Finite Group Databasebeta

← C4×#90413 #13513799

Subgroups — C4×#90413 #13513799

Order 1792.

2324 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90413C211yesmaximal, characteristic
2C4×C7×C4⋊Q8C211yesmaximal, characteristic
3#11740675C211yesmaximal, characteristic
4C4×#6507C214yesmaximal
5#11733939C214yesmaximal
6#11733432C214yesmaximal
7#11733426C214yesmaximal
8#11731768C212yesmaximal
9C4×#6451C214yesmaximal
10C4×#6450C214yesmaximal
11C42×Dic14C212yesmaximal
12C2×C7×C4⋊Q8C2211yescharacteristic
13C2×C4×C7×Q8C2212yes—
14C2×#6507C2214yes—
15#90413C4116yesdirect product factor
16C2×#6451C2214yes—
17C2×#6450C2214yes—
18C2×#6450C2214yes—
19C2×C4×Dic14C2212yes—
20C2×C4×Dic14C2214yes—
21C2×C4×Dic14C2212yes—
22C2×C4×Dic14C2212yes—
23C7×#391C2212yes—
24C7×#389C2214yes—
25C7×#384C2211yescharacteristic
26C4×C7×C4⋊C4C2214yes—
27C43×C7C2211yescharacteristic
28#90002C2214yes—
29#89757C2214yes—
30#89748C2214yes—
31#89748C2214yes—
32C4⋊C4×Dic7C2214yes—
33C4⋊C4×Dic7C2214yes—
34#89746C2214yes—
35#89745C2214yes—
36#89744C2218yes—
37#89744C2218yes—
38C4×C4⋊Dic7C2212yes—
39C4×C4⋊Dic7C2212yes—
40C4×C4⋊Dic7C2212yes—
41C4×Dic7⋊C4C2214yes—
42C4×Dic7⋊C4C2214yes—
43C4×Dic7⋊C4C2214yes—
44C4×Dic7⋊C4C2218yes—
45C42×Dic7C2214yes—
46C42×Dic7C2214yes—
47#89421C2218yes—
48#89421C2218yes—
49#89419C2218yes—
50#89418C2218yes—
51C4×Q82—71nomaximal, Sylow
52C22×C7×Q8C2312yes—
53C22×Dic14C2314yes—
54C22×Dic14C2312yes—
55C7×C4⋊Q8C2×C418yes—
56C4×C7×Q8—44no—
57C2×C7×C4⋊C4C2314yes—
58C2×C7×C4⋊C4C2312yes—
59C2×C7×C4⋊C4C2314yes—
60C2×C7×C4⋊C4C2314yes—
61C2×C42×C7C2314yes—
62C2×C42×C7C2312yes—
63C2×C42×C7C2311yescharacteristic
64C2×C42×C7C2311yescharacteristic
65C2×C42×C7C2311yescharacteristic
66C2×C42×C7C2312yes—
67#6507C2×C4132yes—
68C2×C4⋊Dic7C2312yes—
69C2×C4⋊Dic7C2314yes—
70C2×C4⋊Dic7C2312yes—
71C2×C4⋊Dic7C2312yes—
72C2×Dic7⋊C4C2314yes—
73C2×Dic7⋊C4C2318yes—
74C2×Dic7⋊C4C2318yes—
75C2×Dic7⋊C4C2314yes—
76C2×Dic7⋊C4C2318yes—
77C2×Dic7⋊C4C2314yes—
78C2×C4×Dic7C2314yes—
79C2×C4×Dic7C2314yes—
80C2×C4×Dic7C2318yes—
81C2×C4×Dic7C2314yes—
82C2×C4×Dic7C2314yes—
83C2×C4×Dic7C2314yes—
84C2×C4×Dic7C2314yes—
85C2×C4×Dic7C2314yes—
86C2×C4×Dic7C2314yes—
87#6451C2×C4132yes—
88#6450—216no—
89#6450C2×C4132yes—
90C4×Dic14—28no—
91C4×Dic14—48no—
