Finite Group Databasebeta

← #110543

Subgroups — #110543

Order 512.

594 conjugacy classes of subgroups.

The subgroup lattice has 391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1998C211yesmaximal, characteristic
2#17667C211yesmaximal, characteristic
3C2×#1528C211yesmaximal, characteristic
4M162C211yesmaximal, characteristic
5#8063C211yesmaximal, characteristic
6#7990C211yesmaximal, characteristic
7#7937C211yesmaximal, characteristic
8C22×#125C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14C2×C4×M16C2211yescharacteristic
15#1998—22no—
16#1998—21no—
17#1998—21no—
18C2×#343C412yes—
19C2×#343C412yes—
20#1534C414yes—
21#1528—22no—
22#1528—22no—
23#1528—22no—
24#1528—21no—
25#1528—21no—
26C2×#330C414yes—
27#1455—22no—
28#1451—21no—
29#1451—21no—
30C8×M16—21no—
31C8×M16—21no—
32#1299—22no—
33#1290—22no—
34#1283—22no—
35C22×M16—21no—
36C22×M16C2×C412yes—
37C22×M16C2×C412yes—
38C2×#125—21no—
39C2×#125—21no—
40C2×#125—21no—
41C2×#125—21no—
42C2×#125—21no—
43C2×#125—21no—
44C2×#125—21no—
45C2×#125—21no—
46C2×#125—21no—
47C2×#125—21no—
48C2×#125C2×C412yes—
49C2×#125C2×C412yes—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4C2×C411yescharacteristic
53C22×C4⋊C4C2×C411yescharacteristic
54C22×C42C2311yescharacteristic
55#432—21no—
56#432—21no—
57#432—21no—
58#432—21no—
59#432—21no—
60#432C2×C412yes—
61#432C2×C412yes—
62#432D412yes—
63#431—21no—
64#431—21no—
65#431—21no—
66#431—21no—
67#423—21no—
68#423—21no—
69#423—21no—
70#423—21no—
71#423—21no—
72#423—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76#407—21no—
77#407—21no—
78C2×C22⋊C8—21no—
79C4×M16—21no—
80C4×M16—21no—
81C4×M16—21no—
82C4×M16—21no—
83C4×M16—21no—
84C4×M16D412yes—
85C4×M16D411yescharacteristic
86C4×M16D411yescharacteristic
87C4×M16D412yes—
88C4×M16D411yescharacteristic
89C4×M16D411yescharacteristic
90C4×M16D412yes—
91C2×#97—21no—
92C2×#97C2×C412yes—
93C2×#97C2×C412yes—
94C2×C4×C8—21no—
95C2×C4×C8—21no—
96#343—22no—
97#343—22no—
98#343—22no—
99#343—22no—
100#330—24no—
101#330—24no—
102#330—28no—
103#322—22no—
104#322—22no—
105#322—22no—
106C82—22no—
107C23×C4—21no—
108C23×C4—21no—
109C23×C4C22×C411yescharacteristic
110C23×C4#4111yescharacteristic
111C23×C4#4111yescharacteristic
112C2×M16—21no—
113C2×M16—22no—
114C2×M16—22no—
115C2×M16—21no—
116C2×M16—22no—
117C2×M16—24no—
118C2×M16—22no—
119C2×M16—22no—
120C2×M16—42no—
121C2×M16—44no—
122C2×M16—41no—
123C2×M16—44no—
124C2×M16C22⋊C412yes—
125C2×M16C22⋊C412yes—
126C22×C8—22no—
127C22×C8—22no—
128C22×C8—22no—
129C22×C8—22no—
130#125—22no—
131#125—22no—
132#125—22no—
133#125—22no—
134#125—22no—
135#125—22no—
136#125—22no—
137#125—22no—
138#125—41no—
139#125—41no—
140#125—41no—
141#125—41no—
142#125—41no—
143#125—41no—
144#125—41no—
145#125—41no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—41no—
161C2×C4⋊C4—41no—
162C2×C4⋊C4—41no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4—41no—
165C2×C4⋊C4—41no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4C4212yes—
169C2×C4⋊C4C4212yes—
170C2×C42C22×C411yescharacteristic
171C2×C42C22×C411yescharacteristic
172C2×C42C2×D411yescharacteristic
173C2×C42C2×D411yescharacteristic
174C2×C42C2×D411yescharacteristic
175C2×C42C2×D411yescharacteristic
176C2×C42C2×D411yescharacteristic
177C2×C42C2×D411yescharacteristic
178C2×C42#4111yescharacteristic
179C2×C42#4111yescharacteristic
180C2×C42#4111yescharacteristic
181C2×C42#4111yescharacteristic
182C4⋊C8—22no—
