Finite Group Databasebeta

← #15684948

Subgroups — #15684948

Order 2944.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625122C211yesmaximal, characteristic, complemented
2C2×#10625121C211yesmaximal, characteristic, complemented
3#13093076C211yesmaximal, characteristic, complemented
4#13092809C211yesmaximal, characteristic, complemented
5#13092665C211yesmaximal, characteristic, complemented
6#13092656C211yesmaximal, characteristic, complemented
7#13092632C211yesmaximal, characteristic, complemented
8#13092624C211yesmaximal, characteristic, complemented
9#13092579C211yesmaximal, characteristic, complemented
10#13092577C211yesmaximal, characteristic, complemented
11#13092572C211yesmaximal, characteristic, complemented
12#13092562C211yesmaximal, characteristic, complemented
13#13092517C211yesmaximal, characteristic, complemented
14#13092489C211yesmaximal, characteristic, complemented
15C23×#547C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×#41×C23C2211yescharacteristic
18C2×#67288C2211yescharacteristic
19C22×Dic46C2211yescharacteristic
20C23×C4⋊Q8C2211yescharacteristic
21C23×#123—21no—
22C23×#123—21no—
23C23×C22⋊Q8C2211yescharacteristic
24C23×C22⋊Q8C2211yescharacteristic
25C23×#121—21no—
26C4×D4×C23C2211yescharacteristic
27C4×D4×C23C2211yescharacteristic
28C2×C4⋊C4×C23—21no—
29#10625122—24no—
30#10625121—24no—
31C2×#67275C2211yescharacteristic
32C2×#67275C2211yescharacteristic
33C2×#67275C2211yescharacteristic
34C2×#67275C2211yescharacteristic
35C2×#67274C2211yescharacteristic
36C2×#67274C2211yescharacteristic
37#10625110—21no—
38C2×#67273C2211yescharacteristic
39C2×#67273C2211yescharacteristic
40C2×#67272C2211yescharacteristic
41#10625101C2211yescharacteristic
42#10625095C2211yescharacteristic
43C2×#67267C2211yescharacteristic
44C22×C23⋊C8C2211yescharacteristic
45#10625067—21no—
46#10625056—21no—
47(C22⋊D23)⋊C4—21no—
48#10625046C2211yescharacteristic
49C4×Dic46C2211yescharacteristic
50#10625017C2211yescharacteristic
51#10625017C2211yescharacteristic
52#10625014C2211yescharacteristic
53C22⋊(C23⋊C8)C2211yescharacteristic
54C22⋊(C23⋊C8)C2211yescharacteristic
55#10624992C2211yescharacteristic
56#10624992C2211yescharacteristic
57#10624991C2211yescharacteristic
58#10624989C2211yescharacteristic
59C4⋊(C23⋊C8)C2211yescharacteristic
60#10624985C2211yescharacteristic
61#41×C23—22no—
62#41×C23—22no—
63#41×C23—41no—
64#41×C23—41no—
65C2×Q8×C23C2311yescharacteristic
66C2×Q8×C23C2311yescharacteristic
67C2×D4×C23—21no—
68C2×D4×C23—21no—
69C2×D4×C23D411yescharacteristic
70C2×D4×C23C2311yescharacteristic
71C22×C4×C23—21no—
72C22×C4×C23—21no—
73C22×C4×C23—21no—
74C22×C4×C23C2311yescharacteristic
75C22×C4×C23C2311yescharacteristic
76C2×C22⋊D23—21no—
77C2×C22⋊D23—21no—
78C22×Dic23—21no—
79#67288—22no—
80#67288—41no—
81C2×D92C2311yescharacteristic
82C2×C4×D23—21no—
83C2×Dic46—22no—
84C2×Dic46—21no—
85C2×Dic46—41no—
86C2×Dic46C2311yescharacteristic
87C2×Dic46C2311yescharacteristic
88C4⋊C4×C23—21no—
89C4⋊C4×C23—21no—
90C4⋊C4×C23—21no—
91C4⋊C4×C23—21no—
92C4⋊C4×C23D411yescharacteristic
93C4⋊C4×C23C2311yescharacteristic
94C22⋊C4×C23—21no—
95C22⋊C4×C23—21no—
96C22⋊C4×C23—21no—
97C22⋊C4×C23D411yescharacteristic
98C22⋊C4×C23D411yescharacteristic
