Finite Group Databasebeta

← C2×#22625395 #34017412

Subgroups — C2×#22625395 #34017412

Order 18688.

1050 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989608C211yesmaximal, characteristic
2C2×C4×#11924037C211yesmaximal, characteristic
3#22625395C218yesmaximal, direct product factor
4C2×#17989444C214yesmaximal, complemented
5C22×#14556582C211yesmaximal, characteristic
6C22×#11924037—21no—
7#17989608—22no—
8#17989608C2214yes—
9C2×C4⋊#10596833—21no—
10C2×C22⋊#10596833—21no—
11C4×#11924037—22no—
12C4×#11924037C2214yes—
13C2×#14556646C2212yes—
14C2×#14556646C2212yes—
15C2×C4×#10596833—21no—
16#17989444C22116yescomplemented
17C2×#14556582—21no—
18C2×#14556582—22no—
19C2×#14556582—21no—
20C2×#14556582—22no—
21C2×#14556582C412yes—
22C2×#14556582C414yes—
23C2×#14556582C2212yes—
24C2×#14556582C2214yes—
25C22×C4⋊Dic73—21no—
26C22×C4⋊Dic73C411yescharacteristic
27C22×#11924007—21no—
28C22×C4×Dic73C2211yescharacteristic
29C22×C4⋊C4×C73C411yescharacteristic
30C2×#11924037—28no—
31C2×#11924037—24no—
32C22×#10596833—22no—
33C22×#10596833—22no—
34C4⋊#10596833—24no—
35C22⋊#10596833—24no—
36#14556646—22no—
37#14556646—22no—
38#14556646C2314yes—
39#14556646C2314yes—
40C4×#10596833—24no—
41C23×Dic73—21no—
42C23×Dic73D411yescharacteristic
43C23×Dic73D411yescharacteristic
44#14556582—24no—
45#14556582—24no—
46#14556582—24no—
47#14556582—24no—
48#14556582—22no—
49#14556582—22no—
50#14556582—24no—
51#14556582C2×C414yes—
52#14556582C2×C418yes—
53#14556582C2314yes—
54C2×C4⋊Dic73—24no—
55C2×C4⋊Dic73—22no—
56C2×C4⋊Dic73—22no—
57C2×C4⋊Dic73—24no—
58C2×C4⋊Dic73—22no—
59C2×C4⋊Dic73—21no—
60C2×C4⋊Dic73C2×C412yes—
61C2×C4⋊Dic73C2×C414yes—
62C2×#11924007—22no—
63C2×#11924007—24no—
64C2×#11924007—22no—
65C2×#11924007—24no—
66C2×C4×Dic73C2×C411yescharacteristic
67C2×C4×Dic73C2×C412yes—
68C2×C4×Dic73D411yescharacteristic
69C2×C4×Dic73D412yes—
70C2×C4×Dic73D411yescharacteristic
71C2×C4×Dic73D412yes—
72C2×C4×Dic73C2311yescharacteristic
73C2×C4×Dic73C2312yes—
74C23×C4×C73—21no—
75C23×C4×C73C2×C411yescharacteristic
76C2×C4⋊C4×C73—22no—
77C2×C4⋊C4×C73—21no—
78C2×C4⋊C4×C73C2×C412yes—
79C2×C4⋊C4×C73C2×C414yes—
80#11924037—216no—
81C2×#10596833—28no—
82C2×#10596833—24no—
83C2×#10596833—24no—
84C2×#10596833—44no—
85C22×Dic73—24no—
86C22×Dic73—24no—
87C22×Dic73—22no—
88C22×Dic73—42no—
89C22×Dic73—44no—
90C22×Dic73C22⋊C411yescharacteristic
91C22×Dic73C22⋊C412yes—
92C22×Dic73C22⋊C411yescharacteristic
93C22×Dic73C22⋊C412yes—
94C22×Dic73C2×D411yescharacteristic
95C22×Dic73C2×D411yescharacteristic
96C22×Dic73C2×D412yes—
97C22×Dic73C2×D412yes—
98C4⋊Dic73—22no—
99C4⋊Dic73—24no—
100C4⋊Dic73—24no—
101C4⋊Dic73—28no—
102C4⋊Dic73—24no—
103C4⋊Dic73C22×C414yes—
104#11924007—28no—
105#11924007—24no—
106#11924007—24no—
107C4×Dic73C22⋊C412yes—
108C4×Dic73C22⋊C412yes—
109C4×Dic73C22⋊C412yes—
110C4×Dic73C22×C411yescharacteristic
111C4×Dic73C22×C412yes—
112C4×Dic73C2×D412yes—
113C4×Dic73C2×D411yescharacteristic
