Finite Group Databasebeta

← C2×#11725856 #13319639

Subgroups — C2×#11725856 #13319639

Order 1792.

1326 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6440C211yesmaximal, characteristic
2C2×#89491C212yesmaximal, complemented
3C2×C7×#323C211yesmaximal, characteristic
4C2×#89320C211yesmaximal, characteristic
5C2×#89264C212yesmaximal, complemented
6#11725856C218yesmaximal, direct product factor
7C24×Dic7C411yescharacteristic
8C22×C7×C22⋊C4C2211yescharacteristic
9C22×C22⋊Dic7C411yescharacteristic
10C22×Dic7⋊C4C411yescharacteristic
11C22×Dic7⋊C4C2211yescharacteristic
12C22×C4×Dic7C411yescharacteristic
13C22×C4×Dic7C2211yescharacteristic
14C2×#6440—22no—
15C2×#6440—22no—
16C2×#6440—24no—
17C2×#6440C414yes—
18C2×#6440C2214yes—
19C2×C7×C22⋊C8C2212yes—
20C2×C22⋊(C7⋊C8)C2212yes—
21C2×#6389—22no—
22C2×Dic7⋊C8—22no—
23#89491—24no—
24#89491C2218yescomplemented
25C7×#323C2214yes—
26#89320C2214yes—
27#89264C2218yescomplemented
28C2×#1464—71nomaximal, Sylow
29C25×C7C2×C411yescharacteristic
30C23×C4×C7C2×C411yescharacteristic
31C23×C4×C7C2311yescharacteristic
32C23×Dic7—24no—
33C23×Dic7—22no—
34C23×Dic7—21no—
35C23×Dic7—21no—
36C23×Dic7—24no—
37C23×Dic7C2×C414yes—
38C23×Dic7C2×C411yescharacteristic
39C23×Dic7C2×C411yescharacteristic
40C23×Dic7C2×C411yescharacteristic
41C23×Dic7C2×C411yescharacteristic
42C22×C7×C8—22no—
43C2×C7×C22⋊C4—22no—
44C2×C7×C22⋊C4—22no—
45C2×C7×C22⋊C4C2×C412yes—
46C2×C7×C22⋊C4C2312yes—
47C2×C22⋊Dic7—22no—
48C2×C22⋊Dic7—22no—
49C2×C22⋊Dic7C2×C414yes—
50C2×Dic7⋊C4—22no—
51C2×Dic7⋊C4—22no—
52C2×Dic7⋊C4—22no—
53C2×Dic7⋊C4—22no—
54C2×Dic7⋊C4C2×C412yes—
55C2×Dic7⋊C4C2×C414yes—
56C2×Dic7⋊C4C2312yes—
57C2×C4×Dic7—22no—
58C2×C4×Dic7—21no—
59C2×C4×Dic7—21no—
60C2×C4×Dic7C2×C414yes—
61C2×C4×Dic7C2×C412yes—
62C2×C4×Dic7D412yes—
63C2×C4×Dic7D412yes—
64C2×C4×Dic7D414yes—
65C2×C4×Dic7C2312yes—
66C22×C7⋊C8—22no—
67#6440—28no—
68#6440—28no—
69#6440—28no—
70#6440—28no—
71C7×C22⋊C8—22no—
72C7×C22⋊C8C2314yes—
73C22⋊(C7⋊C8)—22no—
74C22⋊(C7⋊C8)C2314yes—
75#6389—28no—
76Dic7⋊C8—28no—
77C22×#117—71no—
78C2×#432—72no—
79#1464—78no—
80C2×#324—72no—
81C2×#323—71no—
82C2×#323D711yescharacteristic
83C24×C7—21no—
84C24×C7—21no—
85C24×C7—22no—
86C24×C7—42no—
87C24×C7—42no—
88C24×C7M1614yes—
89C24×C7C22×C411yescharacteristic
90C24×C7C22×C412yes—
91C22×C4×C7—21no—
92C22×C4×C7—21no—
93C22×C4×C7—42no—
94C22×C4×C7—42no—
95C22×C4×C7C22×C412yes—
