Finite Group Databasebeta

← C2×#22608941 #33058215

Subgroups — C2×#22608941 #33058215

Order 18688.

1028 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1028 conjugacy classes of subgroups — too many to draw. Only its 203 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989218C211yesmaximal, characteristic
2C2×#17988918C212yesmaximal
3C2×#17988517C211yesmaximal, characteristic
4#22608941C218yesmaximal, direct product factor
5C2×#17988325C212yesmaximal
6C2×#324×C73C211yesmaximal, characteristic
7#17989218—24no—
8#17989218—22no—
9#17989218C2214yes—
10C2×#14556590—22no—
11C2×#14556582—22no—
12C2×#14556570—21no—
13C2×#14556570C2212yes—
14C2×#14556550—21no—
15C22×C4⋊Dic73C2211yescharacteristic
16C22×#11924007—21no—
17#17988918—24no—
18#17988918C2218yes—
19C2×#14556523—22no—
20C2×#14556516—22no—
21#17988517—22no—
22#17988517C2214yes—
23C2×#14556498—21no—
24C2×#14556498C2211yescharacteristic
25#17988325C2218yes—
26C22×C4⋊C4×C73C2211yescharacteristic
27C2×C22⋊C8×C73C2212yes—
28#324×C73C2214yes—
29C22×Dic146—21no—
30C22×Dic146D412yes—
31C23×Dic73—21no—
32C23×Dic73—21no—
33#14556590—28no—
34#14556590—28no—
35#14556582—28no—
36#14556582—28no—
37#14556570—24no—
38#14556570—22no—
39#14556570—22no—
40#14556570—24no—
41#14556570D414yes—
42#14556570C2314yes—
43#14556550—24no—
44#14556550—24no—
45C2×C4⋊Dic73—21no—
46C2×C4⋊Dic73—21no—
47C2×C4⋊Dic73—21no—
48C2×C4⋊Dic73—22no—
49C2×C4⋊Dic73—22no—
50C2×C4⋊Dic73—21no—
51C2×C4⋊Dic73D412yes—
52C2×C4⋊Dic73C2312yes—
53C2×#11924007—22no—
54C2×#11924007—22no—
55C2×#11924007—24no—
56C2×#11924007—44no—
57C2×C22⋊Dic73—22no—
58C2×C4×Dic73—22no—
59#14556523—28no—
60#14556516—28no—
61#14556498—24no—
62#14556498—21no—
63#14556498C2312yes—
64C23×C4×C73D411yescharacteristic
65C23×C4×C73D411yescharacteristic
66C23×C4×C73C2311yescharacteristic
67C22×C8×C73—22no—
68C2×C4⋊C4×C73—22no—
69C2×C4⋊C4×C73—22no—
70C2×C4⋊C4×C73D412yes—
71C2×C4⋊C4×C73C2312yes—
72C22⋊C8×C73—22no—
73C22⋊C8×C73C2314yes—
74C2×Dic146—24no—
75C2×Dic146—22no—
76C2×Dic146—44no—
77C2×Dic146—82no—
78C2×Dic146C2×D414yes—
79C22×Dic73—24no—
80C22×Dic73—22no—
81C22×Dic73—22no—
82C22×Dic73—22no—
83C22×Dic73—22no—
84C22×Dic73—42no—
85C22×Dic73—42no—
86C22×Dic73—41no—
87C22×Dic73—41no—
88C22×Dic73—42no—
89C22×Dic73—42no—
90C4⋊Dic73—24no—
91C4⋊Dic73—24no—
92C4⋊Dic73—24no—
93C4⋊Dic73—22no—
94C4⋊Dic73—24no—
95C4⋊Dic73—42no—
96C4⋊Dic73C2×D414yes—
97#11924007—28no—
98#11924007—24no—
99#11924007—24no—
100#11924007—48no—
101C22⋊Dic73—24no—
102C22⋊Dic73—24no—
103C4×Dic73—28no—
104C24×C73C2×D411yescharacteristic
105C22×C4×C73—21no—
106C22×C4×C73—21no—
107C22×C4×C73—22no—
108C22×C4×C73—21no—
109C22×C4×C73—21no—
110C22×C4×C73—42no—
111C22×C4×C73—42no—
112C22×C4×C73SD1614yes—
113C22×C4×C73C2×D412yes—
114C22×C4×C73C2×D412yes—
115C22×C4×C73C2×D412yes—
