Finite Group Databasebeta

← C2×#22608921 #33058110

Subgroups — C2×#22608921 #33058110

Order 18688.

1136 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1136 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×#17989213C211yesmaximal, characteristic
2C2×#17988917C212yesmaximal, complemented
3#22608921C218yesmaximal, direct product factor
4C2×#17988323C212yesmaximal, complemented
5C2×#17988311C211yesmaximal, characteristic
6C2×#397×C73C211yesmaximal, characteristic
7#17989213—24no—
8#17989213—22no—
9#17989213C2214yes—
10C2×#14556570—21no—
11C2×#14556570C2212yes—
12C2×#14556568—22no—
13C2×#14556568—22no—
14C22×C22⋊Dic73—21no—
15#17988917—24no—
16#17988917C2218yescomplemented
17C2×#14556522—22no—
18C2×#14556514—22no—
19C2×C22⋊#10596831C2212yes—
20#17988323C2218yescomplemented
21#17988311C2214yes—
22C22×C4⋊C4×C73C2211yescharacteristic
23C22×C22⋊C4×C73—21no—
24C22×C22⋊C4×C73C2211yescharacteristic
25#397×C73—22no—
26#397×C73C2214yes—
27C2×#95×C73—21no—
28C2×#95×C73C2211yescharacteristic
29C22×Dic146—21no—
30C22×Dic146D412yes—
31C23×Dic73—21no—
32C23×Dic73—21no—
33C22×#10596831—22no—
34#14556570—24no—
35#14556570—22no—
36#14556570—22no—
37#14556570—24no—
38#14556570D414yes—
39#14556570C2314yes—
40#14556568—28no—
41#14556568—28no—
42#14556568—28no—
43#14556568—28no—
44C2×C4⋊Dic73—21no—
45C2×C4⋊Dic73D412yes—
46C2×#11924007—22no—
47C2×#11924007—22no—
48C2×C22⋊Dic73—24no—
49C2×C22⋊Dic73—22no—
50C2×C22⋊Dic73—24no—
51C2×C22⋊Dic73—22no—
52#14556522—28no—
53#14556514—28no—
54C22⋊#10596831—22no—
55C22⋊#10596831C2314yes—
56C25×C73D411yescharacteristic
57C23×C4×C73—21no—
58C23×C4×C73—21no—
59C23×C4×C73D411yescharacteristic
60C23×C4×C73C2311yescharacteristic
61C2×C4⋊C4×C73—22no—
62C2×C4⋊C4×C73—22no—
63C2×C4⋊C4×C73—21no—
64C2×C4⋊C4×C73C2312yes—
65C2×C22⋊C4×C73—22no—
66C2×C22⋊C4×C73—22no—
67C2×C22⋊C4×C73—24no—
68C2×C22⋊C4×C73—44no—
69C2×C22⋊C4×C73D412yes—
70C2×C22⋊C4×C73C2312yes—
71#95×C73—21no—
72#95×C73—24no—
73#95×C73C2312yes—
74C2×Dic146—24no—
75C2×Dic146—22no—
76C2×Dic146—44no—
77C2×Dic146—82no—
78C2×Dic146C2×D414yes—
79C22×Dic73—22no—
80C22×Dic73—22no—
81C22×Dic73—24no—
82C22×Dic73—24no—
83C22×Dic73—82no—
84C22×Dic73—82no—
85C2×#10596831—24no—
86C2×#10596831—44no—
87C4⋊Dic73—24no—
88C4⋊Dic73—22no—
89C4⋊Dic73C2×D414yes—
90#11924007—28no—
91#11924007—24no—
92#11924007—24no—
93C22⋊Dic73—28no—
94C22⋊Dic73—24no—
95C22⋊Dic73—24no—
96C24×C73—21no—
97C24×C73—21no—
98C24×C73—22no—
99C24×C73—42no—
100C24×C73—42no—
101C24×C73SD1614yes—
102C24×C73C2×D411yescharacteristic
103C24×C73C2×D412yes—
104C22×C4×C73—21no—
105C22×C4×C73—21no—
106C22×C4×C73—22no—
107C22×C4×C73—22no—
108C22×C4×C73—42no—
109C22×C4×C73—42no—
110C22×C4×C73—42no—
111C22×C4×C73—42no—
112C22×C4×C73—41no—
113C22×C4×C73—41no—
114C22×C4×C73—42no—
115C22×C4×C73—42no—
116C22×C4×C73—42no—
117C22×C4×C73C2×D412yes—
118C22×C4×C73C2×D412yes—
119C22×C4×C73C2×D412yes—
120C22×C4×C73C2×D411yescharacteristic
121C22×C4×C73C2411yescharacteristic
122C4⋊C4×C73—24no—
123C4⋊C4×C73—42no—
124C22⋊C4×C73—24no—
125C22⋊C4×C73—24no—
