Finite Group Databasebeta

← C2×#11729326 #13319642

Subgroups — C2×#11729326 #13319642

Order 1792.

1326 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#117C211yesmaximal, characteristic
2C2×#89698C212yesmaximal, complemented
3#11729326C218yesmaximal, direct product factor
4C2×#89323C212yesmaximal, complemented
5C2×#89320C212yesmaximal
6C24×C4×C7C411yescharacteristic
7C2×C7×#117—22no—
8C2×C7×#117—22no—
9C2×C7×#117—24no—
10C2×C7×#117C414yes—
11C2×C7×#117C2214yes—
12C22×C7×C4⋊C4C411yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C22⋊C4C411yescharacteristic
15C22×C7×C22⋊C4C2211yescharacteristic
16C22×C42×C7C411yescharacteristic
17C22×C42×C7C2211yescharacteristic
18C2×C22⋊(C7⋊C8)C2214yes—
19#89698—24no—
20#89698C2218yescomplemented
21C2×C4⋊(C7⋊C8)—22no—
22C2×#6377—22no—
23#89323C2218yescomplemented
24#89320C2218yes—
25C2×#1464—71nomaximal, Sylow
26C25×C7C2×C411yescharacteristic
27C23×C4×C7—24no—
28C23×C4×C7—22no—
29C23×C4×C7—21no—
30C23×C4×C7—21no—
31C23×C4×C7—24no—
32C23×C4×C7C2×C414yes—
33C23×C4×C7C2×C411yescharacteristic
34C23×C4×C7C2×C411yescharacteristic
35C23×C4×C7C2×C411yescharacteristic
36C23×C4×C7C2×C411yescharacteristic
37C23×C4×C7C2×C411yescharacteristic
38C23×C4×C7C2311yescharacteristic
39C7×#117—28no—
40C7×#117—28no—
41C7×#117—28no—
42C7×#117—28no—
43C2×C7×C4⋊C4—22no—
44C2×C7×C4⋊C4—22no—
45C2×C7×C4⋊C4—22no—
46C2×C7×C4⋊C4—22no—
47C2×C7×C4⋊C4C2×C414yes—
48C2×C7×C4⋊C4C2×C412yes—
49C2×C7×C4⋊C4C2312yes—
50C2×C7×C22⋊C4—22no—
51C2×C7×C22⋊C4—22no—
52C2×C7×C22⋊C4—22no—
53C2×C7×C22⋊C4—22no—
54C2×C7×C22⋊C4C2×C414yes—
55C2×C7×C22⋊C4C2×C412yes—
56C2×C7×C22⋊C4C2312yes—
57C2×C42×C7—22no—
58C2×C42×C7—21no—
59C2×C42×C7—21no—
60C2×C42×C7C2×C414yes—
61C2×C42×C7C2×C412yes—
62C2×C42×C7D412yes—
63C2×C42×C7D412yes—
64C2×C42×C7D414yes—
65C2×C42×C7C2312yes—
66C22×C7⋊C8—24no—
67C22⋊(C7⋊C8)—24no—
68C22⋊(C7⋊C8)C2318yes—
69C4⋊(C7⋊C8)—28no—
70#6377—28no—
71C22×#117D711yescharacteristic
72C2×#432—72no—
73#1464—78no—
74C2×#324—72no—
75C2×#323—72no—
76C24×C7—21no—
77C24×C7—21no—
78C24×C7—22no—
79C24×C7—42no—
80C24×C7—42no—
81C24×C7M1614yes—
82C24×C7C22×C411yescharacteristic
83C24×C7C22×C412yes—
84C22×C4×C7—216no—
85C22×C4×C7—28no—
86C22×C4×C7—28no—
87C22×C4×C7—21no—
88C22×C4×C7—21no—
89C22×C4×C7—28no—
90C22×C4×C7—22no—
91C22×C4×C7—22no—
92C22×C4×C7—22no—
93C22×C4×C7—24no—
94C22×C4×C7—24no—
95C22×C4×C7—28no—
96C22×C4×C7—21no—
97C22×C4×C7—21no—
98C22×C4×C7—21no—
99C22×C4×C7—21no—
100C22×C4×C7—42no—
101C22×C4×C7—42no—
102C22×C4×C7—42no—
103C22×C4×C7—42no—
104C22×C4×C7C22⋊C412yes—
105C22×C4×C7C22⋊C411yescharacteristic
106C22×C4×C7C22⋊C411yescharacteristic
107C22×C4×C7C22⋊C412yes—
108C22×C4×C7C22⋊C412yes—
109C22×C4×C7M1614yes—
110C22×C4×C7C22×C412yes—
111C22×C4×C7C22×C412yes—
112C22×C4×C7C22×C412yes—
113C22×C4×C7C22×C412yes—
114C22×C4×C7C22×C411yescharacteristic
115C22×C4×C7C22×C412yes—
116C22×C4×C7C2×D412yes—
117C22×C4×C7C2×D412yes—
118C22×C4×C7C2411yescharacteristic
119C7×C4⋊C4—24no—
120C7×C4⋊C4—28no—
121C7×C4⋊C4—24no—
122C7×C22⋊C4—24no—
123C7×C22⋊C4—28no—
124C7×C22⋊C4—24no—
125C42×C7—24no—
126C42×C7—24no—
127C42×C7C22⋊C414yes—
