Finite Group Databasebeta

← #119481

Subgroups — #119481

Order 512.

617 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1801C211yesmaximal, characteristic
2#17449C211yesmaximal, characteristic
3C2×#1491C211yesmaximal, characteristic
4#8121C211yesmaximal, characteristic
5#8063C211yesmaximal, characteristic
6#7990C211yesmaximal, characteristic
7#7938C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×#423C2211yescharacteristic
14C22×#101C412yes—
15C2×C4×M16C2211yescharacteristic
16#1801—21no—
17#1801—21no—
18#1801—21no—
19#1801—21no—
20C2×#343C412yes—
21#1491—22no—
22#1491—22no—
23#1491—22no—
24#1487—22no—
25#1479—21no—
26#1479—21no—
27C2×Q8⋊C8—21no—
28C2×Q8⋊C8—21no—
29#1307—22no—
30#1299—22no—
31#1290—22no—
32#1283—22no—
33C23×Q8C2×C411yescharacteristic
34C22×M16—21no—
35C22×M16C2×C412yes—
36C22×M16C2×C412yes—
37C2×C4×Q8—21no—
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×Q8—21no—
45C2×C4×Q8—21no—
46C2×C4×Q8—21no—
47C2×C4×Q8D411yescharacteristic
48C2×C4×Q8D411yescharacteristic
49C2×C4×Q8D411yescharacteristic
50C2×C4×Q8D411yescharacteristic
51C22×C4⋊C4—21no—
52C22×C4⋊C4C2×C411yescharacteristic
53C22×C42—21no—
54C22×C42C2311yescharacteristic
55#432—21no—
56#432—21no—
57#432—21no—
58#432—21no—
59#432—21no—
60#432—21no—
61#432D412yes—
62#432D412yes—
63#431—21no—
64#431—21no—
65#431—21no—
66#431D412yes—
67#423—21no—
68#423—21no—
69#423—21no—
70#423—21no—
71#423—21no—
72#423—21no—
73#423—21no—
74#423—21no—
75#423—21no—
76#423—21no—
77C2×C4⋊C8—21no—
78C2×C4⋊C8—21no—
79C2×C4⋊C8—21no—
80C2×C4⋊C8—21no—
81C2×C4⋊C8—21no—
82C2×#101—22no—
83C2×#101—22no—
84C2×#101—44no—
85#407—21no—
86#407—21no—
87C2×C22⋊C8—21no—
88C4×M16—21no—
89C4×M16—21no—
90C4×M16—21no—
91C4×M16—21no—
92C4×M16—21no—
93C4×M16D412yes—
94C2×#97—21no—
95C2×#97—21no—
96C2×C4×C8—21no—
97#343—22no—
98#343—22no—
99Q8⋊C8—24no—
100Q8⋊C8—24no—
101Q8⋊C8—24no—
102Q8⋊C8—24no—
103C22×Q8—22no—
104C22×Q8—22no—
105C22×Q8—21no—
106C22×Q8—21no—
107C22×Q8—21no—
108C22×Q8—21no—
109C22×Q8—21no—
110C22×Q8—41no—
111C22×Q8—41no—
112C22×Q8C22⋊C411yescharacteristic
113C22×Q8C22⋊C411yescharacteristic
114C23×C4—21no—
115C23×C4—21no—
116C23×C4C22×C411yescharacteristic
117C23×C4#4111yescharacteristic
118C23×C4#4111yescharacteristic
119C2×M16—22no—
120C2×M16—22no—
121C2×M16—22no—
122C2×M16—22no—
123C2×M16—22no—
124C2×M16—44no—
125C2×M16—41no—
126C2×M16—41no—
127C2×M16—41no—
128C2×M16—42no—
129C2×M16—42no—
130C2×M16—42no—
131C2×M16—42no—
132C22×C8—22no—
133C22×C8—22no—
134C22×C8—41no—
135C22×C8—41no—
136C4×Q8—21no—
137C4×Q8—21no—
138C4×Q8—21no—
139C4×Q8—21no—
140C4×Q8—21no—
141C4×Q8—21no—
142C4×Q8—21no—
143C4×Q8—21no—
144C4×Q8—21no—
145C4×Q8—21no—
146C4×Q8—21no—
147C4×Q8—21no—
148C4×Q8—21no—
149C4×Q8—21no—
150C4×Q8—21no—
151C4×Q8—21no—
152C4×Q8—41no—
153C4×Q8—41no—
154C4×Q8—41no—
155C4×Q8—41no—
156C4×Q8—41no—
157C4×Q8—41no—
158C4×Q8—41no—
159C4×Q8—41no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
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×C4⋊C4—41no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4C22⋊C411yescharacteristic
174C2×C4⋊C4C22⋊C411yescharacteristic
175C2×C42—21no—
176C2×C42—21no—
177C2×C42—21no—
178C2×C42—21no—
179C2×C42—41no—
180C2×C42—41no—
181C2×C42—41no—
182C2×C42—41no—
183C2×C42C2×D411yescharacteristic
184C2×C42C2×D411yescharacteristic
185C2×C42C2×D411yescharacteristic
186C2×C42C2×D411yescharacteristic
187C2×C42C2×D411yescharacteristic
188C2×C42C2×D411yescharacteristic
189C2×C42#4111yescharacteristic
190C2×C42#4111yescharacteristic
191C2×C42#4111yescharacteristic
192C2×C42#4111yescharacteristic
193C2×C42#4111yescharacteristic
194C2×C42#4111yescharacteristic
195C4⋊C8—22no—
196C4⋊C8—22no—
197C4⋊C8—22no—
198C4⋊C8—41no—
199C4⋊C8—41no—
200C4⋊C8—41no—
201C4⋊C8—41no—
202C4⋊C8—41no—
203C4⋊C8—41no—
204C4⋊C8—41no—
205C4⋊C8—41no—
206C4⋊C8—41no—
207C4⋊C8—41no—
208C4⋊C8—41no—
209#101—44no—
210#101—44no—
211C22⋊C8—22no—
212C22⋊C8—22no—
213C22⋊C8—22no—
214C22⋊C8—41no—
215C22⋊C8—41no—
216C22⋊C8—41no—
217#97—22no—
218#97—22no—
