Finite Group Databasebeta

← C2×#21462122 #30624018

Subgroups — C2×#21462122 #30624018

Order 15616.

1198 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 216 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×#16840749C212yesmaximal
2#21462122C218yesmaximal, direct product factor
3C2×#16840673C212yesmaximal, complemented
4C2×#16840672C212yesmaximal, complemented
5C2×#16840332C211yesmaximal, characteristic
6C22×#11758217—22no—
7#16840749—24no—
8#16840749C2218yes—
9C2×#14519838C2214yes—
10C2×#14519837—22no—
11#16840673C2218yescomplemented
12#16840672C2218yescomplemented
13C22×#11758224C2211yescharacteristic
14C22×Q8×D61C411yescharacteristic
15#16840332—24no—
16#16840332C414yes—
17#16840332C2214yes—
18C2×#14519777C2211yescharacteristic
19C2×#14519775C2211yescharacteristic
20C2×#14519764C411yescharacteristic
21C2×#14519759—22no—
22C2×#14519754—22no—
23C2×#14519734C411yescharacteristic
24C2×#124×C61C411yescharacteristic
25C2×#11758217—24no—
26C2×#11758217—28no—
27C2×#11758217—42no—
28C2×#11758217—44no—
29C22×#92420—42no—
30#14519838—24no—
31#14519838C2318yes—
32#14519837—28no—
33C2×#11758224—42no—
34C2×#11758224—42no—
35C2×#11758224C2×C412yes—
36C2×#11758224D414yes—
37C2×#11758224C2312yes—
38C22×Dic122—21no—
39C22×Dic122C2×C411yescharacteristic
40C22×Dic122C2311yescharacteristic
41C2×Q8×D61—22no—
42C2×Q8×D61—42no—
43C2×Q8×D61—42no—
44C2×Q8×D61C2×C414yes—
45C22×C22⋊D61D412yes—
46C23×Dic61D412yes—
47C22×C4×D61—21no—
48C22×C4×D61C2×C411yescharacteristic
49#14519777—22no—
50#14519777C2×C412yes—
51#14519777C2312yes—
52#14519775—22no—
53#14519775C2×C412yes—
54#14519775C2312yes—
55#14519764—22no—
56#14519764C2×C414yes—
57#14519759—28no—
58#14519759—28no—
59#14519754—28no—
60#14519754—28no—
61#14519734—22no—
62#14519734C2×C414yes—
63C2×C4⋊Dic61—22no—
64C2×#11758196—21no—
65C2×#11758196—22no—
66C2×C22⋊Dic61—22no—
67C2×#11758198—21no—
68C2×C4×Dic61C2×C411yescharacteristic
69C22×Q8×C61C2×C411yescharacteristic
70C22×D4×C61C2×C411yescharacteristic
71#124×C61—22no—
72#124×C61C2×C414yes—
73C2×C22⋊C4×C61—22no—
74C2×C42×C61C2×C411yescharacteristic
75C24×C61C22⋊C412yes—
76C23×D61C22⋊C411yescharacteristic
77C2×Q8×C61—21no—
78C2×Q8×C61—41no—
79C2×Q8×C61—41no—
80C2×Q8×C61C22×C412yes—
81C2×D4×C61—41no—
82C2×D4×C61—41no—
83C2×D4×C61C22⋊C412yes—
84C2×D4×C61C22×C412yes—
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61C22×C411yescharacteristic
88C2×C22⋊D61—42no—
89C2×C22⋊D61—42no—
90C2×C22⋊D61C22⋊C414yes—
91C2×C22⋊D61C2×D414yes—
92C22×Dic61—22no—
93C22×Dic61—22no—
94C22×Dic61—24no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61C22⋊C414yes—
98C22×Dic61C22⋊C411yescharacteristic
99C22×Dic61C2×D412yes—
100C22×Dic61C2×D414yes—
101Q8×D61—48no—
102Q8×D61—48no—
103#11758224—44no—
104#11758224—44no—
105#11758224—44no—
106#11758224—44no—
107C2×C4×D61—22no—
108C2×C4×D61—22no—
109C2×C4×D61—24no—
110C2×C4×D61—42no—
111C2×C4×D61—42no—
112C2×C4×D61C22⋊C412yes—
113C2×C4×D61C22×C412yes—
114C2×Dic122—21no—
115C2×Dic122—24no—
116C2×Dic122—41no—
117C2×Dic122—41no—
118C2×Dic122—42no—
119C2×Dic122—42no—
120C2×Dic122—41no—
121C2×Dic122—41no—
122C2×Dic122C22×C412yes—
123C2×Dic122C22×C411yescharacteristic
124C2×Dic122C2×D412yes—
125C2×Dic122C2411yescharacteristic