96C22×C4×C7C22×C411yescharacteristic
97C22×C4×C7C2×D412yes—
98C22×C4×C7C2×D412yes—
99C22×C4×C7C2411yescharacteristic
100C22×Dic7—216no—
101C22×Dic7—28no—
102C22×Dic7—28no—
103C22×Dic7—21no—
104C22×Dic7—21no—
105C22×Dic7—28no—
106C22×Dic7—22no—
107C22×Dic7—22no—
108C22×Dic7—22no—
109C22×Dic7—24no—
110C22×Dic7—24no—
111C22×Dic7—28no—
112C22×Dic7—21no—
113C22×Dic7—21no—
114C22×Dic7—42no—
115C22×Dic7—42no—
116C22×Dic7C22⋊C412yes—
117C22×Dic7C22⋊C411yescharacteristic
118C22×Dic7C22⋊C411yescharacteristic
119C22×Dic7C22⋊C412yes—
120C22×Dic7C22⋊C412yes—
121C22×Dic7M1614yes—
122C22×Dic7C22×C412yes—
123C22×Dic7C22×C412yes—
124C22×Dic7C22×C412yes—
125C22×Dic7C22×C412yes—
126C2×C7×C8—24no—
127C2×C7×C8—44no—
128C7×C22⋊C4—24no—
129C7×C22⋊C4—24no—
130C22⋊Dic7—28no—
131Dic7⋊C4—24no—
132Dic7⋊C4—24no—
133Dic7⋊C4—28no—
134C4×Dic7—24no—
135C4×Dic7—24no—
136C4×Dic7C22⋊C414yes—
137C4×Dic7C22⋊C414yes—
138C4×Dic7C2×D414yes—
139C4×Dic7C2×D414yes—
140C2×C7⋊C8—24no—
141C2×C7⋊C8—44no—
142C24×C4—71no—
143C2×#117—74no—
144C2×#117—74no—
145C2×#117—142no—
146C2×#117—142no—
147C2×#117—144no—
148C22×C4⋊C4—71no—
149C22×C4⋊C4—71no—
150C22×C22⋊C4—71no—
151C22×C22⋊C4C2×D711yescharacteristic
152C22×C42—71no—
153C22×C42—71no—
154#432—78no—
155#432—144no—
156C2×C4⋊C8—142no—
157C2×C22⋊C8—72no—
158C2×C22⋊C8C2×D712yes—
159C2×#97—142no—
160#324—78no—
161#323—74no—
162#323C2×D714yes—
163C23×C7—22no—
164C23×C7—22no—
165C23×C7—22no—
166C23×C7—22no—
167C23×C7—24no—
168C23×C7—24no—
169C23×C7—48no—
170C23×C7—42no—
171C23×C7—42no—
172C23×C7—42no—
173C23×C7—42no—
174C23×C7—48no—
175C23×C7—42no—
176C23×C7—42no—
177C23×C7C2×C22⋊C411yescharacteristic
178C23×C7C2×C22⋊C411yescharacteristic
179C23×C7C2×M1612yes—
180C23×C7C2×M1614yes—
181C23×C7C2×M1612yes—
182C23×C7C23×C411yescharacteristic
183C2×C4×C7—24no—
184C2×C4×C7—22no—
185C2×C4×C7—41no—
186C2×C4×C7—42no—
187C2×C4×C7—41no—
188C2×C4×C7—42no—
189C2×C4×C7—42no—
190C2×C4×C7—42no—
191C2×C4×C7C2×C22⋊C412yes—
192C2×C4×C7C22×D412yes—
193C2×Dic7—216no—
194C2×Dic7—216no—
195C2×Dic7—22no—
196C2×Dic7—22no—
197C2×Dic7—22no—
198C2×Dic7—22no—
199C2×Dic7—24no—
200C2×Dic7—22no—
201C2×Dic7—22no—
202C2×Dic7—24no—
203C2×Dic7—24no—
204C2×Dic7—24no—
205C2×Dic7—22no—
206C2×Dic7—42no—
207C2×Dic7—42no—
208C2×Dic7—42no—
209C2×Dic7—42no—
210C2×Dic7—42no—
211C2×Dic7C2×C22⋊C412yes—
212C2×Dic7C2×C22⋊C412yes—
213C2×Dic7C2×C22⋊C414yes—
214C2×Dic7C2×M1614yes—