116C22×C4×C73C2×D412yes—
117C22×C4×C73C2×D411yescharacteristic
118C22×C4×C73C2411yescharacteristic
119C2×C8×C73—24no—
120C2×C8×C73—44no—
121C4⋊C4×C73—24no—
122C4⋊C4×C73—24no—
123C23×C73—22no—
124C23×C73—22no—
125C23×C73#12011yescharacteristic
126C23×C73#12011yescharacteristic
127C23×C73C2×SD1612yes—
128C23×C73#13712yes—
129C23×C73C22×D411yescharacteristic
130C2×C4×C73—22no—
131C2×C4×C73—22no—
132C2×C4×C73—24no—
133C2×C4×C73—24no—
134C2×C4×C73—24no—
135C2×C4×C73—22no—
136C2×C4×C73—42no—
137C2×C4×C73—41no—
138C2×C4×C73—41no—
139C2×C4×C73—42no—
140C2×C4×C73—42no—
141C2×C4×C73—81no—
142C2×C4×C73#12012yes—
143C2×C4×C73C2×SD1614yes—
144C2×C4×C73C22×D412yes—
145C2×Dic73—24no—
146C2×Dic73—24no—
147C2×Dic73—24no—
148C2×Dic73—48no—
149C2×Dic73—42no—
150C2×Dic73—42no—
151C2×Dic73—44no—
152C2×Dic73—44no—
153C2×Dic73—42no—
154C2×Dic73—42no—
155C2×Dic73—42no—
156C2×Dic73—82no—
157C2×Dic73—82no—
158Dic146—44no—
159Dic146—82no—
160Dic146—84no—
161C8×C73—44no—
162C22×C73—24no—
163C22×C73—24no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73—21no—
168C22×C73#44812yes—
169C22×C73#44812yes—
170C22×C73#45612yes—
171C22×C73#45812yes—
172C22×C73C2×#12011yescharacteristic
173C22×C73C22×SD1611yescharacteristic
174C22×C73C2×#13711yescharacteristic
175C4×C73—24no—
176C4×C73—22no—
177C4×C73—22no—
178C4×C73—42no—
179Dic73—44no—
180Dic73—44no—
181Dic73—44no—
182Dic73—82no—
183C2×#1611—731nomaximal, Sylow
184C2×C73—21no—
185C2×C73—21no—
186C2×C73—22no—
187C2×C73#161114yescomplemented
188C2×C73C2×#44811yescharacteristic
189C2×C73C2×#45611yescharacteristic
190C2×C73C2×#45811yescharacteristic
191C2×#544—731no—
192C2×#483—732no—
193C2×#398—731no—
194#1611—738no—
195C2×#328—732no—
196C2×#324D7311yescharacteristic
197C73C2×#161111yescharacteristic, complemented, Sylow
198#544—734no—
199#544—1464no—
200#544—1462no—
201C2×C4⋊Q8—1462no—
202C2×#125—1462no—
203C2×C22⋊Q8—732no—
204C2×C22⋊Q8—1461no—
205C2×#117—1461no—
206C22×C4⋊C4—731no—
207C22×C4⋊C4—1461no—
208C22×C4⋊C4C2×D7311yescharacteristic
209#483—738no—
210#483—1464no—
211C2×#106—1462no—
212C2×#103—1462no—
213C2×C22⋊C8C2×D7312yes—
214#398—734no—
215#398—1462no—
216C2×#95—731no—
217C2×#95—1461no—
218#328—738no—
219#324C2×D7314yes—
220C22×Q8—732no—
221C22×Q8—1461no—
222C23×C4—1461no—
223C23×C4—1461no—
224C23×C4D29211yescharacteristic
225C23×C4D29211yescharacteristic
226C23×C4C22×D7311yescharacteristic
227C22×C8—22no—
228C4⋊Q8—1468no—
229C4⋊Q8—1468no—
230#125—1468no—
231#125—1468no—
232C22⋊Q8—734no—
233C22⋊Q8—734no—
234C22⋊Q8—1464no—
235C22⋊Q8—1462no—
236C22⋊Q8—1462no—
237C22⋊Q8—1464no—
238#117—1464no—
239#117—1464no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—2924no—
243C2×C4⋊C4—732no—
244C2×C4⋊C4—732no—
245C2×C4⋊C4—1461no—
246C2×C4⋊C4—1464no—
247C2×C4⋊C4—1462no—
248C2×C4⋊C4—1462no—