92C4×Dic14C2×C4116yes—
93C4×Dic14Q8116yescomplemented
94C7×#95C2318yes—
95C7⋊#95C2314yes—
96C7⋊#95C2318yes—
97C7⋊#95C2318yes—
98C7⋊#95C2314yes—
99C7⋊#95C2314yes—
100C2×Q82—71no—
101#2369—74no—
102#2369—74no—
103#2369—71no—
104Q8×C4⋊C4—74no—
105Q8×C4⋊C4—72no—
106C4×C4⋊Q8—74no—
107C4×C4⋊Q8—74no—
108C4×C4⋊Q8D711yescharacteristic
109C42×Q8—74no—
110C42×Q8—72no—
111C2×C7×Q8—42no—
112C2×C7×Q8—42no—
113C2×C7×Q8C22×C418yes—
114C22×C4×C7C2411yescharacteristic
115C22×C4×C7C2414yes—
116C22×C4×C7C2411yescharacteristic
117C22×C4×C7C2414yes—
118C22×C4×C7C2412yes—
119C22×C4×C7C2412yes—
120C22×C4×C7C2411yescharacteristic
121C22×Dic7C2414yes—
122C22×Dic7C2414yes—
123C22×Dic7C2414yes—
124C22×Dic7C2414yes—
125C2×Dic14—44no—
126C2×Dic14—44no—
127C2×Dic14C22×C4116yes—
128C2×Dic14C22×C418yes—
129C2×Dic14C2×Q818yes—
130C2×Dic14#4118yes—
131C7×C4⋊C4—28no—
132C7×C4⋊C4—44no—
133C7×C4⋊C4—42no—
134C7×C4⋊C4C22×C4116yes—
135C42×C7—24no—
136C42×C7—28no—
137C42×C7—22no—
138C42×C7—41no—
139C42×C7C22×C414yes—
140C42×C7C2×Q818yes—
141C4⋊Dic7—24no—
142C4⋊Dic7—44no—
143C4⋊Dic7C22×C418yes—
144C4⋊Dic7C2×Q818yes—
145Dic7⋊C4—28no—
146Dic7⋊C4—216no—
147Dic7⋊C4—48no—
148Dic7⋊C4C22×C4116yes—
149Dic7⋊C4C22×C4132yes—
150Dic7⋊C4C2×Q8116yes—
151C4×Dic7—28no—
152C4×Dic7—28no—
153C4×Dic7—28no—
154C4×Dic7—216no—
155C4×Dic7—44no—
156C4×Dic7—44no—
157C4×Dic7C22×C4116yes—
158C4×Dic7C22×C4116yes—
159C4×Dic7C2×Q8116yes—
160Q82—716no—
161C2×C4⋊Q8—74no—
162C2×C4⋊Q8—74no—
163C2×C4⋊Q8C2×D711yescharacteristic
164C2×C4×Q8—74no—
165C2×C4×Q8—74no—
166C2×C4×Q8—72no—
167C2×C4×Q8—72no—
168C2×C4×Q8—72no—
169C2×C4×Q8—74no—
170C2×C4×Q8C2×D712yes—
171#391—74no—
172#391—74no—
173#391—78no—
174#391C2×D712yes—
175#389—78no—
176#389—78no—
177#389—74no—
178#389—74no—
179#389—78no—
180#389C2×D714yes—
181#384—74no—
182#384—74no—
183#384C2×D711yescharacteristic
184C4×C4⋊C4—74no—
185C4×C4⋊C4—74no—
186C4×C4⋊C4—78no—
187C4×C4⋊C4—74no—
188C4×C4⋊C4—72no—
189C4×C4⋊C4—74no—
190C4×C4⋊C4—72no—
191C4×C4⋊C4—74no—
192C4×C4⋊C4—72no—
193C4×C4⋊C4—78no—
194C4×C4⋊C4—78no—
195C4×C4⋊C4C2×D714yes—
196C43—74no—
197C43—74no—
198C43C2×D711yescharacteristic
199C23×C7C2511yescharacteristic
200C7×Q8—48no—
201C2×C4×C7—22no—
202C2×C4×C7—24no—
203C2×C4×C7—21no—
204C2×C4×C7—22no—
205C2×C4×C7—24no—
