Finite Group Databasebeta

← #106927

Subgroups — #106927

Order 512.

767 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2984C211yesmaximal, characteristic
2#17449C211yesmaximal, characteristic
3C2×#1479C211yesmaximal, characteristic
4#8090C211yesmaximal, characteristic
5#8076C211yesmaximal, characteristic
6#8054C211yesmaximal, characteristic
7#7964C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9#2984—22no—
10#2984—22no—
11#2984—22no—
12#2984C414yes—
13C2×#446—22no—
14C2×#446—21no—
15C2×C8×Q8—21no—
16#2920C2211yescharacteristic
17#2920C2211yescharacteristic
18C2×#432—21no—
19C2×#432C2211yescharacteristic
20C2×#431—21no—
21C2×#431C2211yescharacteristic
22C2×#431C2211yescharacteristic
23C2×#431C2211yescharacteristic
24#1491—22no—
25#1487C414yes—
26#1479—22no—
27#1479—21no—
28#1479—21no—
29#1479C412yes—
30#1479C412yes—
31C2×Q8⋊C8—22no—
32#1302—22no—
33#1301—22no—
34#1298—21no—
35#1298—21no—
36#1287—22no—
37C23×Q8Q811yescharacteristic
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×Q8C2×C412yes—
45C2×C4×Q8C2×C411yescharacteristic
46C2×C4×Q8C2×C411yescharacteristic
47C2×C4×Q8C2×C412yes—
48C2×C4×Q8D411yescharacteristic
49C2×C4×Q8D411yescharacteristic
50C2×C4×Q8D412yes—
51C2×C4×Q8D412yes—
52C22×C4⋊C4—21no—
53C22×C4⋊C4Q811yescharacteristic
54C22×C42—21no—
55C22×C42C2311yescharacteristic
56#446—28no—
57#446—24no—
58#446—24no—
59#446—28no—
60C8×Q8—24no—
61C8×Q8—24no—
62#432—24no—
63#432—21no—
64#432—21no—
65#432—24no—
66#432—21no—
67#432—21no—
68#432—21no—
69#432—21no—
70#432C2×C412yes—
71#432D412yes—
72#431—24no—
73#431—21no—
74#431—21no—
75#431—24no—
76#431—21no—
77#431—21no—
78#431—21no—
79#431—21no—
80#431—21no—
81#431—21no—
82#431—21no—
83#431—21no—
84#431—21no—
85#431C2×C412yes—
86#431C2×C412yes—
87#431C2×C412yes—
88#431C2×C412yes—
89#431D412yes—
90#423—21no—
91#423C2×C412yes—
92C2×C4⋊C8—22no—
93C2×C4⋊C8—22no—
94C2×C4⋊C8—21no—
95C2×C4⋊C8—21no—
96C2×C4⋊C8—21no—
97C2×C4⋊C8—21no—
98#407—21no—
99#407—21no—
100C2×C22⋊C8—21no—
101C2×C22⋊C8—21no—
102C2×C22⋊C8—21no—
103C2×C22⋊C8D411yescharacteristic
104C2×C22⋊C8D411yescharacteristic
105C4×M16—21no—
106C4×M16—21no—
107C2×#97—22no—
108C2×#97D412yes—
109C2×C4×C8—22no—
110C2×C4×C8—21no—
111C2×C4×C8—21no—
112C2×C4×C8—21no—
113Q8⋊C8—24no—
114Q8⋊C8—24no—
115Q8⋊C8—24no—
116Q8⋊C8—24no—
117C22×Q8—21no—
118C22×Q8—21no—
119C22×Q8—21no—
120C22×Q8—24no—
121C22×Q8—42no—
122C22×Q8C4⋊C411yescharacteristic
123C22×Q8C4⋊C412yes—
124C22×Q8C4⋊C412yes—
125C22×Q8C4⋊C411yescharacteristic
126C23×C4—21no—
127C23×C4—21no—
128C23×C4C2×D411yescharacteristic
129C23×C4C2×Q811yescharacteristic
130C23×C4#4111yescharacteristic
131C2×M16—22no—
132C2×M16—41no—
133C22×C8—21no—
134C22×C8—21no—
135C22×C8—22no—