249C2×C4⋊C4—1461no—
250C2×C4⋊C4—1461no—
251C2×C4⋊C4—1461no—
252C2×C4⋊C4—1462no—
253C2×C4⋊C4—1462no—
254C2×C4⋊C4D29212yes—
255C2×C4⋊C4C22×D7312yes—
256C2×C22⋊C4—1462no—
257C2×C42—1462no—
258#106—1468no—
259#103—1468no—
260C22⋊C8—22no—
261C22⋊C8C22×D7314yes—
262#95—732no—
263#95—1461no—
264#95—1464no—
265C24C2×D29211yescharacteristic
266C2×Q8—2924no—
267C2×Q8—5842no—
268C2×Q8—734no—
269C2×Q8—1464no—
270C2×Q8—1462no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—2922no—
279C22×C4—2922no—
280C22×C4—2921no—
281C22×C4—2921no—
282C22×C4—2922no—
283C22×C4—2922no—
284C22×C4—1462no—
285C22×C4—1464no—
286C22×C4—1462no—
287C22×C4—1462no—
288C22×C4—1462no—
289C22×C4#1192401714yes—
290C22×C4D4×D7312yes—
291C22×C4D4×D7312yes—
292C22×C4C2×D29212yes—
293C22×C4C2×D29212yes—
294C22×C4C2×D29211yescharacteristic
295C22×C4C23×D7311yescharacteristic
296C2×C8—24no—
297C2×C8—44no—
298C4⋊C4—24no—
299C4⋊C4—24no—
300C4⋊C4—2922no—
301C4⋊C4—2928no—
302C4⋊C4—734no—
303C4⋊C4—1468no—
304C4⋊C4—1464no—
305C4⋊C4—1464no—
306C4⋊C4—1464no—
307C4⋊C4—1464no—
308C4⋊C4—1464no—
309C4⋊C4—1462no—
310C4⋊C4—1464no—
311C22⋊C4—1464no—
312C22⋊C4—1464no—
313C42—1468no—
314C23—22no—
315C23—22no—
316C23#1455656111yescharacteristic
317C23#1455656111yescharacteristic
318C23C2×#1192401712yes—
319C23#1455662412yes—
320C23C22×D29211yescharacteristic
321Q8—2924no—
322Q8—5842no—
323Q8—5844no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—2928no—
337C2×C4—2922no—
338C2×C4—2924no—
339C2×C4—2924no—
340C2×C4—2922no—
341C2×C4—2922no—
342C2×C4—2922no—
343C2×C4—2922no—
344C2×C4—5842no—
345C2×C4—5842no—
346C2×C4—1464no—
347C2×C4—1464no—
348C2×C4—1464no—
349C2×C4#1455656112yes—
350C2×C4C2×#1192401714yes—
351C2×C4C2×D4×D7312yes—
352C8—44no—
353C22—24no—
354C22—24no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22#1798872812yes—
360C22#1798872812yes—
361C22#1798877212yes—
362C22#1798877812yes—
363C22C2×#1455656111yescharacteristic
364C22C22×#1192401711yescharacteristic
365C22C2×#1455662411yescharacteristic
366C4—22no—
367C4—22no—
368C4—24no—
369C4—42no—
370C4—2924no—
371C4—2924no—
372C4—2924no—
373C4—5842no—
374C2—21no—
375C2—21no—
376C2—22no—
377C2#2260894114yesdirect product factor
378C2C2×#1798872811yescharacteristic
379C2C2×#1798877211yescharacteristic
380C2C2×#1798877811yescharacteristic
subgroupG/H
centerC23#14556561
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC2×#324×C73C2
socleC23×C73#120
prime radicalC24×C73C2×D4
hypercenterC2×#324D73
hypocenterC73C2×#1611
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
4. #22608941C2direct (N × H)
187. C2×C73#1611semidirect
197. C73C2×#1611semidirect
377. C2#22608941direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892182
C2×#179889182
C2×#179885172
#226089412
C2×#179883252
C2×#324×C732
C2×#161173