Finite Group Databasebeta

← #98235

Subgroups — #98235

Order 512.

627 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36563C211yesmaximal, characteristic
2#9691C211yesmaximal, characteristic
3#9691C211yesmaximal, characteristic
4#8586C211yesmaximal, characteristic
5#8564C211yesmaximal, characteristic
6#8564C211yesmaximal, characteristic
7#7570C211yesmaximal, characteristic
8#2868C2211yescharacteristic
9#2859—21no—
10#2582—21no—
11#2567C412yes—
12#2552—21no—
13#2550—22no—
14#2507—22no—
15#2451—22no—
16#2369C412yes—
17#2355—21no—
18Q8×C4⋊C4—21no—
19C4×C4⋊Q8—21no—
20C4×C4⋊Q8C2211yescharacteristic
21C42×Q8C2211yescharacteristic
22#1842C2211yescharacteristic
23#1842C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25C4×C4⋊C8C2211yescharacteristic
26C2×#333—22no—
27C2×#333—22no—
28C2×#332—21no—
29C2×Q8⋊C8—21no—
30C2×Q8⋊C8—21no—
31#1296—21no—
32#1279—21no—
33#1279—21no—
34#1271—22no—
35C2×C4⋊Q8C2×C412yes—
36C2×C4⋊Q8D412yes—
37C2×C4⋊Q8D412yes—
38C2×C4⋊Q8D411yescharacteristic
39C2×#125—22no—
40C2×C4×Q8—22no—
41C2×C4×Q8—21no—
42C2×C4×Q8C2×C411yescharacteristic
43C2×C4×Q8D411yescharacteristic
44C2×C4×Q8D411yescharacteristic
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8—21no—
50C2×C4⋊C8—21no—
51C2×C4⋊C8—21no—
52C2×C4⋊C8—21no—
53C2×C4×C8—21no—
54C2×C4×C8—21no—
55#398—24no—
56#398—24no—
57#395—24no—
58#391—22no—
59#391—22no—
60#391—24no—
61#391—21no—
62#389—22no—
63#389—22no—
64#389—22no—
65#389—24no—
66#389—22no—
67#389—22no—
68#389—22no—
69#389—22no—
70#389—21no—
71#389D412yes—
72#387—24no—
73#384—22no—
74#384—21no—
75#384—21no—
76#384—21no—
77#384—21no—
78#384D411yescharacteristic
79#382—22no—
80C4×C4⋊C4—22no—
81C4×C4⋊C4—22no—
82C4×C4⋊C4—22no—
83C4×C4⋊C4—21no—
84C4×C4⋊C4—21no—
85C4×C4⋊C4—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4C2×C412yes—
88C4×C4⋊C4C2×C411yescharacteristic
89C4×C4⋊C4D411yescharacteristic
90C4×C4⋊C4D411yescharacteristic
91C43—21no—
92C43C2311yescharacteristic
93#336—21no—
94#336—21no—
95#333—44no—
96#333—44no—
97#332—42no—
98Q8⋊C8—42no—
99Q8⋊C8—42no—
100C22×Q8—21no—
101C22×Q8C22⋊C411yescharacteristic
102C22×Q8C22⋊C414yes—
103C22×C8—41no—
104C22×C8—41no—
105C22×C8—41no—
106C22×C8—41no—
107C4⋊Q8—21no—
108C4⋊Q8—21no—
109C4⋊Q8—42no—
110C4⋊Q8—42no—
111C4⋊Q8—42no—
112C4⋊Q8—42no—
113C4⋊Q8—42no—
114C4⋊Q8—42no—
115C4⋊Q8SD1612yes—
116C4⋊Q8Q1612yes—
117#125—82no—
118#125—82no—
119C4×Q8—21no—
120C4×Q8—21no—
121C4×Q8—21no—
122C4×Q8—21no—
123C4×Q8—21no—
124C4×Q8—21no—
125C4×Q8—41no—
126C4×Q8—41no—
127C4×Q8—41no—
128C4×Q8—41no—
129C4×Q8—41no—
130C4×Q8—41no—
131C4×Q8—82no—
132C4×Q8—82no—
133C4×Q8SD1612yes—
134C4×Q8Q1612yes—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—24no—
147C2×C4⋊C4—24no—
148C2×C4⋊C4—24no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4C22⋊C411yescharacteristic
152C2×C4⋊C4C22⋊C411yescharacteristic
153C2×C4⋊C4C22⋊C411yescharacteristic
154C2×C4⋊C4C22⋊C412yes—
155C2×C4⋊C4C22⋊C412yes—
156C2×C42—21no—
157C2×C42—22no—
158C2×C42—21no—
159C2×C42—21no—
160C2×C42—21no—
161C2×C42—21no—
162C2×C42—21no—
163C2×C42—24no—
164C2×C42C22×C411yescharacteristic
165C2×C42C2×D411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42C2×D411yescharacteristic
169C2×C42C2×D411yescharacteristic
170C2×C42C2×D411yescharacteristic
171C4⋊C8—22no—
172C4⋊C8—22no—
173C4⋊C8—41no—
174C4⋊C8—41no—
175C4⋊C8—42no—
176C4⋊C8—42no—
177C4⋊C8—41no—
178C4⋊C8—41no—
179C4⋊C8—41no—
180C4⋊C8—41no—
181C4⋊C8—41no—
182C4⋊C8—41no—
183C4⋊C8—41no—
184C4⋊C8—41no—
185C4×C8—41no—
186C4×C8—41no—
187C4×C8—41no—
188C4×C8—41no—
189#95—24no—
190#95—24no—
191#95—24no—
192#95—24no—
193#95—21no—
194#95—22no—
195#95—21no—
196#95—21no—
197#95—22no—
198C2×Q8—21no—
199C2×Q8—22no—
200C2×Q8—22no—
201C2×Q8—21no—
202C2×Q8—21no—
203C2×Q8—21no—
204C2×Q8—21no—
205C2×Q8—44no—
206C2×Q8—44no—
207C2×Q8—44no—
