Finite Group Databasebeta

← C4×#17988377 #33001121

Subgroups — C4×#17988377 #33001121

Order 18688.

576 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988377C212yesmaximal
2C4×#14556508C211yesmaximal, characteristic
3C4×#14556506C211yesmaximal, characteristic
4#22608049C212yesmaximal
5C4×#123×C73C211yesmaximal, characteristic
6C2×#14556508C2212yes—
7C2×#14556506C2212yes—
8C4×#11924012—21no—
9C4×C22⋊Dic73—21no—
10#17988377C418yesdirect product factor
11#17988356—21no—
12#17988354—21no—
13C2×#123×C73C2211yescharacteristic
14C2×C4×D4×C73C2211yescharacteristic
15C22×C42×C73C411yescharacteristic, complemented
16#388×C73—21no—
17#387×C73—21no—
18#386×C73C2211yescharacteristic
19#385×C73C411yescharacteristic, complemented
20#381×C73C411yescharacteristic, complemented
21C4×C4⋊C4×C73—21no—
22C4×C22⋊C4×C73—21no—
23C4×C22⋊C4×C73C411yescharacteristic, complemented
24C2×#11924012—22no—
25C2×C22⋊Dic73—22no—
26C2×C4×Dic73—41no—
27#14556508—22no—
28#14556508C2×C414yes—
29#14556506—22no—
30#14556506C2×C414yes—
31#14556502—41no—
32C4×#10596831—41no—
33#14556498—41no—
34C22×D4×C73C2311yescharacteristic
35C23×C4×C73C2×C411yescharacteristic
36C23×C4×C73C2×C411yescharacteristic
37C23×C4×C73C2×C411yescharacteristic
38C23×C4×C73D411yescharacteristic
39#123×C73—22no—
40#123×C73C2×C414yes—
41C4×D4×C73—41no—
42C4×D4×C73—41no—
43C2×C4⋊C4×C73—21no—
44C2×C4⋊C4×C73—21no—
45C2×C4⋊C4×C73D411yescharacteristic
46C2×C22⋊C4×C73—21no—
47C2×C22⋊C4×C73—21no—
48C2×C22⋊C4×C73C2×C411yescharacteristic
49C2×C22⋊C4×C73C2×C411yescharacteristic
50C2×C22⋊C4×C73C2×C411yescharacteristic
51C2×C22⋊C4×C73D411yescharacteristic
52C2×C42×C73—21no—
53C2×C42×C73—21no—
54C2×C42×C73—21no—
55C2×C42×C73—41no—
56C2×C42×C73—41no—
57C2×C42×C73D411yescharacteristic
58#95×C73—21no—
59#95×C73—21no—
60#95×C73—21no—
61#95×C73—21no—
62#95×C73—21no—
63C22×Dic73—42no—
64#11924012—24no—
65#11924012—42no—
66C2×#10596831—42no—
67C22⋊Dic73—24no—
68C22⋊Dic73—42no—
69C4×Dic73—82no—
70C24×C73C22×C411yescharacteristic
71C24×C73C2×D411yescharacteristic
72C2×D4×C73—41no—
73C2×D4×C73—41no—
74C2×D4×C73C22×C412yes—
75C2×D4×C73#4112yes—
76C22×C4×C73—21no—
77C22×C4×C73—21no—
78C22×C4×C73—21no—
79C22×C4×C73—21no—
80C22×C4×C73—21no—
81C22×C4×C73—21no—
82C22×C4×C73—21no—
83C22×C4×C73—21no—
84C22×C4×C73—21no—
85C22×C4×C73—42no—
86C22×C4×C73—42no—
87C22×C4×C73—42no—
88C22×C4×C73—41no—
89C22×C4×C73—41no—
90C22×C4×C73—41no—
91C22×C4×C73C4212yescomplemented
92C22×C4×C73C22⋊C411yescharacteristic
93C22×C4×C73C22⋊C411yescharacteristic
94C22×C4×C73C22⋊C411yescharacteristic
95C22×C4×C73C22⋊C411yescharacteristic
96C22×C4×C73C2×D411yescharacteristic
97C4⋊C4×C73—24no—
98C4⋊C4×C73—41no—
99C4⋊C4×C73—42no—
100C22⋊C4×C73—21no—
101C22⋊C4×C73—24no—
102C22⋊C4×C73—41no—
103C22⋊C4×C73—41no—
104C22⋊C4×C73—42no—
105C22⋊C4×C73—41no—
106C22⋊C4×C73C4212yescomplemented
107C42×C73—21no—
108C42×C73—21no—
109C42×C73—42no—
110C42×C73—42no—
111C42×C73—41no—
112C42×C73—41no—
113C23×C73—21no—
114C23×C73—21no—
115C23×C73—21no—
