
517C22×D7—416no—
518C22×D7—832no—
519C22×D7C22×D418yes—
520C22×D7C22×D414yes—
521C22×D7C22×D4132yescomplemented
522C22×D7C2514yes—
523C22×D7C2514yes—
524C22×D7C2512yes—
525C7×D4—232no—
526C7×D4—216no—
527C7×D4—216no—
528C7×D4—28no—
529C7×D4—416no—
530C7×D4—48no—
531C7×D4C22×D4116yescomplemented
532C2×C4×C7—24no—
533C2×C4×C7—24no—
534C2×C4×C7—22no—
535C2×C4×C7—216no—
536C2×C4×C7—216no—
537C2×C4×C7C22×D414yes—
538C2×C4×C7H(5,𝔽2)14yescomplemented
539C2×C4×C7C2512yes—
540C2×C4×C7C2514yes—
541C2×C4×C7C2514yes—
542C2×C4×C7C2512yes—
543C2×C4×C7C2512yes—
544C22⋊D7—232no—
545C22⋊D7—232no—
546C22⋊D7—216no—
547C22⋊D7—232no—
548C22⋊D7—232no—
549C22⋊D7—216no—
550C22⋊D7—416no—
551C22⋊D7—48no—
552C22⋊D7C22×D4132yescomplemented
553C2×Dic7—28no—
554C2×Dic7—24no—
555C2×Dic7—232no—
556C2×Dic7—22no—
557C2×Dic7—24no—
558C2×Dic7—22no—
559C2×Dic7—232no—
560C2×Dic7—48no—
561C2×Dic7C22×D414yes—
562C2×Dic7C2512yes—
563C2×Dic7C2512yes—
564C2×Dic7C2514yes—
565C2×Dic7C2518yes—
566C2×Dic7C2514yes—
567C2×Dic7C2512yes—
568D28—216no—
569D28—28no—
570D28C22×D4116yescomplemented
571C4×D7—232no—
572C4×D7—216no—
573C4×D7—28no—
574C4×D7—216no—
575C4×D7—48no—
576C4×D7—48no—
577C4×D7—44no—
578C4×D7C22×D4116yescomplemented
579Dic14—216no—
580Dic14—216no—
581C25—72no—
582C25—74no—
583C25C22×D714yes—
584H(5,𝔽2)—14256no—
585C2×#41—716no—
586C2×#41—716no—
587C2×#41—732no—
588C2×#41—716no—
589C2×#41—716no—
590C2×#41—1416no—
591C2×#41—1416no—
592C2×#41—1416no—
593C2×#41—1432no—
594C2×#41—1416no—
595C22×Q8—72no—
596C22×Q8—72no—
597C22×D4—216no—
598C22×D4—48no—
599C22×D4—72no—
600C22×D4—716no—
601C22×D4—78no—
602C22×D4—74no—
603C22×D4—74no—
604C22×D4—74no—
605C22×D4—74no—
606C22×D4—72no—
607C22×D4—72no—
608C22×D4—732no—
609C22×D4—732no—
610C22×D4—72no—
611C22×D4—74no—
612C22×D4—732no—
613C22×D4—716no—
614C22×D4—716no—
615C22×D4—71no—
616C22×D4—71no—
617C22×D4—72no—
618C22×D4—1416no—
619C22×D4—1432no—
620C22×D4—1432no—
621C22×D4—1432no—
622C22×D4—288no—
623C22×D4C22×D712yes—
624C22×D4C22×D711yescharacteristic
625C22×D4C22×D714yes—
626C22×D4C22×D712yes—
627C22×D4C22×D712yes—
628C22×D4C22×D714yes—
629C22×D4C22×D711yescharacteristic
630C22×D4C22×D7116yescomplemented
631C22×D4C22×D7116yescomplemented
632C23×C4—71no—
633C23×C4—74no—
634C23×C4—74no—
635C23×C4—72no—
636C23×C4—74no—
637C23×C4—72no—
638C23×C4—72no—
639C23×C4—71no—
640C23×C4—72no—
641C23×C4—71no—
642C23×C4—72no—
643C23×C4—716no—
644C23×C4—288no—
645C23×C4C22×D712yes—
646C23×C4C22×D712yes—
647C4⋊Q8—78no—
648C4⋊Q8—78no—
649#127—78no—
650#127C22×D718yescomplemented
651#124—716no—
652#124—716no—
653#123—732no—
654#123—732no—