208C2×Q8—41no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×Q8#10312yes—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—21no—
217C22×C4—22no—
218C22×C4—24no—
219C22×C4—21no—
220C22×C4C2×C22⋊C411yescharacteristic
221C22×C4C2×C22⋊C411yescharacteristic
222C22×C4C2×C22⋊C411yescharacteristic
223C22×C4#12011yescharacteristic
224C22×C4#12011yescharacteristic
225C22×C4#12011yescharacteristic
226C22×C4#12011yescharacteristic
227C2×C8—42no—
228C2×C8—42no—
229C2×C8—81no—
230C2×C8—81no—
231C2×C8—81no—
232C2×C8—81no—
233C2×C8—81no—
234C2×C8—81no—
235C2×C8—81no—
236C2×C8—81no—
237C2×C8—81no—
238C2×C8—81no—
239C4⋊C4—21no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—44no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C4⋊C4—42no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C4⋊C4—41no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—82no—
267C4⋊C4—82no—
268C4⋊C4—84no—
269C4⋊C4—84no—
270C4⋊C4—84no—
271C4⋊C4#10312yes—
272C4⋊C4#10314yes—
273C42—21no—
274C42—21no—
275C42—22no—
276C42—22no—
277C42—21no—
278C42—21no—
279C42—21no—
280C42—21no—
281C42—41no—
282C42—42no—
283C42—42no—
284C42—42no—
285C42—42no—
286C42—41no—
287C42—41no—
288C42—41no—
289C42—41no—
290C42—41no—
291C42—41no—
292C42—84no—
293C42C2×SD1611yescharacteristic
294C42C2×SD1611yescharacteristic
295C42C2×Q1611yescharacteristic
296C42C2×Q1611yescharacteristic
297C42#13511yescharacteristic
298C42#13511yescharacteristic
299C42AGL(1,ℤ/8)11yescharacteristic
300C42#13711yescharacteristic
301C42#13711yescharacteristic
302C42#13711yescharacteristic
303C42#13711yescharacteristic
304C42#13711yescharacteristic
305C23#37911yescharacteristic
306Q8—22no—
307Q8—22no—
308Q8—41no—
309Q8—41no—
310Q8—42no—
311Q8—42no—
312Q8—42no—
313Q8—42no—
314Q8—164no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—24no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—44no—
337C2×C4—42no—
338C2×C4—44no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—44no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4#41311yescharacteristic
346C2×C4#41311yescharacteristic
347C2×C4C2×#10311yescharacteristic
348C2×C4C2×#10311yescharacteristic
349C2×C4#41611yescharacteristic
350C2×C4#41711yescharacteristic
351C2×C4#41911yescharacteristic
352C2×C4#41911yescharacteristic
353C2×C4#44811yescharacteristic
354C2×C4#44811yescharacteristic
355C2×C4#44811yescharacteristic
356C2×C4#44811yescharacteristic
357C2×C4#44911yescharacteristic
358C2×C4#44911yescharacteristic
359C2×C4#45111yescharacteristic
360C2×C4#45111yescharacteristic
361C2×C4#45111yescharacteristic
362C2×C4#45111yescharacteristic
363C2×C4#45211yescharacteristic
364C2×C4#45211yescharacteristic
365C2×C4#45311yescharacteristic
366C2×C4#45311yescharacteristic
367C2×C4#45511yescharacteristic
368C2×C4#45511yescharacteristic
369C8—82no—
370C8—82no—
371C8—161no—
372C8—161no—
373C22#178511yescharacteristic
374C22#178711yescharacteristic
375C22#178711yescharacteristic
376C22#178811yescharacteristic
377C22#179211yescharacteristic
378C22#179211yescharacteristic
379C22#179611yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—44no—
387C4—41no—
388C4—42no—
389C4—42no—
390C4—81no—
391C4—84no—
392C4—81no—
393C4—82no—
394C4#154211yescharacteristic
395C4#155011yescharacteristic
396C4#155411yescharacteristic
397C4#155911yescharacteristic
398C4#162211yescharacteristic
399C4#162311yescharacteristic
400C4#163211yescharacteristic
401C4#163311yescharacteristic
402C4#164311yescharacteristic
403C4#164411yescharacteristic
404C4#164511yescharacteristic
405C4#164511yescharacteristic
406C2#834311yescharacteristic
407C2#839211yescharacteristic
408C2#842311yescharacteristic
409C2#842511yescharacteristic
410C2#845011yescharacteristic
411C2#845111yescharacteristic
412C2#847211yescharacteristic
subgroupG/H
center, socle, prime radicalC23#379
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#365632
#96912
#85862
#85642
#75702