126C22⋊C4×C73—48no—
127C23×C73—22no—
128C23×C73—22no—
129C23×C73—22no—
130C23×C73—24no—
131C23×C73—22no—
132C23×C73—24no—
133C23×C73—48no—
134C23×C73—42no—
135C23×C73—42no—
136C23×C73—42no—
137C23×C73—42no—
138C23×C73—84no—
139C23×C73—81no—
140C23×C73—81no—
141C23×C73#12011yescharacteristic
142C23×C73#12011yescharacteristic
143C23×C73C2×SD1612yes—
144C23×C73C2×SD1614yes—
145C23×C73#13712yes—
146C23×C73C22×D411yescharacteristic
147C2×C4×C73—24no—
148C2×C4×C73—22no—
149C2×C4×C73—42no—
150C2×C4×C73—41no—
151C2×C4×C73—41no—
152C2×C4×C73—42no—
153C2×C4×C73—42no—
154C2×C4×C73—42no—
155C2×C4×C73—42no—
156C2×C4×C73—42no—
157C2×C4×C73—42no—
158C2×C4×C73—42no—
159C2×C4×C73—42no—
160C2×C4×C73—81no—
161C2×C4×C73—84no—
162C2×C4×C73—82no—
163C2×C4×C73—82no—
164C2×C4×C73#12012yes—
165C2×C4×C73C22×D412yes—
166C2×Dic73—24no—
167C2×Dic73—24no—
168C2×Dic73—44no—
169C2×Dic73—44no—
170C2×Dic73—84no—
171C2×Dic73—84no—
172Dic146—44no—
173Dic146—82no—
174Dic146—84no—
175#10596831—44no—
176C22×C73—24no—
177C22×C73—24no—
178C22×C73—21no—
179C22×C73—21no—
180C22×C73—21no—
181C22×C73—21no—
182C22×C73—24no—
183C22×C73—44no—
184C22×C73—48no—
185C22×C73—42no—
186C22×C73—42no—
187C22×C73—82no—
188C22×C73—84no—
189C22×C73#44812yes—
190C22×C73#44812yes—
191C22×C73#45512yes—
192C22×C73#45812yes—
193C22×C73C2×#12011yescharacteristic
194C22×C73C22×SD1611yescharacteristic
195C22×C73C2×#13711yescharacteristic
196C4×C73—22no—
197C4×C73—22no—
198C4×C73—42no—
199C4×C73—82no—
200C4×C73—82no—
201Dic73—44no—
202Dic73—44no—
203C2×#1608—731nomaximal, Sylow
204C2×C73—21no—
205C2×C73—21no—
206C2×C73—22no—
207C2×C73—44no—
208C2×C73#160814yescomplemented
209C2×C73C2×#44811yescharacteristic
210C2×C73C2×#45511yescharacteristic
211C2×C73C2×#45811yescharacteristic
212C2×#543—731no—
213C2×#483—732no—
214C2×#397D7311yescharacteristic
215#1608—738no—
216C2×#328—732no—
217C2×#323—731no—
218C73C2×#160811yescharacteristic, complemented, Sylow
219#543—734no—
220#543—1464no—
221#543—1462no—
222C2×C22⋊Q8—732no—
223C2×C22⋊Q8—1462no—
224C2×C22⋊Q8—1462no—
225C2×C22⋊Q8—1461no—
226C22×C4⋊C4C2×D7311yescharacteristic
227C22×C22⋊C4—21no—
228C22×C22⋊C4—1461no—
229C22×C22⋊C4C2×D7311yescharacteristic
230#483—738no—
231#483—1464no—
232C2×#106—1462no—
233C2×#103—1462no—
234C2×C22⋊C8—732no—
235#397—22no—
236#397C2×D7314yes—
237C2×#95—21no—
238C2×#95C2×D7311yescharacteristic
239#328—738no—
240#323—734no—
241C25C22⋊D7311yescharacteristic
242C22×Q8—732no—
243C22×Q8—1461no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—1461no—
247C23×C4—1461no—
248C23×C4C22⋊D7311yescharacteristic
249C23×C4C22×D7311yescharacteristic
250C22×C8—1462no—
251C22⋊Q8—734no—
252C22⋊Q8—734no—
253C22⋊Q8—1468no—
254C22⋊Q8—1468no—
255C22⋊Q8—1468no—
256C22⋊Q8—1468no—
257C22⋊Q8—1464no—
258C22⋊Q8—1462no—
259C22⋊Q8—1462no—
260C22⋊Q8—1464no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—732no—
265C2×C4⋊C4—1462no—
266C2×C4⋊C4—1461no—
267C2×C4⋊C4—1462no—
268C2×C4⋊C4C22×D7312yes—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—24no—