114C4×Dic73C2×D411yescharacteristic
115C4×Dic73C2×D412yes—
116C4×Dic73C2411yescharacteristic
117C24×C73C22⋊C411yescharacteristic
118C22×C4×C73—24no—
119C22×C4×C73—24no—
120C22×C4×C73—22no—
121C22×C4×C73—44no—
122C22×C4×C73C22⋊C412yes—
123C22×C4×C73C22⋊C411yescharacteristic
124C22×C4×C73C22×C412yes—
125C22×C4×C73C22×C411yescharacteristic
126C4⋊C4×C73—22no—
127C4⋊C4×C73—24no—
128C4⋊C4×C73C22×C414yes—
129C23×C73—22no—
130C23×C73—22no—
131C23×C73#10414yes—
132C23×C73C2×C22⋊C412yes—
133C23×C73C2×C22⋊C411yescharacteristic
134C2×C4×C73—22no—
135C2×C4×C73—24no—
136C2×C4×C73—24no—
137C2×C4×C73—24no—
138C2×C4×C73—48no—
139C2×C4×C73—44no—
140C2×C4×C73#10114yes—
141C2×C4×C73C2×C22⋊C411yescharacteristic
142C2×C4×C73C2×C22⋊C412yes—
143C2×C4×C73C23×C411yescharacteristic
144C2×Dic73—24no—
145C2×Dic73—22no—
146C2×Dic73—22no—
147C2×Dic73—24no—
148C2×Dic73—22no—
149C2×Dic73—22no—
150C2×Dic73—24no—
151C2×Dic73—42no—
152C2×Dic73—42no—
153C2×Dic73—48no—
154C2×Dic73—44no—
155C2×Dic73C2×C22⋊C412yes—
156C2×Dic73C2×C22⋊C411yescharacteristic
157C2×Dic73C2×C22⋊C411yescharacteristic
158C2×Dic73C2×C22⋊C412yes—
159C2×Dic73C22×D411yescharacteristic
160C2×Dic73C22×D411yescharacteristic
161#10596833—28no—
162#10596833—44no—
163C22×C73—22no—
164C22×C73—22no—
165C22×C73—28no—
166C22×C73C2×#10112yes—
167C22×C73C2×#10414yes—
168C22×C73C2×#10412yes—
169C22×C73#42112yes—
170C22×C73C22×C22⋊C411yescharacteristic
171C4×C73—21no—
172C4×C73—21no—
173C4×C73—44no—
174C4×C73C2×#10114yes—
175Dic73—21no—
176Dic73—21no—
177Dic73—22no—
178Dic73—21no—
179Dic73—22no—
180Dic73—21no—
181Dic73—44no—
182C2×#1528—731nomaximal, Sylow
183C2×C73—24no—
184C2×C73#152814yescomplemented
185C2×C73C22×#10111yescharacteristic
186C2×C73C22×#10411yescharacteristic
187C2×C73C2×#42111yescharacteristic
188C22×#125—731no—
189C2×#432—731no—
190C2×C4×M16—731no—
191#1528—738no—
192C2×#330—734no—
193C73C2×#152811yescharacteristic, complemented, Sylow
194C22×M16—1461no—
195C2×#125—732no—
196C2×#125—734no—
197C2×#125—732no—
198C2×#125—734no—
199C2×#125—1461no—
200C2×#125—1462no—
201C2×#125—1461no—
202C2×#125—1462no—
203C22×C4⋊C4—731no—
204C22×C4⋊C4—1461no—
205C22×C4⋊C4—1461no—
206C22×C4⋊C4#6440811yescharacteristic
207C22×C42—731no—
208#432—734no—
209#432—1462no—
210C2×C4⋊C8—1461no—
211C2×C22⋊C8—1461no—
212C4×M16—734no—
213C4×M16—1462no—
214C2×#97—732no—
215C2×#97—732no—
216C2×C4×C8—1461no—
217#330—7316no—
218C23×C4—21no—
219C23×C4—731no—
220C23×C4—731no—
221C23×C4—1461no—
222C23×C4C2×#6440811yescharacteristic
223C2×M16—1464no—
224C2×M16—1468no—
225C22×C8—1462no—
226C22×C8—1462no—
227#125—734no—
228#125—734no—
229#125—738no—
230#125—1464no—
231#125—1464no—
232#125—1464no—
233#125—1464no—
234#125—1462no—
235#125—1462no—
236#125—1464no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—734no—
240C2×C4⋊C4—732no—
241C2×C4⋊C4—1464no—
242C2×C4⋊C4—1464no—
243C2×C4⋊C4—1462no—
244C2×C4⋊C4—1462no—
245C2×C4⋊C4—1464no—
246C2×C4⋊C4—1464no—
247C2×C4⋊C4—1462no—
