Finite Group Databasebeta

← #99901

Subgroups — #99901

Order 512.

501 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
1#22629C211yesmaximal, characteristic
2C2×#1928C211yesmaximal, characteristic
3#9878C211yesmaximal, characteristic
4#8707C211yesmaximal, characteristic
5#7575C211yesmaximal, characteristic
6#7020C211yesmaximal, characteristic
7#7016C211yesmaximal, characteristic
8C22×#107C411yescharacteristic
9C22×#103C411yescharacteristic
10C22×#103C411yescharacteristic
11C2×#391C2211yescharacteristic
12C2×C4×C4⋊C4C2211yescharacteristic
13#1939—21no—
14#1928—21no—
15#1928—21no—
16#1928—21no—
17#1928—21no—
18#1917—22no—
19#1797—21no—
20#1797C2211yescharacteristic
21#1797C2211yescharacteristic
22#1770—21no—
23#1749—21no—
24C4×C22⋊C8C2211yescharacteristic
25C4×C22⋊C8C2211yescharacteristic
26C2×#340C411yescharacteristic
27C2×#336C2211yescharacteristic
28#1280—21no—
29#1280—21no—
30#1279—21no—
31#1279—21no—
32#1272—22no—
33C23×Q8C2×C411yescharacteristic
34C23×C8C2×C411yescharacteristic
35C23×C8C2×C411yescharacteristic
36C22×C4⋊C4C2×C411yescharacteristic
37C22×C4⋊C4C2×C411yescharacteristic
38C22×C4⋊C4C2×C411yescharacteristic
39C22×C42—21no—
40C22×C42C2311yescharacteristic
41C2×#107—21no—
42C2×#107—21no—
43C2×#107—42no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—22no—
47C2×#103—22no—
48C2×#103—22no—
49C2×#103—21no—
50C2×#103—21no—
51C2×#103—21no—
52C2×#103—21no—
53C2×#103—42no—
54C2×C22⋊C8—21no—
55C2×C22⋊C8—21no—
56C2×C22⋊C8—21no—
57C2×C22⋊C8D411yescharacteristic
58C2×C22⋊C8D411yescharacteristic
59C2×#97—22no—
60C2×C4×C8—21no—
61C2×C4×C8—21no—
62#391—21no—
63#391—21no—
64#391—21no—
65#391—21no—
66C4×C4⋊C4—21no—
67C4×C4⋊C4—21no—
68C4×C4⋊C4D411yescharacteristic
69C4×C4⋊C4D411yescharacteristic
70C4×C4⋊C4D411yescharacteristic
71C4×C4⋊C4D411yescharacteristic
72C2×#95—21no—
73C2×#95—21no—
74C2×#95—21no—
75#340—21no—
76#340—21no—
77#336—22no—
78#336—22no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336—21no—
84#336D412yes—
85C22×Q8—21no—
86C22×Q8—21no—
87C22×Q8—21no—
88C22×Q8—21no—
89C22×Q8—21no—
90C22×Q8—41no—
91C22×Q8—41no—
92C22×Q8—41no—
93C22×Q8—41no—
94C22×Q8M1612yes—
95C23×C4—21no—
96C23×C4—21no—
97C23×C4—21no—
98C23×C4—21no—
99C23×C4C22×C411yescharacteristic
100C23×C4C2×D411yescharacteristic
101C23×C4#4111yescharacteristic
102C22×C8—21no—
103C22×C8—21no—
104C22×C8—21no—
105C22×C8—21no—
106C22×C8—21no—
107C22×C8—22no—
108C22×C8—21no—
109C22×C8—21no—
110C22×C8—41no—
111C22×C8—41no—
112C22×C8—41no—
113C22×C8—41no—
114C22×C8—41no—
115C22×C8—41no—
116C22×C8M1612yes—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4—41no—
128C2×C4⋊C4—41no—
129C2×C4⋊C4C22⋊C411yescharacteristic
130C2×C4⋊C4C22⋊C411yescharacteristic
131C2×C4⋊C4C22⋊C411yescharacteristic
132C2×C4⋊C4C22⋊C411yescharacteristic
133C2×C42—21no—
134C2×C42—21no—
135C2×C42—21no—
136C2×C42—21no—
137C2×C42—41no—
138C2×C42—41no—
139C2×C42—82no—
140C2×C42C2×D411yescharacteristic
141C2×C42C2×D411yescharacteristic
142C2×C42C2×D411yescharacteristic
143C2×C42#4111yescharacteristic
144#107—42no—
145#107—42no—
146C4⋊C8—41no—
147C4⋊C8—41no—
148C4⋊C8—41no—
149C4⋊C8—41no—
150C4⋊C8—82no—
151#103—24no—
152#103—24no—
153#103—42no—
154#103—42no—
155C22⋊C8—21no—
156C22⋊C8—22no—
157C22⋊C8—21no—
158C22⋊C8—21no—
159C22⋊C8—41no—
160C22⋊C8—41no—
161C22⋊C8—41no—
162C22⋊C8—41no—
163C22⋊C8—41no—
164C22⋊C8Q1612yes—
165#97—82no—
166C4×C8—41no—
167C4×C8—41no—
168C4×C8—41no—
169C4×C8—41no—
170#95—21no—
171#95—21no—
172#95—21no—
173#95—21no—
174#95—41no—
175#95—41no—
176#95—41no—
177#95—41no—
