Finite Group Databasebeta

← C4×#17989673 #34033262

Subgroups — C4×#17989673 #34033262

Order 18688.

730 conjugacy classes of subgroups.

The subgroup lattice has 438 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#17989673C418yesdirect product factor
9C22×C4⋊#64408C411yescharacteristic
10C22×C4⋊#64408C2211yescharacteristic
11C22×C4×#64408C411yescharacteristic
12C22×C4×#64408C2211yescharacteristic
13C4×C4⋊#64408—22no—
14C4×C4⋊#64408—22no—
15C2×(C2×#64408)⋊C4C411yescharacteristic
16C2×(C2×#64408)⋊C4C2211yescharacteristic
17C2×C42×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⋊#64408—22no—
29C2×C4⋊#64408—22no—
30C2×C4⋊#64408C814yescomplemented
31C2×C4⋊#64408C2×C414yes—
32C2×C4×#64408—21no—
33C2×C4×#64408—21no—
34C2×C4×#64408—42no—
35C2×C4×#64408—42no—
36C2×C4×#64408D412yes—
37C2×C4×#64408D412yes—
38(C2×#64408)⋊C4—22no—
39(C2×#64408)⋊C4—22no—
40C22×C4×D73C2×C411yescharacteristic
41C22×C4×D73C2×C411yescharacteristic
42C22×C4×D73C2×C411yescharacteristic
43C2×C4×Dic73C811yescharacteristic, complemented
44C2×C4×Dic73C811yescharacteristic, complemented
45C2×C4×Dic73C811yescharacteristic, complemented
46C42×D73—21no—
47C42×D73—21no—
48C42×D73—21no—
49C42×D73—21no—
50C2×C42×C73C811yescharacteristic, complemented
51C2×#10596842—28no—
52C2×#10596842—44no—
53C2×#10596842—44no—
54C22×#64408—21no—
55C22×#64408—21no—
56C22×#64408—21no—
57C22×#64408—21no—
58C22×#64408—41no—
59C22×#64408—41no—
60C22×#64408—41no—
61C22×#64408—41no—
62C22×#64408—41no—
63C22×#64408—41no—
64C22×#64408—41no—
65C22×#64408—41no—
66C22×#64408C4212yes—
67C22×#64408C22⋊C412yes—
68C22×#64408C2×C812yes—
69C22×#64408C2×C812yes—
70C22×#64408M1612yes—
71C22×#64408C22×C412yes—
72C22×#64408C2×D412yes—
73C22×#64408#4112yes—
74C4⋊#64408—28no—
75C4⋊#64408—28no—
76C4×#64408—24no—
77C4×#64408—42no—
78C4×#64408—42no—
79C4×#64408—42no—
80C23×D73C22×C411yescharacteristic
81C22×Dic73C2×C811yescharacteristic
82C22×Dic73C2×C811yescharacteristic
83C22×Dic73C2×C811yescharacteristic
84C2×C4×D73—21no—
85C2×C4×D73—21no—
86C2×C4×D73—21no—
87C2×C4×D73—21no—
88C2×C4×D73—22no—
89C2×C4×D73—22no—
90C2×C4×D73—21no—
91C2×C4×D73—21no—
92C2×C4×D73—41no—
93C2×C4×D73—41no—
94C2×C4×D73C4212yes—
95C2×C4×D73C22⋊C411yescharacteristic
96C2×C4×D73C22⋊C411yescharacteristic
97C2×C4×D73C2×C812yes—
98C2×C4×D73M1611yescharacteristic
99C2×C4×D73M1611yescharacteristic
100C4×Dic73—21no—
101C4×Dic73—21no—
102C4×Dic73—21no—
103C4×Dic73—21no—
104C4×Dic73—21no—
105C4×Dic73—21no—
106C22×C4×C73C2×C811yescharacteristic
107C22×C4×C73C2×C811yescharacteristic
108C22×C4×C73C2×C811yescharacteristic
109C42×C73—21no—
110C42×C73—21no—
111C23×C73C22×C811yescharacteristic
112C22×D73—21no—
113C22×D73—21no—
114C22×D73—21no—
115C22×D73—21no—
116C22×D73C2×C4211yescharacteristic
117C22×D73C2×C22⋊C411yescharacteristic
118C22×D73#11711yescharacteristic
119C22×D73C22×C811yescharacteristic
120C22×D73C2×M1611yescharacteristic
121C22×D73C2×M1611yescharacteristic
122C2×#64408—22no—
123C2×#64408—22no—
124C2×#64408—22no—
125C2×#64408—22no—
126C2×#64408—22no—
127C2×#64408—22no—
128C2×#64408—42no—
129C2×#64408—42no—
130C2×#64408—42no—
131C2×#64408—42no—
132C2×#64408—42no—
133C2×#64408—42no—
134C2×#64408—41no—
135C2×#64408—41no—
136C2×#64408—41no—
137C2×#64408—41no—
138C2×#64408—42no—
139C2×#64408—42no—
