Finite Group Databasebeta

← C2×#11729356 #13319653

Subgroups — C2×#11729356 #13319653

Order 1792.

1738 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×D4C211yesmaximal, characteristic
2C2×#89979C212yesmaximal, complemented
3#11729356C218yesmaximal, direct product factor
4C2×#89323C212yesmaximal, complemented
5C2×#89320C212yesmaximal, complemented
6C23×C7×D4C411yescharacteristic
7C24×C4×C7C411yescharacteristic
8C24×C4×C7C2211yescharacteristic
9C2×C4×C7×D4—22no—
10C2×C4×C7×D4—22no—
11C2×C4×C7×D4—24no—
12C2×C4×C7×D4C414yes—
13C2×C4×C7×D4C2214yes—
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C22⋊C4C411yescharacteristic
16C22×C7×C22⋊C4C2211yescharacteristic
17C22×C42×C7C411yescharacteristic
18C22×#1136—22no—
19#89979—24no—
20#89979C2218yescomplemented
21C2×C22⋊(C7⋊C8)—22no—
22C2×C22⋊(C7⋊C8)C2214yes—
23#89323C2218yescomplemented
24#89320C2218yescomplemented
25C2×#1465—71nomaximal, Sylow
26C25×C7C2×C411yescharacteristic
27C25×C7C2×C411yescharacteristic
28C22×C7×D4—22no—
29C22×C7×D4—22no—
30C22×C7×D4—24no—
31C22×C7×D4—24no—
32C22×C7×D4C2×C414yes—
33C23×C4×C7—22no—
34C23×C4×C7—21no—
35C23×C4×C7—21no—
36C23×C4×C7—44no—
37C23×C4×C7—44no—
38C23×C4×C7C2×C411yescharacteristic
39C23×C4×C7C2×C411yescharacteristic
40C23×C4×C7C2×C411yescharacteristic
41C23×C4×C7C2×C411yescharacteristic
42C23×C4×C7C2×C414yes—
43C23×C4×C7C2×C412yes—
44C23×C4×C7D412yes—
45C23×C4×C7D412yes—
46C23×C4×C7D414yes—
47C23×C4×C7C2311yescharacteristic
48C23×C4×C7C2312yes—
49C4×C7×D4—28no—
50C4×C7×D4—28no—
51C4×C7×D4—28no—
52C4×C7×D4—28no—
53C2×C7×C4⋊C4—22no—
54C2×C7×C4⋊C4—22no—
55C2×C7×C4⋊C4C2×C412yes—
56C2×C7×C4⋊C4C2312yes—
57C2×C7×C22⋊C4—22no—
58C2×C7×C22⋊C4—22no—
59C2×C7×C22⋊C4—22no—
60C2×C7×C22⋊C4—22no—
61C2×C7×C22⋊C4C2×C414yes—
62C2×C7×C22⋊C4C2×C412yes—
63C2×C7×C22⋊C4C2312yes—
64C2×C42×C7—22no—
65C2×C42×C7—21no—
66C2×C42×C7—21no—
67C2×C42×C7C2×C414yes—
68C2×#1136—28no—
69C2×#1136—48no—
70C22×C7⋊C8—24no—
71C22⋊(C7⋊C8)—28no—
72C22⋊(C7⋊C8)—24no—
73C22⋊(C7⋊C8)C2318yes—
74C22×C4×D4D711yescharacteristic
75C2×#407—72no—
76#1465—78no—
77C2×#324—72no—
78C2×#323—72no—
79C24×C7—21no—
80C24×C7—21no—
81C24×C7—22no—
82C24×C7—22no—
83C24×C7—22no—
84C24×C7—42no—
85C24×C7—42no—
86C24×C7—42no—
87C24×C7—42no—
88C24×C7C22⋊C412yes—
89C24×C7C22⋊C412yes—
90C24×C7M1614yescomplemented
91C24×C7C22×C411yescharacteristic
92C24×C7C22×C412yes—
93C24×C7C22×C412yes—
94C2×C7×D4—216no—
95C2×C7×D4—216no—
96C2×C7×D4—28no—
97C2×C7×D4—28no—
98C2×C7×D4—28no—
99C22×C4×C7—21no—
100C22×C4×C7—21no—
101C22×C4×C7—22no—
102C22×C4×C7—28no—
103C22×C4×C7—24no—
104C22×C4×C7—21no—
105C22×C4×C7—21no—
106C22×C4×C7—21no—
107C22×C4×C7—21no—
108C22×C4×C7—24no—
109C22×C4×C7—24no—
110C22×C4×C7—44no—
111C22×C4×C7—48no—
112C22×C4×C7—44no—
113C22×C4×C7—44no—
114C22×C4×C7—42no—
115C22×C4×C7—44no—
