Finite Group Databasebeta

← #110785

Subgroups — #110785

Order 512.

844 conjugacy classes of subgroups.

The subgroup lattice has 487 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20700C211yesmaximal, characteristic
2C2×#1824C211yesmaximal, characteristic
3C2×#1821C211yesmaximal, characteristic
4#20527C211yesmaximal, characteristic
5C2×#1305C211yesmaximal, characteristic
6#8016C211yesmaximal, characteristic
7C2×#1293C211yesmaximal, characteristic
8C23×C4⋊C4C2211yescharacteristic
9C2×#407C2211yescharacteristic
10C2×#407C2211yescharacteristic
11C2×#407C2211yescharacteristic
12C22×C22⋊C8C2211yescharacteristic
13#2280C2211yescharacteristic
14C2×#380C2211yescharacteristic
15#1824—22no—
16#1824—22no—
17#1824C414yescomplemented
18#1823C414yescomplemented
19#1821—22no—
20#1821C414yescomplemented
21#1753—22no—
22#1752—21no—
23C8×C22⋊C4—21no—
24#1750—22no—
25C2×#343—22no—
26#1736—22no—
27C2×#340—21no—
28C2×#340—21no—
29#1305—22no—
30#1294—22no—
31#1293—22no—
32C24×C4—21no—
33C24×C4C2311yescharacteristic
34C22×M16—21no—
35C22×M16—21no—
36C22×M16D412yes—
37C23×C8D411yescharacteristic
38C23×C8D411yescharacteristic
39C2×#117D412yes—
40C22×C4⋊C4—21no—
41C22×C4⋊C4—21no—
42C22×C4⋊C4—21no—
43C22×C4⋊C4—21no—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4C2×C412yes—
53C22×C4⋊C4C2×C412yes—
54C22×C4⋊C4C2×C412yes—
55C22×C22⋊C4—21no—
56#407—21no—
57#407—21no—
58#407—21no—
59#407—21no—
60#407—21no—
61#407—21no—
62#407—21no—
63#407—21no—
64#407—21no—
65#407C2×C412yes—
66#407C2×C412yes—
67#407D412yes—
68C2×C22⋊C8—21no—
69C2×C22⋊C8—21no—
70C2×C22⋊C8—21no—
71C2×C22⋊C8—21no—
72C2×C22⋊C8—21no—
73C2×C22⋊C8—21no—
74C2×C22⋊C8—21no—
75C2×C22⋊C8—21no—
76C2×C22⋊C8—21no—
77C2×C22⋊C8C2×C412yes—
78C2×C22⋊C8C2×C412yes—
79C2×C22⋊C8D412yes—
80C2×#97—22no—
81C2×C4×C8—22no—
82#381—21no—
83#380—21no—
84#380—21no—
85#380—21no—
86#380C2×C412yes—
87#380C2×C412yes—
88#380D412yes—
89#379—21no—
90C4×C22⋊C4—21no—
91C4×C22⋊C4—21no—
92C2×#95—21no—
93#343—28no—
94#340—24no—
95#340—24no—
96#340—28no—
97#336—22no—
98#336—22no—
99C25#4111yescharacteristic
100C23×C4—22no—
101C23×C4—22no—
102C23×C4—22no—
103C23×C4—42no—
104C23×C4—42no—
105C23×C4—41no—
106C23×C4—41no—
107C23×C4—41no—
108C23×C4—41no—
109C23×C4—41no—
110C23×C4—84no—
111C23×C4C22×C411yescharacteristic
112C23×C4C22×C411yescharacteristic
113C23×C4C22×C411yescharacteristic
114C23×C4C2×D411yescharacteristic
115C23×C4C2×D411yescharacteristic
116C23×C4C2×D411yescharacteristic
117C23×C4C2×D411yescharacteristic
118C23×C4C2×D411yescharacteristic
119C23×C4C2×D411yescharacteristic
120C23×C4#4111yescharacteristic
121C23×C4#4111yescharacteristic
122C23×C4#4111yescharacteristic
123C23×C4#4111yescharacteristic
124C23×C4#4111yescharacteristic
125C2×M16—22no—
126C2×M16—22no—
127C2×M16—42no—
128C2×M16—42no—
129C2×M16—41no—
130C2×M16—41no—
131C2×M16—41no—
132C2×M16—42no—
133C2×M16—42no—
134C2×M16—42no—
135C2×M16—42no—
136C2×M16C22⋊C414yes—
137C22×C8—21no—
138C22×C8—21no—
139C22×C8—22no—
140C22×C8—21no—
141C22×C8—21no—
142C22×C8—22no—
143C22×C8—42no—
144C22×C8—42no—
145C22×C8—41no—
146C22×C8C22⋊C412yes—
147C22×C8C22⋊C412yes—
148#117—42no—
149#117—42no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4—41no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—41no—
176C2×C4⋊C4—41no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—42no—
179C2×C4⋊C4—42no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4C4214yes—
182C2×C4⋊C4C22⋊C414yes—
183C2×C22⋊C4—22no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—41no—
188C2×C22⋊C4—82no—
189C2×C42—22no—
190C22⋊C8—22no—
191C22⋊C8—22no—
192C22⋊C8—22no—
193C22⋊C8—22no—
194C22⋊C8—22no—
195C22⋊C8—22no—
196C22⋊C8—22no—
197C22⋊C8—22no—
198C22⋊C8—22no—
199C22⋊C8—22no—
200C22⋊C8—22no—
201C22⋊C8—22no—
202C22⋊C8—41no—
203C22⋊C8—41no—
204C22⋊C8—41no—
205C22⋊C8—41no—
206#97—82no—
207C4×C8—82no—
208#95—22no—
209#95—22no—
210#95—22no—
211#95—41no—
212C24—22no—
213C24—22no—
214C24—42no—
215C24—42no—
216C24#11711yescharacteristic
217C24C4×D411yescharacteristic
218C24C4×D411yescharacteristic
219C24#12111yescharacteristic
220C24#12311yescharacteristic
221C24#12411yescharacteristic
