Finite Group Databasebeta

← #64408⋊#324 #34033263

Subgroups — #64408⋊#324 #34033263

Order 18688.

730 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊#10596842C212yesmaximal
2C2×#17989673C212yesmaximal
3#22626940C212yesmaximal
4C2×C4⋊C4×#64408C211yesmaximal, characteristic
5C2×C22⋊#10596842C2214yes—
6C2×C4×#10596842—22no—
7(C2×#10596842)⋊C4—22no—
8#17989673C418yescomplemented
9C22×C4⋊#64408C2211yescharacteristic
10C22×C4×#64408C411yescharacteristic
11C22×C4×#64408C411yescharacteristic
12C22×C4×#64408C2211yescharacteristic
13C4⋊C4×#64408—22no—
14C4⋊C4×#64408—22no—
15C2×(C2×#64408)⋊C4C411yescharacteristic
16C2×(C2×#64408)⋊C4C2211yescharacteristic
17C2×C4⋊C4×D73C411yescharacteristic
18C22×#10596842—24no—
19C22⋊#10596842—24no—
20C22⋊#10596842C2×C418yes—
21C4×#10596842—44no—
22C23×#64408C2×C411yescharacteristic
23C23×#64408C2×C411yescharacteristic
24C23×#64408C2×C411yescharacteristic
25C23×#64408C2311yescharacteristic
26C2×C4⋊#64408—22no—
27C2×C4⋊#64408—22no—
28C2×C4⋊#64408C2×C414yes—
29C2×C4×#64408—21no—
30C2×C4×#64408—21no—
31C2×C4×#64408—22no—
32C2×C4×#64408—21no—
33C2×C4×#64408—21no—
34C2×C4×#64408—42no—
35C2×C4×#64408—42no—
36C2×C4×#64408C814yescomplemented
37C2×C4×#64408D412yes—
38C2×C4×#64408D412yes—
39(C2×#64408)⋊C4—22no—
40(C2×#64408)⋊C4—22no—
41C22×C4×D73C2×C411yescharacteristic
42C22×C4×D73C2×C411yescharacteristic
43C22×C4×D73C2×C411yescharacteristic
44C2×C4⋊Dic73C811yescharacteristic, complemented
45C2×#11924007C811yescharacteristic, complemented
46C2×#11924007C811yescharacteristic, complemented
47C4⋊C4×D73—22no—
48C4⋊C4×D73—22no—
49C2×C4⋊C4×C73C811yescharacteristic, complemented
50C2×#10596842—28no—
51C2×#10596842—44no—
52C2×#10596842—44no—
53C22×#64408—22no—
54C22×#64408—22no—
55C22×#64408—21no—
56C22×#64408—21no—
57C22×#64408—21no—
58C22×#64408—21no—
59C22×#64408—41no—
60C22×#64408—41no—
61C22×#64408—41no—
62C22×#64408—41no—
63C22×#64408—41no—
64C22×#64408—41no—
65C22×#64408C4212yes—
66C22×#64408C22⋊C411yescharacteristic
67C22×#64408C22⋊C411yescharacteristic
68C22×#64408C2×C812yes—
69C22×#64408C2×C812yes—
70C22×#64408M1612yes—
71C22×#64408C22×C412yes—
72C22×#64408C2×D412yes—
73C22×#64408#4112yes—
74C4⋊#64408—28no—
75C4×#64408—24no—
76C4×#64408—24no—
77C4×#64408—24no—
78C4×#64408—42no—
79C4×#64408—42no—
80C4×#64408—42no—
81C23×D73C22×C411yescharacteristic
82C22×Dic73C2×C811yescharacteristic
83C22×Dic73C2×C811yescharacteristic
84C22×Dic73C2×C811yescharacteristic
85C2×C4×D73—21no—
86C2×C4×D73—21no—
87C2×C4×D73—21no—
88C2×C4×D73—21no—
89C2×C4×D73—21no—
90C2×C4×D73—21no—
91C2×C4×D73—41no—
92C2×C4×D73—41no—
93C2×C4×D73—41no—
94C2×C4×D73—41no—
95C2×C4×D73C4212yes—
96C2×C4×D73C22⋊C412yes—
97C2×C4×D73C2×C812yes—
98C2×C4×D73M1612yes—
99C4⋊Dic73—22no—
100#11924007—22no—
101#11924007—22no—
102C22×C4×C73C2×C811yescharacteristic
103C22×C4×C73C2×C811yescharacteristic
104C22×C4×C73C2×C811yescharacteristic
105C4⋊C4×C73—22no—
106C23×C73C22×C811yescharacteristic
107C22×D73—21no—
108C22×D73—21no—
109C22×D73—21no—
110C22×D73—21no—
111C22×D73C2×C4211yescharacteristic
112C22×D73C2×C22⋊C411yescharacteristic
113C22×D73#11711yescharacteristic
114C22×D73C22×C811yescharacteristic
115C22×D73C2×M1611yescharacteristic
116C22×D73C2×M1611yescharacteristic
117C2×#64408—22no—
118C2×#64408—21no—
