Finite Group Databasebeta

← C2×#22626226 #34029978

Subgroups — C2×#22626226 #34029978

Order 18688.

1198 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556652C212yesmaximal, complemented
2#22626226C218yesmaximal, direct product factor
3C2×#17989497C212yesmaximal, complemented
4C2×#17989495C212yesmaximal, complemented
5C2×#17989158C211yesmaximal, characteristic
6C22×#11924037—22no—
7C2×#14556652—22no—
8C2×#14556652—24no—
9C2×#14556652C2214yes—
10C2×#14556652C2218yescomplemented
11#17989497C2218yescomplemented
12#17989495C2218yescomplemented
13C23×Dic146C2211yescharacteristic
14#17989158—24no—
15#17989158C414yes—
16#17989158C2214yes—
17C2×#14556589C411yescharacteristic
18C2×#14556589C2211yescharacteristic
19C2×#14556578C411yescharacteristic
20C2×#14556578C2211yescharacteristic
21C2×#14556572—22no—
22C2×#14556570—22no—
23C2×#14556550C411yescharacteristic
24C22×#41×C73C411yescharacteristic
25C2×#11924037—24no—
26C2×#11924037—28no—
27C2×#11924037—42no—
28C2×#11924037—44no—
29C22×#10596833—42no—
30#14556652—24no—
31#14556652—28no—
32#14556652C2318yes—
33C22×Dic146—42no—
34C22×Dic146—42no—
35C22×Dic146C2×C411yescharacteristic
36C22×Dic146C2×C412yes—
37C22×Dic146D414yes—
38C22×Dic146D412yes—
39C22×Dic146C2311yescharacteristic
40C22×Dic146C2312yes—
41C23×Dic73D412yes—
42#14556589—22no—
43#14556589—22no—
44#14556589C2×C414yes—
45#14556589C2×C412yes—
46#14556589C2312yes—
47#14556578—22no—
48#14556578—22no—
49#14556578C2×C412yes—
50#14556578C2×C414yes—
51#14556578C2312yes—
52#14556572—28no—
53#14556572—28no—
54#14556570—28no—
55#14556570—28no—
56#14556550—22no—
57#14556550C2×C414yes—
58C2×C4⋊Dic73—21no—
59C2×#11924007—22no—
60C2×#11924007—22no—
61C2×C22⋊Dic73—22no—
62C2×C22⋊Dic73—22no—
63C2×C22⋊Dic73—21no—
64C2×C4×Dic73C2×C411yescharacteristic
65C2×C4×Dic73C2×C411yescharacteristic
66C2×#41×C73—22no—
67C2×#41×C73—42no—
68C2×#41×C73—42no—
69C2×#41×C73C2×C414yes—
70C22×Q8×C73C2×C411yescharacteristic
71C22×D4×C73—21no—
72C22×D4×C73C2×C411yescharacteristic
73C23×C4×C73—21no—
74C23×C4×C73C2×C411yescharacteristic
75#11924037—28no—
76#11924037—44no—
77#11924037—48no—
78C2×#10596833—44no—
79C2×#10596833—48no—
80C2×Dic146—41no—
81C2×Dic146—41no—
82C2×Dic146—44no—
83C2×Dic146—42no—
84C2×Dic146—44no—
85C2×Dic146—42no—
86C2×Dic146—44no—
87C2×Dic146—41no—
88C2×Dic146—44no—
89C2×Dic146—41no—
90C2×Dic146C22⋊C414yes—
91C2×Dic146C22⋊C412yes—
92C2×Dic146C22×C411yescharacteristic
93C2×Dic146C22×C412yes—
94C2×Dic146C2×D414yes—
95C2×Dic146C2×D412yes—
96C2×Dic146C2411yescharacteristic
97C22×Dic73—22no—
98C22×Dic73—22no—
99C22×Dic73—24no—
100C22×Dic73—21no—
101C22×Dic73—21no—
102C22×Dic73C22⋊C412yes—
103C22×Dic73C22⋊C414yes—
104C22×Dic73C2×D412yes—
105C22×Dic73C2×D414yes—
106C4⋊Dic73—24no—
107#11924007—28no—
108#11924007—24no—
109#11924007—24no—
110C22⋊Dic73—24no—
111C22⋊Dic73—28no—
112C22⋊Dic73—24no—
113C22⋊Dic73—24no—
114C4×Dic73—21no—
115C4×Dic73—21no—
116C4×Dic73C22×C412yes—
117C4×Dic73C22×C412yes—
118C24×C73—21no—
119C24×C73C22⋊C411yescharacteristic
120#41×C73—48no—
121#41×C73—48no—
122C2×Q8×C73—21no—
123C2×Q8×C73—41no—
124C2×Q8×C73—41no—
125C2×Q8×C73C22×C412yes—
126C2×D4×C73—24no—
127C2×D4×C73—21no—
128C2×D4×C73—41no—
129C2×D4×C73—41no—
130C2×D4×C73—42no—
131C2×D4×C73—42no—
132C2×D4×C73C22×C412yes—