116C22×C4×C7—48no—
117C22×C4×C7—48no—
118C22×C4×C7—44no—
119C22×C4×C7—42no—
120C22×C4×C7—42no—
121C22×C4×C7C22⋊C411yescharacteristic
122C22×C4×C7C22⋊C412yes—
123C22×C4×C7C22⋊C414yes—
124C22×C4×C7C22⋊C414yes—
125C22×C4×C7C22⋊C411yescharacteristic
126C22×C4×C7M1614yescomplemented
127C22×C4×C7C22×C412yes—
128C22×C4×C7C22×C412yes—
129C22×C4×C7C22×C412yes—
130C22×C4×C7C22×C412yes—
131C22×C4×C7C22×C411yescharacteristic
132C22×C4×C7C2×D412yes—
133C22×C4×C7C2×D414yes—
134C22×C4×C7C2×D412yes—
135C22×C4×C7C2×D414yes—
136C22×C4×C7C2411yescharacteristic
137C7×C4⋊C4—24no—
138C7×C4⋊C4—24no—
139C7×C22⋊C4—28no—
140C7×C22⋊C4—24no—
141C7×C22⋊C4—24no—
142C42×C7—24no—
143C42×C7—24no—
144#1136—416no—
145C2×C7⋊C8—28no—
146C2×C7⋊C8—48no—
147C23×D4Dic711yescharacteristic
148C24×C4Dic711yescharacteristic
149C24×C4C2×D711yescharacteristic
150C22×M16—142no—
151C2×C4×D4—22no—
152C2×C4×D4—22no—
153C2×C4×D4—24no—
154C2×C4×D4Dic714yes—
155C2×C4×D4C2×D714yes—
156C22×C4⋊C4C2×D711yescharacteristic
157C22×C22⋊C4Dic711yescharacteristic
158C22×C22⋊C4C2×D711yescharacteristic
159C22×C42Dic711yescharacteristic
160#407—78no—
161#407—144no—
162C2×C22⋊C8—74no—
163C2×C22⋊C8—142no—
164#324—78no—
165#323—78no—
166C23×C7—22no—
167C23×C7—22no—
168C23×C7—22no—
169C23×C7—22no—
170C23×C7—22no—
171C23×C7—22no—
172C23×C7—24no—
173C23×C7—24no—
174C23×C7—24no—
175C23×C7—24no—
176C23×C7—24no—
177C23×C7—24no—
178C23×C7—42no—
179C23×C7—42no—
180C23×C7—42no—
181C23×C7—42no—
182C23×C7—42no—
183C23×C7—48no—
184C23×C7—42no—
185C23×C7—42no—
186C23×C7—42no—
187C23×C7—48no—
188C23×C7—48no—
189C23×C7—48no—
190C23×C7—42no—
191C23×C7—42no—
192C23×C7C2×C22⋊C414yes—
193C23×C7C2×C22⋊C411yescharacteristic
194C23×C7C2×C22⋊C411yescharacteristic
195C23×C7C2×M1612yes—
196C23×C7C2×M1612yes—
197C23×C7C2×M1614yescomplemented
198C23×C7C23×C411yescharacteristic
199C7×D4—232no—
200C2×C4×C7—22no—
201C2×C4×C7—22no—
202C2×C4×C7—24no—
203C2×C4×C7—24no—
204C2×C4×C7—24no—
205C2×C4×C7—22no—
206C2×C4×C7—28no—
207C2×C4×C7—24no—
208C2×C4×C7—24no—
209C2×C4×C7—28no—
210C2×C4×C7—22no—
211C2×C4×C7—22no—
212C2×C4×C7—44no—
213C2×C4×C7—41no—
214C2×C4×C7—44no—
215C2×C4×C7—42no—
216C2×C4×C7—41no—
217C2×C4×C7—48no—
218C2×C4×C7—42no—
219C2×C4×C7—42no—
220C2×C4×C7—42no—
221C2×C4×C7—42no—
222C2×C4×C7—48no—
223C2×C4×C7—42no—
224C2×C4×C7—42no—
225C2×C4×C7#9914yes—
226C2×C4×C7C2×C22⋊C412yes—
227C2×C4×C7C2×C22⋊C412yes—
228C2×C4×C7C2×C22⋊C412yes—
229C2×C4×C7C2×M1614yescomplemented
230C2×C4×C7C22×D412yes—
231C7⋊C8—48no—
232C25C2×Dic711yescharacteristic
233C25C2×Dic711yescharacteristic
234C22×D4—24no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—24no—
238C22×D4C2×Dic714yes—
239C23×C4—22no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—44no—
243C23×C4—44no—
244C23×C4C2×Dic711yescharacteristic