655#123—732no—
656#123—732no—
657C22⋊Q8—716no—
658C22⋊Q8—716no—
659C22⋊Q8—732no—
660#121—716no—
661#121—78no—
662#121—732no—
663#121—716no—
664#121—716no—
665#121—732no—
666#121—732no—
667#121—716no—
668#121—716no—
669#121—732no—
670#121—716no—
671#121—78no—
672#121—732no—
673#121—716no—
674#121C22×D7116yescomplemented
675#121C22×D7116yescomplemented
676#120—732no—
677#120—732no—
678#120—732no—
679#120C22×D7132yescomplemented
680C4×D4—78no—
681C4×D4—716no—
682C4×D4—716no—
683C4×D4—716no—
684C4×D4—716no—
685C4×D4—78no—
686C4×D4—716no—
687C4×D4—78no—
688C4×D4—78no—
689C4×D4C22×D718yescomplemented
690C4×D4C22×D718yescomplemented
691C2×C4⋊C4—71no—
692C2×C4⋊C4—72no—
693C2×C4⋊C4—72no—
694C2×C4⋊C4—71no—
695C2×C4⋊C4—74no—
696C2×C4⋊C4—74no—
697C2×C4⋊C4—716no—
698C2×C4⋊C4—72no—
699C2×C4⋊C4—72no—
700C2×C4⋊C4—78no—
701C2×C4⋊C4—716no—
702C2×C4⋊C4C22×D711yescharacteristic
703C2×C4⋊C4C22×D711yescharacteristic
704C2×C22⋊C4—74no—
705C2×C22⋊C4—72no—
706C2×C22⋊C4—72no—
707C2×C22⋊C4—74no—
708C2×C22⋊C4—74no—
709C2×C22⋊C4—732no—
710C2×C22⋊C4—74no—
711C2×C22⋊C4—72no—
712C2×C22⋊C4—72no—
713C2×C22⋊C4—72no—
714C2×C22⋊C4—74no—
715C2×C22⋊C4—72no—
716C2×C22⋊C4—716no—
717C2×C22⋊C4—732no—
718C2×C22⋊C4C22×D712yes—
719C2×C22⋊C4C22×D714yes—
720C2×C22⋊C4C22×D712yes—
721C2×C42—71no—
722C2×C42—71no—
723C2×C42—71no—
724C2×C42—78no—
725C2×C42C22×D711yescharacteristic
726C22×C7—24no—
727C22×C7—24no—
728C22×C7—216no—
729C22×C7—28no—
730C22×C7—24no—
731C22×C7—28no—
732C22×C7—24no—
733C22×C7—24no—
734C22×C7—28no—
735C22×C7—416no—
736C22×C7—48no—
737C22×C7—832no—
738C22×C7C23×D418yes—
739C22×C7C23×D412yes—
740C22×C7C2×H(5,𝔽2)12yes—
741C22×C7#58512yes—
742C22×C7C2611yescharacteristic
743C2×D7—22no—
744C2×D7—24no—
745C2×D7—22no—
746C2×D7—24no—
747C2×D7—28no—
748C2×D7—216no—
749C2×D7—24no—
750C2×D7—24no—
751C2×D7—24no—
752C2×D7—432no—
753C2×D7—48no—
754C2×D7—832no—
755C2×D7C23×D418yes—
756C2×D7C23×D414yes—
757C4×C7—24no—
758C4×C7—24no—
759C4×C7—22no—
760C4×C7C23×D414yes—
761C4×C7C2×H(5,𝔽2)14yescomplemented
762Dic7—28no—
763Dic7—24no—
764Dic7—22no—
765Dic7—24no—
766Dic7—22no—
767Dic7C23×D414yes—
768C24—216no—
769C24—48no—
770C24—48no—
771C24—72no—
772C24—71no—
773C24—716no—
774C24—78no—
775C24—72no—
776C24—716no—
777C24—1416no—
778C24—284no—
779C24—284no—
780C24—288no—
781C24—288no—
782C24C23×D714yes—
783C24C23×D712yes—
784C24C23×D712yes—
785C24C23×D7116yes—
786#41—1464no—
787#41—1464no—
788#41—1464no—
789#41—14128no—
790#41—1464no—
791C2×Q8—78no—
792C2×Q8—78no—
793C2×Q8—148no—
794C2×Q8—148no—
795C2×D4—216no—
796C2×D4—264no—
797C2×D4—28no—
798C2×D4—24no—
799C2×D4—28no—
