Finite Group Databasebeta

← #120066

Subgroups — #120066

Order 512.

522 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21356C211yesmaximal, characteristic
2#21172C211yesmaximal, characteristic
3C2×#1307C211yesmaximal, characteristic
4C2×#1299C211yesmaximal, characteristic
5#8033C211yesmaximal, characteristic
6#7914C211yesmaximal, characteristic
7#7902C211yesmaximal, characteristic
8C2×#432C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#428C411yescharacteristic
12C2×#428C411yescharacteristic
13C2×#423C2211yescharacteristic
14C2×C4×M16C2211yescharacteristic
15C2×#382C2211yescharacteristic
16C4×#117C2211yescharacteristic
17#1949—21no—
18#1949—21no—
19#1949—21no—
20#1949—21no—
21#1939—21no—
22#1939—21no—
23#1851—22no—
24#1767—21no—
25#1767—21no—
26#1736C411yescharacteristic
27#1736C411yescharacteristic
28#1307—22no—
29#1299—22no—
30#1295—21no—
31#1295—21no—
32#1280—22no—
33#1279—21no—
34#1279—21no—
35C22×M16—21no—
36C22×M16C2×C411yescharacteristic
37C22×M16C2×C411yescharacteristic
38C2×#117C2×C411yescharacteristic
39C2×#117C2×C411yescharacteristic
40C22×C4⋊C4C2×C411yescharacteristic
41C22×C4⋊C4C2×C411yescharacteristic
42C22×C42C2311yescharacteristic
43#432—21no—
44#432—21no—
45#432—21no—
46#432—21no—
47#432—21no—
48#432—21no—
49#432—21no—
50#432Q812yes—
51#431—21no—
52#431—21no—
53#431—21no—
54#431Q812yes—
55#428—42no—
56#428—42no—
57C2×#107—21no—
58C2×#107—21no—
59C2×#106—21no—
60C2×#106—21no—
61#423—21no—
62#423—21no—
63#423D412yes—
64#423Q812yes—
65C2×C4⋊C8—21no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—22no—
70C2×C4⋊C8—22no—
71C2×C4⋊C8—21no—
72C2×C22⋊C8—21no—
73C2×C22⋊C8—21no—
74C2×C22⋊C8D412yes—
75C4×M16—21no—
76C4×M16—21no—
77C4×M16—21no—
78C4×M16—21no—
79C2×#97—21no—
80C2×#97—21no—
81C2×#97D411yescharacteristic
82C2×#97D411yescharacteristic
83C2×C4×C8—21no—
84C2×C4×C8—21no—
85#382—21no—
86#382—21no—
87#382—21no—
88#382—21no—
89C4×C4⋊C4D411yescharacteristic
90C4×C4⋊C4D411yescharacteristic
91C4×C4⋊C4D411yescharacteristic
92C4×C4⋊C4D411yescharacteristic
93C4×C22⋊C4—21no—
94C4×C22⋊C4—21no—
95#376—21no—
96C2×#95—21no—
97C2×#95—21no—
98C43—21no—
99#340—21no—
100#340—21no—
101#340—21no—
102#340—21no—
103#336—22no—
104#336—22no—
105C23×C4—21no—
106C23×C4—21no—
107C23×C4C22×C411yescharacteristic
108C23×C4C2×D411yescharacteristic
109C23×C4#4111yescharacteristic
110C2×M16—21no—
111C2×M16—21no—
112C2×M16—42no—
113C2×M16—42no—
114C2×M16—41no—
115C2×M16—41no—
116C2×M16—41no—
117C2×M16—41no—
118C2×M16—41no—
119C2×M16—41no—
120C2×M16C4⋊C412yes—
121C2×M16C4⋊C412yes—
122C22×C8—21no—
123C22×C8—21no—
124C22×C8—21no—
125C22×C8—21no—
126C22×C8—22no—
127C22×C8—41no—
128C22×C8—41no—
129#117—22no—
130#117—22no—
131#117—41no—
132#117—41no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4C22⋊C411yescharacteristic
142C2×C4⋊C4C22⋊C411yescharacteristic
143C2×C4⋊C4C22⋊C411yescharacteristic
144C2×C4⋊C4C22⋊C411yescharacteristic
145C2×C22⋊C4—21no—
146C2×C22⋊C4—21no—
147C2×C42—21no—
148C2×C42—21no—
149C2×C42—21no—
150C2×C42—21no—
151C2×C42—21no—
152C2×C42—21no—
153C2×C42C2×D411yescharacteristic
154C2×C42C2×D411yescharacteristic
155C2×C42C2×D411yescharacteristic
156C2×C42C2×D411yescharacteristic
157C2×C42C2×Q811yescharacteristic
158C2×C42C2×Q811yescharacteristic
159C2×C42C2×Q811yescharacteristic
160C2×C42#4111yescharacteristic
161C2×C42#4111yescharacteristic
162C2×C42#4111yescharacteristic
163C2×C42#4111yescharacteristic
164C2×C42#4111yescharacteristic
165#107—42no—
166#107—42no—
167#106—42no—
168#106—42no—
169C4⋊C8—22no—
170C4⋊C8—22no—
171C4⋊C8—22no—
172C4⋊C8—22no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—44no—
176C4⋊C8—44no—
177C4⋊C8—41no—
178C4⋊C8—41no—
179C4⋊C8—41no—
180C4⋊C8—41no—
181C22⋊C8—22no—
182C22⋊C8—22no—
183C22⋊C8—22no—
184C22⋊C8—22no—
185C22⋊C8—41no—
