Finite Group Databasebeta

← #98786

Subgroups — #98786

Order 512.

754 conjugacy classes of subgroups.

The subgroup lattice has 477 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#389C211yesmaximal, characteristic
2#10832C211yesmaximal, characteristic
3#10795C211yesmaximal, characteristic
4C2×#1271C212yesmaximal
5#7025C212yesmaximal
6C22×C4⋊C8—21no—
7C2×#389C411yescharacteristic
8C2×#389C2211yescharacteristic
9C2×C4×C4⋊C4—21no—
10C2×C4×C4⋊C4C411yescharacteristic
11C2×C4×C4⋊C4C411yescharacteristic
12C2×C43C2211yescharacteristic
13C2×#336—21no—
14C2×#336—21no—
15C2×#336—21no—
16C2×#336C2212yes—
17C2×#336C2212yes—
18#1436—21no—
19#1436—21no—
20C4⋊#95C411yescharacteristic
21C4⋊#95C2211yescharacteristic
22C4×#95—21no—
23#1271—24no—
24C23×C8—22no—
25C23×C8—22no—
26C22×C4⋊C4—21no—
27C22×C4⋊C4—21no—
28C22×C4⋊C4C2×C411yescharacteristic
29C22×C4⋊C4C2×C411yescharacteristic
30C22×C4⋊C4C2×C411yescharacteristic
31C22×C4⋊C4C2×C411yescharacteristic
32C22×C42—21no—
33C22×C42—21no—
34C22×C42C2×C411yescharacteristic
35C22×C42C2×C411yescharacteristic
36C22×C42D411yescharacteristic
37C22×C42D411yescharacteristic
38C22×C42D411yescharacteristic
39C22×C42D411yescharacteristic
40C22×C42C2311yescharacteristic
41C2×C4⋊C8—24no—
42C2×C4⋊C8—42no—
43C2×C4⋊C8—42no—
44#389—22no—
45#389—22no—
46#389—21no—
47#389—21no—
48#389D412yes—
49#389Q812yes—
50C4×C4⋊C4—22no—
51C4×C4⋊C4—44no—
52C4×C4⋊C4—42no—
53C4×C4⋊C4C814yescomplemented
54C2×#95—21no—
55C2×#95—21no—
56C2×#95—21no—
57C2×#95—21no—
58C2×#95—21no—
59C2×#95—21no—
60C2×#95—21no—
61C2×#95—21no—
62C43—42no—
63#336—24no—
64#336—22no—
65#336—22no—
66#336—22no—
67#336—22no—
68#336—42no—
69#336—42no—
70C23×C4—21no—
71C23×C4—21no—
72C23×C4—21no—
73C23×C4—21no—
74C23×C4C22⋊C411yescharacteristic
75C23×C4C22⋊C411yescharacteristic
76C23×C4C22⋊C411yescharacteristic
77C23×C4C22⋊C411yescharacteristic
78C23×C4C22×C411yescharacteristic
79C23×C4C2×D411yescharacteristic
80C23×C4C2×D411yescharacteristic
81C22×C8—24no—
82C22×C8—24no—
83C22×C8—42no—
84C22×C8—42no—
85C22×C8—42no—
86C22×C8—42no—
87C22×C8—42no—
88C22×C8—42no—
89C22×C8—42no—
90C22×C8—42no—
91C22×C8—42no—
92C22×C8—42no—
93C22×C8—42no—
94C22×C8—42no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—24no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—41no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—42no—
111C2×C4⋊C4—42no—
112C2×C4⋊C4—42no—
113C2×C4⋊C4—42no—
114C2×C4⋊C4C4⋊C412yes—
115C2×C4⋊C4C4⋊C412yes—
116C2×C4⋊C4C2×C812yes—
117C2×C4⋊C4C2×C812yes—
118C2×C4⋊C4M1612yes—
119C2×C4⋊C4M1612yes—
120C2×C42—22no—
121C2×C42—22no—
122C2×C42—22no—
123C2×C42—22no—
124C2×C42—21no—
125C2×C42—21no—
126C2×C42—24no—
127C2×C42—22no—
128C2×C42—22no—
129C2×C42—21no—
130C2×C42—21no—
131C2×C42—22no—
132C2×C42—22no—
133C2×C42—41no—
134C2×C42—41no—
135C2×C42—41no—
136C2×C42—41no—
137C2×C42—41no—
138C2×C42—41no—
139C2×C42—41no—
140C2×C42—41no—
141C2×C42—42no—
142C2×C42—42no—
143C2×C42—42no—
144C2×C42—42no—
145C2×C42—42no—
146C2×C42C2×C812yes—
147C2×C42M1612yes—
148C2×C42SD1612yes—
149C2×C42Q1612yes—
150C2×C42C2×D411yescharacteristic
151C2×C42C2×Q811yescharacteristic
152C2×C42#4111yescharacteristic
153C2×C42#4111yescharacteristic
154C4⋊C8—48no—
155#95—24no—
156#95—24no—
157#95—22no—
158#95—22no—
159#95—42no—
160#95—42no—
161#95—42no—
162#95—41no—
163#95—42no—
164#95—41no—
165C24C2×C22⋊C411yescharacteristic
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—21no—
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
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×C4C22⋊C812yes—
227C22×C4C22⋊C812yes—
228C22×C4#9912yes—
229C22×C4#10112yes—
230C22×C4#10312yes—
231C22×C4#10312yes—
232C22×C4#10412yes—
233C22×C4#10412yes—
234C22×C4C2×C4⋊C411yescharacteristic
235C22×C4#11711yescharacteristic
236C22×C4#12111yescharacteristic
237C22×C4#12111yescharacteristic
238C22×C4C22⋊Q811yescharacteristic
239C22×C4C22⋊Q811yescharacteristic
240C22×C4C22×C811yescharacteristic
241C22×C4C2×M1611yescharacteristic
242C22×C4C2×M1611yescharacteristic