128C42×C7C22⋊C414yes—
129C42×C7C2×D414yes—
130C42×C7C2×D414yes—
131C2×C7⋊C8—28no—
132C2×C7⋊C8—48no—
133C24×C4Dic711yescharacteristic
134C2×#117—22no—
135C2×#117—22no—
136C2×#117—24no—
137C2×#117Dic714yes—
138C2×#117C2×D714yes—
139C22×C4⋊C4Dic711yescharacteristic
140C22×C4⋊C4C2×D711yescharacteristic
141C22×C22⋊C4Dic711yescharacteristic
142C22×C22⋊C4C2×D711yescharacteristic
143C22×C42Dic711yescharacteristic
144C22×C42C2×D711yescharacteristic
145#432—78no—
146#432—144no—
147C2×C4⋊C8—142no—
148C2×C22⋊C8—74no—
149C2×#97—142no—
150#324—78no—
151#323—78no—
152C23×C7—22no—
153C23×C7—22no—
154C23×C7—22no—
155C23×C7—22no—
156C23×C7—24no—
157C23×C7—24no—
158C23×C7—48no—
159C23×C7—42no—
160C23×C7—42no—
161C23×C7—42no—
162C23×C7—42no—
163C23×C7—48no—
164C23×C7—42no—
165C23×C7—42no—
166C23×C7C2×C22⋊C411yescharacteristic
167C23×C7C2×C22⋊C411yescharacteristic
168C23×C7C2×M1612yes—
169C23×C7C2×M1612yes—
170C23×C7C2×M1614yes—
171C23×C7C23×C411yescharacteristic
172C2×C4×C7—216no—
173C2×C4×C7—216no—
174C2×C4×C7—22no—
175C2×C4×C7—22no—
176C2×C4×C7—22no—
177C2×C4×C7—22no—
178C2×C4×C7—24no—
179C2×C4×C7—22no—
180C2×C4×C7—22no—
181C2×C4×C7—24no—
182C2×C4×C7—24no—
183C2×C4×C7—24no—
184C2×C4×C7—24no—
185C2×C4×C7—22no—
186C2×C4×C7—22no—
187C2×C4×C7—42no—
188C2×C4×C7—41no—
189C2×C4×C7—42no—
190C2×C4×C7—42no—
191C2×C4×C7—41no—
192C2×C4×C7—42no—
193C2×C4×C7—42no—
194C2×C4×C7—42no—
195C2×C4×C7—42no—
196C2×C4×C7—42no—
197C2×C4×C7—42no—
198C2×C4×C7C2×C22⋊C412yes—
199C2×C4×C7C2×C22⋊C412yes—
200C2×C4×C7C2×C22⋊C412yes—
201C2×C4×C7C2×C22⋊C414yes—
202C2×C4×C7C2×M1614yes—
203C2×C4×C7C22×D412yes—
204C7⋊C8—48no—
205C25C2×Dic711yescharacteristic
206C23×C4—24no—
207C23×C4—24no—
208C23×C4—22no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4C2×Dic714yes—
212C23×C4C2×Dic711yescharacteristic
213C23×C4C2×Dic711yescharacteristic
214C23×C4C2×Dic711yescharacteristic
215C23×C4C2×Dic711yescharacteristic
216C23×C4C2×Dic711yescharacteristic
217C23×C4C22×D711yescharacteristic
218C22×C8—144no—
219#117—28no—
220#117—28no—
221#117—28no—
222#117—28no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4C2×Dic714yes—
228C2×C4⋊C4C2×Dic712yes—
229C2×C4⋊C4C22×D712yes—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—22no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4C2×Dic714yes—
235C2×C22⋊C4C2×Dic712yes—
236C2×C22⋊C4C22×D712yes—
237C2×C42—22no—
238C2×C42—21no—
239C2×C42—21no—
240C2×C42C2×Dic714yes—
241C2×C42C2×Dic712yes—
242C2×C42C22⋊D712yes—
243C2×C42C22⋊D712yes—
244C2×C42C22⋊D714yes—
245C2×C42C22×D712yes—
246C4⋊C8—148no—
247C22⋊C8—78no—
248C22⋊C8—144no—
249#97—148no—
250C22×C7—21no—
251C22×C7—21no—
252C22×C7—21no—
253C22×C7—21no—
254C22×C7—24no—
255C22×C7—24no—
256C22×C7—24no—
257C22×C7—44no—
258C22×C7—44no—
259C22×C7—48no—
260C22×C7—42no—
261C22×C7—42no—
262C22×C7—48no—
263C22×C7#40712yes—
264C22×C7#40712yes—
265C22×C7#41012yes—
266C22×C7#41312yes—
267C22×C7C22×C22⋊C411yescharacteristic
268C22×C7C22×M1611yescharacteristic
269C22×C7C22×M1611yescharacteristic
270C4×C7—22no—
271C4×C7—22no—
272C4×C7—24no—
273C4×C7—22no—
274C4×C7—22no—
275C4×C7—24no—