140C2×#64408C22⋊C814yes—
141C2×#64408C4×D414yes—
142#10596842—48no—
143C2×C4×C73—21no—
144C2×C4×C73—21no—
145C2×C4×C73—22no—
146C2×C4×C73—21no—
147C2×C4×C73—41no—
148C2×C4×C73C4×C812yescomplemented
149C2×C4×C73C22⋊C811yescharacteristic
150C2×C4×C73C22⋊C811yescharacteristic
151C2×Dic73—21no—
152C2×Dic73—21no—
153C2×Dic73—22no—
154C2×Dic73—21no—
155C2×Dic73—41no—
156C2×Dic73C4×C812yescomplemented
157C2×Dic73C22⋊C811yescharacteristic
158C2×Dic73C22⋊C811yescharacteristic
159C4×D73—22no—
160C4×D73—22no—
161C4×D73—22no—
162C4×D73—21no—
163C4×D73—21no—
164C4×D73—22no—
165C4×D73—22no—
166C4×D73—22no—
167C4×D73—42no—
168C4×D73—41no—
169C4×D73—41no—
170C4×D73#9912yes—
171C4×D73#10112yes—
172C22×C73—21no—
173C22×C73—21no—
174C22×C73C2×C4×C811yescharacteristic
175C22×C73C2×C22⋊C811yescharacteristic
176C22×C73#43111yescharacteristic
177C2×D73—21no—
178C2×D73—21no—
179C2×D73—21no—
180C2×D73—21no—
181C2×D73—21no—
182C2×D73—21no—
183C2×D73—21no—
184C2×D73—21no—
185C2×D73—21no—
186C2×D73—21no—
187C2×D73C4×C22⋊C411yescharacteristic
188C2×D73C4×M1611yescharacteristic
189C2×D73C2×C22⋊C811yescharacteristic
190C2×D73C2×#9911yescharacteristic
191C2×D73#41011yescharacteristic
192C2×D73C2×#10111yescharacteristic
193C2×D73#41311yescharacteristic
194C2×D73#43111yescharacteristic
195#64408—24no—
196#64408—24no—
197#64408—42no—
198#64408—42no—
199C4×C73—21no—
200C4×C73—22no—
201C4×C73—41no—
202C4×C73#32412yescomplemented
203Dic73—21no—
204Dic73—22no—
205Dic73—41no—
206Dic73#32412yescomplemented
207C4×#324—731nomaximal, Sylow
208C2×C73—21no—
209C2×C73—21no—
210C2×C73C2×#32411yescharacteristic
211C2×C73#145811yescharacteristic
212C2×C73C4×C22⋊C811yescharacteristic
213D73—21no—
214D73—21no—
215D73#145911yescharacteristic
216D73#146111yescharacteristic
217D73C4×#9911yescharacteristic
218D73C4×#10111yescharacteristic
219C2×C4×C4⋊C4—731no—
220C4×C22⋊C8—732no—
221C2×#324—732no—
222#1280—732no—
223C73C4×#32411yescharacteristic, complemented, Sylow
224C22×C4⋊C4—731no—
225C22×C4⋊C4—731no—
226C22×C42—731no—
227C22×C42—731no—
228C22×C42—731no—
229C2×C22⋊C8—734no—
230C2×C4×C8—1462no—
231C4×C4⋊C4—1462no—
232C4×C4⋊C4—1462no—
233C2×#95—731no—
234C2×#95—731no—
235#336—1462no—
236#324—738no—
237C23×C4—731no—
238C23×C4—731no—
239C23×C4—731no—
240C23×C4—731no—
241C23×C4—731no—
242C23×C4—731no—
243C23×C4—731no—
244C22×C8—1464no—
245C2×C4⋊C4—734no—
246C2×C4⋊C4—734no—
247C2×C4⋊C4—1462no—
248C2×C4⋊C4—1462no—
249C2×C4⋊C4—1462no—
250C2×C4⋊C4—1462no—
251C2×C42—2922no—
252C2×C42—2922no—
253C2×C42—732no—
254C2×C42—732no—
255C2×C42—731no—
256C2×C42—731no—
257C2×C42—731no—
258C2×C42—1461no—
259C2×C42—1461no—
260C2×C42—1461no—
261C2×C42—1461no—
262C2×C42—1461no—
263C2×C42—1461no—
264C2×C42#1059684211yescharacteristic, complemented
265C22⋊C8—738no—
266C22⋊C8—1464no—
267C4×C8—2924no—
268#95—1462no—
269#95—1462no—
270C24—731no—
271C22×C4—2921no—
272C22×C4—2921no—
273C22×C4—2921no—
274C22×C4—2921no—
275C22×C4—2921no—
276C22×C4—2921no—
277C22×C4—2921no—
278C22×C4—2921no—
279C22×C4—2921no—
280C22×C4—2921no—
281C22×C4—732no—
282C22×C4—732no—
283C22×C4—732no—
284C22×C4—732no—
285C22×C4—732no—
286C22×C4—732no—
287C22×C4—731no—
288C22×C4—731no—
289C22×C4—732no—
290C22×C4—732no—
291C22×C4—731no—
292C22×C4—731no—
293C22×C4—732no—
294C22×C4—732no—
