Finite Group Databasebeta

← C2×#22608933 #33058200

Subgroups — C2×#22608933 #33058200

Order 18688.

1308 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1308 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×#17989168C211yesmaximal, characteristic
2C2×#17988900C212yesmaximal, complemented
3#22608933C218yesmaximal, direct product factor
4C2×#17988320C212yesmaximal, complemented
5C2×#17988313C211yesmaximal, characteristic, complemented
6C2×#398×C73C211yesmaximal, characteristic, complemented
7C22×#11924028—21no—
8#17989168—24no—
9#17989168—22no—
10#17989168C2214yes—
11C2×#14556571—22no—
12C2×#14556566—22no—
13C2×#14556565—21no—
14C2×#14556565C2212yes—
15#17988900—24no—
16#17988900C2218yescomplemented
17C2×#14556524—22no—
18C2×#14556511—22no—
19C2×C22⋊#10596831C2212yes—
20#17988320C2218yescomplemented
21#17988313C2214yescomplemented
22C22×C4⋊C4×C73—21no—
23C22×C4⋊C4×C73C2211yescharacteristic
24C22×C4⋊C4×C73C2211yescharacteristic
25#398×C73—22no—
26#398×C73C2214yescomplemented
27C2×#95×C73—21no—
28C2×#95×C73C2211yescharacteristic
29C2×#11924028—24no—
30C2×#11924028—24no—
31C2×#11924028—44no—
32C2×#11924028—44no—
33C22×Dic146—21no—
34C22×D292—21no—
35C22×D292—21no—
36C22×D292D412yes—
37C22×C22⋊D73—22no—
38C22×C4×D73—22no—
39C22×#10596831—22no—
40#14556571—28no—
41#14556571—28no—
42#14556566—28no—
43#14556566—28no—
44#14556565—24no—
45#14556565—22no—
46#14556565—22no—
47#14556565—24no—
48#14556565D414yes—
49#14556565C2314yes—
50C2×C4⋊Dic73—21no—
51C2×C4⋊Dic73D412yes—
52C2×#11924005—22no—
53C2×#11924005—22no—
54#14556524—28no—
55#14556511—28no—
56C22⋊#10596831—22no—
57C22⋊#10596831C2314yes—
58C23×C4×C73—21no—
59C23×C4×C73—21no—
60C23×C4×C73D411yescharacteristic
61C23×C4×C73D411yescharacteristic
62C23×C4×C73C2311yescharacteristic
63C2×C4⋊C4×C73—22no—
64C2×C4⋊C4×C73—22no—
65C2×C4⋊C4×C73—22no—
66C2×C4⋊C4×C73—22no—
67C2×C4⋊C4×C73—21no—
68C2×C4⋊C4×C73—24no—
69C2×C4⋊C4×C73—44no—
70C2×C4⋊C4×C73D412yes—
71C2×C4⋊C4×C73C2312yes—
72C2×C4⋊C4×C73C2312yes—
73#95×C73—21no—
74#95×C73—24no—
75#95×C73C2312yes—
76C23×D73—22no—
77#11924028—48no—
78#11924028—416no—
79#11924028—48no—
80C2×Dic146—24no—
81C2×Dic146—44no—
82C2×D292—24no—
83C2×D292—24no—
84C2×D292—22no—
85C2×D292—44no—
86C2×D292—44no—
87C2×D292—82no—
88C2×D292C2×D414yes—
89C2×C22⋊D73—24no—
90C2×C22⋊D73—24no—
91C2×C22⋊D73—44no—
92C2×C22⋊D73—44no—
93C22×Dic73—22no—
94C2×C4×D73—28no—
95C2×C4×D73—48no—
96C2×#10596831—24no—
97C2×#10596831—44no—
98C4⋊Dic73—24no—
99C4⋊Dic73—22no—
100C4⋊Dic73C2×D414yes—
101#11924005—28no—
102#11924005—24no—
103#11924005—24no—
104C24×C73C2×D411yescharacteristic
105C22×C4×C73—21no—
106C22×C4×C73—21no—
107C22×C4×C73—22no—
108C22×C4×C73—24no—
109C22×C4×C73—21no—
110C22×C4×C73—22no—
111C22×C4×C73—21no—
112C22×C4×C73—22no—
113C22×C4×C73—42no—
114C22×C4×C73—42no—
115C22×C4×C73—42no—
116C22×C4×C73—42no—
117C22×C4×C73—41no—
118C22×C4×C73—41no—
119C22×C4×C73—42no—
120C22×C4×C73—42no—
121C22×C4×C73D814yes—
122C22×C4×C73C2×D412yes—
123C22×C4×C73C2×D412yes—
124C22×C4×C73C2×D412yes—
125C22×C4×C73C2×D412yes—
126C22×C4×C73C2×D411yescharacteristic
127C22×C4×C73C2411yescharacteristic
128C4⋊C4×C73—24no—
