Finite Group Databasebeta

← #117514

Subgroups — #117514

Order 512.

600 conjugacy classes of subgroups.

The subgroup lattice has 433 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1574C211yesmaximal, characteristic
2C2×#1544C211yesmaximal, characteristic
3C2×#1493C211yesmaximal, characteristic
4C2×#1485C211yesmaximal, characteristic
5C2×#1299C211yesmaximal, characteristic
6C2×#1278C211yesmaximal, characteristic
7#7849C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14C22×C4×C8C2211yescharacteristic
15#1574—22no—
16#1574—22no—
17C2×#335—21no—
18C2×#334—21no—
19#1544—22no—
20#1544—22no—
21C2×#332C411yescharacteristic
22C2×#332C411yescharacteristic
23C2×#332C411yescharacteristic
24C2×#332C411yescharacteristic
25#1493—22no—
26#1493—22no—
27#1485—22no—
28#1485—22no—
29C2×Q8⋊C8—21no—
30C2×Q8⋊C8—21no—
31C2×Q8⋊C8—22no—
32#1299—22no—
33#1278—22no—
34#1273—22no—
35C22×M16—21no—
36C22×M16—21no—
37C23×C8—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42#533—21no—
43#533—21no—
44#533D412yes—
45#533Q812yes—
46C2×C4⋊Q8C2×C411yescharacteristic
47C2×C4⋊Q8C2×C411yescharacteristic
48C2×#125—21no—
49C2×C22⋊Q8—21no—
50C2×C22⋊Q8—21no—
51C2×C4×Q8—21no—
52C2×C4×Q8—21no—
53C2×#117—21no—
54C22×C42C2311yescharacteristic
55#431—21no—
56#431—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#431D412yes—
66#431D412yes—
67#423—21no—
68#423—21no—
69#423—21no—
70#423D412yes—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8C2×C411yescharacteristic
74C2×C4⋊C8C2×C411yescharacteristic
75C2×C4⋊C8C2×C411yescharacteristic
76C2×C4⋊C8C2×C411yescharacteristic
77C2×C4⋊C8D411yescharacteristic
78C2×C4⋊C8D411yescharacteristic
79C2×C22⋊C8—21no—
80C2×C22⋊C8—21no—
81C2×C22⋊C8—21no—
82C4×M16—21no—
83C4×M16—21no—
84C4×M16—21no—
85C4×M16D412yes—
86C2×#97—21no—
87C2×C4×C8—21no—
88C2×C4×C8—21no—
89C2×C4×C8—21no—
90C2×C4×C8—21no—
91C2×C4×C8—21no—
92C2×C4×C8—21no—
93C2×C4×C8—21no—
94C2×C4×C8—21no—
95C2×C4×C8—21no—
96C2×C4×C8D412yes—
97#335—24no—
98#334—24no—
99#332—22no—
100#332—22no—
101#332—22no—
102#332—22no—
103Q8⋊C8—24no—
104Q8⋊C8—24no—
105Q8⋊C8—28no—
106C22×Q8—21no—
107C22×Q8—21no—
108C23×C4#4111yescharacteristic
109C23×C4#4111yescharacteristic
110C23×C4#4111yescharacteristic
111C2×M16—24no—
112C2×M16—22no—
113C2×M16—22no—
114C2×M16—42no—
115C2×M16—41no—
116C2×M16—41no—
117C2×M16—82no—
118C22×C8—22no—
119C22×C8—22no—
120C22×C8—21no—
121C22×C8—21no—
122C22×C8—22no—
123C22×C8—21no—
124C22×C8—21no—
125C22×C8—21no—
126C22×C8—21no—
127C22×C8—41no—
128C22×C8—41no—
129C22×C8—41no—
130C22×C8—41no—
131C22×C8—41no—
132C22×C8—41no—
133C4⋊Q8—21no—
134C4⋊Q8—21no—
135C4⋊Q8—21no—
136C4⋊Q8—21no—
137C4⋊Q8—21no—
138C4⋊Q8—21no—
139C4⋊Q8C4⋊C412yes—
140C4⋊Q8C4⋊C412yes—
141#125—22no—
142#125—22no—
143#125—41no—
144#125—41no—
145C22⋊Q8—22no—
146C22⋊Q8—22no—
147C22⋊Q8—22no—
148C22⋊Q8—22no—
149C22⋊Q8—41no—
150C22⋊Q8—41no—
151C22⋊Q8—41no—
152C22⋊Q8—41no—
153C4×Q8—22no—
154C4×Q8—22no—
155C4×Q8—22no—
156C4×Q8—22no—
157C4×Q8—41no—
158C4×Q8—41no—
159C4×Q8—41no—
160C4×Q8—41no—
161#117—22no—
162#117—22no—
163#117—41no—
164#117—41no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—41no—
170C2×C4⋊C4—41no—
171C2×C22⋊C4—41no—
172C2×C42—41no—
173C2×C42C22×C411yescharacteristic
174C2×C42C2×D411yescharacteristic
175C2×C42C2×D411yescharacteristic
176C2×C42C2×D411yescharacteristic
177C2×C42C2×D411yescharacteristic
178C2×C42C2×D411yescharacteristic
179C2×C42C2×D411yescharacteristic
180C2×C42C2×D411yescharacteristic
181C2×C42C2×Q811yescharacteristic
182C2×C42#4111yescharacteristic
183C2×C42#4111yescharacteristic
184C2×C42#4111yescharacteristic
185C4⋊C8—21no—
186C4⋊C8—21no—
187C4⋊C8—21no—
188C4⋊C8—21no—
189C4⋊C8—21no—
190C4⋊C8—21no—
191C4⋊C8—22no—
192C4⋊C8—21no—
193C4⋊C8—21no—
194C4⋊C8—21no—
195C4⋊C8—22no—
196C4⋊C8—21no—
197C4⋊C8—41no—
198C4⋊C8—41no—
199C4⋊C8C22⋊C412yes—
200C4⋊C8C22⋊C412yes—
201C22⋊C8—22no—
202C22⋊C8—22no—
203C22⋊C8—41no—
204C22⋊C8—41no—
205C22⋊C8—41no—
206C22⋊C8—41no—
207#97—22no—
208#97—41no—
209C4×C8—22no—
210C4×C8—22no—
211C4×C8—22no—
212C4×C8—22no—
213C4×C8—22no—
