Finite Group Databasebeta

← #117349

Subgroups — #117349

Order 512.

608 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1574C211yesmaximal, characteristic
2C2×#1549C211yesmaximal, characteristic
3C2×#1548C211yesmaximal, characteristic
4C2×#1546C211yesmaximal, characteristic
5C2×#1309C211yesmaximal, characteristic
6#7880C211yesmaximal, characteristic
7#7880C211yesmaximal, characteristic
8C22×C4⋊Q8C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×#423C2211yescharacteristic
14C2×#423C2211yescharacteristic
15#1574—22no—
16#1574—22no—
17C2×#335—21no—
18C2×#334—21no—
19#1549—22no—
20#1549—22no—
21#1548—22no—
22#1548—22no—
23#1546—22no—
24#1546C414yes—
25C2×#333—21no—
26C2×#333—21no—
27C2×#332—21no—
28C2×#332—21no—
29C2×#332—22no—
30#1309—22no—
31#1277—22no—
32#1277—21no—
33#1277—21no—
34C23×Q8—21no—
35C22×M16—21no—
36C22×M16—21no—
37C22×M16—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⋊Q8C2×C412yes—
48C2×C4⋊Q8D412yes—
49C2×C4⋊Q8Q812yes—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C42C2311yescharacteristic
53#431—21no—
54#431—21no—
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#431C2×C412yes—
64#431D412yes—
65#423—21no—
66#423—21no—
67#423—21no—
68#423—21no—
69#423—21no—
70#423—21no—
71#423—21no—
72#423—21no—
73#423—21no—
74#423C2×C412yes—
75#423D412yes—
76#423D412yes—
77C2×C4⋊C8—21no—
78C2×C4⋊C8—21no—
79C2×C4⋊C8—21no—
80C2×C4⋊C8—21no—
81C2×C4⋊C8—21no—
82C2×C4⋊C8—21no—
83C2×C4⋊C8D412yes—
84C2×C4⋊C8D411yescharacteristic
85C2×C4⋊C8D411yescharacteristic
86C2×C4⋊C8D411yescharacteristic
87C2×C4⋊C8D411yescharacteristic
88C2×C22⋊C8—21no—
89C2×C22⋊C8—21no—
90C2×C22⋊C8—21no—
91C2×C4×C8—21no—
92C2×C4×C8—21no—
93C2×C4×C8—21no—
94#335—24no—
95#334—24no—
96#333—24no—
97#333—24no—
98#332—28no—
99#332—24no—
100#332—24no—
101C22×Q8—22no—
102C22×Q8—22no—
103C22×Q8—22no—
104C22×Q8—41no—
105C22×Q8—41no—
106C22×Q8—41no—
107C22×Q8—82no—
108C22×Q8—82no—
109C23×C4—41no—
110C23×C4#4111yescharacteristic
111C23×C4#4111yescharacteristic
112C23×C4#4111yescharacteristic
113C2×M16—22no—
114C2×M16—22no—
115C2×M16—22no—
116C2×M16—41no—
117C2×M16—41no—
118C2×M16—41no—
119C2×M16—82no—
120C2×M16—81no—
121C2×M16—81no—
122C2×M16—82no—
123C22×C8—21no—
124C22×C8—21no—
125C22×C8—21no—
126C22×C8—21no—
127C22×C8—22no—
128C22×C8—41no—
129C22×C8—41no—
130C22×C8—41no—
131C4⋊Q8—22no—
132C4⋊Q8—22no—
133C4⋊Q8—22no—
134C4⋊Q8—22no—
135C4⋊Q8—22no—
136C4⋊Q8—22no—
137C4⋊Q8—22no—
138C4⋊Q8—22no—
139C4⋊Q8—22no—
140C4⋊Q8—41no—
141C4⋊Q8—41no—
142C4⋊Q8—41no—
143C4⋊Q8—41no—
144C4⋊Q8—41no—
145C4⋊Q8—41no—
146C4⋊Q8C4⋊C414yes—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C42C22×C411yescharacteristic
160C2×C42C2×D411yescharacteristic
161C2×C42C2×D411yescharacteristic
162C2×C42C2×D411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×D411yescharacteristic
165C2×C42C2×D411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42C2×Q811yescharacteristic
168C2×C42#4111yescharacteristic
169C2×C42#4111yescharacteristic
170C2×C42#4111yescharacteristic
171C4⋊C8—22no—
172C4⋊C8—22no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—21no—
177C4⋊C8—21no—
178C4⋊C8—21no—
179C4⋊C8—22no—
180C4⋊C8—21no—
181C4⋊C8—21no—
182C4⋊C8—21no—
183C4⋊C8—22no—
184C4⋊C8—22no—
185C4⋊C8—41no—
186C4⋊C8—41no—
187C4⋊C8—41no—
188C4⋊C8—41no—
189C4⋊C8—41no—
190C4⋊C8—41no—
191C4⋊C8C22⋊C412yes—
192C4⋊C8C22⋊C412yes—
193C22⋊C8—22no—
194C22⋊C8—22no—
195C22⋊C8—41no—
196C22⋊C8—41no—
197C22⋊C8—41no—
198C22⋊C8—41no—
199C4×C8—22no—
200C4×C8—22no—
201C4×C8—41no—
202C4×C8—41no—
203C4×C8—41no—
204C4×C8—41no—
205C24#12611yescharacteristic
206C2×Q8—24no—
207C2×Q8—42no—
208C2×Q8—42no—
209C2×Q8—42no—
210C2×Q8—84no—