129C4⋊C4×C73—24no—
130C4⋊C4×C73—24no—
131C4⋊C4×C73—42no—
132C4⋊C4×C73—48no—
133C23×C73—22no—
134C23×C73—22no—
135C23×C73#12011yescharacteristic
136C23×C73#12011yescharacteristic
137C23×C73C2×D812yes—
138C23×C73AGL(1,ℤ/8)12yes—
139C23×C73C22×D411yescharacteristic
140C22×D73—24no—
141C22×D73—44no—
142C22×D73—44no—
143C22×D73—44no—
144C2×C4×C73—22no—
145C2×C4×C73—22no—
146C2×C4×C73—24no—
147C2×C4×C73—24no—
148C2×C4×C73—24no—
149C2×C4×C73—24no—
150C2×C4×C73—22no—
151C2×C4×C73—42no—
152C2×C4×C73—41no—
153C2×C4×C73—41no—
154C2×C4×C73—48no—
155C2×C4×C73—42no—
156C2×C4×C73—42no—
157C2×C4×C73—42no—
158C2×C4×C73—42no—
159C2×C4×C73—42no—
160C2×C4×C73—42no—
161C2×C4×C73—42no—
162C2×C4×C73—81no—
163C2×C4×C73—82no—
164C2×C4×C73—82no—
165C2×C4×C73#12012yes—
166C2×C4×C73C2×D814yes—
167C2×C4×C73C22×D412yes—
168C22⋊D73—44no—
169C22⋊D73—44no—
170C22⋊D73—48no—
171C2×Dic73—24no—
172C2×Dic73—44no—
173D292—44no—
174D292—48no—
175D292—82no—
176D292—84no—
177C4×D73—416no—
178Dic146—48no—
179#10596831—44no—
180C22×C73—24no—
181C22×C73—24no—
182C22×C73—21no—
183C22×C73—21no—
184C22×C73—21no—
185C22×C73—21no—
186C22×C73#44712yes—
187C22×C73#44712yes—
188C22×C73#45612yes—
189C22×C73#45812yes—
190C22×C73C2×#12011yescharacteristic
191C22×C73C22×D811yescharacteristic
192C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
193C2×D73—44no—
194C2×D73—44no—
195C2×D73—44no—
196C2×D73—88no—
197C4×C73—24no—
198C4×C73—22no—
199C4×C73—22no—
200C4×C73—44no—
201C4×C73—42no—
202C4×C73—82no—
203Dic73—44no—
204C2×#1610—731nomaximal, Sylow
205C2×C73—21no—
206C2×C73—21no—
207C2×C73—22no—
208C2×C73#161014yescomplemented
209C2×C73C2×#44711yescharacteristic
210C2×C73C2×#45611yescharacteristic
211C2×C73C2×#45811yescharacteristic
212D73—84no—
213C2×#537—731no—
214C2×#480—732no—
215C2×#398D7311yescharacteristic, complemented
216#1610—738no—
217C2×#327—732no—
218C2×#324—731no—
219C73C2×#161011yescharacteristic, complemented, Sylow
220C22×#41—1461no—
221#537—734no—
222#537—1464no—
223#537—1462no—
224C2×C22⋊Q8—1462no—
225C2×#121—732no—
226C2×#121—1462no—
227C2×#121—1461no—
228C22×C4⋊C4—21no—
229C22×C4⋊C4C2×D7311yescharacteristic
230C22×C4⋊C4C2×D7311yescharacteristic
231#480—738no—
232#480—1464no—
233C2×#107—1462no—
234C2×#102—1462no—
235C2×C22⋊C8—732no—
236#398—22no—
237#398C2×D7314yescomplemented
238C2×#95—21no—
239C2×#95C2×D7311yescharacteristic
240#327—738no—
241#324—734no—
242C2×#41—2924no—
243C2×#41—2924no—
244C2×#41—1464no—
245C2×#41—1464no—
246C22×Q8—1461no—
247C22×D4—732no—
248C22×D4—1461no—
249C22×D4—1461no—
250C22×D4—1462no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—1462no—
254C23×C4C22⋊D7311yescharacteristic
255C23×C4C22⋊D7311yescharacteristic
256C23×C4C22×D7311yescharacteristic
257C22×C8—1462no—
258C22⋊Q8—1468no—
259C22⋊Q8—1468no—
260#121—734no—
261#121—734no—
262#121—1468no—
263#121—1468no—
264#121—1464no—
265#121—1462no—
266#121—1462no—
267#121—1464no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—44no—
275C2×C4⋊C4—732no—
276C2×C4⋊C4—1461no—
277C2×C4⋊C4C22⋊D7312yes—
278C2×C4⋊C4C22×D7312yes—
279C2×C4⋊C4C22×D7312yes—
280C2×C22⋊C4—1462no—
281C2×C22⋊C4—1462no—
282#107—1468no—
283#102—1468no—
284C22⋊C8—734no—
