Finite Group Databasebeta

← #98784

Subgroups — #98784

Order 512.

754 conjugacy classes of subgroups.

The subgroup lattice has 482 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—42no—
52C4×C4⋊C4—42no—
53C4×C4⋊C4—42no—
54C4×C4⋊C4C814yescomplemented
55C2×#95—21no—
56C2×#95—21no—
57C2×#95—21no—
58C2×#95—21no—
59C2×#95—21no—
60C2×#95—21no—
61C2×#95—21no—
62C2×#95—21no—
63C43—42no—
64#336—24no—
65#336—22no—
66#336—22no—
67#336—22no—
68#336—22no—
69#336—42no—
70#336—42no—
71C23×C4—21no—
72C23×C4—21no—
73C23×C4—21no—
74C23×C4—21no—
75C23×C4C22⋊C411yescharacteristic
76C23×C4C22⋊C411yescharacteristic
77C23×C4C22⋊C411yescharacteristic
78C23×C4C22⋊C411yescharacteristic
79C23×C4C22×C411yescharacteristic
80C23×C4C2×D411yescharacteristic
81C23×C4C2×D411yescharacteristic
82C22×C8—24no—
83C22×C8—24no—
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—
95C22×C8—42no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—24no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—41no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—42no—
112C2×C4⋊C4—42no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4C4⋊C412yes—
118C2×C4⋊C4C4⋊C412yes—
119C2×C4⋊C4C2×C812yes—
120C2×C4⋊C4C2×C812yes—
121C2×C4⋊C4M1612yes—
122C2×C4⋊C4M1612yes—
123C2×C42—22no—
124C2×C42—22no—
125C2×C42—22no—
126C2×C42—22no—
127C2×C42—21no—
128C2×C42—21no—
129C2×C42—24no—
130C2×C42—22no—
131C2×C42—22no—
132C2×C42—21no—
133C2×C42—21no—
134C2×C42—22no—
135C2×C42—22no—
136C2×C42—41no—
137C2×C42—41no—
138C2×C42—41no—
139C2×C42—41no—
140C2×C42—41no—
141C2×C42—41no—
142C2×C42—41no—
143C2×C42—41no—
144C2×C42—42no—
145C2×C42—42no—
146C2×C42—42no—
147C2×C42—42no—
148C2×C42—42no—
149C2×C42C2×C812yes—
150C2×C42M1612yes—
151C2×C42D812yes—
152C2×C42SD1612yes—
153C2×C42C2×D411yescharacteristic
154C2×C42C2×Q811yescharacteristic
155C2×C42#4111yescharacteristic
156C2×C42#4111yescharacteristic
157C4⋊C8—48no—
158#95—24no—
159#95—24no—
160#95—22no—
161#95—22no—
162#95—42no—
163#95—42no—
164#95—42no—
165#95—41no—
166#95—41no—
167#95—42no—
168C24C2×C22⋊C411yescharacteristic
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—21no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—21no—
192C22×C4—22no—
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—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
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×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4C22⋊C812yes—
230C22×C4C22⋊C812yes—
231C22×C4#9912yes—
232C22×C4#10112yes—
233C22×C4#10212yes—
234C22×C4#10212yes—
235C22×C4#10412yes—
236C22×C4#10412yes—
237C22×C4C2×C4⋊C411yescharacteristic
238C22×C4#11711yescharacteristic
239C22×C4#12111yescharacteristic
240C22×C4#12111yescharacteristic
241C22×C4C22⋊Q811yescharacteristic
242C22×C4C22⋊Q811yescharacteristic
243C22×C4C22×C811yescharacteristic
244C22×C4C2×M1611yescharacteristic
245C22×C4C2×M1611yescharacteristic
246C22×C4C2×M1611yescharacteristic
247C22×C4C2×D811yescharacteristic
248C22×C4C2×SD1611yescharacteristic
249C22×C4#13512yes—
250C22×C4AGL(1,ℤ/8)11yescharacteristic
251C22×C4#13711yescharacteristic
252C22×C4#13712yes—
253C2×C8—44no—
254C2×C8—44no—
255C2×C8—44no—
256C2×C8—44no—
257C2×C8—44no—
258C2×C8—44no—
259C2×C8—82no—
260C2×C8—82no—
261C2×C8—82no—
262C2×C8—82no—
263C2×C8—82no—
