Finite Group Databasebeta

← #110546

Subgroups — #110546

Order 512.

643 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1997C211yesmaximal, characteristic
2#17742C211yesmaximal, characteristic
3C2×#1546C211yesmaximal, characteristic
4#17327C211yesmaximal, characteristic
5#8065C211yesmaximal, characteristic
6#8004C211yesmaximal, characteristic
7#7938C211yesmaximal, characteristic
8C22×C4⋊Q8C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×#423C2211yescharacteristic
14C2×C4×M16C2211yescharacteristic
15#1997—22no—
16#1997—21no—
17#1997—21no—
18C2×#343C414yes—
19#1556C414yes—
20#1549—22no—
21#1546—22no—
22#1546—21no—
23#1546—21no—
24#1546—22no—
25C2×#332C414yes—
26#1453—22no—
27#1451—21no—
28#1451—21no—
29C8×M16—21no—
30C8×M16—21no—
31#1299—22no—
32#1292—22no—
33#1283—22no—
34C23×Q8—21no—
35C22×M16—21no—
36C22×M16C2×C412yes—
37C22×M16C2×C412yes—
38C2×C4⋊Q8—21no—
39C2×C4⋊Q8—21no—
40C2×C4⋊Q8—21no—
41C2×C4⋊Q8—21no—
42C2×C4⋊Q8—21no—
43C2×C4⋊Q8—21no—
44C2×C4⋊Q8—21no—
45C2×C4⋊Q8—21no—
46C2×C4⋊Q8—21no—
47C2×C4⋊Q8—21no—
48C2×C4⋊Q8C2×C412yes—
49C2×C4⋊Q8C2×C412yes—
50C22×C4⋊C4—21no—
51C22×C4⋊C4C2×C412yes—
52C22×C42C2311yescharacteristic
53#432—21no—
54#432—21no—
55#432C2×C412yes—
56#432C2×C412yes—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431D412yes—
63#431D411yescharacteristic
64#431D411yescharacteristic
65#431D412yes—
66#423—21no—
67#423—21no—
68#423—21no—
69#423—21no—
70#423—21no—
71#423—21no—
72#423—21no—
73#423—21no—
74#423—21no—
75#423D412yes—
76C2×C4⋊C8—21no—
77C2×C4⋊C8—21no—
78C2×C4⋊C8—21no—
79C2×C4⋊C8C2×C412yes—
80C2×C4⋊C8C2×C412yes—
81#407—21no—
82#407—21no—
83C2×C22⋊C8—21no—
84C4×M16—21no—
85C4×M16—21no—
86C4×M16—21no—
87C4×M16—21no—
88C4×M16D412yes—
89C4×M16D411yescharacteristic
90C4×M16D411yescharacteristic
91C2×#97—21no—
92C2×C4×C8—21no—
93C2×C4×C8—21no—
94#343—24no—
95#343—24no—
96#332—24no—
97#332—24no—
98#332—28no—
99#322—22no—
100#322—22no—
101#322—22no—
102C82—22no—
103C22×Q8—22no—
104C22×Q8—22no—
105C22×Q8—41no—
106C22×Q8—41no—
107C22×Q8—41no—
108C22×Q8—41no—
109C22×Q8—82no—
110C22×Q8—82no—
111C23×C4—22no—
112C23×C4C22×C411yescharacteristic
113C23×C4#4111yescharacteristic
114C23×C4#4111yescharacteristic
115C2×M16—22no—
116C2×M16—22no—
117C2×M16—24no—
118C2×M16—22no—
119C2×M16—22no—
120C2×M16—42no—
121C2×M16—41no—
122C2×M16—41no—
123C2×M16—41no—
124C2×M16—44no—
125C2×M16—82no—
126C2×M16C22⋊C412yes—
127C2×M16C22⋊C412yes—
128C22×C8—22no—
129C22×C8—22no—
130C22×C8—22no—
131C22×C8—22no—
132C4⋊Q8—22no—
133C4⋊Q8—22no—
134C4⋊Q8—22no—
135C4⋊Q8—22no—
136C4⋊Q8—22no—
137C4⋊Q8—22no—
138C4⋊Q8—22no—
139C4⋊Q8—22no—
140C4⋊Q8—41no—
141C4⋊Q8—41no—
142C4⋊Q8—41no—
143C4⋊Q8—41no—
144C4⋊Q8—41no—
145C4⋊Q8—41no—
146C4⋊Q8—41no—
147C4⋊Q8—41no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4C4214yes—
160C2×C42C22×C411yescharacteristic
161C2×C42C22×C411yescharacteristic
162C2×C42C2×D411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×D411yescharacteristic
165C2×C42C2×D411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42#4111yescharacteristic
169C2×C42#4111yescharacteristic
170C2×C42#4111yescharacteristic
171C2×C42#4111yescharacteristic
172C4⋊C8—22no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—41no—
178C4⋊C8—41no—
179C4⋊C8—41no—
180C4⋊C8—41no—
181C4⋊C8—41no—
182C4⋊C8—41no—
183C4⋊C8—41no—
184C4⋊C8C22⋊C412yes—
185C4⋊C8C22⋊C412yes—
186C4⋊C8C22⋊C414yes—
187C22⋊C8—22no—
188C22⋊C8—22no—
189C22⋊C8—21no—
190C22⋊C8—21no—
191C22⋊C8—22no—
192C22⋊C8—22no—
193C22⋊C8—41no—
194#97—22no—
195#97—22no—
196#97—22no—
197#97—21no—
198#97—21no—
199C4×C8—21no—
200C4×C8—21no—
201C4×C8—22no—
202C4×C8—21no—
203C4×C8—21no—