215C7×C8—44no—
216C7⋊C8—44no—
217C25C4×D711yescharacteristic
218C23×C4—71no—
219C23×C4—71no—
220C23×C4—71no—
221C23×C4—74no—
222C23×C4—71no—
223C23×C4—142no—
224C23×C4—141no—
225C23×C4—141no—
226C23×C4—144no—
227C23×C4—144no—
228C23×C4C4×D711yescharacteristic
229C23×C4C22×D711yescharacteristic
230C22×C8—22no—
231C22×C8—142no—
232#117—148no—
233#117—148no—
234#117—148no—
235#117—148no—
236C2×C4⋊C4—74no—
237C2×C4⋊C4—72no—
238C2×C4⋊C4—72no—
239C2×C4⋊C4—142no—
240C2×C4⋊C4—142no—
241C2×C4⋊C4—142no—
242C2×C4⋊C4—142no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—74no—
246C2×C22⋊C4—142no—
247C2×C22⋊C4—142no—
248C2×C22⋊C4C4×D712yes—
249C2×C22⋊C4C22×D712yes—
250C2×C42—72no—
251C2×C42—72no—
252C2×C42—72no—
253C2×C42—74no—
254C2×C42—72no—
255C2×C42—74no—
256C2×C42—142no—
257C2×C42—141no—
258C2×C42—141no—
259C4⋊C8—148no—
260C22⋊C8—22no—
261C22⋊C8—74no—
262C22⋊C8—142no—
263C22⋊C8C22×D714yes—
264#97—148no—
265C22×C7—21no—
266C22×C7—21no—
267C22×C7—21no—
268C22×C7—21no—
269C22×C7—24no—
270C22×C7—24no—
271C22×C7—24no—
272C22×C7—44no—
273C22×C7—44no—
274C22×C7—48no—
275C22×C7—42no—
276C22×C7—42no—
277C22×C7—48no—
278C22×C7#40712yes—
279C22×C7#40712yes—
280C22×C7#41012yes—
281C22×C7#41312yes—
282C22×C7C22×C22⋊C411yescharacteristic
283C22×C7C22×M1611yescharacteristic
284C22×C7C22×M1611yescharacteristic
285C4×C7—22no—
286C4×C7—22no—
287C4×C7—42no—
288Dic7—22no—
289Dic7—22no—
290Dic7—24no—
291Dic7—24no—
292Dic7—42no—
293C24—21no—
294C24—21no—
295C24—22no—
296C24—42no—
297C24—42no—
298C24#113114yes—
299C24C2×C4×D711yescharacteristic
300C24C2×C4×D712yes—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—72no—
306C22×C4—71no—
307C22×C4—71no—
308C22×C4—72no—
309C22×C4—74no—
310C22×C4—72no—
311C22×C4—72no—
312C22×C4—72no—
313C22×C4—72no—
314C22×C4—72no—
315C22×C4—144no—
316C22×C4—144no—
317C22×C4—148no—
318C22×C4—1416no—
319C22×C4—148no—
320C22×C4—148no—
321C22×C4—141no—
322C22×C4—141no—
323C22×C4—148no—
324C22×C4—142no—
325C22×C4—142no—
326C22×C4—142no—
327C22×C4—141no—
328C22×C4—141no—
329C22×C4—282no—
330C22×C4—282no—
331C22×C4C2×C4×D712yes—
332C22×C4C2×C4×D711yescharacteristic
333C22×C4D4×D712yes—
334C22×C4D4×D712yes—
335C22×C4C23×D711yescharacteristic
336C2×C8—24no—
337C2×C8—44no—
338C2×C8—144no—
339C2×C8—284no—
340C4⋊C4—148no—
341C4⋊C4—144no—
342C4⋊C4—144no—
343C22⋊C4—24no—
344C22⋊C4—24no—
345C22⋊C4—148no—
346C42—74no—