276C4×C7—42no—
277C4×C7—42no—
278C24—22no—
279C24—21no—
280C24—21no—
281C24—42no—
282C24—42no—
283C24#113614yes—
284C24C22×Dic711yescharacteristic
285C24C22×Dic712yes—
286C22×C4—216no—
287C22×C4—28no—
288C22×C4—28no—
289C22×C4—28no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—28no—
296C22×C4—24no—
297C22×C4—24no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4#113614yes—
307C22×C4C22⋊Dic712yes—
308C22×C4C22⋊Dic711yescharacteristic
309C22×C4C22⋊Dic711yescharacteristic
310C22×C4C22⋊Dic712yes—
311C22×C4C22⋊Dic712yes—
312C22×C4C22×Dic712yes—
313C22×C4C22×Dic712yes—
314C22×C4C22×Dic712yes—
315C22×C4C22×Dic712yes—
316C22×C4C22×Dic711yescharacteristic
317C22×C4C22×Dic712yes—
318C22×C4C2×C22⋊D712yes—
319C22×C4C2×C22⋊D712yes—
320C22×C4C23×D711yescharacteristic
321C2×C8—148no—
322C2×C8—288no—
323C4⋊C4—24no—
324C4⋊C4—28no—
325C4⋊C4—24no—
326C22⋊C4—24no—
327C22⋊C4—28no—
328C22⋊C4—24no—
329C42—24no—
330C42—24no—
331C42C22⋊Dic714yes—
332C42C22⋊Dic714yes—
333C42C2×C22⋊D714yes—
334C42C2×C22⋊D714yes—
335C2×C7—21no—
336C2×C7—21no—
337C2×C7—22no—
338C2×C7—44no—
339C2×C7#146414yescomplemented
340C2×C7C2×#40711yescharacteristic
341C2×C7C2×#41011yescharacteristic
342C2×C7C2×#41311yescharacteristic
343C23—22no—
344C23—22no—
345C23—22no—
346C23—24no—
347C23—24no—
348C23—22no—
349C23—48no—
350C23—42no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23—48no—
355C23—42no—
356C23—42no—
357C23C2×#113612yes—
358C23C2×#113612yes—
359C23C2×#113614yes—
360C23C2×C22⋊Dic711yescharacteristic
361C23C2×C22⋊Dic711yescharacteristic
362C23C23×Dic711yescharacteristic
363C2×C4—216no—
364C2×C4—216no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4C2×#113614yes—
390C2×C4C2×C22⋊Dic712yes—
391C2×C4C2×C22⋊Dic712yes—
392C2×C4C2×C22⋊Dic712yes—
393C2×C4C2×C22⋊Dic714yes—
394C2×C4C22×C22⋊D712yes—
395C8—288no—
396C7C2×#146411yescharacteristic, complemented, Sylow
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—24no—
402C22—24no—
403C22—24no—
404C22—44no—
405C22—44no—
406C22—48no—
407C22—42no—
408C22—42no—
409C22—48no—
410C22#8997912yes—
411C22#8997912yes—
412C22#9000912yes—
413C22#9001212yes—
414C22C22×#113611yescharacteristic
415C22C22×#113611yescharacteristic
416C22C22×C22⋊Dic711yescharacteristic
417C4—24no—
418C4—22no—
419C4—22no—
420C4—24no—
421C4—22no—
422C4—22no—
423C4—42no—
424C4—42no—
425C2—21no—
426C2—21no—
427C2—22no—
428C2—44no—
429C2#1172932614yesdirect product factor
430C2C2×#8997911yescharacteristic
431C2C2×#9000911yescharacteristic
432C2C2×#9001211yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic7
commutatorC23×C7C23×C4
FrattiniC22×C4C23×D7
FittingC22×C7×#117C2
socleC23×C7C2×C22⋊C4
prime radicalC25×C7C2×C4
cosocleC22×C4×C7C24
hypercenterC22×#117D7
hypocenterC7C2×#1464
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. C2×#89698C2semidirect
3. #11729326C2direct (N × H)
4. C2×#89323C2semidirect
20. #89698C22semidirect
23. #89323C22semidirect
339. C2×C7#1464semidirect
396. C7C2×#1464semidirect
429. C2#11729326direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1172
C2×#896982
#117293262
C2×#893232
C2×#893202
C2×#14647