245C23×C4C2×Dic711yescharacteristic
246C23×C4C2×Dic711yescharacteristic
247C23×C4C2×Dic711yescharacteristic
248C23×C4C2×Dic714yes—
249C23×C4C2×Dic712yes—
250C23×C4C22⋊D712yes—
251C23×C4C22⋊D712yes—
252C23×C4C22⋊D714yes—
253C23×C4C22×D711yescharacteristic
254C23×C4C22×D712yes—
255C2×M16—148no—
256C2×M16—288no—
257C22×C8—144no—
258C4×D4—28no—
259C4×D4—28no—
260C4×D4—28no—
261C4×D4—28no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4C2×Dic712yes—
265C2×C4⋊C4C22×D712yes—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4C2×Dic714yes—
271C2×C22⋊C4C2×Dic712yes—
272C2×C22⋊C4C22×D712yes—
273C2×C42—22no—
274C2×C42—21no—
275C2×C42—21no—
276C2×C42C2×Dic714yes—
277C22⋊C8—78no—
278C22⋊C8—144no—
279C22⋊C8—148no—
280C22×C7—21no—
281C22×C7—21no—
282C22×C7—21no—
283C22×C7—21no—
284C22×C7—24no—
285C22×C7—24no—
286C22×C7—24no—
287C22×C7—24no—
288C22×C7—24no—
289C22×C7—24no—
290C22×C7—44no—
291C22×C7—44no—
292C22×C7—44no—
293C22×C7—44no—
294C22×C7—48no—
295C22×C7—48no—
296C22×C7—42no—
297C22×C7—42no—
298C22×C7—48no—
299C22×C7—48no—
300C22×C7#40712yes—
301C22×C7#40712yes—
302C22×C7C2×#9912yes—
303C22×C7#41312yes—
304C22×C7C22×C22⋊C411yescharacteristic
305C22×C7C22×M1611yescharacteristic
306C22×C7C22×M1611yescharacteristic
307C4×C7—24no—
308C4×C7—22no—
309C4×C7—22no—
310C4×C7—22no—
311C4×C7—42no—
312C4×C7—42no—
313C4×C7C2×#9914yes—
314C24—22no—
315C24—22no—
316C24—22no—
317C24—21no—
318C24—21no—
319C24—42no—
320C24—42no—
321C24—42no—
322C24—42no—
323C24#113614yescomplemented
324C24C22⋊Dic712yes—
325C24C22⋊Dic712yes—
326C24C22×Dic711yescharacteristic
327C24C22×Dic712yes—
328C24C22×Dic712yes—
329C2×D4—216no—
330C2×D4—216no—
331C2×D4—28no—
332C2×D4—28no—
333C2×D4—28no—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—28no—
338C22×C4—24no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—44no—
346C22×C4—48no—
347C22×C4—44no—
348C22×C4—44no—
349C22×C4—42no—
350C22×C4—44no—
351C22×C4—48no—
352C22×C4—48no—
353C22×C4—44no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4#113614yescomplemented
357C22×C4C22⋊Dic712yes—
358C22×C4C22⋊Dic714yes—
359C22×C4C22⋊Dic711yescharacteristic
360C22×C4C22⋊Dic714yes—
361C22×C4C22⋊Dic711yescharacteristic
362C22×C4C22×Dic712yes—
363C22×C4C22×Dic712yes—
364C22×C4C22×Dic712yes—
365C22×C4C22×Dic712yes—
366C22×C4C22×Dic711yescharacteristic
367C22×C4C2×C22⋊D714yes—
368C22×C4C2×C22⋊D712yes—
369C22×C4C2×C22⋊D712yes—
370C22×C4C2×C22⋊D714yes—
371C22×C4C23×D711yescharacteristic
372M16—2816no—
373C2×C8—148no—
374C2×C8—288no—
375C4⋊C4—24no—
376C4⋊C4—24no—
377C22⋊C4—28no—
378C22⋊C4—24no—
379C22⋊C4—24no—
380C42—24no—
381C42—24no—
382C2×C7—21no—
383C2×C7—21no—
384C2×C7—22no—
385C2×C7—44no—
386C2×C7—44no—
387C2×C7#146514yescomplemented
388C2×C7C2×#40711yescharacteristic
389C2×C7C22×#9911yescharacteristic
