Finite Group Databasebeta

← C2×#7792 #165702

Subgroups — C2×#7792 #165702

Order 512.

947 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2726C211yesmaximal, characteristic
2C2×#2099C211yesmaximal, characteristic
3C2×#2083C211yesmaximal, characteristic
4C2×#2083C211yesmaximal, characteristic
5#7792C218yesmaximal, direct product factor
6C2×#1271C211yesmaximal, characteristic
7C2×#1271C211yesmaximal, characteristic
8C2×#1271C211yesmaximal, characteristic
9C22×#125—21no—
10C22×#107—21no—
11C22×#107—21no—
12#2726—22no—
13#2726—22no—
14#2726—22no—
15#2726C2214yes—
16C2×#398—21no—
17C2×#398—21no—
18C2×#398—21no—
19C2×#389—21no—
20C2×#389C2211yescharacteristic
21C2×#389C2211yescharacteristic
22C2×#389C2211yescharacteristic
23C2×#387—21no—
24C2×#384C2211yescharacteristic
25#2099—22no—
26#2099C2214yes—
27#2083—22no—
28#2083—22no—
29#2083C2214yes—
30#2083C2214yes—
31C2×#340—21no—
32C2×#340—21no—
33C2×#340—21no—
34C2×#340—21no—
35C2×#336C2211yescharacteristic
36C2×#336C2211yescharacteristic
37C2×#336C2211yescharacteristic
38#1271C2214yes—
39#1271C2214yes—
40#1271C2214yes—
41C23×C8—21no—
42C23×C8—21no—
43C23×C8—21no—
44C2×#125—24no—
45C2×#125—24no—
46C2×#125—44no—
47C2×#125—44no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4D411yescharacteristic
59C22×C4⋊C4D411yescharacteristic
60C22×C4⋊C4D411yescharacteristic
61C22×C4⋊C4D411yescharacteristic
62C22×C4⋊C4D411yescharacteristic
63C22×C4⋊C4D411yescharacteristic
64C22×C42—21no—
65C22×C42C2311yescharacteristic
66C2×#107—24no—
67C2×#107—24no—
68C2×#107—44no—
69C2×#107—44no—
70#398—24no—
71#398—24no—
72#398—24no—
73#398—24no—
74#398—24no—
75#398—24no—
76#389—24no—
77#389—24no—
78#389—21no—
79#389—21no—
80#389—21no—
81#389—21no—
82#389—21no—
83#389—21no—
84#389D412yes—
85#389D412yes—
86#389D412yes—
87#389C2312yes—
88#389C2312yes—
89#389C2312yes—
90#387—24no—
91#387—24no—
92#384—21no—
93#384—21no—
94#384—21no—
95#384C2312yes—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95—21no—
102#340—24no—
103#340—24no—
104#340—24no—
105#340—24no—
106#336—21no—
107#336—21no—
108#336—21no—
109#336C2312yes—
110#336C2312yes—
111#336C2312yes—
112C23×C4—21no—
113C23×C4—21no—
114C23×C4—21no—
115C23×C4—21no—
116C23×C4—21no—
117C23×C4—21no—
118C23×C4—41no—
119C23×C4C2×D411yescharacteristic
120C23×C4C2×D411yescharacteristic
121C23×C4C2×D411yescharacteristic
122C22×C8—24no—
123C22×C8—24no—
124C22×C8—22no—
125C22×C8—22no—
126C22×C8—22no—
127C22×C8—42no—
128C22×C8—42no—
129C22×C8—42no—
130C22×C8—42no—
131C22×C8—42no—
132C22×C8—42no—
133C22×C8—42no—
134#125—48no—
135#125—416no—
136#125—48no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—24no—
144C2×C4⋊C4—24no—
145C2×C4⋊C4—24no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—24no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—44no—
161C2×C4⋊C4—44no—
162C2×C4⋊C4—44no—
163C2×C4⋊C4—42no—
164C2×C4⋊C4—42no—
165C2×C4⋊C4—42no—
166C2×C4⋊C4—42no—
167C2×C4⋊C4—42no—
168C2×C4⋊C4—42no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4—42no—
171C2×C4⋊C4—42no—
172C2×C4⋊C4—44no—
173C2×C4⋊C4—42no—
174C2×C4⋊C4—42no—
175C2×C4⋊C4—42no—
176C2×C4⋊C4—42no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—82no—
181C2×C4⋊C4D814yes—
182C2×C4⋊C4Q1614yes—
183C2×C4⋊C4C2×D412yes—
184C2×C4⋊C4C2×D412yes—
185C2×C4⋊C4C2×D412yes—
186C2×C4⋊C4C2×D412yes—
187C2×C4⋊C4C2×D412yes—
188C2×C4⋊C4C2×D412yes—