214C4×C8—41no—
215C4×C8—41no—
216C4×C8—41no—
217C4×C8—41no—
218C4×C8—41no—
219C4×C8—41no—
220C4×C8—41no—
221C24#12611yescharacteristic
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8—42no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—42no—
230C2×Q8—41no—
231C2×Q8—41no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4#11711yescharacteristic
243C22×C4C4×D411yescharacteristic
244C22×C4C4×D411yescharacteristic
245C22×C4#12111yescharacteristic
246C22×C4#12111yescharacteristic
247C22×C4#12111yescharacteristic
248C22×C4#12111yescharacteristic
249C22×C4#12111yescharacteristic
250C22×C4C22⋊Q811yescharacteristic
251C22×C4C22⋊Q811yescharacteristic
252C22×C4C22⋊Q811yescharacteristic
253C22×C4#12311yescharacteristic
254C22×C4#12311yescharacteristic
255C22×C4#12311yescharacteristic
256C22×C4#12311yescharacteristic
257C22×C4#12411yescharacteristic
258C22×C4#12411yescharacteristic
259C22×C4#12611yescharacteristic
260M16—24no—
261M16—44no—
262M16—42no—
263M16—82no—
264M16—82no—
265C2×C8—24no—
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—44no—
274C2×C8—42no—
275C2×C8—42no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—42no—
285C2×C8—42no—
286C2×C8—42no—
287C2×C8—42no—
288C2×C8—42no—
289C2×C8—82no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—42no—
299C4⋊C4—42no—
300C4⋊C4—42no—
301C4⋊C4—42no—
302C22⋊C4—42no—
303C22⋊C4—42no—
304C42—42no—
305C42—42no—
306C42C2×C22⋊C411yescharacteristic
307C42C2×C4⋊C411yescharacteristic
308C42C4×D411yescharacteristic
309C42C4×D411yescharacteristic
310C42#12011yescharacteristic
311C42#12011yescharacteristic
312C42#12011yescharacteristic
313C42#12111yescharacteristic
314C42#12111yescharacteristic
315C42#12111yescharacteristic
316C42C22⋊Q811yescharacteristic
317C42C22⋊Q811yescharacteristic
318C42C22⋊Q811yescharacteristic
319C42#12311yescharacteristic
320C42#12411yescharacteristic
321C42#12711yescharacteristic
322C23—22no—
323C23—22no—
324C23—21no—
325C23—21no—
326C23#38811yescharacteristic
327C23#39611yescharacteristic
328C23#39711yescharacteristic
329Q8—42no—
330Q8—42no—
331Q8—44no—
332Q8—81no—
333Q8—81no—
334Q8—81no—
335Q8—81no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—22no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—22no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—82no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4#38011yescharacteristic
366C2×C4#38511yescharacteristic
367C2×C4#38511yescharacteristic
368C2×C4#38611yescharacteristic
369C2×C4#38811yescharacteristic
370C2×C4#39011yescharacteristic
371C2×C4#39211yescharacteristic
372C2×C4#39311yescharacteristic
373C2×C4#39411yescharacteristic
374C2×C4#39411yescharacteristic
375C2×C4#39611yescharacteristic
376C2×C4#39911yescharacteristic
377C2×C4#44311yescharacteristic
378C2×C4#44311yescharacteristic
379C2×C4#44312yes—
380C2×C4#44411yescharacteristic
381C2×C4#44411yescharacteristic
382C2×C4#44412yes—
383C2×C4#47112yes—
384C2×C4#47312yes—
385C8—44no—
386C8—44no—
387C8—42no—
388C8—42no—
389C8—81no—
390C8—81no—
391C8—81no—
392C8—82no—
393C8—81no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—42no—
401C22—42no—
402C22#143911yescharacteristic
403C22#192912yes—
404C22#193012yes—
405C22#193711yescharacteristic
406C22#193811yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—82no—
414C4—82no—
415C4#186611yescharacteristic
416C4#186611yescharacteristic
417C4#186612yes—
418C4#187611yescharacteristic
419C4#187611yescharacteristic
420C4#197411yescharacteristic
421C4#197511yescharacteristic
422C4#201911yescharacteristic
423C4#202011yescharacteristic
424C4#206412yes—
425C2—41no—
426C2—41no—
427C2#958512yes—
428C2#958712yes—
429C2#1106811yescharacteristic
430C2#1112511yescharacteristic
431C2#1114511yescharacteristic
subgroupG/H
centerC22×C4#121
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC23#388
prime radicalC24#126
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×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×#15742
C2×#15442
C2×#14932
C2×#14852
C2×#12992
C2×#12782
#78492