116C23×C73—21no—
117C23×C73—41no—
118C23×C73—41no—
119C23×C73—41no—
120C23×C73—41no—
121C23×C73C2×C4211yescharacteristic
122C23×C73C2×C22⋊C411yescharacteristic
123C23×C73#11711yescharacteristic
124C23×C73C4×D412yes—
125D4×C73—42no—
126D4×C73—42no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—22no—
130C2×C4×C73—22no—
131C2×C4×C73—22no—
132C2×C4×C73—22no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—42no—
137C2×C4×C73—41no—
138C2×C4×C73—41no—
139C2×C4×C73—41no—
140C2×C4×C73—42no—
141C2×C4×C73—42no—
142C2×C4×C73—41no—
143C2×C4×C73—41no—
144C2×C4×C73—41no—
145C2×C4×C73—42no—
146C2×C4×C73—42no—
147C2×C4×C73—41no—
148C2×C4×C73—42no—
149C2×C4×C73—41no—
150C2×C4×C73—41no—
151C2×C4×C73—42no—
152C2×C4×C73—41no—
153C2×C4×C73—41no—
154C2×C4×C73—41no—
155C2×C4×C73—81no—
156C2×C4×C73#9911yescharacteristic
157C2×C4×C73#9911yescharacteristic
158C2×C4×C73C4×D412yes—
159C2×Dic73—44no—
160C2×Dic73—82no—
161C2×Dic73—82no—
162#10596831—44no—
163C22×C73—21no—
164C22×C73—21no—
165C22×C73—22no—
166C22×C73—21no—
167C22×C73—21no—
168C22×C73—41no—
169C22×C73—41no—
170C22×C73—42no—
171C22×C73—42no—
172C22×C73—41no—
173C22×C73—41no—
174C22×C73—41no—
175C22×C73—41no—
176C22×C73—81no—
177C22×C73C4×C22⋊C411yescharacteristic
178C22×C73C2×#9911yescharacteristic
179C22×C73#41011yescharacteristic
180C4×C73—21no—
181C4×C73—22no—
182C4×C73—42no—
183C4×C73—41no—
184C4×C73—41no—
185C4×C73—41no—
186C4×C73—42no—
187C4×C73—42no—
188C4×C73—81no—
189C4×C73#35212yescomplemented
190Dic73—84no—
191C4×#352—731nomaximal, Sylow
192C2×C73—21no—
193C2×C73—21no—
194C2×C73—42no—
195C2×C73—41no—
196C2×C73—41no—
197C2×C73C4×#9911yescharacteristic
198C2×C73C2×#35211yescharacteristic
199C2×C73#212011yescharacteristic
200C4×#123D7311yescharacteristic
201C2×#352—732no—
202C4×#100—731no—
203C4×#99—731no—
204#1390—732no—
205C73C4×#35211yescharacteristic, complemented, Sylow
206C2×#123C2×D7311yescharacteristic
207C2×C4×D4C2×D7311yescharacteristic
208C22×C42Dic7311yescharacteristic, complemented
209C2×#100—732no—
210C2×#99—732no—
211C4×M16—1461no—
212#388—21no—
213#387—21no—
214#386C2×D7311yescharacteristic
215#385Dic7311yescharacteristic, complemented
216#381Dic7311yescharacteristic, complemented
217C4×C4⋊C4—21no—
218C4×C22⋊C4—21no—
219C4×C22⋊C4—1461no—
220C4×C22⋊C4Dic7311yescharacteristic, complemented
221#352—738no—
222#343—1461no—
223#342—1461no—
224C22×D4C22×D7311yescharacteristic
225C23×C4C2×Dic7311yescharacteristic
226C23×C4C2×Dic7311yescharacteristic
227C23×C4C2×Dic7311yescharacteristic
228C23×C4C22⋊D7311yescharacteristic
229C2×M16—1462no—
230#123—22no—
231#123C4×D7314yes—
232C4×D4—41no—
233C4×D4—41no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C22⋊D7311yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—1462no—
240C2×C22⋊C4C2×Dic7311yescharacteristic
241C2×C22⋊C4C2×Dic7311yescharacteristic
242C2×C22⋊C4C2×Dic7311yescharacteristic
243C2×C22⋊C4C22⋊D7311yescharacteristic
244C2×C42—21no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42—41no—
