Finite Group Databasebeta

← C2×#22608922 #33058111

Subgroups — C2×#22608922 #33058111

Order 18688.

1136 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988915C212yesmaximal, complemented
2C2×#17988512C211yesmaximal, characteristic
3#22608922C218yesmaximal, direct product factor
4C2×#17988324C212yesmaximal, complemented
5C2×#17988311C211yesmaximal, characteristic
6C2×#543×C73C211yesmaximal, characteristic
7C22×C4⋊Dic73C2211yescharacteristic
8C22×C22⋊Dic73—21no—
9#17988915—24no—
10#17988915C2218yescomplemented
11C2×#14556522—22no—
12C2×#14556515—22no—
13C2×C22⋊#10596831C2212yes—
14#17988512—22no—
15#17988512C2214yes—
16C2×#14556498—21no—
17C2×#14556498C2211yescharacteristic
18#17988324C2218yescomplemented
19#17988311C2214yes—
20#543×C73—24no—
21#543×C73—22no—
22#543×C73C2214yes—
23C2×C22⋊Q8×C73—22no—
24C2×C22⋊Q8×C73—21no—
25C2×C22⋊Q8×C73—22no—
26C2×C22⋊Q8×C73C2212yes—
27C22×C22⋊C4×C73—21no—
28C22×C22⋊C4×C73C2211yescharacteristic
29C23×Dic73—21no—
30C23×Dic73—21no—
31C22×#10596831—22no—
32C2×C4⋊Dic73—22no—
33C2×C4⋊Dic73—22no—
34C2×C4⋊Dic73—21no—
35C2×C4⋊Dic73C2312yes—
36C2×C22⋊Dic73—24no—
37C2×C22⋊Dic73—44no—
38#14556522—28no—
39#14556515—28no—
40C22⋊#10596831—22no—
41C22⋊#10596831C2314yes—
42#14556498—24no—
43#14556498—21no—
44#14556498C2312yes—
45C25×C73D411yescharacteristic
46C22×Q8×C73—21no—
47C22×Q8×C73D412yes—
48C23×C4×C73—21no—
49C23×C4×C73—21no—
50C23×C4×C73D411yescharacteristic
51C23×C4×C73C2311yescharacteristic
52C22⋊Q8×C73—28no—
53C22⋊Q8×C73—28no—
54C22⋊Q8×C73—24no—
55C22⋊Q8×C73—28no—
56C22⋊Q8×C73—24no—
57C22⋊Q8×C73—22no—
58C22⋊Q8×C73—22no—
59C22⋊Q8×C73—28no—
60C22⋊Q8×C73D414yes—
61C22⋊Q8×C73C2314yes—
62C2×C4⋊C4×C73—21no—
63C2×C4⋊C4×C73—22no—
64C2×C4⋊C4×C73—22no—
65C2×C4⋊C4×C73D412yes—
66C2×C22⋊C4×C73—22no—
67C2×C22⋊C4×C73—24no—
68C2×C22⋊C4×C73—22no—
69C2×C22⋊C4×C73—24no—
70C2×C22⋊C4×C73—22no—
71C2×C22⋊C4×C73—22no—
72C2×C22⋊C4×C73D412yes—
73C2×C22⋊C4×C73C2312yes—
74C22×Dic73—22no—
75C22×Dic73—22no—
76C22×Dic73—42no—
77C22×Dic73—42no—
78C22×Dic73—41no—
79C22×Dic73—41no—
80C22×Dic73—42no—
81C22×Dic73—42no—
82C22×Dic73—42no—
83C2×#10596831—24no—
84C2×#10596831—44no—
85C4⋊Dic73—24no—
86C4⋊Dic73—42no—
87C22⋊Dic73—48no—
88C24×C73—21no—
89C24×C73—21no—
90C24×C73—22no—
91C24×C73—42no—
92C24×C73—42no—
93C24×C73SD1614yes—
94C24×C73C2×D411yescharacteristic
95C24×C73C2×D412yes—
96C2×Q8×C73—24no—
97C2×Q8×C73—22no—
98C2×Q8×C73—44no—
99C2×Q8×C73—82no—
100C2×Q8×C73C2×D414yes—
101C22×C4×C73—22no—
102C22×C4×C73—21no—
103C22×C4×C73—22no—
104C22×C4×C73—24no—
105C22×C4×C73—24no—
106C22×C4×C73—21no—
107C22×C4×C73—42no—
108C22×C4×C73—42no—
109C22×C4×C73—82no—
110C22×C4×C73—82no—
111C22×C4×C73C2×D412yes—
112C22×C4×C73C2×D412yes—
113C22×C4×C73C2×D411yescharacteristic
114C22×C4×C73C2×D412yes—
115C22×C4×C73C2411yescharacteristic
116C4⋊C4×C73—24no—
117C4⋊C4×C73—28no—
118C4⋊C4×C73—24no—
119C4⋊C4×C73—22no—
120C4⋊C4×C73—24no—
121C4⋊C4×C73C2×D414yes—
122C22⋊C4×C73—28no—
123C22⋊C4×C73—24no—
124C22⋊C4×C73—24no—
125C22⋊C4×C73—24no—
126C22⋊C4×C73—24no—
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
147Q8×C73—44no—
148Q8×C73—82no—
149Q8×C73—84no—
150C2×C4×C73—24no—
151C2×C4×C73—24no—
152C2×C4×C73—22no—
153C2×C4×C73—24no—
154C2×C4×C73—42no—
155C2×C4×C73—41no—
156C2×C4×C73—41no—
157C2×C4×C73—42no—
158C2×C4×C73—44no—
159C2×C4×C73—44no—
160C2×C4×C73—42no—
161C2×C4×C73—81no—
162C2×C4×C73—84no—
163C2×C4×C73—84no—
164C2×C4×C73#12012yes—
165C2×C4×C73C22×D412yes—
166C2×Dic73—42no—
167C2×Dic73—42no—
168C2×Dic73—42no—
169C2×Dic73—42no—
170C2×Dic73—42no—
171C2×Dic73—42no—
172C2×Dic73—84no—
173C2×Dic73—82no—
174C2×Dic73—82no—
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—44no—
200C4×C73—44no—
201Dic73—82no—
202Dic73—82no—
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×#543D7311yescharacteristic
213C2×#483—732no—
214C2×#397—731no—
215#1608—738no—
216C2×#328—732no—
217C2×#323—731no—
218C73C2×#160811yescharacteristic, complemented, Sylow
219#543—24no—