183C4⋊C8—22no—
184C4⋊C8—22no—
185C4⋊C8—41no—
186C4⋊C8—41no—
187C4⋊C8—41no—
188C4⋊C8—41no—
189C4⋊C8—41no—
190C4⋊C8—41no—
191C4⋊C8—41no—
192C22⋊C8—22no—
193C22⋊C8—22no—
194C22⋊C8—22no—
195C22⋊C8—41no—
196C22⋊C8—41no—
197C22⋊C8—41no—
198#97—22no—
199#97—22no—
200#97—22no—
201#97—22no—
202#97—22no—
203#97—21no—
204#97—21no—
205#97C22⋊C412yes—
206#97C22⋊C412yes—
207#97C22⋊C414yes—
208C4×C8—21no—
209C4×C8—21no—
210C4×C8—22no—
211C4×C8—21no—
212C4×C8—21no—
213C4×C8—22no—
214C4×C8—22no—
215C4×C8—41no—
216C24#11711yescharacteristic
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—42no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—81no—
227C22×C4—82no—
228C22×C4—82no—
229C22×C4C2×C4211yescharacteristic
230C22×C4C2×C22⋊C411yescharacteristic
231C22×C4C4×D411yescharacteristic
232C22×C4C4×D411yescharacteristic
233C22×C4C4×D411yescharacteristic
234C22×C4C4×D411yescharacteristic
235C22×C4C4×D411yescharacteristic
236C22×C4C4×D411yescharacteristic
237C22×C4C4×D411yescharacteristic
238C22×C4C4×D411yescharacteristic
239C22×C4#12111yescharacteristic
240C22×C4#12111yescharacteristic
241C22×C4#12311yescharacteristic
242C22×C4#12311yescharacteristic
243C22×C4#12411yescharacteristic
244C22×C4#12411yescharacteristic
245C22×C4#12611yescharacteristic
246C22×C4#12611yescharacteristic
247M16—24no—
248M16—22no—
249M16—22no—
250M16—22no—
251M16—44no—
252M16—44no—
253M16—42no—
254M16—44no—
255M16—82no—
256M16—82no—
257M16—82no—
258M16#10114yes—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8—24no—
264C2×C8—44no—
265C2×C8—44no—
266C2×C8—42no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—82no—
270C2×C8—82no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—42no—
286C4⋊C4—42no—
287C42C2×C22⋊C411yescharacteristic
288C42C2×C22⋊C411yescharacteristic
289C42#11711yescharacteristic
290C42#11711yescharacteristic
291C42C4×D411yescharacteristic
292C42C4×D411yescharacteristic
293C42C4×D411yescharacteristic
294C42C4×D411yescharacteristic
295C42#12011yescharacteristic
296C42#12111yescharacteristic
297C42#12111yescharacteristic
298C42#12111yescharacteristic
299C42#12111yescharacteristic
300C42#12311yescharacteristic
301C42#12411yescharacteristic
302C42#12711yescharacteristic
303C23—22no—
304C23—22no—
305C23—41no—
306C23C4×C22⋊C411yescharacteristic
307C23#38811yescharacteristic
308C23#38811yescharacteristic
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4C4×C22⋊C411yescharacteristic
337C2×C4C4×C22⋊C411yescharacteristic
338C2×C4#38611yescharacteristic
339C2×C4#38611yescharacteristic
340C2×C4#38611yescharacteristic
341C2×C4#38811yescharacteristic
342C2×C4#38811yescharacteristic
343C2×C4#38811yescharacteristic
344C2×C4#38811yescharacteristic
345C2×C4#39011yescharacteristic
346C2×C4#39011yescharacteristic
347C2×C4#39011yescharacteristic
348C2×C4C2×#10112yes—
349C2×C4#41312yes—
350C8—24no—
351C8—24no—
352C8—42no—
353C8—44no—
354C8—42no—
355C8—82no—
356C8—82no—
357C8—82no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—44no—
366C22#143711yescharacteristic
367C22C4×#10112yes—
368C22#193212yes—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—82no—
380C4—82no—
381C4#190112yes—
382C4#196611yescharacteristic
383C4#196711yescharacteristic
384C2—22no—
385C2—22no—
386C2—41no—
387C2#1094611yescharacteristic
388C2#1095511yescharacteristic
389C2#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×#19982
#176672
C2×#15282
M1622
#80632
#79902
#79372