99C42×C23C2311yescharacteristic
100C22⋊Dic23—21no—
101#67275—22no—
102#67275—22no—
103#67275—22no—
104#67275—41no—
105#67274—22no—
106#67274—41no—
107#67273—22no—
108#67273D414yescomplemented
109#67272—22no—
110(C2×D23)⋊C4—21no—
111(C2×D23)⋊C4—21no—
112(C2×D23)⋊C4—21no—
113C4⋊Dic23C2311yescharacteristic
114Dic23⋊C4—21no—
115Dic23⋊C4—21no—
116C4×Dic23—21no—
117#67267—22no—
118C2×C23⋊C8—22no—
119C2×C23⋊C8C2311yescharacteristic
120C2×C23⋊C8C2311yescharacteristic
121C2×C23⋊C8C2311yescharacteristic
122C2×C23⋊C8C2311yescharacteristic
123C23×C23—21no—
124C23×C23C2×D411yescharacteristic
125C23×C23C2×D411yescharacteristic
126C22×D23—21no—
127Q8×C23—21no—
128Q8×C23—21no—
129Q8×C23—21no—
130Q8×C23—21no—
131D4×C23—21no—
132D4×C23—41no—
133D4×C23—42no—
134D4×C23—42no—
135D4×C23C2×D412yes—
136C2×C4×C23—21no—
137C2×C4×C23—21no—
138C2×C4×C23—21no—
139C2×C4×C23—21no—
140C2×C4×C23—21no—
141C2×C4×C23—21no—
142C2×C4×C23—21no—
143C2×C4×C23—42no—
144C2×C4×C23—42no—
145C2×C4×C23—42no—
146C2×C4×C23C2×D411yescharacteristic
147C2×C4×C23C2×D411yescharacteristic
148C2×C4×C23C2×D411yescharacteristic
149C2×C4×C23C2×D411yescharacteristic
150C2×C4×C23C2411yescharacteristic
151C22⋊D23—42no—
152C22⋊D23—42no—
153C2×Dic23—21no—
154C2×Dic23—21no—
155C2×Dic23—21no—
156C2×Dic23—42no—
157D92—21no—
158D92—21no—
159C4×D23—42no—
160Dic46—21no—
161Dic46—21no—
162Dic46—21no—
163Dic46—42no—
164Dic46C2×D412yes—
165C23⋊C8—21no—
166C23⋊C8—21no—
167C23⋊C8—21no—
168C23⋊C8C2×D412yes—
169#3269—231nomaximal, Sylow
170C22×C23—21no—
171C22×C23—21no—
172C22×C23—22no—
173C22×C23—21no—
174C22×C23—21no—
175C22×C23—21no—
176C22×C23—21no—
177C22×C23—41no—
178C22×C23—41no—
179C22×C23C22×D411yescharacteristic
180C2×D23—41no—
181C2×D23—41no—
182C2×D23—41no—
183C4×C23—21no—
184C4×C23—21no—
185C4×C23—21no—
186C4×C23—21no—
187C4×C23—41no—
188C4×C23—41no—
189C4×C23—41no—
190C4×C23C22×D411yescharacteristic
191C4×C23H(5,𝔽2)11yescharacteristic
192Dic23—22no—
193Dic23—41no—
194Dic23—41no—
195C2×#137—231no—
196C2×#135—231no—
197#548—231no—
198#547D2311yescharacteristic, complemented
199#497—231no—
200#468—231no—
201#467—231no—
202#463—231no—
203#462—231no—
204#452—231no—
205#452—231no—
206#451—231no—
207#449—231no—
208#440—231no—
209#435—231no—
210C2×C23—41no—
211C2×C23—41no—
212C2×C23—42no—
213C2×C23D4211yescharacteristic
214C2×C23#57511yescharacteristic
215C2×C23#57811yescharacteristic
216D23—81no—
217C2×#41—231no—
218C2×#41C2×D2311yescharacteristic
219C2×#41C2×D2311yescharacteristic
220C22×Q8—231no—
221#137—464no—
222#135—464no—
223C2×Q16—231no—
224C2×Q16—231no—
225C2×Q16—231no—
226C2×Q16—231no—
227C2×SD16—231no—
228C2×SD16—231no—
229C2×SD16—231no—
230C2×SD16—231no—
231C2×D8—231no—
232C2×M16—231no—
233C22×C8—231no—
234C4⋊Q8C2×D2311yescharacteristic
235#124—231no—
236#124—461no—
237#123—21no—
238#123—21no—
239C22⋊Q8—231no—
240C22⋊Q8—461no—
241C22⋊Q8C2×D2311yescharacteristic
242C22⋊Q8C2×D2311yescharacteristic
243#121—21no—
244#121—231no—
245#121—461no—
246C4×Q8—231no—
247C4×D4—461no—
248C4×D4C2×D2311yescharacteristic
249C4×D4C2×D2311yescharacteristic
250C2×C4⋊C4—21no—
251#107—231no—
252C4⋊C8—231no—
253#103—231no—
254#103—231no—
255#103—231no—
256#103—231no—
257#102—231no—
258#102—231no—
259C22⋊C8—231no—