136C22×C8—41no—
137C22×C8—41no—
138C4×Q8—22no—
139C4×Q8—22no—
140C4×Q8—21no—
141C4×Q8—21no—
142C4×Q8—22no—
143C4×Q8—21no—
144C4×Q8—21no—
145C4×Q8—22no—
146C4×Q8—21no—
147C4×Q8—22no—
148C4×Q8—21no—
149C4×Q8—22no—
150C4×Q8—22no—
151C4×Q8—22no—
152C4×Q8—21no—
153C4×Q8—21no—
154C4×Q8C4212yes—
155C4×Q8C4212yes—
156C4×Q8C22⋊C412yes—
157C4×Q8C22⋊C412yes—
158C4×Q8C22⋊C412yes—
159C4×Q8C22⋊C412yes—
160C4×Q8C22⋊C412yes—
161C4×Q8C22⋊C412yes—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4C4⋊C412yes—
174C2×C4⋊C4C4⋊C412yes—
175C2×C4⋊C4C4⋊C411yescharacteristic
176C2×C4⋊C4C4⋊C411yescharacteristic
177C2×C42—22no—
178C2×C42—21no—
179C2×C42—21no—
180C2×C42—22no—
181C2×C42—21no—
182C2×C42—21no—
183C2×C42—22no—
184C2×C42—22no—
185C2×C42C22×C411yescharacteristic
186C2×C42C22×C411yescharacteristic
187C2×C42C22×C411yescharacteristic
188C2×C42C2×D411yescharacteristic
189C2×C42C2×D411yescharacteristic
190C2×C42C2×D411yescharacteristic
191C2×C42C2×D411yescharacteristic
192C2×C42C2×D411yescharacteristic
193C2×C42C2×D411yescharacteristic
194C2×C42#4111yescharacteristic
195C2×C42#4111yescharacteristic
196C2×C42#4111yescharacteristic
197C4⋊C8—28no—
198C4⋊C8—28no—
199C4⋊C8—22no—
200C4⋊C8—22no—
201C4⋊C8—22no—
202C4⋊C8—22no—
203C4⋊C8—22no—
204C4⋊C8—22no—
205C4⋊C8—22no—
206C4⋊C8—22no—
207C4⋊C8—22no—
208C4⋊C8—41no—
209C4⋊C8—41no—
210C4⋊C8—41no—
211C22⋊C8—22no—
212C22⋊C8—22no—
213C22⋊C8—21no—
214C22⋊C8—21no—
215C22⋊C8—22no—
216C22⋊C8—22no—
217C22⋊C8—22no—
218C22⋊C8—41no—
219C22⋊C8—41no—
220C22⋊C8—41no—
221C22⋊C8—41no—
222C22⋊C8—41no—
223C22⋊C8C22⋊C412yes—
224C22⋊C8C22⋊C412yes—
225#97—28no—
226#97—22no—
227#97—41no—
228#97—41no—
229#97C22⋊C414yes—
230C4×C8—28no—
231C4×C8—22no—
232C4×C8—22no—
233C4×C8—22no—
234C4×C8—22no—
235C4×C8—22no—
236C4×C8—41no—
237C4×C8—41no—
238C4×C8—41no—
239C24C22⋊Q811yescharacteristic
240C2×Q8—22no—
241C2×Q8—21no—
242C2×Q8—22no—
243C2×Q8—21no—
244C2×Q8—22no—
245C2×Q8—24no—
246C2×Q8—24no—
247C2×Q8—22no—
248C2×Q8—22no—
249C2×Q8—44no—
250C2×Q8—42no—
251C2×Q8—42no—
252C2×Q8—44no—
253C2×Q8—44no—
254C2×Q8#9512yes—
255C2×Q8#9512yes—
256C2×Q8#10814yes—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—44no—
270C22×C4—44no—
271C22×C4C2×C22⋊C411yescharacteristic
272C22×C4C2×C4⋊C411yescharacteristic
273C22×C4C2×C4⋊C411yescharacteristic
274C22×C4C2×C4⋊C411yescharacteristic
275C22×C4#11711yescharacteristic
276C22×C4C4×D411yescharacteristic
277C22×C4C4×D411yescharacteristic
278C22×C4C4×D411yescharacteristic
279C22×C4C4×D411yescharacteristic
280C22×C4#12011yescharacteristic
281C22×C4#12011yescharacteristic
282C22×C4#12111yescharacteristic
283C22×C4#12111yescharacteristic
284C22×C4C22⋊Q811yescharacteristic
285C22×C4C22⋊Q811yescharacteristic
286C22×C4C22⋊Q811yescharacteristic