126#11758217—28no—
127#11758217—44no—
128#11758217—48no—
129C2×#92420—44no—
130C2×#92420—48no—
131C22⋊C4×C61—28no—
132C42×C61—21no—
133C42×C61C22×C412yes—
134C22⋊Dic61—28no—
135#11758198—24no—
136C4⋊Dic61—24no—
137C4⋊Dic61—24no—
138#11758196—24no—
139#11758196—24no—
140#11758196—24no—
141C4×Dic61—21no—
142C4×Dic61C22×C412yes—
143C23×C61—22no—
144C23×C61—22no—
145C23×C61—44no—
146C23×C61C2×C22⋊C411yescharacteristic
147C23×C61C2×C22⋊C414yes—
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—42no—
151C22×D61C2×C22⋊C412yes—
152Q8×C61—42no—
153Q8×C61—42no—
154D4×C61—42no—
155D4×C61—42no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—22no—
159C2×C4×C61—22no—
160C2×C4×C61—42no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61C2×C22⋊C411yescharacteristic
164C2×C4×C61C23×C411yescharacteristic
165C22⋊D61—44no—
166C22⋊D61—44no—
167C2×Dic61—22no—
168C2×Dic61—22no—
169C2×Dic61—24no—
170C2×Dic61—24no—
171C2×Dic61—24no—
172C2×Dic61—24no—
173C2×Dic61—22no—
174C2×Dic61—22no—
175C2×Dic61—42no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61#9912yes—
179C2×Dic61#9912yes—
180C2×Dic61C2×C22⋊C412yes—
181C2×Dic61C2×C22⋊C412yes—
182C2×Dic61C22×D412yes—
183C4×D61—24no—
184C4×D61—24no—
185C4×D61—48no—
186Dic122—41no—
187Dic122—42no—
188Dic122—41no—
189Dic122—42no—
190Dic122—48no—
191Dic122—42no—
192#92420—48no—
193C2×#2135—611nomaximal, Sylow
194C22×C61—22no—
195C22×C61—24no—
196C22×C61—44no—
197C22×C61—44no—
198C22×C61—82no—
199C22×C61C2×#9911yescharacteristic
200C22×C61C2×#9911yescharacteristic
201C22×C61C22×C22⋊C411yescharacteristic
202C2×D61—22no—
203C2×D61—42no—
204C2×D61—42no—
205C2×D61—42no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—42no—
209C4×C61—42no—
210Dic61—22no—
211Dic61—22no—
212Dic61—42no—
213Dic61—42no—
214Dic61C2×#9914yes—
215C2×#536—611no—
216C2×#413—612no—
217#2135—618no—
218C2×#356—612no—
219C2×#356—612no—
220C2×C61—21no—
221C2×C61—21no—
222C2×C61—44no—
223C2×C61#213512yescomplemented
224C2×C61C22×#9911yescharacteristic
225D61—42no—
226C22×#41—611no—
227C23×Q8—611no—
228C22×M16—1222no—
229#536—614no—
230#536—614no—
231#536—1224no—
232C2×C4⋊Q8—611no—
233C2×C4⋊Q8—611no—
234C2×#124—611no—
235C2×#124#692311yescharacteristic
236C2×#123—1222no—
237C2×C22⋊Q8—1222no—
238C2×#117—611no—
239#413—618no—
240#413—1224no—
241C2×#101—614no—
242C2×#100—1222no—
243#356—618no—
244#356—618no—
245C61C2×#213511yescharacteristic, complemented, Sylow
246C2×#41—614no—
247C2×#41—612no—
248C2×#41—612no—
249C2×#41—2442no—
250C2×#41—2442no—
251C22×Q8—611no—
252C22×Q8—614no—
253C22×Q8—611no—
254C22×Q8—1221no—
255C22×Q8—1222no—
256C22×Q8—2442no—
257C22×Q8—2442no—
258C22×Q8C2×#692311yescharacteristic
259C22×D4—612no—
260C22×D4C2×#692311yescharacteristic
261C23×C4—612no—
262C23×C4—611no—
263C23×C4—1221no—
264C2×M16—1224no—
265C2×M16—1228no—
266C2×M16—2444no—
267C2×M16—2442no—
268C22×C8—2442no—
269C4⋊Q8—612no—
270C4⋊Q8—612no—
271C4⋊Q8—612no—
272C4⋊Q8—612no—
273C4⋊Q8—1222no—
274C4⋊Q8—1222no—
275#124—22no—
276#124—614no—
277#124—1222no—
278#124C2×#692314yes—
279#123—1228no—
280#123—1228no—
281C22⋊Q8—1228no—
282C22⋊Q8—1228no—
283#117—614no—
284#117—1222no—
285C2×C4⋊C4—1221no—
286C2×C4⋊C4—1222no—