119C2×#64408—22no—
120C2×#64408—21no—
121C2×#64408—24no—
122C2×#64408—24no—
123C2×#64408—22no—
124C2×#64408—22no—
125C2×#64408—42no—
126C2×#64408—42no—
127C2×#64408—42no—
128C2×#64408—42no—
129C2×#64408—41no—
130C2×#64408—41no—
131C2×#64408—41no—
132C2×#64408—41no—
133C2×#64408—42no—
134C2×#64408—42no—
135C2×#64408C22⋊C812yes—
136C2×#64408C22⋊C812yes—
137C2×#64408#9912yes—
138C2×#64408#10112yes—
139C2×#64408C4×D414yes—
140#10596842—48no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73—41no—
145C2×C4×C73—41no—
146C2×C4×C73C4×C812yescomplemented
147C2×C4×C73C22⋊C812yes—
148C2×Dic73—21no—
149C2×Dic73—21no—
150C2×Dic73—21no—
151C2×Dic73—41no—
152C2×Dic73—41no—
153C2×Dic73C4×C812yescomplemented
154C2×Dic73C22⋊C812yes—
155C4×D73—22no—
156C4×D73—22no—
157C4×D73—22no—
158C4×D73—22no—
159C4×D73—22no—
160C4×D73—22no—
161C4×D73—42no—
162C4×D73—42no—
163C4×D73—41no—
164C4×D73—41no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73C2×C4×C811yescharacteristic
168C22×C73C2×C22⋊C811yescharacteristic
169C22×C73#43111yescharacteristic
170C2×D73—21no—
171C2×D73—21no—
172C2×D73—21no—
173C2×D73—21no—
174C2×D73—21no—
175C2×D73—21no—
176C2×D73—21no—
177C2×D73—21no—
178C2×D73—21no—
179C2×D73—21no—
180C2×D73C4×C22⋊C411yescharacteristic
181C2×D73C4×M1611yescharacteristic
182C2×D73C2×C22⋊C811yescharacteristic
183C2×D73C2×#9911yescharacteristic
184C2×D73#41011yescharacteristic
185C2×D73C2×#10111yescharacteristic
186C2×D73#41311yescharacteristic
187C2×D73#43111yescharacteristic
188#64408—22no—
189#64408—24no—
190#64408—42no—
191#64408—42no—
192#64408#32414yescomplemented
193C4×C73—22no—
194C4×C73—22no—
195C4×C73—41no—
196Dic73—22no—
197Dic73—22no—
198Dic73—41no—
199C4×#324—731nomaximal, Sylow
200C2×C73—21no—
201C2×C73—21no—
202C2×C73#145911yescharacteristic
203C2×C73#146111yescharacteristic
204C2×C73C4×C22⋊C811yescharacteristic
205D73—21no—
206D73—21no—
207D73C2×#32411yescharacteristic
208D73#145811yescharacteristic
209D73C4×#9911yescharacteristic
210D73C4×#10111yescharacteristic
211C2×C4×C4⋊C4—731no—
212C4×C22⋊C8—732no—
213C2×#324—732no—
214#1280—732no—
215C73C4×#32411yescharacteristic, complemented, Sylow
216C22×C4⋊C4—731no—
217C22×C4⋊C4—731no—
218C22×C42—731no—
219C22×C42—731no—
220C22×C42—731no—
221C2×C22⋊C8—734no—
222C2×C4×C8—1462no—
223C4×C4⋊C4—1462no—
224C4×C4⋊C4—1462no—
225C2×#95—731no—
226C2×#95—731no—
227#336—1462no—
228#324—738no—
229C23×C4—731no—
230C23×C4—731no—
231C23×C4—731no—
232C23×C4—731no—
233C23×C4—731no—
234C23×C4—731no—
235C23×C4—731no—
236C22×C8—1464no—
237C2×C4⋊C4—734no—
238C2×C4⋊C4—731no—
239C2×C4⋊C4—731no—
240C2×C4⋊C4—731no—
241C2×C4⋊C4—1462no—
242C2×C4⋊C4—1462no—
243C2×C4⋊C4—1462no—
244C2×C4⋊C4—1462no—
245C2×C4⋊C4#1059684211yescharacteristic, complemented
246C2×C42—2922no—
247C2×C42—2922no—
248C2×C42—732no—
249C2×C42—732no—
250C2×C42—734no—
251C2×C42—1461no—
252C2×C42—1461no—
253C2×C42—1461no—
254C2×C42—1461no—
255C2×C42—1462no—
256C22⋊C8—738no—
257C22⋊C8—1464no—
258C4×C8—2924no—
259#95—1462no—
260#95—1462no—
261C24—731no—
262C22×C4—2921no—
263C22×C4—2921no—
264C22×C4—2921no—
265C22×C4—2921no—
266C22×C4—2921no—
267C22×C4—2921no—
268C22×C4—2921no—
269C22×C4—2921no—
270C22×C4—2921no—
271C22×C4—2921no—
272C22×C4—732no—
273C22×C4—732no—
274C22×C4—731no—
275C22×C4—732no—
276C22×C4—732no—