347C42—74no—
348C42—74no—
349C42—74no—
350C42—144no—
351C42—144no—
352C2×C7—21no—
353C2×C7—21no—
354C2×C7—22no—
355C2×C7—44no—
356C2×C7#146414yescomplemented
357C2×C7C2×#40711yescharacteristic
358C2×C7C2×#41011yescharacteristic
359C2×C7C2×#41311yescharacteristic
360C23—22no—
361C23—22no—
362C23—22no—
363C23—22no—
364C23—24no—
365C23—24no—
366C23—48no—
367C23—42no—
368C23—42no—
369C23—48no—
370C23—42no—
371C23—42no—
372C23—42no—
373C23—42no—
374C23D7×C22⋊C411yescharacteristic
375C23D7×C22⋊C411yescharacteristic
376C23C2×#113112yes—
377C23C2×#113114yes—
378C23D7×M1612yes—
379C23C22×C4×D711yescharacteristic
380C2×C4—24no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—72no—
389C2×C4—72no—
390C2×C4—74no—
391C2×C4—74no—
392C2×C4—1416no—
393C2×C4—1416no—
394C2×C4—142no—
395C2×C4—142no—
396C2×C4—142no—
397C2×C4—142no—
398C2×C4—144no—
399C2×C4—144no—
400C2×C4—142no—
401C2×C4—142no—
402C2×C4—144no—
403C2×C4—144no—
404C2×C4—142no—
405C2×C4—282no—
406C2×C4—282no—
407C2×C4—282no—
408C2×C4—282no—
409C2×C4—282no—
410C2×C4D7×C22⋊C412yes—
411C2×C4C2×D4×D712yes—
412C8—44no—
413C8—284no—
414C7C2×#146411yescharacteristic, complemented, Sylow
415C22—24no—
416C22—24no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—24no—
422C22—44no—
423C22—44no—
424C22—48no—
425C22—48no—
426C22—42no—
427C22—42no—
428C22#8949812yes—
429C22#8949812yes—
430C22#8951212yes—
431C22#8951712yes—
432C22C2×D7×C22⋊C411yescharacteristic
433C22C22×#113111yescharacteristic
434C22C2×D7×M1611yescharacteristic
435C4—22no—
436C4—22no—
437C4—42no—
438C4—144no—
439C4—142no—
440C4—142no—
441C4—144no—
442C4—282no—
443C2—21no—
444C2—21no—
445C2—22no—
446C2—44no—
447C2#1172585614yesdirect product factor
448C2C2×#8949811yescharacteristic
449C2C2×#8951211yescharacteristic
450C2C2×#8951711yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC23×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#323C2
socleC23×C7C2×C22⋊C4
prime radicalC25×C7C2×C4
cosocleC22×C4×C7C24
hypercenterC2×#323D7
hypocenterC7C2×#1464
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. C2×#89491C2semidirect
5. C2×#89264C2semidirect
6. #11725856C2direct (N × H)
24. #89491C22semidirect
27. #89264C22semidirect
356. C2×C7#1464semidirect
414. C7C2×#1464semidirect
447. C2#11725856direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64402
C2×#894912
C2×C7×#3232
C2×#893202
C2×#892642
#117258562
C2×#14647