800C2×D4—432no—
801C2×D4—48no—
802C2×D4—44no—
803C2×D4—716no—
804C2×D4—78no—
805C2×D4—764no—
806C2×D4—716no—
807C2×D4—716no—
808C2×D4—716no—
809C2×D4—716no—
810C2×D4—78no—
811C2×D4—78no—
812C2×D4—78no—
813C2×D4—716no—
814C2×D4—78no—
815C2×D4—74no—
816C2×D4—74no—
817C2×D4—78no—
818C2×D4—148no—
819C2×D4—148no—
820C2×D4—1464no—
821C2×D4—14128no—
822C2×D4—14128no—
823C2×D4—148no—
824C2×D4—1416no—
825C2×D4—1416no—
826C2×D4—1416no—
827C2×D4—14128no—
828C2×D4—1416no—
829C2×D4—144no—
830C2×D4—2832no—
831C2×D4—288no—
832C2×D4—284no—
833C2×D4D4×D718yescomplemented
834C2×D4C23×D718yes—
835C2×D4C23×D714yes—
836C2×D4C23×D7116yes—
837C2×D4C23×D718yes—
838C2×D4C23×D718yes—
839C2×D4C23×D7116yes—
840C2×D4C23×D714yes—
841C22×C4—28no—
842C22×C4—28no—
843C22×C4—71no—
844C22×C4—78no—
845C22×C4—74no—
846C22×C4—716no—
847C22×C4—716no—
848C22×C4—71no—
849C22×C4—71no—
850C22×C4—72no—
851C22×C4—72no—
852C22×C4—74no—
853C22×C4—78no—
854C22×C4—74no—
855C22×C4—716no—
856C22×C4—78no—
857C22×C4—78no—
858C22×C4—74no—
859C22×C4—78no—
860C22×C4—78no—
861C22×C4—1416no—
862C22×C4—1416no—
863C22×C4—1416no—
864C22×C4—148no—
865C22×C4—144no—
866C22×C4—148no—
867C22×C4—2832no—
868C22×C4—282no—
869C22×C4—284no—
870C22×C4—284no—
871C22×C4—284no—
872C22×C4C23×D718yes—
873C22×C4C23×D718yes—
874C22×C4C23×D711yescharacteristic
875C22×C4C23×D712yes—
876C22×C4C23×D712yes—
877C22×C4C23×D711yescharacteristic
878C22×C4C23×D711yescharacteristic
879C4⋊C4—78no—
880C4⋊C4—716no—
881C4⋊C4—78no—
882C4⋊C4—78no—
883C4⋊C4—74no—
884C4⋊C4—74no—
885C4⋊C4—716no—
886C4⋊C4—78no—
887C4⋊C4C23×D714yes—
888C4⋊C4C23×D714yes—
889C22⋊C4—716no—
890C22⋊C4—78no—
891C22⋊C4—78no—
892C22⋊C4—716no—
893C22⋊C4—716no—
894C22⋊C4—716no—
895C22⋊C4—78no—
896C22⋊C4—78no—
897C22⋊C4—78no—
898C22⋊C4—716no—
899C22⋊C4—78no—
900C22⋊C4C23×D718yes—
901C22⋊C4C23×D7116yes—
902C22⋊C4C23×D718yes—
903C42—74no—
904C42—74no—
905C42—74no—
906C42C23×D714yes—
907C2×C7—28no—
908C2×C7—48no—
909C2×C7—44no—
910C2×C7#349614yescomplemented
911C2×C7C24×D411yescharacteristic
912C2×C7C22×H(5,𝔽2)11yescharacteristic
913C2×C7C2×#58511yescharacteristic
914D7—24no—
915D7—28no—
916D7—44no—
917C23—24no—
918C23—24no—
919C23—24no—
920C23—28no—
921C23—24no—
922C23—28no—
923C23—28no—
924C23—24no—
925C23—232no—
926C23—416no—
927C23—416no—
928C23—74no—
929C23—72no—
930C23—74no—
931C23—78no—
932C23—732no—
933C23—74no—
934C23—832no—
935C23—1432no—
936C23—142no—
937C23—144no—
938C23—142no—
939C23—144no—
940C23—144no—
941C23—144no—
942C23—144no—
943C23—288no—
944C23—288no—
945C23—2832no—
946C23—2816no—
947C23—2816no—
948C23—5632no—
949C23C2×D4×D718yes—
