Finite Group Databasebeta

← C2×#11739184 #14223069

Subgroups — C2×#11739184 #14223069

Order 1792.

2118 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×C4⋊Q8C211yesmaximal, characteristic
2C2×#90379C211yesmaximal, characteristic
3C2×C7×#491C211yesmaximal, characteristic, complemented
4C2×#89854C211yesmaximal, characteristic, complemented
5C2×#89841C211yesmaximal, characteristic, complemented
6#11739184C2116yesmaximal, direct product factor
7C2×#89574C214yesmaximal
8C2×#89564C214yesmaximal, complemented
9C2×#89475C211yesmaximal, characteristic, complemented
10C2×#89479C211yesmaximal, characteristic
11C22×Q8×D7C2212yes—
12C2×C7×C4⋊Q8C2211yescharacteristic
13C2×C7×#125C2211yescharacteristic
14C2×#6507C2212yes—
15C22×#1131C2212yes—
16D7×C4⋊Q8—24no—
17D7×C4⋊Q8C2218yes—
18#90379—24no—
19#90379C2218yes—
20C2×#6459—22no—
21C2×#6455C2212yes—
22C2×D7×C4⋊C4—22no—
23C2×#6451—22no—
24C2×#6451C2212yes—
25C2×#6450—22no—
26C2×C42×D7C2211yescharacteristic
27C2×#6433C2211yescharacteristic
28C2×#6432C2211yescharacteristic
29C7×#491C2218yescomplemented
30C2×C7×#103C2214yes—
31C2×C7×#97C2211yescharacteristic
32C2×#6409C2214yes—
33C2×#6390C2214yes—
34C2×C8×Dic7C2212yes—
35#89854C2218yescomplemented
36#89841C2218yescomplemented
37C2×#6384C2214yes—
38C2×#6377C2211yescharacteristic
39#89574C22132yes—
40#89564C22132yescomplemented
41#89479C2218yes—
42#89475C2218yescomplemented
43C2×#3139—71nomaximal, Sylow
44C22×C7×Q8C2312yes—
45C2×Q8×D7—24no—
46C2×Q8×D7—216no—
47C2×Q8×D7C2318yes—
48C22×C4×D7—22no—
49C22×C4×D7D412yes—
50C22×C4×D7C2311yescharacteristic
51C22×Dic14—22no—
52C22×Dic14—22no—
53C22×Dic14C2312yes—
54C22×C7×C8C2312yes—
55C7×C4⋊Q8—22no—
56C7×C4⋊Q8C2314yes—
57C7×#125—22no—
58C7×#125C2314yes—
59C2×C7×C4⋊C4—22no—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4C2312yes—
62C2×C42×C7C2311yescharacteristic
63#6507—24no—
64#6507C2318yes—
65C2×(C2×D7)⋊C4—22no—
66C2×C4⋊Dic7—22no—
67C2×C4⋊Dic7C2312yes—
68C2×Dic7⋊C4—22no—
69C2×Dic7⋊C4—22no—
70C2×Dic7⋊C4—24no—
71C2×C4×Dic7—22no—
72C2×C4×Dic7D412yes—
73C2×C4×Dic7C2311yescharacteristic
74C22×C7⋊C8C2312yes—
75C2×#1131—28no—
76C2×#1131C2318yes—
77#6459—216no—
78#6455—24no—
79#6455C2318yes—
80D7×C4⋊C4—216no—
81#6451—24no—
82#6451—216no—
83#6451C2318yes—
84#6450—216no—
85C42×D7D414yes—
86C42×D7C2314yes—
87#6433—22no—
88#6433C2314yes—
89#6432—22no—
90#6432C2314yes—
91C7×#103C23116yes—
92C7×#97C2314yes—
93#6409C23116yes—
94#6390C23116yes—
95C8×Dic7C2318yes—
96#6384C23116yes—
97#6377C2314yes—
98C2×#533—71no—
99C22×C4⋊Q8—71no—
100#3139—716no—
101C2×#491—71no—
102C2×#491—71no—
103C2×#491—71no—
104C2×#491D711yescharacteristic, complemented
105C2×#487—74no—
106C2×#419—74no—
107C2×C4×M16—71no—
108C23×D7C2×D411yescharacteristic
109C2×C7×Q8—22no—
110C2×C7×Q8—28no—
111C2×C7×Q8C2414yes—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7C2×D412yes—
115C22×C4×C7C2411yescharacteristic
116C22×Dic7—22no—
117C22×Dic7—22no—
118C22×Dic7C2×D411yescharacteristic
119C22×Dic7C2×D412yes—