260C22⋊C8—231no—
261#97—231no—
262C23#326911yescharacteristic, complemented, Sylow
263#41—22no—
264#41—22no—
265#41—41no—
266#41—41no—
267#41—462no—
268#41—921no—
269C2×Q8—231no—
270C2×Q8—231no—
271C2×Q8—462no—
272C2×Q8—461no—
273C2×Q8—921no—
274C2×Q8C22×D2311yescharacteristic
275C2×Q8C22×D2311yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—231no—
279C2×D4—461no—
280C2×D4—461no—
281C2×D4C22⋊D2311yescharacteristic
282C2×D4C22×D2311yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—461no—
287C22×C4—461no—
288C22×C4C22×D2311yescharacteristic
289C22×C4C22×D2311yescharacteristic
290Q16—462no—
291Q16—462no—
292Q16—462no—
293Q16—921no—
294SD16—234no—
295SD16—462no—
296SD16—462no—
297SD16—921no—
298D8—462no—
299M16—462no—
300C2×C8—231no—
301C2×C8—231no—
302C2×C8—231no—
303C2×C8—231no—
304C2×C8—462no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—231no—
310C4⋊C4—461no—
311C4⋊C4—461no—
312C4⋊C4C22⋊D2311yescharacteristic
313C4⋊C4C22×D2311yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—461no—
318C22⋊C4—461no—
319C22⋊C4—461no—
320C22⋊C4—461no—
321C22⋊C4C22⋊D2311yescharacteristic
322C22⋊C4C22⋊D2311yescharacteristic
323C42—461no—
324C42C22×D2311yescharacteristic
325C23—21no—
326C23—461no—
327C23C2×C22⋊D2311yescharacteristic
328C23C2×C22⋊D2311yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—232no—
334Q8—461no—
335Q8—461no—
336Q8—461no—
337Q8—922no—
338D4—21no—
339D4—41no—
340D4—42no—
341D4—42no—
342D4—461no—
343D4—461no—
344D4—922no—
345D4—922no—
346D4D4×D2312yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—461no—
358C2×C4—461no—
359C2×C4—461no—
360C2×C4—922no—
361C2×C4—922no—
362C2×C4C2×C22⋊D2311yescharacteristic
363C2×C4C2×C22⋊D2311yescharacteristic
364C2×C4C2×C22⋊D2311yescharacteristic
365C2×C4C2×C22⋊D2311yescharacteristic
366C2×C4C23×D2311yescharacteristic
367C8—232no—
368C8—461no—
369C8—461no—
370C8—461no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—22no—
378C22—41no—
379C22—41no—
380C22—921no—
381C22—921no—
382C22—921no—
383C22C22×C22⋊D2311yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—462no—
392C4—921no—
393C4—921no—
394C4C2×D4×D2311yescharacteristic
395C4#1062515511yescharacteristic
396C2—41no—
397C2—41no—
398C2—42no—
399C2—1841no—
400C2D4×C22⋊D2311yescharacteristic
401C2#1309321511yescharacteristic
402C2#1309323211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#547C2
socleC22×C23C22×D4
hypercenter#547D23
hypocenterC23#3269
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C2×#10625122C2semidirect
2. C2×#10625121C2semidirect
3. #13093076C2semidirect
4. #13092809C2semidirect
5. #13092665C2semidirect
6. #13092656C2semidirect
7. #13092632C2semidirect
8. #13092624C2semidirect
9. #13092579C2semidirect
10. #13092577C2semidirect
11. #13092572C2semidirect
12. #13092562C2semidirect
13. #13092517C2semidirect
14. #13092489C2semidirect
15. C23×#547C2semidirect
108. #67273D4semidirect
198. #547D23semidirect
262. C23#3269semidirect

Maximal subgroups

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

subgroupindex
C2×#106251222
C2×#106251212
#130930762
#130928092
#130926652
#130926562
#130926322
#130926242
#130925792
#130925772
#130925722
#130925622
#130925172
#130924892
C23×#5472
#326923