206C2×C4×C7—21no—
207C2×C4×C7—28no—
208C2×C4×C7—22no—
209C2×C4×C7—24no—
210C2×C4×C7—21no—
211C2×C4×C7C23×C418yes—
212C2×C4×C7C23×C412yes—
213C2×C4×C7C23×C414yes—
214C2×C4×C7C22×Q814yes—
215C2×C4×C7C22×Q814yes—
216C2×C4×C7C22×Q814yes—
217C2×C4×C7C2×#4114yes—
218C2×C4×C7H(5,𝔽2)12yes—
219C2×Dic7—24no—
220C2×Dic7—24no—
221C2×Dic7—24no—
222C2×Dic7—24no—
223C2×Dic7—24no—
224C2×Dic7—24no—
225C2×Dic7—24no—
226C2×Dic7C23×C418yes—
227C2×Dic7C23×C418yes—
228C2×Dic7C22×Q818yes—
229C2×Dic7C22×Q818yes—
230C2×Dic7C2×#4118yes—
231Dic14—416no—
232Dic14C4×Q8132yescomplemented
233C22×Q8—72no—
234C22×Q8—74no—
235C22×Q8C22×D712yes—
236C4⋊Q8—732no—
237C4⋊Q8—732no—
238C4⋊Q8C4×D718yes—
239C4×Q8—44no—
240C4×Q8—732no—
241C4×Q8—716no—
242C4×Q8—716no—
243C4×Q8—148no—
244C4×Q8—1416no—
245C4×Q8—288no—
246C2×C4⋊C4—74no—
247C2×C4⋊C4—78no—
248C2×C4⋊C4—72no—
249C2×C4⋊C4—74no—
250C2×C4⋊C4—72no—
251C2×C4⋊C4—74no—
252C2×C4⋊C4—78no—
253C2×C4⋊C4—72no—
254C2×C4⋊C4—78no—
255C2×C4⋊C4—74no—
256C2×C4⋊C4C22×D714yes—
257C2×C4⋊C4C22×D714yes—
258C2×C4⋊C4C22×D712yes—
259C2×C4⋊C4C22×D714yes—
260C2×C42—74no—
261C2×C42—74no—
262C2×C42—74no—
263C2×C42—78no—
264C2×C42—74no—
265C2×C42—74no—
266C2×C42—74no—
267C2×C42—74no—
268C2×C42—74no—
269C2×C42C22×D712yes—
270C2×C42C22×D714yes—
271C2×C42C22×D711yescharacteristic
272C2×C42C22×D711yescharacteristic
273C2×C42C22×D711yescharacteristic
274C2×C42C22×D712yes—
275#95—74no—
276#95—78no—
277#95—74no—
278#95—78no—
279#95—74no—
280#95C22×D718yes—
281C22×C7C24×C411yescharacteristic
282C22×C7C23×Q812yes—
283C22×C7C22×#4112yes—
284C22×C7C2×H(5,𝔽2)11yescharacteristic
285C22×C7#58511yescharacteristic
286C4×C7—28no—
287C4×C7—22no—
288C4×C7—24no—
289C4×C7—44no—
290C4×C7—41no—
291C4×C7C2×C4×Q818yes—
292C4×C7Q8214yescomplemented
293Dic7—28no—
294Dic7—28no—
295Dic7—44no—
296Dic7C2×C4×Q8116yes—
297C2×Q8—42no—
298C2×Q8—42no—
299C2×Q8—78no—
300C2×Q8—716no—
301C2×Q8—78no—
302C2×Q8—78no—
303C2×Q8—284no—
304C2×Q8—284no—
305C2×Q8C2×C4×D718yes—
306C22×C4—74no—
307C22×C4—74no—
308C22×C4—74no—
309C22×C4—74no—
310C22×C4C23×D711yescharacteristic
311C22×C4C23×D714yes—
312C22×C4C23×D711yescharacteristic
313C22×C4C23×D714yes—
314C22×C4C23×D712yes—
315C22×C4C23×D712yes—
316C22×C4C23×D711yescharacteristic
317C4⋊C4—28no—
318C4⋊C4—42no—