178C24C4×D411yescharacteristic
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—42no—
182C2×Q8—42no—
183C2×Q8—42no—
184C2×Q8—42no—
185C2×Q8—41no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8—81no—
192C2×Q8—81no—
193C2×Q8—81no—
194C2×Q8—81no—
195C2×Q8—81no—
196C2×Q8—81no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—42no—
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—81no—
223C22×C4—81no—
224C22×C4—81no—
225C22×C4—81no—
226C22×C4—81no—
227C22×C4—81no—
228C22×C4—81no—
229C22×C4C2×C22⋊C411yescharacteristic
230C22×C4C4×D411yescharacteristic
231C22×C4#12011yescharacteristic
232C22×C4#12111yescharacteristic
233C22×C4#12111yescharacteristic
234C22×C4#12311yescharacteristic
235C22×C4C2×M1611yescharacteristic
236C22×C4C2×M1611yescharacteristic
237C22×C4#13111yescharacteristic
238C22×C4#13111yescharacteristic
239C22×C4C2×Q1611yescharacteristic
240C22×C4#13511yescharacteristic
241C22×C4#13711yescharacteristic
242C22×C4#13711yescharacteristic
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—42no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—42no—
251C2×C8—41no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—42no—
261C2×C8—81no—
262C2×C8—81no—
263C2×C8—81no—
264C2×C8—81no—
265C2×C8—81no—
266C2×C8—81no—
267C2×C8—81no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—81no—
281C4⋊C4#10012yes—
282C42—21no—
283C42—21no—
284C42—21no—
285C42—21no—
286C42—41no—
287C42—41no—
288C42—42no—
289C42—42no—
290C42—81no—
291C42—81no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23#38611yescharacteristic
297C23#43511yescharacteristic
298C23#43611yescharacteristic
299C23C4×Q1611yescharacteristic
300C23#44111yescharacteristic
301C23#44311yescharacteristic
302C23#44411yescharacteristic
303Q8—42no—
304Q8—42no—
305Q8—82no—
306Q8—82no—
307Q8—81no—
308Q8—81no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—82no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—82no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—161no—
360C2×C4—161no—
361C2×C4#40711yescharacteristic
362C2×C4#40811yescharacteristic
363C2×C4#41011yescharacteristic
364C2×C4#41011yescharacteristic
365C2×C4C2×#10011yescharacteristic
366C2×C4#41311yescharacteristic
367C2×C4#43511yescharacteristic
368C2×C4#43611yescharacteristic
369C2×C4#45111yescharacteristic
370C2×C4#45211yescharacteristic
371C2×C4#46211yescharacteristic
372C2×C4#46411yescharacteristic
373C8—42no—
374C8—42no—
375C8—81no—
376C8—82no—
377C8—82no—
378C8—81no—
379C8—161no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22#158411yescharacteristic
393C22#158711yescharacteristic
394C22#159111yescharacteristic
395C22#159311yescharacteristic
396C22#187011yescharacteristic
397C22#187611yescharacteristic
398C22#187811yescharacteristic
399C22#189911yescharacteristic
400C22#190011yescharacteristic
401C22#190211yescharacteristic
402C22#190411yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—41no—
410C4—41no—
411C4—42no—
412C4—81no—
413C4—82no—
414C4—81no—
415C4—81no—
416C4—161no—
417C4#146411yescharacteristic
418C4#146611yescharacteristic
419C4#146911yescharacteristic
420C4#147311yescharacteristic
421C2—21no—
422C2—21no—
423C2—21no—
424C2—21no—
425C2#895011yescharacteristic
426C2#908411yescharacteristic
427C2#909111yescharacteristic
428C2#924011yescharacteristic
429C2#924311yescharacteristic
430C2#924811yescharacteristic
431C2#925711yescharacteristic
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 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#226292
C2×#19282
#98782
#87072
#75752
#70202
#70162