Finite Group Databasebeta

← #21457368

Subgroups — #21457368

Order 7808.

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×#14519798C211yesmaximal, characteristic, complemented
2#16840423C211yesmaximal, characteristic, complemented
3#16840411C211yesmaximal, characteristic, complemented
4#16840155C211yesmaximal, characteristic, complemented
5#16840008C211yesmaximal, characteristic, complemented
6#16840000C211yesmaximal, characteristic, complemented
7#16839979C211yesmaximal, characteristic, complemented
8#16839970C211yesmaximal, characteristic, complemented
9#16839923C211yesmaximal, characteristic, complemented
10#16839921C211yesmaximal, characteristic, complemented
11#16839918C211yesmaximal, characteristic, complemented
12#16839907C211yesmaximal, characteristic, complemented
13#16839863C211yesmaximal, characteristic, complemented
14#16839831C211yesmaximal, characteristic, complemented
15C2×#137×C61C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18#14519798—24no—
19C2×#11758202C2211yescharacteristic
20C2×#11758202C2211yescharacteristic
21C2×#11758190C2211yescharacteristic
22C2×#11758201C2211yescharacteristic
23C2×#11758199C2211yescharacteristic
24C2×C8×D61C2211yescharacteristic
25#14519775C2211yescharacteristic
26#14519766—21no—
27#14519766C2211yescharacteristic
28#14519760—21no—
29#14519758—21no—
30#14519756C2211yescharacteristic
31#14519753—21no—
32#14519753C2211yescharacteristic
33#14519753C2211yescharacteristic
34#14519751—21no—
35#14519751C2211yescharacteristic
36#14519749—21no—
37Q8×Dic61C2211yescharacteristic
38D4×Dic61C2211yescharacteristic
39C4×C22⋊D61—21no—
40C4×C22⋊D61C2211yescharacteristic
41C2×#11758196—21no—
42#14519711C2211yescharacteristic
43#14519706C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519701C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519698C2211yescharacteristic
50C22⋊#92418C2211yescharacteristic
51#14519689C2211yescharacteristic
52#14519687C2211yescharacteristic
53C2×#41×C61C2211yescharacteristic
54C22×Q8×C61C2211yescharacteristic
55#137×C61—24no—
56C2×Q16×C61C2211yescharacteristic
57C2×Q16×C61C2211yescharacteristic
58C2×SD16×C61C2211yescharacteristic
59C2×SD16×C61C2211yescharacteristic
60C2×M16×C61C2211yescharacteristic
61#41×C61—22no—
62#41×C61—41no—
63C2×Q8×C61—21no—
64C2×Q8×C61—22no—
65C2×Q8×C61—41no—
66C2×Q8×C61C2311yescharacteristic
67C2×Q8×C61C2311yescharacteristic
68C2×Q8×C61C2311yescharacteristic
69C2×D4×C61—21no—
70C2×D4×C61C2311yescharacteristic
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61C2311yescharacteristic
74C2×C22⋊D61—21no—
75C2×C22⋊D61—21no—
76C2×C22⋊D61D411yescharacteristic
77C22×Dic61—21no—
78C22×Dic61—21no—
79#11758226—22no—
80#11758226—41no—
81#11758224—22no—
82#11758224—41no—
83C2×D244—21no—
84C2×D244C2311yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61C2311yescharacteristic
87C2×Dic122C2311yescharacteristic
88Q16×C61—22no—
89Q16×C61—22no—
90SD16×C61—22no—
91SD16×C61D414yescomplemented
92M16×C61—22no—
93C2×C8×C61C2311yescharacteristic
94C2×C8×C61C2311yescharacteristic
95C22⋊Dic61—21no—
96C22⋊Dic61—21no—
97C22⋊Dic61D411yescharacteristic
98#11758202—22no—
99#11758202—41no—
100#11758201—41no—
101#11758199—22no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107#11758198D411yescharacteristic
108C4⋊Dic61—21no—
109C4⋊Dic61C2311yescharacteristic
110C4⋊Dic61C2311yescharacteristic
111#11758196—21no—
112#11758196—21no—
113#11758196—21no—
114#11758196—21no—
115#11758196—21no—
116#11758196D411yescharacteristic
117C4×Dic61—21no—
118C4×Dic61C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120C2×#92418C2311yescharacteristic
121#11758190—22no—
122C8×D61—22no—
123C23×C61—21no—
124C23×C61C2×D411yescharacteristic
125C22×D61—21no—
126C22×D61C2×D411yescharacteristic
127Q8×C61—21no—
128Q8×C61—21no—
129Q8×C61—21no—
130Q8×C61—21no—
131Q8×C61—21no—
132Q8×C61—42no—
133Q8×C61C2×D412yes—
134D4×C61—21no—
135D4×C61—42no—
136D4×C61C2×D412yes—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—42no—
143C2×C4×C61—42no—
144C2×C4×C61C2×D411yescharacteristic
145C2×C4×C61C2411yescharacteristic
146C22⋊D61—41no—
147C22⋊D61—42no—
148C22⋊D61—42no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—42no—
153C2×Dic61—42no—
154C2×Dic61C2×D411yescharacteristic
155C2×Dic61C2×D411yescharacteristic
156C2×Dic61C2×D411yescharacteristic
157D244—21no—
158D244—21no—
159D244—42no—
160C4×D61—21no—
161C4×D61—21no—
162C4×D61—42no—
163Dic122—21no—
164Dic122—21no—
165C8×C61—21no—
166C8×C61C2×D412yes—
167#92418—21no—
168#92418—21no—
169C22×C61—22no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61C22×D411yescharacteristic