390C2×C7C2×#41311yescharacteristic
391C23—22no—
392C23—22no—
393C23—22no—
394C23—22no—
395C23—22no—
396C23—24no—
397C23—24no—
398C23—24no—
399C23—24no—
400C23—24no—
401C23—24no—
402C23—22no—
403C23—42no—
404C23—42no—
405C23—42no—
406C23—42no—
407C23—42no—
408C23—48no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—48no—
413C23—48no—
414C23—48no—
415C23—42no—
416C23—42no—
417C23C2×#113612yes—
418C23C2×#113612yes—
419C23C2×#113614yescomplemented
420C23C2×C22⋊Dic714yes—
421C23C2×C22⋊Dic711yescharacteristic
422C23C2×C22⋊Dic711yescharacteristic
423C23C23×Dic711yescharacteristic
424D4—232no—
425C2×C4—22no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—28no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—28no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—44no—
438C2×C4—41no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—48no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—48no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4#640814yes—
451C2×C4C2×#113614yescomplemented
452C2×C4C2×C22⋊Dic712yes—
453C2×C4C2×C22⋊Dic712yes—
454C2×C4C2×C22⋊Dic712yes—
455C2×C4C22×C22⋊D712yes—
456C8—288no—
457C7C2×#146511yescharacteristic, complemented, Sylow
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—24no—
463C22—24no—
464C22—24no—
465C22—24no—
466C22—24no—
467C22—24no—
468C22—44no—
469C22—44no—
470C22—44no—
471C22—44no—
472C22—48no—
473C22—48no—
474C22—42no—
475C22—42no—
476C22—48no—
477C22—48no—
478C22#8997912yes—
479C22#8997912yes—
480C22C2×#640812yes—
481C22#9000912yes—
482C22C22×#113611yescharacteristic
483C22C22×#113611yescharacteristic
484C22C22×C22⋊Dic711yescharacteristic
485C4—24no—
486C4—22no—
487C4—22no—
488C4—22no—
489C4—42no—
490C4—42no—
491C4C2×#640814yes—
492C2—21no—
493C2—21no—
494C2—22no—
495C2—44no—
496C2—44no—
497C2#1172935614yesdirect product factor
498C2C2×#8997911yescharacteristic
499C2C22×#640811yescharacteristic
500C2C2×#9000911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic7
commutatorC23×C7C23×C4
FrattiniC22×C4C23×D7
FittingC22×C4×C7×D4C2
socleC23×C7C2×C22⋊C4
prime radicalC23×C7×D4C4
cosocleC22×C4×C7C24
hypercenterC22×C4×D4D7
hypocenterC7C2×#1465
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#89979C2semidirect
3. #11729356C2direct (N × H)
4. C2×#89323C2semidirect
5. C2×#89320C2semidirect
20. #89979C22semidirect
23. #89323C22semidirect
24. #89320C22semidirect
90. C24×C7M16semidirect
126. C22×C4×C7M16semidirect
197. C23×C7C2×M16semidirect
229. C2×C4×C7C2×M16semidirect
323. C24#1136semidirect
356. C22×C4#1136semidirect
387. C2×C7#1465semidirect
419. C23C2×#1136semidirect
451. C2×C4C2×#1136semidirect
457. C7C2×#1465semidirect
497. C2#11729356direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C7×D42
C2×#899792
#117293562
C2×#893232
C2×#893202
C2×#14657