272C2×C22⋊C4—44no—
273C2×C22⋊C4—1462no—
274C2×C22⋊C4—1464no—
275C2×C22⋊C4—1462no—
276C2×C22⋊C4—1464no—
277C2×C22⋊C4C22⋊D7312yes—
278C2×C22⋊C4C22×D7312yes—
279#106—1468no—
280#103—1468no—
281C22⋊C8—734no—
282C22⋊C8—1462no—
283#95—24no—
284#95—21no—
285#95C22×D7312yes—
286C24—21no—
287C24—21no—
288C24—22no—
289C24—42no—
290C24—42no—
291C24#1192401614yes—
292C24C2×C22⋊D7311yescharacteristic
293C24C2×C22⋊D7312yes—
294C2×Q8—2924no—
295C2×Q8—5842no—
296C2×Q8—734no—
297C2×Q8—1464no—
298C2×Q8—1462no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—5842no—
313C22×C4—5842no—
314C22×C4—1462no—
315C22×C4—1462no—
316C22×C4—1464no—
317C22×C4—1464no—
318C22×C4D4×D7312yes—
319C22×C4D4×D7312yes—
320C22×C4C2×C22⋊D7312yes—
321C22×C4C2×C22⋊D7311yescharacteristic
322C22×C4C23×D7311yescharacteristic
323C2×C8—2924no—
324C2×C8—1464no—
325C4⋊C4—24no—
326C4⋊C4—42no—
327C4⋊C4—734no—
328C4⋊C4—1468no—
329C4⋊C4—1464no—
330C4⋊C4—1464no—
331C4⋊C4—1462no—
332C4⋊C4—1464no—
333C22⋊C4—24no—
334C22⋊C4—24no—
335C22⋊C4—48no—
336C22⋊C4—1468no—
337C22⋊C4—1464no—
338C22⋊C4—1464no—
339C23—22no—
340C23—22no—
341C23—24no—
342C23—22no—
343C23—22no—
344C23—24no—
345C23—48no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—84no—
351C23—81no—
352C23—81no—
353C23#1455655911yescharacteristic
354C23#1455655911yescharacteristic
355C23C2×#1192401612yes—
356C23C2×#1192401614yes—
357C23#1455662112yes—
358C23C22×C22⋊D7311yescharacteristic
359Q8—2924no—
360Q8—5842no—
361Q8—5844no—
362C2×C4—24no—
363C2×C4—22no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—81no—
376C2×C4—84no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4—2924no—
380C2×C4—2924no—
381C2×C4—5844no—
382C2×C4—5844no—
383C2×C4—1464no—
384C2×C4—1464no—
385C2×C4#1455655912yes—
386C2×C4C2×D4×D7312yes—
387C8—2924no—
388C22—24no—
389C22—24no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—24no—
395C22—44no—
396C22—48no—
397C22—42no—
398C22—42no—
399C22—82no—
400C22—84no—
401C22#1798872512yes—
402C22#1798872512yes—
403C22#1798876412yes—
404C22#1798877612yes—
405C22C2×#1455655911yescharacteristic
406C22C22×#1192401611yescharacteristic
407C22C2×#1455662111yescharacteristic
408C4—22no—
409C4—22no—
410C4—42no—
411C4—82no—
412C4—82no—
413C4—2924no—
414C4—2924no—
415C2—21no—
416C2—21no—
417C2—22no—
418C2—44no—
419C2#2260892114yesdirect product factor
420C2C2×#1798872511yescharacteristic
421C2C2×#1798876411yescharacteristic
422C2C2×#1798877611yescharacteristic
subgroupG/H
centerC23#14556559
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC2×#397×C73C2
socleC23×C73#120
prime radicalC25×C73D4
hypercenterC2×#397D73
hypocenterC73C2×#1608
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
2. C2×#17988917C2semidirect
3. #22608921C2direct (N × H)
4. C2×#17988323C2semidirect
16. #17988917C22semidirect
20. #17988323C22semidirect
208. C2×C73#1608semidirect
218. C73C2×#1608semidirect
419. C2#22608921direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892132
C2×#179889172
#226089212
C2×#179883232
C2×#179883112
C2×#397×C732
C2×#160873