220#543—22no—
221#543C2×D7314yes—
222C2×C22⋊Q8—22no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—22no—
225C2×C22⋊Q8C2×D7312yes—
226C22×C4⋊C4—731no—
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—734no—
236#397—1462no—
237C2×#95—731no—
238C2×#95—1461no—
239#328—738no—
240#323—734no—
241C25C22⋊D7311yescharacteristic
242C22×Q8—21no—
243C22×Q8C22⋊D7312yes—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—1461no—
247C23×C4—1461no—
248C23×C4C22⋊D7311yescharacteristic
249C23×C4C22×D7311yescharacteristic
250C22×C8—1462no—
251C22⋊Q8—28no—
252C22⋊Q8—28no—
253C22⋊Q8—24no—
254C22⋊Q8—28no—
255C22⋊Q8—24no—
256C22⋊Q8—22no—
257C22⋊Q8—22no—
258C22⋊Q8—28no—
259C22⋊Q8C22⋊D7314yes—
260C22⋊Q8C22×D7314yes—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—732no—
265C2×C4⋊C4—1461no—
266C2×C4⋊C4—1462no—
267C2×C4⋊C4—1462no—
268C2×C4⋊C4C22⋊D7312yes—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—24no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—24no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—2924no—
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—732no—
284#95—1461no—
285#95—1464no—
286C24—21no—
287C24—21no—
288C24—22no—
289C24—42no—
290C24—42no—
291C24#1192401514yes—
292C24C2×C22⋊D7311yescharacteristic
293C24C2×C22⋊D7312yes—
294C2×Q8—24no—
295C2×Q8—22no—
296C2×Q8—44no—
297C2×Q8—82no—
298C2×Q8C2×C22⋊D7314yes—
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—21no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—82no—
308C22×C4—82no—
309C22×C4—2922no—
310C22×C4—2922no—
311C22×C4—2921no—
312C22×C4—2921no—
313C22×C4—2922no—
314C22×C4—2922no—
315C22×C4—2922no—
316C22×C4—1462no—
317C22×C4—1462no—
318C22×C4C2×C22⋊D7312yes—
319C22×C4C2×C22⋊D7312yes—
320C22×C4C2×C22⋊D7311yescharacteristic
321C22×C4C2×C22⋊D7312yes—
322C22×C4C23×D7311yescharacteristic
323C2×C8—2924no—
324C2×C8—1464no—
325C4⋊C4—24no—
326C4⋊C4—28no—
327C4⋊C4—24no—
328C4⋊C4—22no—
329C4⋊C4—24no—
330C4⋊C4—2922no—
331C4⋊C4—1464no—
332C4⋊C4C2×C22⋊D7314yes—
333C22⋊C4—28no—
334C22⋊C4—24no—
335C22⋊C4—24no—
336C22⋊C4—24no—
337C22⋊C4—24no—
338C22⋊C4—2928no—
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#1455656011yescharacteristic
354C23#1455656011yescharacteristic
355C23C2×#1192401512yes—
356C23C2×#1192401514yes—
357C23#1455662212yes—
358C23C22×C22⋊D7311yescharacteristic
359Q8—44no—
360Q8—82no—
361Q8—84no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—22no—
365C2×C4—24no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4—42no—
373C2×C4—81no—
374C2×C4—84no—
375C2×C4—84no—
376C2×C4—2922no—
377C2×C4—2922no—
378C2×C4—2922no—
379C2×C4—2922no—
380C2×C4—2922no—
381C2×C4—2922no—
382C2×C4—5844no—
383C2×C4—5842no—
384C2×C4—5842no—
385C2×C4#1455656012yes—
386C2×C4C22×C22⋊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#1798872612yes—
402C22#1798872612yes—
403C22#1798876512yes—
404C22#1798877712yes—
405C22C2×#1455656011yescharacteristic
406C22C22×#1192401511yescharacteristic
407C22C2×#1455662211yescharacteristic
408C4—22no—
409C4—22no—
410C4—42no—
411C4—44no—
412C4—44no—
413C4—5842no—
414C4—5842no—
415C2—21no—
416C2—21no—
417C2—22no—
418C2—44no—
419C2#2260892214yesdirect product factor
420C2C2×#1798872611yescharacteristic
421C2C2×#1798876511yescharacteristic
422C2C2×#1798877711yescharacteristic
subgroupG/H
centerC23#14556560
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC2×#543×C73C2
socleC23×C73#120
prime radicalC25×C73D4
hypercenterC2×#543D73
hypocenterC73C2×#1608
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#543

Complements

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

NH ≅ G/Ntype
1. C2×#17988915C2semidirect
3. #22608922C2direct (N × H)
4. C2×#17988324C2semidirect
10. #17988915C22semidirect
18. #17988324C22semidirect
208. C2×C73#1608semidirect
218. C73C2×#1608semidirect
419. C2#22608922direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179889152
C2×#179885122
#226089222
C2×#179883242
C2×#179883112
C2×#543×C732
C2×#160873