120Q8×D7—232no—
121Q8×D7—416no—
122C2×C4×D7—28no—
123C2×C4×D7—28no—
124C2×C4×D7—48no—
125C2×C4×D7C2×D418yes—
126C2×C4×D7C2×D412yes—
127C2×C4×D7#4118yes—
128C2×C4×D7C2412yes—
129C2×Dic14—28no—
130C2×Dic14—22no—
131C2×Dic14—28no—
132C2×Dic14—28no—
133C2×Dic14—48no—
134C2×Dic14—48no—
135C2×Dic14C2414yes—
136C2×C7×C8—24no—
137C2×C7×C8C2414yes—
138C7×C4⋊C4—28no—
139C7×C4⋊C4—28no—
140C7×C4⋊C4—22no—
141C7×C4⋊C4C2414yes—
142C42×C7C2×D412yes—
143C42×C7C2412yes—
144(C2×D7)⋊C4—28no—
145C4⋊Dic7—28no—
146C4⋊Dic7—22no—
147C4⋊Dic7C2414yes—
148Dic7⋊C4—28no—
149Dic7⋊C4—28no—
150Dic7⋊C4—216no—
151C4×Dic7—28no—
152C4×Dic7C2×D412yes—
153C4×Dic7C2×D418yes—
154C4×Dic7C2412yes—
155C2×C7⋊C8—24no—
156C2×C7⋊C8C2414yes—
157#1131—216no—
158C23×Q8—72no—
159C22×M16—72no—
160#533—78no—
161#533—144no—
162C2×C4⋊Q8—72no—
163C2×C4⋊Q8—72no—
164C2×C4⋊Q8—78no—
165C2×C4⋊Q8—71no—
166C2×C4⋊Q8—142no—
167C2×C4⋊Q8—144no—
168C2×C4⋊Q8C2×D711yescharacteristic
169C2×#125—71no—
170C2×#125C2×D711yescharacteristic
171C2×C22⋊Q8—142no—
172C2×C4×Q8—142no—
173C2×#117—72no—
174C22×C4⋊C4—142no—
175C22×C42—71no—
176#491—78no—
177#491—78no—
178#491—78no—
179#491C2×D718yescomplemented
180#487—732no—
181#419—732no—
182C2×#103—74no—
183C2×#103—74no—
184C2×#103—74no—
185C2×#103C2×D714yes—
186C4×M16—78no—
187C2×#97—71no—
188C2×#97C2×D711yescharacteristic
189C2×C4×C8—72no—
190C23×C7C22×D411yescharacteristic
191C22×D7—24no—
192C22×D7#12414yes—
193C22×D7C22×D412yes—
194C7×Q8—28no—
195C7×Q8—44no—
196C2×C4×C7—24no—
197C2×C4×C7—24no—
198C2×C4×C7—24no—
199C2×C4×C7—44no—
200C2×C4×C7—44no—
201C2×C4×C7C22×D414yes—
202C2×C4×C7C22×D411yescharacteristic
203C2×C4×C7C2×#4114yes—
204C2×C4×C7C2511yescharacteristic
205C2×Dic7—24no—
206C2×Dic7—24no—
207C2×Dic7—44no—
208C2×Dic7—44no—
209C2×Dic7#12414yes—
210C2×Dic7#13718yes—
211C2×Dic7C22×D412yes—
212C2×Dic7C22×D414yes—
213C4×D7—216no—
214C4×D7—416no—
215C4×D7#12418yes—
216C4×D7C2×#4118yes—
217Dic14—28no—
218Dic14—44no—
219Dic14—416no—
220Dic14—416no—
221C7×C8—24no—
222C7⋊C8—24no—
223C22×Q8—78no—
224C22×Q8—72no—
225C22×Q8—142no—
226C22×Q8—142no—
227C22×Q8—144no—
228C22×Q8—1416no—
229C22×Q8C22×D712yes—
230C23×C4—71no—
231C23×C4—72no—
232C23×C4—142no—
233C2×M16—78no—
234C2×M16—148no—
235C22×C8—72no—
236C22×C8C22×D712yes—
237C4⋊Q8—22no—
238C4⋊Q8—78no—
239C4⋊Q8—78no—
240C4⋊Q8—74no—
241C4⋊Q8—1416no—
242C4⋊Q8—144no—
243C4⋊Q8—144no—
244C4⋊Q8—142no—
245C4⋊Q8C22×D714yes—
246#125—22no—
247#125—74no—
248#125—142no—
249#125C22×D714yes—
250C22⋊Q8—1416no—
251C4×Q8—1416no—
252#117—78no—
253#117—144no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—72no—
257C2×C4⋊C4—1416no—
258C2×C4⋊C4—144no—
259C2×C4⋊C4—142no—
260C2×C4⋊C4—142no—
261C2×C4⋊C4—142no—
262C2×C4⋊C4C22×D712yes—
263C2×C22⋊C4—142no—
264C2×C42—72no—
265C2×C42—71no—
266C2×C42—74no—
267C2×C42—74no—
268C2×C42—142no—
269C2×C42C22×D711yescharacteristic
270#103—716no—
271#103—716no—
272#103—716no—
273#103C22×D7116yes—
274#97—74no—
275#97C22×D714yes—
276C4×C8—78no—