222C24#12611yescharacteristic
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—24no—
230C22×C4—24no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—42no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—84no—
254C22×C4—84no—
255C22×C4—84no—
256C22×C4—84no—
257C22×C4—84no—
258C22×C4—84no—
259C22×C4—84no—
260C22×C4—82no—
261C22×C4—82no—
262C22×C4—82no—
263C22×C4C2×C4211yescharacteristic
264C22×C4C2×C22⋊C411yescharacteristic
265C22×C4C2×C22⋊C411yescharacteristic
266C22×C4C2×C22⋊C411yescharacteristic
267C22×C4#11711yescharacteristic
268C22×C4#11711yescharacteristic
269C22×C4C4×D411yescharacteristic
270C22×C4C4×D411yescharacteristic
271C22×C4C4×D411yescharacteristic
272C22×C4C4×D411yescharacteristic
273C22×C4C4×D411yescharacteristic
274C22×C4C4×D411yescharacteristic
275C22×C4C4×D411yescharacteristic
276C22×C4C4×D411yescharacteristic
277C22×C4C4×D411yescharacteristic
278C22×C4C4×D411yescharacteristic
279C22×C4#12011yescharacteristic
280C22×C4#12111yescharacteristic
281C22×C4#12111yescharacteristic
282C22×C4#12111yescharacteristic
283C22×C4#12111yescharacteristic
284C22×C4#12111yescharacteristic
285C22×C4#12311yescharacteristic
286C22×C4#12311yescharacteristic
287C22×C4#12411yescharacteristic
288C22×C4#12411yescharacteristic
289C22×C4#12611yescharacteristic
290C22×C4#12711yescharacteristic
291M16—44no—
292M16—44no—
293M16—82no—
294M16—81no—
295M16—81no—
296M16—82no—
297M16—81no—
298M16—81no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—24no—
302C2×C8—42no—
303C2×C8—42no—
304C2×C8—42no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—44no—
309C2×C8—42no—
310C2×C8—42no—
311C2×C8—81no—
312C2×C8—81no—
313C2×C8—82no—
314C4⋊C4—24no—
315C4⋊C4—24no—
316C4⋊C4—44no—
317C4⋊C4—42no—
318C4⋊C4—42no—
319C4⋊C4—42no—
320C4⋊C4—42no—
321C4⋊C4—42no—
322C4⋊C4—42no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—82no—
326C22⋊C4—42no—
327C22⋊C4—42no—
328C22⋊C4—82no—
329C22⋊C4—82no—
330C22⋊C4—82no—
331C22⋊C4—82no—
332C42—42no—
333C42—42no—
334C23—22no—
335C23—22no—
336C23—22no—
337C23—22no—
338C23—22no—
339C23—22no—
340C23—22no—
341C23—22no—
342C23—22no—
343C23—22no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—48no—
357C23—48no—
358C23C4×C22⋊C411yescharacteristic
359C23#38611yescharacteristic
360C23#38811yescharacteristic
361C23#38811yescharacteristic
362C23#38811yescharacteristic
363C23#38811yescharacteristic
364C23#39011yescharacteristic
365C23#47112yes—
366C23#47312yes—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—44no—
401C2×C4—44no—
402C2×C4—44no—
403C2×C4—44no—
404C2×C4—84no—
405C2×C4—84no—
406C2×C4—84no—
407C2×C4—84no—
408C2×C4—84no—
409C2×C4—84no—
410C2×C4—84no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—82no—
414C2×C4—164no—
415C2×C4C4×C22⋊C411yescharacteristic
416C2×C4C4×C22⋊C411yescharacteristic
417C2×C4#38611yescharacteristic
418C2×C4#38611yescharacteristic
419C2×C4#38811yescharacteristic
420C2×C4#38811yescharacteristic
421C2×C4#39011yescharacteristic
422C2×C4#39011yescharacteristic
423C2×C4#45812yes—
424C2×C4#45812yes—
425C8—42no—
426C8—42no—
427C8—44no—
428C8—82no—
429C8—82no—
430C22—24no—
431C22—24no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—42no—
449C22—42no—
450C22—44no—
451C22—44no—
452C22—42no—
453C22—42no—
454C22—44no—
455C22—44no—
456C22#143711yescharacteristic
457C22#189012yes—
458C22#190312yes—
459C22#190812yes—
460C22#193012yes—
461C22#197711yescharacteristic
462C22#197911yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—84no—
470C4—84no—
471C4—162no—
472C4#189011yescharacteristic
473C4#189011yescharacteristic
474C4#189012yes—
475C2—21no—
476C2—22no—
477C2—21no—
478C2—41no—
479C2—41no—
480C2—41no—
481C2—41no—
482C2#952114yes—
483C2#1093611yescharacteristic
484C2#1094211yescharacteristic
485C2#1095311yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
prime radicalC25#41
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
17. #1824C4semidirect
18. #1823C4semidirect
20. #1821C4semidirect

Maximal subgroups

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

subgroupindex
#207002
C2×#18242
C2×#18212
#205272
C2×#13052
#80162
C2×#12932