950C23C24×D718yes—
951C23C24×D714yes—
952C23C24×D714yes—
953C23C24×D711yescharacteristic
954Q8—1416no—
955Q8—1416no—
956D4—232no—
957D4—216no—
958D4—28no—
959D4—216no—
960D4—416no—
961D4—48no—
962D4—732no—
963D4—716no—
964D4—1416no—
965D4—1416no—
966D4—1416no—
967D4—1432no—
968D4—1432no—
969D4—1432no—
970D4—1432no—
971D4—148no—
972D4—288no—
973D4—2816no—
974D4C2×D4×D7116yescomplemented
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—216no—
979C2×C4—216no—
980C2×C4—72no—
981C2×C4—74no—
982C2×C4—716no—
983C2×C4—72no—
984C2×C4—72no—
985C2×C4—74no—
986C2×C4—74no—
987C2×C4—78no—
988C2×C4—1432no—
989C2×C4—1432no—
990C2×C4—148no—
991C2×C4—144no—
992C2×C4—1432no—
993C2×C4—142no—
994C2×C4—144no—
995C2×C4—142no—
996C2×C4—1416no—
997C2×C4—148no—
998C2×C4—1416no—
999C2×C4—284no—
1000C2×C4—288no—
1001C2×C4—288no—
1002C2×C4—288no—
1003C2×C4C2×D4×D714yes—
1004C2×C4#654814yescomplemented
1005C2×C4C24×D712yes—
1006C2×C4C24×D714yes—
1007C2×C4C24×D714yes—
1008C2×C4C24×D712yes—
1009C2×C4C24×D712yes—
1010C7C2×#349611yescharacteristic, complemented, Sylow
1011C22—24no—
1012C22—24no—
1013C22—216no—
1014C22—24no—
1015C22—28no—
1016C22—24no—
1017C22—28no—
1018C22—28no—
1019C22—24no—
1020C22—48no—
1021C22—416no—
1022C22—74no—
1023C22—78no—
1024C22—832no—
1025C22—142no—
1026C22—144no—
1027C22—142no—
1028C22—144no—
1029C22—148no—
1030C22—1416no—
1031C22—144no—
1032C22—144no—
1033C22—144no—
1034C22—2832no—
1035C22—288no—
1036C22—5632no—
1037C22C22×D4×D718yes—
1038C22C22×D4×D712yes—
1039C22C2×#654812yes—
1040C22#9061812yes—
1041C22C25×D711yescharacteristic
1042C4—24no—
1043C4—24no—
1044C4—22no—
1045C4—74no—
1046C4—148no—
1047C4—144no—
1048C4—142no—
1049C4—144no—
1050C4—142no—
1051C4C22×D4×D714yes—
1052C4C2×#654814yescomplemented
1053C2—28no—
1054C2—44no—
1055C2—48no—
1056C2—144no—
1057C2—148no—
1058C2—284no—
1059C2#1174368914yesdirect product factor
1060C2C23×D4×D711yescharacteristic
1061C2C22×#654811yescharacteristic
1062C2C2×#9061811yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×D42C2
socleC23×C7C25
hypercenterC2×D42D7
hypocenterC7C2×#3496
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C22×#6548C2semidirect
2. C2×C7×D42C2semidirect
3. C2×D4×C22⋊D7C2semidirect
4. C22×#6501C2semidirect
5. C2×#90497C2semidirect
6. #11743689C2direct (N × H)
7. C2×#90408C2semidirect
8. C2×#90407C2semidirect
9. C2×#90303C2semidirect
10. C2×#90299C2semidirect
11. C2×D7×#121C2semidirect
12. C2×#90302C2semidirect
13. C2×#90282C2semidirect
14. C2×#90280C2semidirect
15. C2×#90242C2semidirect
16. C2×#90239C2semidirect
17. C2×C4×D4×D7C2semidirect