133C22×C4×C73—22no—
134C22×C4×C73—22no—
135C22×C4×C73—21no—
136C22×C4×C73—24no—
137C22×C4×C73—42no—
138C22×C4×C73—42no—
139C22×C4×C73C22⋊C411yescharacteristic
140C22×C4×C73C22⋊C412yes—
141C22×C4×C73C22×C411yescharacteristic
142C22×C4×C73C22×C412yes—
143C23×C73—22no—
144C23×C73—42no—
145C23×C73—44no—
146C23×C73—41no—
147C23×C73—41no—
148C23×C73#9912yes—
149C23×C73#9912yes—
150C23×C73C2×C22⋊C411yescharacteristic
151C23×C73C2×C22⋊C412yes—
152Q8×C73—42no—
153Q8×C73—42no—
154D4×C73—42no—
155D4×C73—42no—
156D4×C73—48no—
157C2×C4×C73—21no—
158C2×C4×C73—21no—
159C2×C4×C73—24no—
160C2×C4×C73—21no—
161C2×C4×C73—21no—
162C2×C4×C73—24no—
163C2×C4×C73—22no—
164C2×C4×C73—48no—
165C2×C4×C73—41no—
166C2×C4×C73—41no—
167C2×C4×C73C2×C22⋊C412yes—
168C2×C4×C73C2×C22⋊C411yescharacteristic
169C2×C4×C73C23×C411yescharacteristic
170C2×Dic73—22no—
171C2×Dic73—24no—
172C2×Dic73—24no—
173C2×Dic73—22no—
174C2×Dic73—24no—
175C2×Dic73—22no—
176C2×Dic73—22no—
177C2×Dic73—24no—
178C2×Dic73—22no—
179C2×Dic73—22no—
180C2×Dic73—42no—
181C2×Dic73—42no—
182C2×Dic73C2×C22⋊C414yes—
183C2×Dic73C2×C22⋊C412yes—
184C2×Dic73C22×D412yes—
185Dic146—44no—
186Dic146—42no—
187Dic146—42no—
188Dic146—41no—
189Dic146—44no—
190Dic146—42no—
191Dic146—41no—
192#10596833—48no—
193C22×C73—22no—
194C22×C73—24no—
195C22×C73—42no—
196C22×C73—42no—
197C22×C73—44no—
198C22×C73—42no—
199C22×C73—82no—
200C22×C73—82no—
201C22×C73C2×#9911yescharacteristic
202C22×C73C2×#9914yes—
203C22×C73C2×#9911yescharacteristic
204C22×C73C22×C22⋊C411yescharacteristic
205C4×C73—22no—
206C4×C73—21no—
207C4×C73—21no—
208C4×C73—42no—
209Dic73—22no—
210Dic73—24no—
211Dic73—22no—
212Dic73—42no—
213Dic73—42no—
214C2×#2133—731nomaximal, Sylow
215C2×C73—21no—
216C2×C73—21no—
217C2×C73—24no—
218C2×C73—82no—
219C2×C73#213312yescomplemented
220C2×C73C22×#9911yescharacteristic
221C2×#536—731no—
222C22×#101—732no—
223#2133—738no—
224C2×#356—732no—
225C2×#355—732no—
226C73C2×#213311yescharacteristic, complemented, Sylow
227C22×#41#6440811yescharacteristic
228C23×Q8—731no—
229C22×M16—1462no—
230#536—734no—
231#536—734no—
232#536—1464no—
233C2×C4⋊Q8—731no—
234C2×C4⋊Q8—731no—
235C2×#124—731no—
236C2×#124—731no—
237C2×#123—1462no—
238C2×C22⋊Q8—1462no—
239C2×#117—731no—
240C2×#101—734no—
241C2×#101—738no—
242C2×#101—1462no—
243C2×#101—1464no—
244#356—738no—
245#355—738no—
246C2×#41—22no—
247C2×#41—42no—
248C2×#41—42no—
249C2×#41C2×#6440814yes—
250C22×Q8—2922no—
251C22×Q8—2922no—
252C22×Q8—732no—
253C22×Q8—734no—
254C22×Q8—731no—
255C22×Q8—731no—
256C22×Q8—732no—
257C22×Q8—732no—
258C22×Q8C2×#6440811yescharacteristic
259C22×D4—21no—
260C22×D4C2×#6440811yescharacteristic
261C23×C4—21no—
262C23×C4—732no—
263C23×C4C2×#6440811yescharacteristic
264C2×M16—2924no—
265C2×M16—2922no—
266C2×M16—1464no—
267C2×M16—1468no—
268C22×C8—2922no—
269C4⋊Q8—732no—
270C4⋊Q8—734no—
271C4⋊Q8—732no—
272C4⋊Q8—1462no—
273C4⋊Q8—1462no—
274#124—732no—
275#124—732no—
276#124—734no—
277#124—1462no—
278#124—1462no—
279#123—1468no—
280#123—1468no—
281C22⋊Q8—1468no—
282C22⋊Q8—1468no—
283#117—734no—
284#117—1462no—
285C2×C4⋊C4—1462no—
286C2×C4⋊C4—1462no—
287C2×C4⋊C4—1461no—
288C2×C22⋊C4—1462no—
289C2×C22⋊C4—1462no—
290C2×C22⋊C4—1461no—
291C2×C42—731no—
292C2×C42—731no—
293#101—738no—
294#101—1468no—
295#101—1464no—