243C22×C4C2×M1611yescharacteristic
244C22×C4C2×SD1611yescharacteristic
245C22×C4C2×Q1611yescharacteristic
246C22×C4#13512yes—
247C22×C4AGL(1,ℤ/8)11yescharacteristic
248C22×C4AGL(1,ℤ/8)12yes—
249C22×C4#13711yescharacteristic
250C2×C8—44no—
251C2×C8—44no—
252C2×C8—44no—
253C2×C8—44no—
254C2×C8—44no—
255C2×C8—44no—
256C2×C8—82no—
257C2×C8—82no—
258C2×C8—82no—
259C2×C8—82no—
260C2×C8—82no—
261C2×C8—82no—
262C2×C8—82no—
263C2×C8—82no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—48no—
274C4⋊C4—44no—
275C4⋊C4—44no—
276C4⋊C4C4⋊C814yescomplemented
277C42—24no—
278C42—24no—
279C42—24no—
280C42—24no—
281C42—42no—
282C42—42no—
283C42—41no—
284C42—41no—
285C42—41no—
286C42—41no—
287C42—44no—
288C42—44no—
289C42—42no—
290C42—42no—
291C42—48no—
292C42—84no—
293C23#38011yescharacteristic
294C23C2×C22⋊C811yescharacteristic
295C23#40711yescharacteristic
296C23C2×#9911yescharacteristic
297C23#41011yescharacteristic
298C23C2×#10111yescharacteristic
299C23#41311yescharacteristic
300C23C2×#10311yescharacteristic
301C23#41611yescharacteristic
302C23#41711yescharacteristic
303C23#41811yescharacteristic
304C23C2×#10411yescharacteristic
305C23C2×#10411yescharacteristic
306C23#42111yescharacteristic
307C23#42111yescharacteristic
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
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—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—21no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—24no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4#32414yes—
395C2×C4Q8⋊C814yes—
396C2×C4C2×C4⋊C811yescharacteristic
397C2×C4#42311yescharacteristic
398C2×C4#43111yescharacteristic
399C2×C4#43211yescharacteristic
400C2×C4#46011yescharacteristic
401C2×C4#46211yescharacteristic
402C2×C4#46312yes—
403C2×C4#47511yescharacteristic
404C2×C4#47711yescharacteristic
405C2×C4#47812yes—
406C8—84no—
407C8—84no—
408C22C2×#32411yescharacteristic
409C22#145811yescharacteristic
410C22#146511yescharacteristic
411C22#146711yescharacteristic
412C22C2×Q8⋊C811yescharacteristic
413C22#147611yescharacteristic
414C22#147711yescharacteristic
415C22#147811yescharacteristic
416C22#148711yescharacteristic
417C22#148811yescharacteristic
418C22#148911yescharacteristic
419C22#149011yescharacteristic
420C22#150011yescharacteristic
421C22#150311yescharacteristic
422C22#150411yescharacteristic
423C22#150711yescharacteristic
424C22#151211yescharacteristic
425C22#151411yescharacteristic
426C22#151611yescharacteristic
427C22#152011yescharacteristic
428C22#152411yescharacteristic
429C22#152811yescharacteristic
430C22#153111yescharacteristic
431C22#153511yescharacteristic
432C22#154211yescharacteristic
433C22#154911yescharacteristic
434C22#155211yescharacteristic
435C22#155711yescharacteristic
436C22#179711yescharacteristic
437C22#179911yescharacteristic
438C22#180111yescharacteristic
439C22#180311yescharacteristic
440C22#180411yescharacteristic
441C22#180611yescharacteristic
442C22#180611yescharacteristic
443C4—21no—
444C4—21no—
445C4—21no—
446C4—21no—
447C4—22no—
448C4—22no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—21no—
453C4—24no—
454C4—24no—
455C4—44no—
456C4—42no—
457C4—42no—
458C4—82no—
459C4—82no—
460C4—82no—
461C2#756211yescharacteristic
462C2#757611yescharacteristic
463C2#757911yescharacteristic
464C2#759411yescharacteristic
465C2#761911yescharacteristic
466C2#762211yescharacteristic
467C2#763311yescharacteristic
468C2#764811yescharacteristic
469C2#855811yescharacteristic
470C2#856411yescharacteristic
471C2#856511yescharacteristic
472C2#857311yescharacteristic
473C2#857811yescharacteristic
474C2#858211yescharacteristic
475C2#859111yescharacteristic
subgroupG/H
center, socle, prime radicalC24C2×C22⋊C4
commutatorC22×C4C22×C8
Frattini, cosocleC22×C42C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
53. C4×C4⋊C4C8semidirect
276. C4⋊C4C4⋊C8semidirect

Maximal subgroups

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

subgroupindex
C4×#3892
#108322
#107952
C2×#12712
#70252