277C22×C4—732no—
278C22×C4—731no—
279C22×C4—731no—
280C22×C4—731no—
281C22×C4—732no—
282C22×C4—732no—
283C22×C4—732no—
284C22×C4—731no—
285C22×C4—732no—
286C22×C4—732no—
287C22×C4—732no—
288C22×C4—1461no—
289C22×C4—1461no—
290C22×C4—1461no—
291C22×C4—1461no—
292C22×C4—1461no—
293C22×C4—1461no—
294C22×C4—1461no—
295C22×C4—1461no—
296C22×C4—1461no—
297C22×C4—1461no—
298C22×C4—1462no—
299C22×C4—1462no—
300C22×C4C2×#1059684211yescharacteristic
301C22×C4C2×#1059684211yescharacteristic
302C22×C4C2×#1059684211yescharacteristic
303C2×C8—2924no—
304C2×C8—2924no—
305C2×C8—1468no—
306C4⋊C4—22no—
307C4⋊C4—1462no—
308C4⋊C4—1462no—
309C4⋊C4—1468no—
310C4⋊C4—1462no—
311C42—2922no—
312C42—2922no—
313C42—2922no—
314C42—1464no—
315C42—1464no—
316C42—1464no—
317C23—731no—
318C23—731no—
319C23—731no—
320C23—731no—
321C23—731no—
322C23—731no—
323C23—1461no—
324C23—1461no—
325C23—1461no—
326C23—1461no—
327C23C22×#1059684211yescharacteristic
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—2922no—
334C2×C4—2921no—
335C2×C4—2921no—
336C2×C4—2922no—
337C2×C4—2921no—
338C2×C4—2921no—
339C2×C4—2921no—
340C2×C4—2921no—
341C2×C4—2922no—
342C2×C4—2922no—
343C2×C4—2921no—
344C2×C4—2922no—
345C2×C4—2922no—
346C2×C4—2921no—
347C2×C4—2922no—
348C2×C4—2922no—
349C2×C4—732no—
350C2×C4—732no—
351C2×C4—732no—
352C2×C4—732no—
353C2×C4—734no—
354C2×C4—732no—
355C2×C4—732no—
356C2×C4—1462no—
357C2×C4—1462no—
358C2×C4—1462no—
359C2×C4—1462no—
360C2×C4—1462no—
361C2×C4—1462no—
362C2×C4—1462no—
363C2×C4—1462no—
364C2×C4—1461no—
365C2×C4—1464no—
366C2×C4—1464no—
367C2×C4—1461no—
368C2×C4—1462no—
369C2×C4—1462no—
370C2×C4—1461no—
371C2×C4—1461no—
372C2×C4—1461no—
373C2×C4C4×#1059684212yescomplemented
374C2×C4C22⋊#1059684212yes—
375C8—2928no—
376C22—21no—
377C22—21no—
378C22—731no—
379C22—731no—
380C22—731no—
381C22—731no—
382C22—731no—
383C22—731no—
384C22—731no—
385C22—731no—
386C22—1461no—
387C22—1461no—
388C22—1461no—
389C22—1461no—
390C22—1461no—
391C22—1461no—
392C22—1461no—
393C22—1461no—
394C22—1461no—
395C22—1461no—
396C22C2×C4×#1059684211yescharacteristic
397C22C2×C22⋊#1059684211yescharacteristic
398C22#1798970011yescharacteristic
399C4—22no—
400C4—22no—
401C4—41no—
402C4—2922no—
403C4—2922no—
404C4—2921no—
405C4—734no—
406C4—1464no—
407C4—1462no—
408C4—1462no—
409C4—1462no—
410C2—21no—
411C2—21no—
412C2—731no—
413C2—731no—
414C2—731no—
415C2—731no—
416C2—1461no—
417C2—1461no—
418C2#2262704411yescharacteristic
419C2#2262704611yescharacteristic
420C2C4×C22⋊#1059684211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10596842
commutatorC22×C73C2×C4×C8
FrattiniC23C22×#10596842
FittingC2×C4⋊C4×C73C8
socleC22×C73C2×C22⋊C8
prime radicalC23×D73C22×C4
cosocleC23×#64408C23
hypercenterC2×C4⋊C4#10596842
hypocenterC73C4×#324
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
8. #17989673C4semidirect
36. C2×C4×#64408C8semidirect
44. C2×C4⋊Dic73C8semidirect
45. C2×#11924007C8semidirect
46. C2×#11924007C8semidirect
49. C2×C4⋊C4×C73C8semidirect
146. C2×C4×C73C4×C8semidirect
153. C2×Dic73C4×C8semidirect
192. #64408#324semidirect
215. C73C4×#324semidirect
245. C2×C4⋊C4#10596842semidirect
373. C2×C4C4×#10596842semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#105968422
C2×#179896732
#226269402
C2×C4⋊C4×#644082
C4×#32473