285C22⋊C8—1462no—
286#95—24no—
287#95—21no—
288#95C22×D7312yes—
289C24—1462no—
290C24C2×C22⋊D7311yescharacteristic
291#41—29216no—
292#41—2928no—
293#41—2928no—
294C2×Q8—2924no—
295C2×Q8—1464no—
296C2×D4—2924no—
297C2×D4—2924no—
298C2×D4—2924no—
299C2×D4—2924no—
300C2×D4—5842no—
301C2×D4—734no—
302C2×D4—1464no—
303C2×D4—1464no—
304C2×D4—1464no—
305C2×D4—1464no—
306C2×D4—1462no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—24no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—21no—
314C22×C4—22no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—2928no—
324C22×C4—1468no—
325C22×C4—1462no—
326C22×C4#1192401314yes—
327C22×C4D4×D7312yes—
328C22×C4D4×D7312yes—
329C22×C4C2×C22⋊D7312yes—
330C22×C4C2×C22⋊D7312yes—
331C22×C4C2×C22⋊D7311yescharacteristic
332C22×C4C23×D7311yescharacteristic
333C2×C8—2924no—
334C2×C8—1464no—
335C4⋊C4—24no—
336C4⋊C4—24no—
337C4⋊C4—24no—
338C4⋊C4—42no—
339C4⋊C4—48no—
340C4⋊C4—734no—
341C4⋊C4—1464no—
342C4⋊C4—1462no—
343C22⋊C4—1468no—
344C22⋊C4—1464no—
345C22⋊C4—1464no—
346C23—22no—
347C23—22no—
348C23—2924no—
349C23—2924no—
350C23—2924no—
351C23—1464no—
352C23#1455655911yescharacteristic
353C23#1455655911yescharacteristic
354C23C2×#1192401312yes—
355C23#1455661612yes—
356C23C22×C22⋊D7311yescharacteristic
357Q8—2928no—
358D4—2924no—
359D4—2928no—
360D4—2928no—
361D4—2924no—
362D4—2924no—
363D4—5842no—
364D4—5844no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—24no—
371C2×C4—22no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—48no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—81no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4—29216no—
387C2×C4—2924no—
388C2×C4—1464no—
389C2×C4#1455655912yes—
390C2×C4C2×#1192401314yes—
391C2×C4C2×D4×D7312yes—
392C8—2924no—
393C22—24no—
394C22—24no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—2924no—
400C22—2924no—
401C22—2924no—
402C22—5848no—
403C22#1798872012yes—
404C22#1798872012yes—
405C22#1798876912yes—
406C22#1798877612yes—
407C22C2×#1455655911yescharacteristic
408C22C22×#1192401311yescharacteristic
409C22C2×#1455661611yescharacteristic
410C4—22no—
411C4—22no—
412C4—24no—
413C4—44no—
414C4—42no—
415C4—82no—
416C4—2924no—
417C2—21no—
418C2—22no—
419C2—21no—
420C2—5844no—
421C2#2260893314yesdirect product factor
422C2C2×#1798872011yescharacteristic
423C2C2×#1798876911yescharacteristic
424C2C2×#1798877611yescharacteristic
subgroupG/H
centerC23#14556559
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC2×#398×C73C2
socleC23×C73#120
prime radicalC2×#17989168C2
hypercenterC2×#398D73
hypocenterC73C2×#1610
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
2. C2×#17988900C2semidirect
3. #22608933C2direct (N × H)
4. C2×#17988320C2semidirect
5. C2×#17988313C2semidirect
6. C2×#398×C73C2semidirect
16. #17988900C22semidirect
20. #17988320C22semidirect
21. #17988313C22semidirect
26. #398×C73C22semidirect
208. C2×C73#1610semidirect
215. C2×#398D73semidirect
219. C73C2×#1610semidirect
237. #398C2×D73semidirect
421. C2#22608933direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891682
C2×#179889002
#226089332
C2×#179883202
C2×#179883132
C2×#398×C732
C2×#161073