319C4⋊C4—44no—
320C4⋊C4—732no—
321C4⋊C4—716no—
322C4⋊C4—78no—
323C4⋊C4—716no—
324C4⋊C4—78no—
325C4⋊C4—148no—
326C4⋊C4—1416no—
327C4⋊C4—144no—
328C4⋊C4—288no—
329C4⋊C4—284no—
330C4⋊C4C2×C4×D7116yes—
331C42—22no—
332C42—28no—
333C42—24no—
334C42—41no—
335C42—716no—
336C42—716no—
337C42—716no—
338C42—148no—
339C42—1416no—
340C42—148no—
341C42—148no—
342C42—284no—
343C42—284no—
344C42C2×C4×D714yes—
345C42Q8×D718yes—
346C2×C7C22×C4×Q812yes—
347C2×C7C4×H(5,𝔽2)11yescharacteristic
348C2×C7C2×Q8211yescharacteristic
349C2×C7Q8×#4112yes—
350C2×C7#348311yescharacteristic
351C23C24×D711yescharacteristic
352Q8—48no—
353Q8—732no—
354Q8—2816no—
355C2×C4—21no—
356C2×C4—24no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—21no—
360C2×C4—24no—
361C2×C4—21no—
362C2×C4—24no—
363C2×C4—22no—
364C2×C4—28no—
365C2×C4—78no—
366C2×C4—78no—
367C2×C4—78no—
368C2×C4—78no—
369C2×C4—78no—
370C2×C4—144no—
371C2×C4—144no—
372C2×C4—144no—
373C2×C4—144no—
374C2×C4—144no—
375C2×C4—144no—
376C2×C4—144no—
377C2×C4C22×C4×D718yes—
378C2×C4C22×C4×D712yes—
379C2×C4C22×C4×D714yes—
380C2×C4#654812yes—
381C2×C4C2×Q8×D714yes—
382C2×C4C2×Q8×D714yes—
383C2×C4C2×Q8×D714yes—
384C2×C4D7×#4114yes—
385C7C4×Q8211yescharacteristic, complemented, Sylow
386C22C23×C4×D711yescharacteristic
387C22C2×#654811yescharacteristic
388C22C22×Q8×D712yes—
389C22C2×D7×#4112yes—
390C22#9061611yescharacteristic
391C4—22no—
392C4—28no—
393C4—24no—
394C4—41no—
395C4—44no—
396C4—716no—
397C4—148no—
398C4—148no—
399C4—284no—
400C4C4×Q8×D718yes—
401C4#9041314yesdirect product factor
402C2C4×#654811yescharacteristic
403C2C2×C4×Q8×D712yes—
404C2C2×#9041311yescharacteristic
405C2#1174328911yescharacteristic
406C2#1174334512yes—
subgroupG/H
centerC22×C4C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC4×C7×C4⋊Q8C2
socle, prime radical, cosocleC23×C7C25
hypercenterC4×C4⋊Q8D7
hypocenterC7C4×Q82
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
15. #90413C4direct (N × H)
93. C4×Dic14Q8semidirect
232. Dic14C4×Q8semidirect
292. C4×C7Q82semidirect
385. C7C4×Q82semidirect
401. C4#90413direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904132
C4×C7×C4⋊Q82
#117406752
C4×#65072
#117339392
#117334322
#117334262
#117317682
C4×#64512
C4×#64502
C42×Dic142
C4×Q827