18. C2×#90246C2semidirect
19. C23×C7×D4C22semidirect
20. C23×C7×D4C22semidirect
21. C23×C22⋊D7C22semidirect
22. C23×C22⋊D7C22semidirect
24. C2×#6548C22semidirect
25. C22×#1159C22semidirect
26. C22×#1159C22semidirect
27. C22×#1159C22semidirect
29. C22×D4×D7C22semidirect
30. C22×D4×D7C22semidirect
31. C22×D4×D7C22semidirect
32. C22×#1157C22semidirect
33. C22×#1157C22semidirect
34. C23×C4×D7C22semidirect
35. C7×D42C22semidirect
36. C2×C7×#127C22semidirect
37. C2×C7×#121C22semidirect
38. C2×C7×#121C22semidirect
39. C2×C7×#120C22semidirect
40. C2×C4×C7×D4C22semidirect
41. C2×C4×C7×D4C22semidirect
42. C2×#6516C22semidirect
43. C22×C22⋊Dic7C22semidirect
44. #90497C22semidirect
45. C2×#6503C22semidirect
46. C2×#6502C22semidirect
47. C2×#6502C22semidirect
48. D4×C22⋊D7C22semidirect
49. C2×#6501C22semidirect
50. C2×#6501C22semidirect
51. C2×#6501C22semidirect
52. C2×#6501C22semidirect
53. C2×#6501C22semidirect
54. C2×#6501C22semidirect
55. C2×#6501C22semidirect
56. C2×#6501C22semidirect
57. C2×#6501C22semidirect
58. C2×#6500C22semidirect
59. C2×#6500C22semidirect
60. C2×#6499C22semidirect
61. C2×#6498C22semidirect
62. C2×D4×Dic7C22semidirect
63. C2×D4×Dic7C22semidirect
64. C2×D4×Dic7C22semidirect
65. C2×#6493C22semidirect
66. C2×C4×C22⋊D7C22semidirect
67. C2×C4×C22⋊D7C22semidirect
68. C22×C4⋊Dic7C22semidirect
69. C2×#6487C22semidirect
70. #90408C22semidirect
71. #90407C22semidirect
72. #90303C22semidirect
73. #90302C22semidirect
74. #90299C22semidirect
75. D7×#121C22semidirect
76. #90282C22semidirect
77. #90280C22semidirect
78. #90246C22semidirect
79. #90242C22semidirect
80. #90239C22semidirect
81. C4×D4×D7C22semidirect
82. C2×#6460C22semidirect
83. C2×#6458C22semidirect
84. C2×#6456C22semidirect
85. C2×D7×C4⋊C4C22semidirect
86. C2×D7×C4⋊C4C22semidirect
87. C2×#6451C22semidirect
88. C2×#6449C22semidirect
89. C2×#6448C22semidirect
90. C2×#6447C22semidirect
91. C2×#6447C22semidirect
92. C2×#6446C22semidirect
93. C2×#6446C22semidirect
94. C2×(C22⋊D7)⋊C4C22semidirect
95. C2×D7×C22⋊C4C22semidirect
96. C2×D7×C22⋊C4C22semidirect
97. C2×#6441C22semidirect
98. C2×C4×D28C22semidirect
99. C2×C4×D28C22semidirect
100. C2×C42×D7C22semidirect
101. C2×#6432C22semidirect
115. C22×C7×D4C23semidirect
116. C22×C7×D4C23semidirect
130. C22×C22⋊D7C23semidirect
131. C22×C22⋊D7C23semidirect
139. C2×#1159C23semidirect
140. C2×#1159C23semidirect
141. C2×#1159C23semidirect
145. C2×D4×D7D4semidirect
147. C2×D4×D7C23semidirect
148. C2×D4×D7C23semidirect
149. C2×D4×D7C23semidirect
152. C2×#1157C23semidirect
153. C2×#1157C23semidirect
166. C22×C4×D7C23semidirect