211C2×Q8—82no—
212C2×Q8—82no—
213C2×Q8—84no—
214C2×Q8—82no—
215C2×Q8—82no—
216C2×Q8—84no—
217C2×Q8—82no—
218C2×Q8—82no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—84no—
231C22×C4#11711yescharacteristic
232C22×C4C4×D411yescharacteristic
233C22×C4C4×D411yescharacteristic
234C22×C4#12111yescharacteristic
235C22×C4#12111yescharacteristic
236C22×C4#12111yescharacteristic
237C22×C4#12111yescharacteristic
238C22×C4#12111yescharacteristic
239C22×C4C22⋊Q811yescharacteristic
240C22×C4C22⋊Q811yescharacteristic
241C22×C4C22⋊Q811yescharacteristic
242C22×C4#12311yescharacteristic
243C22×C4#12311yescharacteristic
244C22×C4#12311yescharacteristic
245C22×C4#12311yescharacteristic
246C22×C4#12411yescharacteristic
247C22×C4#12411yescharacteristic
248C22×C4#12611yescharacteristic
249M16—82no—
250M16—82no—
251M16—82no—
252M16—82no—
253M16—82no—
254M16—82no—
255C2×C8—22no—
256C2×C8—22no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—42no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—42no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—82no—
272C2×C8—81no—
273C2×C8—81no—
274C2×C8—82no—
275C4⋊C4—24no—
276C4⋊C4—24no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C42C2×C22⋊C411yescharacteristic
284C42C2×C4⋊C411yescharacteristic
285C42C4×D411yescharacteristic
286C42C4×D411yescharacteristic
287C42#12011yescharacteristic
288C42#12011yescharacteristic
289C42#12011yescharacteristic
290C42#12111yescharacteristic
291C42#12111yescharacteristic
292C42#12111yescharacteristic
293C42C22⋊Q811yescharacteristic
294C42C22⋊Q811yescharacteristic
295C42C22⋊Q811yescharacteristic
296C42#12311yescharacteristic
297C42#12411yescharacteristic
298C42#12711yescharacteristic
299C23—22no—
300C23—21no—
301C23—21no—
302C23—22no—
303C23#38811yescharacteristic
304C23#39611yescharacteristic
305C23#39711yescharacteristic
306Q8—84no—
307Q8—84no—
308Q8—84no—
309Q8—82no—
310Q8—82no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—44no—
336C2×C4—84no—
337C2×C4—84no—
338C2×C4—84no—
339C2×C4#38011yescharacteristic
340C2×C4#38511yescharacteristic
341C2×C4#38511yescharacteristic
342C2×C4#38611yescharacteristic
343C2×C4#38811yescharacteristic
344C2×C4#39011yescharacteristic
345C2×C4#39211yescharacteristic
346C2×C4#39311yescharacteristic
347C2×C4#39411yescharacteristic
348C2×C4#39411yescharacteristic
349C2×C4#39611yescharacteristic
350C2×C4#39911yescharacteristic
351C2×C4#47112yes—
352C2×C4#47111yescharacteristic
353C2×C4#47111yescharacteristic
354C2×C4#47112yes—
355C2×C4#47212yes—
356C2×C4#47311yescharacteristic
357C2×C4#47311yescharacteristic
358C2×C4#47312yes—
359C8—42no—
360C8—42no—
361C8—82no—
362C8—82no—
363C8—81no—
364C8—82no—
365C8—81no—
366C8—82no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—42no—
374C22—42no—
375C22#143911yescharacteristic
376C22#206312yes—
377C22#206411yescharacteristic
378C22#206411yescharacteristic
379C22#206412yes—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—84no—
387C4#190811yescharacteristic
388C4#190811yescharacteristic
389C4#193012yes—
390C4#197711yescharacteristic
391C4#197811yescharacteristic
392C4#201911yescharacteristic
393C4#202011yescharacteristic
394C4#204611yescharacteristic
395C4#204711yescharacteristic
396C4#205112yes—
397C2—41no—
398C2—41no—
399C2#1061312yes—
400C2#1061412yes—
401C2#1106211yescharacteristic
402C2#1112711yescharacteristic
403C2#1114511yescharacteristic
subgroupG/H
center, socleC23#396
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#126
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ 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×#15492
C2×#15482
C2×#15462
C2×#13092
#78802