277C22×C7C2×#12412yes—
278C22×C7C2×#13714yes—
279C22×C7C23×D411yescharacteristic
280C2×D7—28no—
281C2×D7—24no—
282C2×D7C2×#12414yes—
283C4×C7—24no—
284C4×C7—44no—
285C4×C7—44no—
286C4×C7C2×#12412yes—
287C4×C7C22×#4112yes—
288Dic7—44no—
289Dic7—44no—
290Dic7C2×#12414yes—
291Dic7C2×#13718yes—
292C24—71no—
293C2×Q8—22no—
294C2×Q8—28no—
295C2×Q8—74no—
296C2×Q8—148no—
297C2×Q8—148no—
298C2×Q8—1432no—
299C2×Q8—142no—
300C2×Q8—148no—
301C2×Q8—288no—
302C2×Q8—288no—
303C2×Q8—2816no—
304C2×Q8C23×D714yes—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—71no—
308C22×C4—72no—
309C22×C4—72no—
310C22×C4—78no—
311C22×C4—72no—
312C22×C4—78no—
313C22×C4—148no—
314C22×C4—148no—
315C22×C4—142no—
316C22×C4—142no—
317C22×C4—288no—
318C22×C4D4×D712yes—
319C22×C4C23×D711yescharacteristic
320M16—1416no—
321C2×C8—24no—
322C2×C8—74no—
323C2×C8—144no—
324C2×C8C23×D714yes—
325C4⋊C4—28no—
326C4⋊C4—28no—
327C4⋊C4—22no—
328C4⋊C4—74no—
329C4⋊C4—1416no—
330C4⋊C4—148no—
331C4⋊C4—148no—
332C4⋊C4—142no—
333C4⋊C4—148no—
334C4⋊C4C23×D714yes—
335C22⋊C4—148no—
336C42—78no—
337C42—72no—
338C42—72no—
339C42—148no—
340C42D4×D712yes—
341C42C23×D712yes—
342C2×C7#313914yescomplemented
343C2×C7C22×#12411yescharacteristic
344C2×C7C22×#13712yes—
345D7—24no—
346C23—72no—
347C23—74no—
348C23—144no—
349C23C2×D4×D711yescharacteristic
350Q8—28no—
351Q8—44no—
352Q8—148no—
353Q8—2816no—
354Q8—2816no—
355Q8—284no—
356C2×C4—24no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—78no—
362C2×C4—72no—
363C2×C4—74no—
364C2×C4—74no—
365C2×C4—78no—
366C2×C4—78no—
367C2×C4—1416no—
368C2×C4—144no—
369C2×C4—144no—
370C2×C4—2816no—
371C2×C4—284no—
372C2×C4—284no—
373C2×C4C2×D4×D714yes—
374C2×C4C2×D4×D711yescharacteristic
375C2×C4D7×#4114yes—
376C2×C4C24×D711yescharacteristic
377C8—24no—
378C8—144no—
379C7C2×#313911yescharacteristic, complemented, Sylow
380C22—74no—
381C22—144no—
382C22—148no—
383C22D7×#12412yes—
384C22D7×#13714yes—
385C22C22×D4×D711yescharacteristic
386C4—24no—
387C4—44no—
388C4—44no—
389C4—78no—
390C4—74no—
391C4—284no—
392C4—284no—
393C4D7×#12412yes—
394C4C2×D7×#4112yes—
395C2—144no—
396C2#1173918414yesdirect product factor
397C2C2×D7×#12411yescharacteristic
398C2C2×D7×#13712yes—
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#491C2
socleC23×C7C22×D4
prime radicalC23×D7C2×D4
hypercenterC2×#491D7
hypocenterC7C2×#3139
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
3. C2×C7×#491C2semidirect
4. C2×#89854C2semidirect
5. C2×#89841C2semidirect
6. #11739184C2direct (N × H)
8. C2×#89564C2semidirect
9. C2×#89475C2semidirect
29. C7×#491C22semidirect
35. #89854C22semidirect
36. #89841C22semidirect
40. #89564C22semidirect
42. #89475C22semidirect
104. C2×#491D7semidirect
179. #491C2×D7semidirect
342. C2×C7#3139semidirect
379. C7C2×#3139semidirect
396. C2#11739184direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D7×C4⋊Q82
C2×#903792
C2×C7×#4912
C2×#898542
C2×#898412
#117391842
C2×#895742
C2×#895642
C2×#894752
C2×#894792
C2×#31397