169. C7×#127C23semidirect
170. C7×#121C23semidirect
171. C7×#121C23semidirect
172. C7×#120C23semidirect
173. C4×C7×D4C23semidirect
174. C4×C7×D4C23semidirect
181. #6516C23semidirect
188. C2×C22⋊Dic7C23semidirect
189. #6503C23semidirect
190. #6502C23semidirect
191. #6502C23semidirect
192. #6501C23semidirect
193. #6501C23semidirect
194. #6501C23semidirect
195. #6501C23semidirect
196. #6501C23semidirect
197. #6501C23semidirect
198. #6501C23semidirect
199. #6501C23semidirect
200. #6500C23semidirect
201. #6500C23semidirect
202. #6499C23semidirect
203. #6498C23semidirect
204. D4×Dic7C23semidirect
205. D4×Dic7C23semidirect
206. D4×Dic7C23semidirect
207. #6493C23semidirect
208. C4×C22⋊D7C23semidirect
209. C4×C22⋊D7C23semidirect
220. C2×C4⋊Dic7C23semidirect
221. #6487C23semidirect
228. #6460C23semidirect
229. #6458C23semidirect
230. #6456C23semidirect
231. D7×C4⋊C4C23semidirect
232. D7×C4⋊C4C23semidirect
233. #6451C23semidirect
234. #6449C23semidirect
235. #6448C23semidirect
236. #6447C23semidirect
237. #6447C23semidirect
238. #6446C23semidirect
239. #6446C23semidirect
240. (C22⋊D7)⋊C4C23semidirect
241. D7×C22⋊C4C23semidirect
242. D7×C22⋊C4C23semidirect
243. #6441C23semidirect
244. C4×D28C23semidirect
245. C4×D28C23semidirect
246. C42×D7C23semidirect
247. #6432C23semidirect
258. C2×D42D7semidirect
278. C23×D7C2×D4semidirect
292. C2×C7×D4C2×D4semidirect
319. C2×C22⋊D7C2×D4semidirect
347. D4×D7C2×D4semidirect
352. C2×D28C2×D4semidirect
364. C2×C4×D7C2×D4semidirect
418. C23×D4C2×D7semidirect
419. C23×D4C2×D7semidirect
429. D42C2×D7semidirect
437. C2×#127C2×D7semidirect
463. C2×#121C2×D7semidirect
464. C2×#121C2×D7semidirect
468. C2×#120C2×D7semidirect
479. C2×C4×D4C2×D7semidirect
480. C2×C4×D4C2×D7semidirect
521. C22×D7C22×D4semidirect
531. C7×D4C22×D4semidirect
538. C2×C4×C7H(5,𝔽2)semidirect
552. C22⋊D7C22×D4semidirect
570. D28C22×D4semidirect
578. C4×D7C22×D4semidirect
630. C22×D4C22×D7semidirect
631. C22×D4C22×D7semidirect
650. #127C22×D7semidirect
674. #121C22×D7semidirect
675. #121C22×D7semidirect
679. #120C22×D7semidirect
689. C4×D4C22×D7semidirect
690. C4×D4C22×D7semidirect
761. C4×C7C2×H(5,𝔽2)semidirect
833. C2×D4D4×D7semidirect
910. C2×C7#3496semidirect
974. D4C2×D4×D7semidirect
1004. C2×C4#6548semidirect
1010. C7C2×#3496semidirect
1052. C4C2×#6548semidirect
1059. C2#11743689direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#65482
C2×C7×D422
C2×D4×C22⋊D72
C22×#65012
C2×#904972
#117436892
C2×#904082
C2×#904072
C2×#903032
C2×#902992
C2×D7×#1212
C2×#903022
C2×#902822
C2×#902802
C2×#902422
C2×#902392
C2×C4×D4×D72
C2×#902462
C2×#34967