248C2×C4⋊C4—1462no—
249C2×C4⋊C4—1462no—
250C2×C4⋊C4—1461no—
251C2×C4⋊C4C2×#6440814yes—
252C2×C4⋊C4C2×#6440812yes—
253C2×C42—731no—
254C2×C42—732no—
255C2×C42—731no—
256C2×C42—732no—
257C2×C42—732no—
258C2×C42—731no—
259C2×C42—731no—
260C2×C42—732no—
261C4⋊C8—1464no—
262C22⋊C8—1464no—
263#97—734no—
264#97—734no—
265#97—1462no—
266#97—1462no—
267C4×C8—1464no—
268C24C22⋊#6440811yescharacteristic
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—22no—
272C22×C4—44no—
273C22×C4—2924no—
274C22×C4—2922no—
275C22×C4—732no—
276C22×C4—732no—
277C22×C4—732no—
278C22×C4—732no—
279C22×C4—731no—
280C22×C4—731no—
281C22×C4—731no—
282C22×C4—731no—
283C22×C4—1464no—
284C22×C4—1462no—
285C22×C4—1464no—
286C22×C4C22⋊#6440812yes—
287C22×C4C22⋊#6440811yescharacteristic
288C22×C4C22×#6440812yes—
289C22×C4C22×#6440811yescharacteristic
290M16—14616no—
291C2×C8—2924no—
292C2×C8—1464no—
293C2×C8—1464no—
294C2×C8—1468no—
295C4⋊C4—22no—
296C4⋊C4—24no—
297C4⋊C4—734no—
298C4⋊C4—1464no—
299C4⋊C4—1468no—
300C4⋊C4—1464no—
301C4⋊C4—1464no—
302C4⋊C4—1464no—
303C4⋊C4—1468no—
304C4⋊C4—1462no—
305C4⋊C4—1464no—
306C4⋊C4C22×#6440814yes—
307C42—731no—
308C42—732no—
309C42—731no—
310C42—732no—
311C42—732no—
312C42—732no—
313C42—732no—
314C42—731no—
315C42—731no—
316C42—732no—
317C23—22no—
318C23—22no—
319C23#1455665614yes—
320C23C2×C22⋊#6440812yes—
321C23C2×C22⋊#6440811yescharacteristic
322C2×C4—22no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—48no—
327C2×C4—44no—
328C2×C4—2928no—
329C2×C4—2924no—
330C2×C4—2922no—
331C2×C4—2922no—
332C2×C4—731no—
333C2×C4—731no—
334C2×C4—731no—
335C2×C4—732no—
336C2×C4—732no—
337C2×C4—731no—
338C2×C4—1464no—
339C2×C4—1462no—
340C2×C4—1464no—
341C2×C4—1464no—
342C2×C4—1462no—
343C2×C4—1462no—
344C2×C4—1462no—
345C2×C4#1455665214yes—
346C2×C4C2×C22⋊#6440811yescharacteristic
347C2×C4C2×C22⋊#6440812yes—
348C2×C4C23×#6440811yescharacteristic
349C8—2924no—
350C8—1468no—
351C22—28no—
352C22—22no—
353C22—22no—
354C22C2×#1455665212yes—
355C22C2×#1455665614yes—
356C22C2×#1455665612yes—
357C22#1798958512yes—
358C22C22×C22⋊#6440811yescharacteristic
359C4—21no—
360C4—21no—
361C4—44no—
362C4—2924no—
363C4—1461no—
364C4—1461no—
365C4—1462no—
366C4—1461no—
367C4—1461no—
368C4—1462no—
369C4C2×#1455665214yes—
370C2—24no—
371C2#2262539514yesdirect product factor
372C2C22×#1455665211yescharacteristic
373C2C22×#1455665611yescharacteristic
374C2C2×#1798958511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
FittingC22×C4⋊C4×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC4×Dic73C24
hypercenterC22×C4⋊C4#64408
hypocenterC73C2×#1528
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #22625395C2direct (N × H)
4. C2×#17989444C2semidirect
16. #17989444C22semidirect
184. C2×C73#1528semidirect
193. C73C2×#1528semidirect
371. C2#22625395direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179896082
C2×C4×#119240372
#226253952
C2×#179894442
C22×#145565822
C2×#152873