186C22⋊C8—41no—
187#97—21no—
188#97—21no—
189#97—22no—
190#97—21no—
191#97—21no—
192#97—41no—
193#97—41no—
194#97—41no—
195C4×C8—22no—
196C4×C8—41no—
197C4×C8—41no—
198C4×C8—41no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—41no—
204#95—41no—
205#95—41no—
206#95—41no—
207C24C4×D411yescharacteristic
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—81no—
225C22×C4—81no—
226C22×C4—81no—
227C22×C4—81no—
228C22×C4C2×C22⋊C411yescharacteristic
229C22×C4C2×C4⋊C411yescharacteristic
230C22×C4#11711yescharacteristic
231C22×C4C4×D411yescharacteristic
232C22×C4C4×Q811yescharacteristic
233C22×C4C4×Q811yescharacteristic
234C22×C4#12011yescharacteristic
235C22×C4#12111yescharacteristic
236C22×C4#12111yescharacteristic
237C22×C4#12111yescharacteristic
238C22×C4C22⋊Q811yescharacteristic
239C22×C4C22⋊Q811yescharacteristic
240C22×C4#12311yescharacteristic
241C22×C4#12311yescharacteristic
242C22×C4#12511yescharacteristic
243C22×C4#12511yescharacteristic
244C22×C4#12611yescharacteristic
245C22×C4C4⋊Q811yescharacteristic
246M16—42no—
247M16—42no—
248M16—44no—
249M16—44no—
250M16—42no—
251M16—42no—
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—42no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—81no—
270C2×C8—81no—
271C2×C8—81no—
272C2×C8—81no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—81no—
284C4⋊C4—81no—
285C4⋊C4#10012yes—
286C4⋊C4#10112yes—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C42—42no—
290C42—42no—
291C42—42no—
292C42—42no—
293C42—81no—
294C42—81no—
295C42#12111yescharacteristic
296C42#12111yescharacteristic
297C42#12111yescharacteristic
298C42C22⋊Q811yescharacteristic
299C42C22⋊Q811yescharacteristic
300C42C22⋊Q811yescharacteristic
301C42C22⋊Q811yescharacteristic
302C42C22⋊Q811yescharacteristic
303C42C22⋊Q811yescharacteristic
304C42#12311yescharacteristic
305C42#12411yescharacteristic
306C42#12511yescharacteristic
307C42#12511yescharacteristic
308C42#12611yescharacteristic
309C42C4⋊Q811yescharacteristic
310C42C4⋊Q811yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23#38611yescharacteristic
318C23#38711yescharacteristic
319C23#38911yescharacteristic
320C2×C4—21no—
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—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—162no—
365C2×C4—162no—
366C2×C4#38011yescharacteristic
367C2×C4#38711yescharacteristic
368C2×C4#38911yescharacteristic
369C2×C4#39111yescharacteristic
370C2×C4#39411yescharacteristic
371C2×C4#39511yescharacteristic
372C2×C4#39611yescharacteristic
373C2×C4#39611yescharacteristic
374C2×C4#39811yescharacteristic
375C2×C4#39811yescharacteristic
376C2×C4#39811yescharacteristic
377C2×C4#40011yescharacteristic
378C2×C4C2×#10011yescharacteristic
379C2×C4C2×#10111yescharacteristic
380C2×C4#41311yescharacteristic
381C2×C4#41311yescharacteristic
382C8—42no—
383C8—42no—
384C8—42no—
385C8—42no—
386C8—82no—
387C8—82no—
388C8—82no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22#144111yescharacteristic
400C22#188111yescharacteristic
401C22#188111yescharacteristic
402C22#190011yescharacteristic
403C22#190111yescharacteristic
404C22#190611yescharacteristic
405C22#190611yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—42no—
417C4—42no—
418C4—81no—
419C4—81no—
420C4—161no—
421C4—161no—
422C4#180011yescharacteristic
423C4#180111yescharacteristic
424C4#199711yescharacteristic
425C4#199811yescharacteristic
426C2—41no—
427C2—41no—
428C2#934911yescharacteristic
429C2#935011yescharacteristic
430C2#935111yescharacteristic
431C2#935211yescharacteristic
432C2#1120411yescharacteristic
433C2#1121511yescharacteristic
434C2#1121811yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ 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
#213562
#211722
C2×#13072
C2×#12992
#80332
#79142
#79022