204C4×C8—22no—
205C4×C8—22no—
206C4×C8—41no—
207C24#11711yescharacteristic
208C2×Q8—42no—
209C2×Q8—42no—
210C2×Q8—42no—
211C2×Q8—42no—
212C2×Q8—84no—
213C2×Q8—82no—
214C2×Q8—82no—
215C2×Q8—84no—
216C2×Q8—84no—
217C2×Q8—82no—
218C2×Q8—82no—
219C2×Q8—82no—
220C2×Q8—82no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—24no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—84no—
230C22×C4C2×C4211yescharacteristic
231C22×C4C2×C22⋊C411yescharacteristic
232C22×C4C4×D411yescharacteristic
233C22×C4C4×D411yescharacteristic
234C22×C4C4×D411yescharacteristic
235C22×C4C4×D411yescharacteristic
236C22×C4C4×D411yescharacteristic
237C22×C4C4×D411yescharacteristic
238C22×C4C4×D411yescharacteristic
239C22×C4C4×D411yescharacteristic
240C22×C4#12111yescharacteristic
241C22×C4#12111yescharacteristic
242C22×C4#12311yescharacteristic
243C22×C4#12311yescharacteristic
244C22×C4#12411yescharacteristic
245C22×C4#12411yescharacteristic
246C22×C4#12611yescharacteristic
247C22×C4#12611yescharacteristic
248M16—22no—
249M16—22no—
250M16—22no—
251M16—44no—
252M16—42no—
253M16—42no—
254M16—44no—
255M16—82no—
256M16—82no—
257M16—82no—
258M16—82no—
259M16#10114yes—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—24no—
265C2×C8—44no—
266C2×C8—42no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—82no—
270C2×C8—82no—
271C2×C8—82no—
272C4⋊C4—24no—
273C4⋊C4—24no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C42C2×C22⋊C411yescharacteristic
281C42C2×C22⋊C411yescharacteristic
282C42#11711yescharacteristic
283C42#11711yescharacteristic
284C42C4×D411yescharacteristic
285C42C4×D411yescharacteristic
286C42C4×D411yescharacteristic
287C42C4×D411yescharacteristic
288C42#12011yescharacteristic
289C42#12111yescharacteristic
290C42#12111yescharacteristic
291C42#12111yescharacteristic
292C42#12111yescharacteristic
293C42#12311yescharacteristic
294C42#12411yescharacteristic
295C42#12711yescharacteristic
296C23—22no—
297C23—22no—
298C23—41no—
299C23C4×C22⋊C411yescharacteristic
300C23#38811yescharacteristic
301C23#38811yescharacteristic
302Q8—84no—
303Q8—84no—
304Q8—84no—
305Q8—82no—
306Q8—82no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
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—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—44no—
328C2×C4—84no—
329C2×C4—84no—
330C2×C4—84no—
331C2×C4C4×C22⋊C411yescharacteristic
332C2×C4C4×C22⋊C411yescharacteristic
333C2×C4#38611yescharacteristic
334C2×C4#38611yescharacteristic
335C2×C4#38611yescharacteristic
336C2×C4#38811yescharacteristic
337C2×C4#38811yescharacteristic
338C2×C4#38811yescharacteristic
339C2×C4#38811yescharacteristic
340C2×C4#39011yescharacteristic
341C2×C4#39011yescharacteristic
342C2×C4#39011yescharacteristic
343C2×C4C2×#10112yes—
344C2×C4#41312yes—
345C2×C4#47112yes—
346C2×C4#47212yes—
347C8—24no—
348C8—42no—
349C8—42no—
350C8—42no—
351C8—44no—
352C8—82no—
353C8—82no—
354C8—82no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—44no—
363C22#143711yescharacteristic
364C22C4×#10112yes—
365C22#193112yes—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—84no—
374C4#190112yes—
375C4#190212yes—
376C4#190712yes—
377C4#196611yescharacteristic
378C4#196711yescharacteristic
379C4#197711yescharacteristic
380C4#197811yescharacteristic
381C2—22no—
382C2—22no—
383C2—41no—
384C2#1094311yescharacteristic
385C2#1095211yescharacteristic
386C2#1096311yescharacteristic
subgroupG/H
center, socleC22#1437
commutatorC22×C4C2×C42
Frattini, cosocleC22×C42C23
prime radicalC24#117
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#19972
#177422
C2×#15462
#173272
#80652
#80042
#79382