264C2×C8—82no—
265C2×C8—82no—
266C2×C8—82no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—48no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4C4⋊C814yescomplemented
282C42—24no—
283C42—24no—
284C42—24no—
285C42—24no—
286C42—42no—
287C42—42no—
288C42—41no—
289C42—41no—
290C42—41no—
291C42—41no—
292C42—44no—
293C42—44no—
294C42—42no—
295C42—42no—
296C42—48no—
297C42—84no—
298C23#38011yescharacteristic
299C23C2×C22⋊C811yescharacteristic
300C23#40711yescharacteristic
301C23C2×#9911yescharacteristic
302C23#41011yescharacteristic
303C23C2×#10111yescharacteristic
304C23#41311yescharacteristic
305C23C2×#10211yescharacteristic
306C23#41611yescharacteristic
307C23#41711yescharacteristic
308C23#41911yescharacteristic
309C23C2×#10411yescharacteristic
310C23C2×#10411yescharacteristic
311C23#42111yescharacteristic
312C23#42111yescharacteristic
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—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—24no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4#32414yes—
400C2×C4D4⋊C814yes—
401C2×C4C2×C4⋊C811yescharacteristic
402C2×C4#42311yescharacteristic
403C2×C4#43111yescharacteristic
404C2×C4#43211yescharacteristic
405C2×C4#45911yescharacteristic
406C2×C4#46111yescharacteristic
407C2×C4#46412yes—
408C2×C4#47411yescharacteristic
409C2×C4#47611yescharacteristic
410C2×C4#47912yes—
411C8—84no—
412C8—84no—
413C22C2×#32411yescharacteristic
414C22#145811yescharacteristic
415C22#146511yescharacteristic
416C22#146711yescharacteristic
417C22C2×D4⋊C811yescharacteristic
418C22#147611yescharacteristic
419C22#147711yescharacteristic
420C22#147911yescharacteristic
421C22#148611yescharacteristic
422C22#148811yescharacteristic
423C22#148911yescharacteristic
424C22#149111yescharacteristic
425C22#150011yescharacteristic
426C22#150211yescharacteristic
427C22#150411yescharacteristic
428C22#150811yescharacteristic
429C22#151211yescharacteristic
430C22#151511yescharacteristic
431C22#151611yescharacteristic
432C22#151911yescharacteristic
433C22#152411yescharacteristic
434C22#152811yescharacteristic
435C22#153111yescharacteristic
436C22#153511yescharacteristic
437C22#154011yescharacteristic
438C22#154611yescharacteristic
439C22#155211yescharacteristic
440C22#155911yescharacteristic
441C22#179711yescharacteristic
442C22#179911yescharacteristic
443C22#180111yescharacteristic
444C22#180211yescharacteristic
445C22#180511yescharacteristic
446C22#180611yescharacteristic
447C22#180611yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—22no—
453C4—22no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—21no—
458C4—24no—
459C4—24no—
460C4—44no—
461C4—42no—
462C4—42no—
463C4—82no—
464C4—82no—
465C4—82no—
466C2#756011yescharacteristic
467C2#757311yescharacteristic
468C2#757911yescharacteristic
469C2#759611yescharacteristic
470C2#761911yescharacteristic
471C2#762511yescharacteristic
472C2#763411yescharacteristic
473C2#764711yescharacteristic
474C2#855811yescharacteristic
475C2#856311yescharacteristic
476C2#856611yescharacteristic
477C2#857411yescharacteristic
478C2#857711yescharacteristic
479C2#858211yescharacteristic
480C2#858911yescharacteristic
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
54. C4×C4⋊C4C8semidirect
281. 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