287C2×C4⋊C4—1222no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—1221no—
290C2×C22⋊C4—1222no—
291C2×C42—611no—
292C2×C42C2×#692311yescharacteristic
293#101—618no—
294#101—1224no—
295#100—1228no—
296C24—611no—
297C24C22⋊#692312yes—
298#41—2444no—
299#41—2444no—
300#41—2444no—
301#41—2444no—
302C2×Q8—21no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—612no—
306C2×Q8—611no—
307C2×Q8—611no—
308C2×Q8—612no—
309C2×Q8—1224no—
310C2×Q8—1221no—
311C2×Q8—2441no—
312C2×Q8—2441no—
313C2×Q8—2441no—
314C2×Q8—2441no—
315C2×Q8—2442no—
316C2×Q8—2442no—
317C2×Q8—2448no—
318C2×Q8—2448no—
319C2×Q8C22×#692312yes—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—614no—
323C2×D4—614no—
324C2×D4—2442no—
325C2×D4—2442no—
326C2×D4C22⋊#692312yes—
327C2×D4C22×#692312yes—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—611no—
331C22×C4—614no—
332C22×C4—614no—
333C22×C4—612no—
334C22×C4—612no—
335C22×C4—612no—
336C22×C4—1222no—
337C22×C4—1222no—
338C22×C4—1224no—
339C22×C4—1222no—
340C22×C4—1224no—
341C22×C4—1222no—
342C22×C4—1221no—
343C22×C4—1221no—
344C22×C4—2442no—
345C22×C4—2442no—
346C22×C4C22×#692311yescharacteristic
347M16—1228no—
348M16—2448no—
349M16—2444no—
350C2×C8—2448no—
351C2×C8—2444no—
352C4⋊C4—1224no—
353C4⋊C4—1224no—
354C4⋊C4—1224no—
355C4⋊C4—1224no—
356C4⋊C4—1224no—
357C22⋊C4—28no—
358C22⋊C4—1224no—
359C22⋊C4—1228no—
360C42—21no—
361C42—612no—
362C42—1221no—
363C42C22×#692312yes—
364C23—22no—
365C23—22no—
366C23—44no—
367C23—612no—
368C23—1221no—
369C23—1221no—
370C23—2442no—
371C23C2×C22⋊#692314yes—
372C23C2×C22⋊#692311yescharacteristic
373Q8—42no—
374Q8—42no—
375Q8—2442no—
376Q8—2441no—
377Q8—2441no—
378Q8—2442no—
379Q8—2442no—
380Q8—2448no—
381D4—42no—
382D4—42no—
383D4—2444no—
384D4—2444no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—612no—
393C2×C4—612no—
394C2×C4—612no—
395C2×C4—612no—
396C2×C4—612no—
397C2×C4—1224no—
398C2×C4—1224no—
399C2×C4—1224no—
400C2×C4—1224no—
401C2×C4—1224no—
402C2×C4—1224no—
403C2×C4—1222no—
404C2×C4—1222no—
405C2×C4—1222no—
406C2×C4—1222no—
407C2×C4—2448no—
408C2×C4—2442no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4C2×C22⋊#692311yescharacteristic
412C2×C4C23×#692311yescharacteristic
413C8—2448no—
414C22—22no—
415C22—24no—
416C22—44no—
417C22—44no—
418C22—82no—
419C22—1222no—
420C22—2442no—
421C22—2442no—
422C22—2442no—
423C22D61⋊#9911yescharacteristic
424C22D61⋊#9911yescharacteristic
425C22C22×C22⋊#692311yescharacteristic
426C4—21no—
427C4—21no—
428C4—42no—
429C4—42no—
430C4—614no—
431C4—1222no—
432C4—1222no—
433C4—2442no—
434C4—2442no—
435C2—21no—
436C2—21no—
437C2—44no—
438C2—2442no—
439C2#2146212212yesdirect product factor
440C2C2×D61⋊#9911yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#124×C61C4
socleC22×C61C2×#99
prime radicalC22×#11758224C22
cosocleC2×Dic122C24
hypercenterC2×#124#6923
hypocenterC61C2×#2135
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. #21462122C2direct (N × H)
3. C2×#16840673C2semidirect
4. C2×#16840672C2semidirect
11. #16840673C22semidirect
12. #16840672C22semidirect
223. C2×C61#2135semidirect
245. C61C2×#2135semidirect
439. C2#21462122direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407492
#214621222
C2×#168406732
C2×#168406722
C2×#168403322
C2×#213561