296C24—21no—
297C24C22⋊#6440811yescharacteristic
298#41—48no—
299#41—48no—
300C2×Q8—21no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—2922no—
304C2×Q8—2924no—
305C2×Q8—2924no—
306C2×Q8—2921no—
307C2×Q8—2921no—
308C2×Q8—2924no—
309C2×Q8—2924no—
310C2×Q8—2922no—
311C2×Q8—2921no—
312C2×Q8—2921no—
313C2×Q8—731no—
314C2×Q8—732no—
315C2×Q8—731no—
316C2×Q8—734no—
317C2×Q8—732no—
318C2×Q8—734no—
319C2×Q8—732no—
320C2×Q8C22×#6440812yes—
321C2×D4—24no—
322C2×D4—21no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—42no—
326C2×D4—42no—
327C2×D4C22×#6440812yes—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—24no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—732no—
335C22×C4—734no—
336C22×C4—732no—
337C22×C4—734no—
338C22×C4—1461no—
339C22×C4—1461no—
340C22×C4—1462no—
341C22×C4—1464no—
342C22×C4—1462no—
343C22×C4C22⋊#6440811yescharacteristic
344C22×C4C22⋊#6440812yes—
345C22×C4C22×#6440811yescharacteristic
346C22×C4C22×#6440812yes—
347M16—2924no—
348M16—2928no—
349M16—1468no—
350C2×C8—2928no—
351C2×C8—2924no—
352C4⋊C4—1464no—
353C4⋊C4—1468no—
354C4⋊C4—1464no—
355C4⋊C4—1464no—
356C22⋊C4—1464no—
357C22⋊C4—1468no—
358C22⋊C4—1464no—
359C22⋊C4—1464no—
360C42—732no—
361C42—732no—
362C42—1461no—
363C42—1461no—
364C23—22no—
365C23—42no—
366C23—44no—
367C23—41no—
368C23—41no—
369C23#1455664912yes—
370C23#1455664912yes—
371C23C2×C22⋊#6440811yescharacteristic
372C23C2×C22⋊#6440812yes—
373Q8—42no—
374Q8—42no—
375Q8—2924no—
376Q8—2924no—
377Q8—2921no—
378Q8—2922no—
379Q8—2921no—
380Q8—2922no—
381Q8—2922no—
382D4—42no—
383D4—42no—
384D4—48no—
385C2×C4—21no—
386C2×C4—24no—
387C2×C4—21no—
388C2×C4—24no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—48no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—2922no—
396C2×C4—2922no—
397C2×C4—732no—
398C2×C4—734no—
399C2×C4—732no—
400C2×C4—1462no—
401C2×C4—1462no—
402C2×C4—1464no—
403C2×C4—1462no—
404C2×C4—1464no—
405C2×C4—1462no—
406C2×C4—1464no—
407C2×C4—1464no—
408C2×C4—1462no—
409C2×C4—1462no—
410C2×C4C2×C22⋊#6440811yescharacteristic
411C2×C4C2×C22⋊#6440812yes—
412C2×C4C23×#6440811yescharacteristic
413C8—2928no—
414C22—22no—
415C22—24no—
416C22—42no—
417C22—42no—
418C22—44no—
419C22—42no—
420C22—82no—
421C22—82no—
422C22C2×#1455664911yescharacteristic
423C22C2×#1455664914yes—
424C22C2×#1455664911yescharacteristic
425C22C22×C22⋊#6440811yescharacteristic
426C4—22no—
427C4—21no—
428C4—21no—
429C4—42no—
430C4—2922no—
431C4—2922no—
432C4—1462no—
433C4—1464no—
434C4—1462no—
435C2—21no—
436C2—21no—
437C2—24no—
438C2—82no—
439C2#2262622612yesdirect product factor
440C2C22×#1455664911yescharacteristic
subgroupG/H
centerC22C2×#14556649
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
Fitting, prime radicalC22×#41×C73C4
socleC22×C73C2×#99
cosocleC2×Dic146C24
hypercenterC22×#41#64408
hypocenterC73C2×#2133
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×#14556652C2semidirect
2. #22626226C2direct (N × H)
3. C2×#17989497C2semidirect
4. C2×#17989495C2semidirect
10. C2×#14556652C22semidirect
11. #17989497C22semidirect
12. #17989495C22semidirect
219. C2×C73#2133semidirect
226. C73C2×#2133semidirect
439. C2#22626226direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145566522
#226262262
C2×#179894972
C2×#179894952
C2×#179891582
C2×#213373