287C22×C4#12311yescharacteristic
288C22×C4#12311yescharacteristic
289M16—82no—
290M16—82no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—24no—
294C2×C8—42no—
295C2×C8—42no—
296C2×C8—44no—
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—82no—
302C2×C8—82no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4#9512yes—
316C4⋊C4#9512yes—
317C42—22no—
318C42—22no—
319C42—22no—
320C42—22no—
321C42—22no—
322C42—22no—
323C42—22no—
324C42—22no—
325C42C2×C4211yescharacteristic
326C42C2×C22⋊C411yescharacteristic
327C42C2×C22⋊C411yescharacteristic
328C42C2×C22⋊C411yescharacteristic
329C42C2×C22⋊C411yescharacteristic
330C42#11711yescharacteristic
331C42C4×D411yescharacteristic
332C42C4×D411yescharacteristic
333C42C4×D411yescharacteristic
334C42C4×D411yescharacteristic
335C42#12011yescharacteristic
336C42#12011yescharacteristic
337C42#12111yescharacteristic
338C42#12111yescharacteristic
339C42#12311yescharacteristic
340C42#12311yescharacteristic
341C23—22no—
342C23—22no—
343C23—41no—
344C23#38011yescharacteristic
345C23#38511yescharacteristic
346C23#38511yescharacteristic
347Q8—24no—
348Q8—22no—
349Q8—22no—
350Q8—22no—
351Q8—44no—
352Q8—44no—
353Q8—42no—
354Q8#34114yes—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—24no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—44no—
380C2×C4—44no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—44no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4C2×#9511yescharacteristic
387C2×C4C4×C22⋊C411yescharacteristic
388C2×C4C4×C22⋊C411yescharacteristic
389C2×C4#37911yescharacteristic
390C2×C4#38011yescharacteristic
391C2×C4#38111yescharacteristic
392C2×C4#38511yescharacteristic
393C2×C4#38511yescharacteristic
394C2×C4#38611yescharacteristic
395C2×C4#38611yescharacteristic
396C2×C4#38611yescharacteristic
397C2×C4#38611yescharacteristic
398C2×C4C2×#10812yes—
399C2×C4#43012yes—
400C8—42no—
401C8—42no—
402C8—44no—
403C8—82no—
404C8—82no—
405C8—82no—
406C8—82no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—44no—
415C22C22⋊#9511yescharacteristic
416C22#181412yes—
417C22#185512yes—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—24no—
428C4—42no—
429C4—42no—
430C4—42no—
431C4C2×#34111yescharacteristic
432C4#173811yescharacteristic
433C4#185512yes—
434C4#190512yes—
435C2—22no—
436C2—22no—
437C2—41no—
438C2#1073411yescharacteristic
439C2#1077311yescharacteristic
440C2#1078611yescharacteristic
subgroupG/H
centerC2×C4#386
commutatorC42C2×C42
Frattini, cosocleC22×C42C23
socleC22C22⋊#95
prime radicalC24C22⋊Q8
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ 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×#29842
#174492
C2×#14792
#80902
#80762
#80542
#79642