295C22×C4—731no—
296C22×C4—731no—
297C22×C4—731no—
298C22×C4—1461no—
299C22×C4—1461no—
300C22×C4—1462no—
301C22×C4—1462no—
302C22×C4—1461no—
303C22×C4—1461no—
304C22×C4—1461no—
305C22×C4—1461no—
306C22×C4—1461no—
307C22×C4—1461no—
308C22×C4—1461no—
309C22×C4—1461no—
310C22×C4C2×#1059684211yescharacteristic
311C22×C4C2×#1059684211yescharacteristic
312C22×C4C2×#1059684211yescharacteristic
313C2×C8—2924no—
314C2×C8—2924no—
315C2×C8—1468no—
316C4⋊C4—1468no—
317C4⋊C4—1468no—
318C42—21no—
319C42—21no—
320C42—2922no—
321C42—2922no—
322C42—2922no—
323C42—1461no—
324C42—1461no—
325C42—1461no—
326C42—1461no—
327C42—1464no—
328C42—1461no—
329C42—1461no—
330C23—731no—
331C23—731no—
332C23—731no—
333C23—731no—
334C23—731no—
335C23—731no—
336C23—1461no—
337C23—1461no—
338C23—1461no—
339C23—1461no—
340C23C22×#1059684211yescharacteristic
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—2921no—
347C2×C4—2921no—
348C2×C4—2922no—
349C2×C4—2921no—
350C2×C4—2921no—
351C2×C4—2921no—
352C2×C4—2921no—
353C2×C4—2922no—
354C2×C4—2922no—
355C2×C4—2921no—
356C2×C4—2922no—
357C2×C4—2922no—
358C2×C4—2922no—
359C2×C4—2922no—
360C2×C4—2922no—
361C2×C4—2922no—
362C2×C4—731no—
363C2×C4—732no—
364C2×C4—732no—
365C2×C4—734no—
366C2×C4—734no—
367C2×C4—732no—
368C2×C4—731no—
369C2×C4—1462no—
370C2×C4—1461no—
371C2×C4—1462no—
372C2×C4—1462no—
373C2×C4—1461no—
374C2×C4—1462no—
375C2×C4—1462no—
376C2×C4—1462no—
377C2×C4—1462no—
378C2×C4—1461no—
379C2×C4—1462no—
380C2×C4—1462no—
381C2×C4—1462no—
382C2×C4—1462no—
383C2×C4—1462no—
384C2×C4—1461no—
385C2×C4—1461no—
386C2×C4—1462no—
387C2×C4C4×#1059684212yescomplemented
388C2×C4C22⋊#1059684211yescharacteristic
389C2×C4C22⋊#1059684211yescharacteristic
390C8—2928no—
391C22—21no—
392C22—21no—
393C22—731no—
394C22—731no—
395C22—731no—
396C22—731no—
397C22—731no—
398C22—731no—
399C22—731no—
400C22—731no—
401C22—1461no—
402C22—1461no—
403C22—1461no—
404C22—1461no—
405C22—1461no—
406C22—1461no—
407C22—1461no—
408C22—1461no—
409C22—1461no—
410C22—1461no—
411C22C2×C4×#1059684211yescharacteristic
412C22C2×C22⋊#1059684211yescharacteristic
413C22#1798970011yescharacteristic
414C4—21no—
415C4—22no—
416C4—41no—
417C4—2922no—
418C4—2922no—
419C4—2921no—
420C4—732no—
421C4—1464no—
422C4—1464no—
423C4—1461no—
424C4—1462no—
425C4#1798967312yesdirect product factor
426C2—21no—
427C2—21no—
428C2—731no—
429C2—731no—
430C2—731no—
431C2—731no—
432C2—1461no—
433C2—1461no—
434C2C2×#1798967311yescharacteristic
435C2#2262704311yescharacteristic
436C2C4×C22⋊#1059684211yescharacteristic
subgroupG/H
centerC2×C4C22⋊#10596842
commutatorC22×C73C2×C4×C8
FrattiniC23C22×#10596842
FittingC2×C42×C73C8
socleC22×C73C2×C22⋊C8
prime radicalC23×D73C22×C4
cosocleC23×#64408C23
hypercenterC2×C42#10596842
hypocenterC73C4×#324
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
8. #17989673C4direct (N × H)
30. C2×C4⋊#64408C8semidirect
43. C2×C4×Dic73C8semidirect
44. C2×C4×Dic73C8semidirect
45. C2×C4×Dic73C8semidirect
50. C2×C42×C73C8semidirect
148. C2×C4×C73C4×C8semidirect
156. C2×Dic73C4×C8semidirect
202. C4×C73#324semidirect
206. Dic73#324semidirect
223. C73C4×#324semidirect
264. C2×C42#10596842semidirect
387. C2×C4C4×#10596842semidirect
425. C4#17989673direct (N × H)

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