248C2×C42—41no—
249C2×C42—2921no—
250C2×C42C22⋊D7311yescharacteristic
251#100—734no—
252#100—1462no—
253#99—734no—
254#99—1462no—
255#97—2921no—
256C4×C8—2921no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—2921no—
263C24C22×Dic7311yescharacteristic
264C24C2×C22⋊D7311yescharacteristic
265C2×D4—41no—
266C2×D4—41no—
267C2×D4C2×C4×D7312yes—
268C2×D4#1192402812yes—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—2922no—
285C22×C4C4×Dic7312yescomplemented
286C22×C4C22⋊Dic7311yescharacteristic
287C22×C4C22⋊Dic7311yescharacteristic
288C22×C4C22⋊Dic7311yescharacteristic
289C22×C4C22⋊Dic7311yescharacteristic
290C22×C4C2×C22⋊D7311yescharacteristic
291M16—2922no—
292M16—1464no—
293C2×C8—2922no—
294C4⋊C4—24no—
295C4⋊C4—41no—
296C4⋊C4—42no—
297C22⋊C4—21no—
298C22⋊C4—24no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—42no—
302C22⋊C4—41no—
303C22⋊C4—2922no—
304C22⋊C4—1464no—
305C22⋊C4C4×Dic7312yescomplemented
306C42—21no—
307C42—21no—
308C42—42no—
309C42—42no—
310C42—41no—
311C42—41no—
312C42—5842no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23C2×C4×Dic7311yescharacteristic
322C23C2×C22⋊Dic7311yescharacteristic
323C23#1455655011yescharacteristic
324C23C4×C22⋊D7312yes—
325D4—42no—
326D4—42no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—2924no—
357C2×C4—5842no—
358C2×C4—5842no—
359C2×C4#1455650611yescharacteristic
360C2×C4#1455650611yescharacteristic
361C2×C4C4×C22⋊D7312yes—
362C8—2924no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—22no—
368C22—41no—
369C22—41no—
370C22—42no—
371C22—42no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—81no—
377C22C4×C22⋊Dic7311yescharacteristic
378C22C2×#1455650611yescharacteristic
379C22#1798856111yescharacteristic
380C4—22no—
381C4—21no—
382C4—42no—
383C4—42no—
384C4—41no—
385C4—41no—
386C4—42no—
387C4—41no—
388C4—81no—
389C4—5844no—
390C4#1798837712yesdirect product factor
391C2—21no—
392C2—21no—
393C2—42no—
394C2—41no—
395C2—41no—
396C2C4×#1455650611yescharacteristic
397C2C2×#1798837711yescharacteristic
398C2#2261157211yescharacteristic
subgroupG/H
centerC2×C4#14556506
commutatorC23×C73C2×C42
FrattiniC22×D4C22×D73
FittingC4×#123×C73C2
socleC22×C73C2×#99
prime radical, cosocleC22×D4×C73C23
hypercenterC4×#123D73
hypocenterC73C4×#352
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#123

Complements

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

NH ≅ G/Ntype
10. #17988377C4direct (N × H)
15. C22×C42×C73C4semidirect
19. #385×C73C4semidirect
20. #381×C73C4semidirect
23. C4×C22⋊C4×C73C4semidirect
91. C22×C4×C73C42semidirect
106. C22⋊C4×C73C42semidirect
189. C4×C73#352semidirect
205. C73C4×#352semidirect
208. C22×C42Dic73semidirect
215. #385Dic73semidirect
216. #381Dic73semidirect
220. C4×C22⋊C4Dic73semidirect
285. C22×C4C4×Dic73semidirect
305. C22⋊C4C4×Dic73semidirect
390. C4#17988377direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179883772
C4×#145565082
C4×#145565062
#226080492
C4×#123×C732
C4×#35273