Finite Group Databasebeta

← #100620

Subgroups — #100620

Order 512.

529 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 529 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#29968C211yesmaximal, characteristic
2#14439C211yesmaximal, characteristic
3#9911C211yesmaximal, characteristic
4#9679C211yesmaximal, characteristic
5#7573C211yesmaximal, characteristic
6#7039C211yesmaximal, characteristic
7#7024C211yesmaximal, characteristic
8#2857C2211yescharacteristic
9C2×#389—21no—
10C2×#389C2211yescharacteristic
11C2×#387—21no—
12#2100C412yescomplemented
13#2088—22no—
14#2058C412yescomplemented
15#1853—21no—
16#1823—21no—
17#1797C2211yescharacteristic
18#1797C2211yescharacteristic
19C4×C22⋊C8C2211yescharacteristic
20C2×#328—21no—
21C2×#328—21no—
22#1442—21no—
23#1441—21no—
24#1441—21no—
25#1436—21no—
26C4⋊#95C2211yescharacteristic
27#1434C2211yescharacteristic
28#1294—21no—
29#1294—21no—
30#1271—22no—
31C2×C4⋊Q8C2×C411yescharacteristic
32C2×C22⋊Q8—21no—
33C22×C4⋊C4—21no—
34C22×C4⋊C4—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4—21no—
37C22×C4⋊C4D411yescharacteristic
38C22×C4⋊C4D411yescharacteristic
39C22×C42—21no—
40C22×C42C2311yescharacteristic
41C2×#106—22no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C22⋊C8—21no—
45C2×C22⋊C8—21no—
46C2×C22⋊C8—21no—
47C2×C4×C8—21no—
48#391—21no—
49#389—21no—
50#389—21no—
51#389—21no—
52#389—21no—
53#389—42no—
54#389—42no—
55#389C2×C412yes—
56#389D412yes—
57#387—42no—
58#387—42no—
59#384C2×C411yescharacteristic
60#380—21no—
61#380—21no—
62C2×#95—21no—
63C2×#95—21no—
64C2×#95—21no—
65C2×#95—21no—
66C2×#95—21no—
67C2×#95—21no—
68C2×#95—21no—
69C2×#95—21no—
70C2×#95—21no—
71C2×#95D411yescharacteristic
72C2×#95D411yescharacteristic
73C2×#95D411yescharacteristic
74C2×#95D411yescharacteristic
75#340—22no—
76#340—22no—
77#340—22no—
78#336—21no—
79#336—21no—
80#336C2×C412yes—
81#328—42no—
82#328—42no—
83C22×Q8—21no—
84C23×C4—21no—
85C23×C4—21no—
86C23×C4—21no—
87C23×C4—21no—
88C23×C4—21no—
89C23×C4—21no—
90C23×C4C2×D411yescharacteristic
91C23×C4C2×D411yescharacteristic
92C23×C4C2×D411yescharacteristic
93C22×C8—22no—
94C22×C8—41no—
95C22×C8—41no—
96C4⋊Q8—81no—
97C22⋊Q8—41no—
98C22⋊Q8—41no—
99C22⋊Q8—41no—
100C22⋊Q8—41no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—42no—
117C2×C4⋊C4—42no—
118C2×C4⋊C4—42no—
119C2×C4⋊C4—42no—
120C2×C4⋊C4—42no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4—81no—
125C2×C4⋊C4—81no—
126C2×C4⋊C4—81no—
127C2×C4⋊C4—81no—
128C2×C4⋊C4C22⋊C412yes—
129C2×C4⋊C4C22⋊C412yes—
130C2×C4⋊C4SD1612yes—
131C2×C4⋊C4Q1612yes—
132C2×C22⋊C4—41no—
133C2×C42—42no—
134C2×C42—42no—
135C2×C42—81no—
136C2×C42—81no—
137C2×C42C22×C411yescharacteristic
138C2×C42C2×D411yescharacteristic
139C2×C42#4111yescharacteristic
140C2×C42#4111yescharacteristic
141#106—82no—
142C4⋊C8—81no—
143C4⋊C8—81no—
144C22⋊C8—22no—
145C22⋊C8—41no—
146C22⋊C8—41no—
147C22⋊C8—41no—
148C22⋊C8—41no—
149C22⋊C8—41no—
150C4×C8—81no—
151#95—22no—
152#95—22no—
153#95—21no—
154#95—21no—
155#95—21no—
156#95—41no—