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C4×C61—22no—
183C4×C61—21no—
184C4×C61—41no—
185C4×C61—41no—
186C4×C61C22×D411yescharacteristic
187C4×C61H(5,𝔽2)11yescharacteristic
188Dic61—21no—
189Dic61—21no—
190Dic61—21no—
191Dic61—41no—
192Dic61—41no—
193Dic61—41no—
194#3269—611nomaximal, Sylow
195C2×C61—41no—
196C2×C61—42no—
197C2×C61D4211yescharacteristic
198C2×C61#57511yescharacteristic
199C2×C61#57811yescharacteristic
200D61—41no—
201D61—81no—
202C2×#137D6111yescharacteristic, complemented
203C2×#135—611no—
204#548—611no—
205#547—611no—
206#497—611no—
207#468—611no—
208#467—611no—
209#463—611no—
210#462—611no—
211#452—611no—
212#452—611no—
213#451—611no—
214#449—611no—
215#440—611no—
216#435—611no—
217C61#326911yescharacteristic, complemented, Sylow
218C2×#41—611no—
219C2×#41—611no—
220C2×#41C2×D6111yescharacteristic
221C22×Q8C2×D6111yescharacteristic
222#137—24no—
223#135—1224no—
224C2×Q16—611no—
225C2×Q16—611no—
226C2×Q16C2×D6111yescharacteristic
227C2×Q16C2×D6111yescharacteristic
228C2×SD16—611no—
229C2×SD16—611no—
230C2×SD16C2×D6111yescharacteristic
231C2×SD16C2×D6111yescharacteristic
232C2×D8—611no—
233C2×M16C2×D6111yescharacteristic
234C22×C8—611no—
235C4⋊Q8—611no—
236#124—611no—
237#124—1221no—
238#123—1221no—
239#123—1221no—
240C22⋊Q8—611no—
241C22⋊Q8—611no—
242C22⋊Q8—611no—
243C22⋊Q8—1221no—
244#121—611no—
245#121—1221no—
246#121—1221no—
247C4×Q8—611no—
248C4×D4—611no—
249C4×D4—611no—
250C4×D4—1221no—
251C2×C4⋊C4—1221no—
252#107—611no—
253C4⋊C8—611no—
254#103—611no—
255#103—611no—
256#103—611no—
257#103—611no—
258#102—611no—
259#102—611no—
260C22⋊C8—611no—
261C22⋊C8—611no—
262#97—611no—
263#41—22no—
264#41—41no—
265#41—1222no—
266#41—1222no—
267#41—2441no—
268#41—2441no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—611no—
273C2×Q8C22×D6111yescharacteristic
274C2×Q8C22×D6111yescharacteristic
275C2×Q8C22×D6111yescharacteristic
276C2×D4—21no—
277C2×D4—611no—
278C2×D4—611no—
279C2×D4—1221no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4C22×D6111yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—611no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4C22×D6111yescharacteristic
290Q16—22no—
291Q16—22no—
292Q16—1222no—
293Q16—2441no—
294SD16—22no—
295SD16—1222no—
296SD16—2441no—
297SD16C22⋊D6114yescomplemented
298D8—1222no—
299M16—22no—
300C2×C8—611no—
301C2×C8—611no—
302C2×C8—1222no—
303C2×C8C22×D6111yescharacteristic
304C2×C8C22×D6111yescharacteristic
305C4⋊C4—611no—
306C4⋊C4—611no—
307C4⋊C4—611no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C4⋊C4—1221no—
314C22⋊C4—611no—
315C22⋊C4—611no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C22⋊C4—1221no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C42—611no—
324C42—1221no—
325C23—21no—
326C23—611no—
327C23—1221no—
328C23D4×D6111yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—42no—
335Q8—1221no—
336Q8—1221no—
337Q8C2×C22⋊D6112yes—
338D4—21no—
339D4—42no—
340D4—1221no—
341D4—1221no—
342D4—2442no—
343D4—2441no—
344D4—2442no—
345D4—2442no—
346D4C2×C22⋊D6112yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—611no—
355C2×C4—611no—
356C2×C4—611no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—2442no—
363C2×C4—2442no—
364C2×C4—2442no—
365C2×C4D4×D6111yescharacteristic
366C2×C4C23×D6111yescharacteristic
367C8—21no—
368C8—1221no—
369C8—1221no—
370C8C2×C22⋊D6112yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—22no—
375C22—41no—
376C22—41no—
377C22—1221no—
378C22—1221no—
379C22—1221no—
380C22—2441no—
381C22—2441no—
382C22—2441no—
383C22C2×D4×D6111yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—41no—
388C4—1221no—
389C4—1221no—
390C4—1221no—
391C4—2441no—
392C4—2441no—
393C4—2441no—
394C4C22×C22⋊D6111yescharacteristic
395C4#1451982211yescharacteristic
396C2—41no—
397C2—42no—
398C2—4881no—
399C2—2441no—
400C2D4×C22⋊D6111yescharacteristic
401C2#1684056111yescharacteristic
402C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#137×C61C2
socleC22×C61C22×D4
hypercenterC2×#137D61
hypocenterC61#3269
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#14519798C2semidirect
2. #16840423C2semidirect
3. #16840411C2semidirect
4. #16840155C2semidirect
5. #16840008C2semidirect
6. #16840000C2semidirect
7. #16839979C2semidirect
8. #16839970C2semidirect
9. #16839923C2semidirect
10. #16839921C2semidirect
11. #16839918C2semidirect
12. #16839907C2semidirect
13. #16839863C2semidirect
14. #16839831C2semidirect
15. C2×#137×C61C2semidirect
91. SD16×C61D4semidirect
202. C2×#137D61semidirect
217. C61#3269semidirect
297. SD16C22⋊D61semidirect