189C2×C42—24no—
190C2×C42—42no—
191C2×C42—44no—
192C2×C42C2×D411yescharacteristic
193C2×C42C2×D411yescharacteristic
194C2×C42C2×D411yescharacteristic
195C2×C42C2411yescharacteristic
196#107—48no—
197#107—48no—
198#95—24no—
199#95—24no—
200#95—24no—
201#95—22no—
202#95—22no—
203#95—22no—
204#95—22no—
205#95—22no—
206#95—22no—
207C24#12011yescharacteristic
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—82no—
240C22×C4—82no—
241C22×C4—82no—
242C22×C4#12011yescharacteristic
243C22×C4#12011yescharacteristic
244C22×C4#12011yescharacteristic
245C22×C4C2×D812yes—
246C22×C4C2×Q1612yes—
247C22×C4#13512yes—
248C22×C4AGL(1,ℤ/8)12yes—
249C22×C4AGL(1,ℤ/8)12yes—
250C22×C4#13712yes—
251C22×C4C22×D411yescharacteristic
252C22×C4C22×D411yescharacteristic
253C22×C4C22×D411yescharacteristic
254C2×C8—24no—
255C2×C8—24no—
256C2×C8—48no—
257C2×C8—48no—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—84no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—24no—
269C4⋊C4—24no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—48no—
276C4⋊C4—48no—
277C4⋊C4—48no—
278C4⋊C4—44no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C4⋊C4—44no—
286C4⋊C4—44no—
287C4⋊C4—42no—
288C4⋊C4—44no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C4⋊C4—42no—
293C4⋊C4—81no—
294C4⋊C4—81no—
295C4⋊C4—81no—
296C4⋊C4—82no—
297C4⋊C4—84no—
298C4⋊C4—82no—
299C4⋊C4—82no—
300C4⋊C4C2×D814yes—
301C4⋊C4C2×Q1614yes—
302C42—41no—
303C42—41no—
304C42—41no—
305C42—41no—
306C42—48no—
307C23#44712yes—
308C23#44912yes—
309C23#45112yes—
310C23#45412yes—
311C23#45612yes—
312C23#45612yes—
313C23#45812yes—
314C23C2×#12011yescharacteristic
315C2×C4—24no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—48no—
336C2×C4—48no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—84no—
354C2×C4—84no—
355C2×C4—84no—
356C2×C4—84no—
357C2×C4—82no—
358C2×C4—82no—
359C2×C4—82no—
360C2×C4—164no—
361C2×C4#44712yes—
362C2×C4#44912yes—
363C2×C4#45112yes—
364C2×C4C22×D811yescharacteristic
365C2×C4C22×Q1611yescharacteristic
366C2×C4C2×#13511yescharacteristic
367C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
368C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
369C2×C4C2×#13711yescharacteristic
370C8—44no—
371C8—44no—
372C8—82no—
373C22#160914yes—
374C22#161014yes—
375C22#161714yes—
376C22#162514yes—
377C22#164814yes—
378C22#164914yes—
379C22#166314yes—
380C22C2×#44711yescharacteristic
381C22C2×#45111yescharacteristic
382C22C2×#44911yescharacteristic
383C22C2×#45411yescharacteristic
384C22C2×#45611yescharacteristic
385C22C2×#45611yescharacteristic
386C22C2×#45811yescharacteristic
387C4—21no—
388C4—21no—
389C4—22no—
390C4—21no—
391C4—21no—
392C4—22no—
393C4—21no—
394C4—21no—
395C4—22no—
396C4—44no—
397C4—44no—
398C4—82no—
399C4—82no—
400C4—82no—
401C4—82no—
402C4—162no—
403C2#779218yesdirect product factor
404C2C2×#160911yescharacteristic
405C2C2×#161011yescharacteristic
406C2C2×#161711yescharacteristic
407C2C2×#162511yescharacteristic
408C2C2×#164911yescharacteristic
409C2C2×#164811yescharacteristic
410C2C2×#166311yescharacteristic
subgroupG/H
center, socle, prime radicalC24#120
commutator, Frattini, cosocleC2×C42C24
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
5. #7792C2direct (N × H)
403. C2#7792direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#27262
C2×#20992
C2×#20832
#77922
C2×#12712