157#95—41no—
158#95—42no—
159#95—42no—
160#95—42no—
161#95—42no—
162#95—41no—
163#95—41no—
164#95—41no—
165#95—41no—
166#95—41no—
167#95—41no—
168#95—81no—
169#95—81no—
170#95SD1612yes—
171C24#12011yescharacteristic
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—81no—
175C2×Q8—81no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4C2×C22⋊C411yescharacteristic
229C22×C4C4×D411yescharacteristic
230C22×C4C4×D411yescharacteristic
231C22×C4#12111yescharacteristic
232C22×C4#12111yescharacteristic
233C22×C4#12311yescharacteristic
234C22×C4C2×SD1611yescharacteristic
235C22×C4C2×SD1611yescharacteristic
236C22×C4C2×Q1611yescharacteristic
237C22×C4#13511yescharacteristic
238C22×C4AGL(1,ℤ/8)11yescharacteristic
239C22×C4AGL(1,ℤ/8)11yescharacteristic
240C22×C4#13711yescharacteristic
241C22×C4#13711yescharacteristic
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—81no—
247C2×C8—81no—
248C2×C8—81no—
249C2×C8—81no—
250C2×C8—81no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—81no—
264C4⋊C4—81no—
265C4⋊C4—81no—
266C4⋊C4—81no—
267C4⋊C4—81no—
268C4⋊C4—82no—
269C4⋊C4—82no—
270C4⋊C4—84no—
271C4⋊C4—84no—
272C4⋊C4#10314yes—
273C22⋊C4—81no—
274C22⋊C4—81no—
275C42—41no—
276C42—41no—
277C42—41no—
278C42—41no—
279C42—84no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23#38611yescharacteristic
285C23#45011yescharacteristic
286C23#45011yescharacteristic
287C23#45111yescharacteristic
288C23#45211yescharacteristic
289C23#45311yescharacteristic
290C23#45411yescharacteristic
291Q8—161no—
292Q8—161no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—24no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4C2×#10311yescharacteristic
366C2×C4#41711yescharacteristic
367C2×C4C4×SD1611yescharacteristic
368C2×C4#44011yescharacteristic
369C2×C4#46111yescharacteristic
370C2×C4#46311yescharacteristic
371C2×C4#48311yescharacteristic
372C2×C4#48411yescharacteristic
373C8—82no—
374C8—82no—
375C8—161no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22#162911yescharacteristic
389C22#163211yescharacteristic
390C22#163511yescharacteristic
391C22#163711yescharacteristic
392C22#187211yescharacteristic
393C22#187711yescharacteristic
394C22#188311yescharacteristic
395C22#190511yescharacteristic
396C22#190611yescharacteristic
397C22#191211yescharacteristic
398C22#191311yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—44no—
408C4—41no—
409C4—41no—
410C4—82no—
411C4—82no—
412C4—82no—
413C4—161no—
414C4—161no—
415C4—161no—
416C4—161no—
417C2—21no—
418C2—21no—
419C2—21no—
420C2—21no—
421C2#897311yescharacteristic
422C2#917611yescharacteristic
423C2#920011yescharacteristic
424C2#927511yescharacteristic
425C2#929611yescharacteristic
426C2#934411yescharacteristic
427C2#938211yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#120
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
12. #2100C4semidirect
14. #2058C4semidirect

Maximal subgroups

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

subgroupindex
#299682
#144392
#99112
#96792
#75732
#70392
#70242