219#97—22no—
220#97—41no—
221#97—41no—
222#97—41no—
223C4×C8—22no—
224C4×C8—22no—
225C4×C8—41no—
226C4×C8—41no—
227C24#11711yescharacteristic
228C2×Q8—24no—
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—21no—
234C2×Q8—21no—
235C2×Q8—21no—
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8—42no—
240C2×Q8—42no—
241C2×Q8—42no—
242C2×Q8—42no—
243C2×Q8—42no—
244C2×Q8—42no—
245C2×Q8—42no—
246C2×Q8—42no—
247C2×Q8—42no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8#10012yes—
251C2×Q8#10112yes—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—24no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—82no—
269C22×C4C2×C22⋊C411yescharacteristic
270C22×C4#11711yescharacteristic
271C22×C4C4×D411yescharacteristic
272C22×C4C4×D411yescharacteristic
273C22×C4C4×D411yescharacteristic
274C22×C4C4×D411yescharacteristic
275C22×C4#12111yescharacteristic
276C22×C4#12111yescharacteristic
277C22×C4#12311yescharacteristic
278C22×C4#12311yescharacteristic
279C22×C4#12311yescharacteristic
280C22×C4#12311yescharacteristic
281C22×C4#12311yescharacteristic
282C22×C4#12311yescharacteristic
283C22×C4#12411yescharacteristic
284C22×C4#12411yescharacteristic
285C22×C4#12611yescharacteristic
286C22×C4#12611yescharacteristic
287M16—24no—
288M16—42no—
289M16—44no—
290M16—42no—
291M16—42no—
292M16—42no—
293M16—42no—
294M16—82no—
295M16—82no—
296M16—82no—
297M16—82no—
298C2×C8—44no—
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—42no—
302C2×C8—42no—
303C2×C8—42no—
304C2×C8—42no—
305C2×C8—82no—
306C2×C8—82no—
307C2×C8—82no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C42—41no—
323C42—41no—
324C42—41no—
325C42—41no—
326C42—41no—
327C42—41no—
328C42—41no—
329C42—41no—
330C42#12011yescharacteristic
331C42#12011yescharacteristic
332C42#12111yescharacteristic
333C42#12111yescharacteristic
334C42#12111yescharacteristic
335C42#12111yescharacteristic
336C42#12111yescharacteristic
337C42#12111yescharacteristic
338C42#12311yescharacteristic
339C42#12311yescharacteristic
340C42#12311yescharacteristic
341C42#12311yescharacteristic
342C42#12411yescharacteristic
343C42#12411yescharacteristic
344C42#12611yescharacteristic
345C42#12611yescharacteristic
346C23—21no—
347C23—21no—
348C23—22no—
349C23—41no—
350C23#38111yescharacteristic
351C23#38811yescharacteristic
352C23#38811yescharacteristic
353Q8—22no—
354Q8—22no—
355Q8—22no—
356Q8—22no—
357Q8—44no—
358Q8—44no—
359Q8—41no—
360Q8—41no—
361Q8—41no—
362Q8—41no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—82no—
396C2×C4—82no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4#38611yescharacteristic
400C2×C4#38611yescharacteristic
401C2×C4#38811yescharacteristic
402C2×C4#38811yescharacteristic
403C2×C4#39411yescharacteristic
404C2×C4#39411yescharacteristic
405C2×C4#39411yescharacteristic
406C2×C4#39411yescharacteristic
407C2×C4#39711yescharacteristic
408C2×C4#39711yescharacteristic
409C2×C4#39711yescharacteristic
410C2×C4#39711yescharacteristic
411C2×C4C2×#10011yescharacteristic
412C2×C4C2×#10111yescharacteristic
413C2×C4#41311yescharacteristic
414C2×C4#41311yescharacteristic
415C8—44no—
416C8—82no—
417C8—82no—
418C8—82no—
419C8—82no—
420C8—82no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—42no—
429C22—42no—
430C22#144011yescharacteristic
431C22#182111yescharacteristic
432C22#182211yescharacteristic
433C22#193212yes—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—21no—
443C4—42no—
444C4—42no—
445C4—81no—
446C4—81no—
447C4#190011yescharacteristic
448C4#190011yescharacteristic
449C4#190111yescharacteristic
450C4#190111yescharacteristic
451C4#208212yes—
452C2—21no—
453C2—21no—
454C2—22no—
455C2—41no—
456C2#1115811yescharacteristic
457C2#1116511yescharacteristic
458C2#1119811yescharacteristic
subgroupG/H
center, socleC22#1440
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#117
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ 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×#18012
#174492
C2×#14912
#81212
#80632
#79902
#79382