Finite Group Databasebeta

← #98781

Subgroups — #98781

Order 512.

782 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#389C211yesmaximal, characteristic
2#10832C211yesmaximal, characteristic
3#10832C211yesmaximal, characteristic
4C2×#1271C212yesmaximal
5#7025C212yesmaximal
6C22×C4⋊C8—21no—
7C22×C4⋊C8—21no—
8C2×#389C411yescharacteristic
9C2×#389C2211yescharacteristic
10C2×C4×C4⋊C4—21no—
11C2×C4×C4⋊C4C411yescharacteristic
12C2×C4×C4⋊C4C411yescharacteristic
13C2×C43C2211yescharacteristic
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—24no—
43C2×C4⋊C8—42no—
44C2×C4⋊C8—42no—
45C2×C4⋊C8—42no—
46C2×C4⋊C8—42no—
47#389—22no—
48#389—22no—
49#389—21no—
50#389—21no—
51#389D412yes—
52#389Q812yes—
53C4×C4⋊C4—22no—
54C4×C4⋊C4—42no—
55C4×C4⋊C4—42no—
56C4×C4⋊C4—42no—
57C4×C4⋊C4C814yescomplemented
58C2×#95—21no—
59C2×#95—21no—
60C2×#95—21no—
61C2×#95—21no—
62C2×#95—21no—
63C2×#95—21no—
64C2×#95—21no—
65C2×#95—21no—
66C43—42no—
67#336—22no—
68#336—22no—
69#336—22no—
70#336—22no—
71#336—42no—
72#336—42no—
73C23×C4—21no—
74C23×C4—21no—
75C23×C4—21no—
76C23×C4—21no—
77C23×C4C22⋊C411yescharacteristic
78C23×C4C22⋊C411yescharacteristic
79C23×C4C22⋊C411yescharacteristic
80C23×C4C22⋊C411yescharacteristic
81C23×C4C22×C411yescharacteristic
82C23×C4C2×D411yescharacteristic
83C23×C4C2×D411yescharacteristic
84C22×C8—24no—
85C22×C8—24no—
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—
96C22×C8—42no—
97C22×C8—42no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—24no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—42no—
114C2×C4⋊C4—42no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4C4⋊C412yes—
120C2×C4⋊C4C4⋊C412yes—
121C2×C4⋊C4C2×C812yes—
122C2×C4⋊C4C2×C812yes—
123C2×C4⋊C4M1612yes—
124C2×C4⋊C4M1612yes—
125C2×C42—22no—
126C2×C42—22no—
127C2×C42—22no—
128C2×C42—22no—
129C2×C42—22no—
130C2×C42—22no—
131C2×C42—24no—
132C2×C42—21no—
133C2×C42—21no—
134C2×C42—21no—
135C2×C42—21no—
136C2×C42—21no—
137C2×C42—21no—
138C2×C42—41no—
139C2×C42—41no—
140C2×C42—41no—
141C2×C42—41no—
142C2×C42—41no—
143C2×C42—41no—
144C2×C42—41no—
145C2×C42—41no—
146C2×C42—42no—
147C2×C42—42no—
148C2×C42—42no—
149C2×C42—42no—
150C2×C42—42no—
151C2×C42C2×C812yes—
152C2×C42M1612yes—
153C2×C42D812yes—
154C2×C42SD1612yes—
155C2×C42SD1612yes—
156C2×C42Q1612yes—
157C2×C42C2×D411yescharacteristic
158C2×C42C2×Q811yescharacteristic
159C2×C42#4111yescharacteristic
160C2×C42#4111yescharacteristic
161C4⋊C8—48no—
162C4⋊C8—48no—
163#95—24no—
164#95—24no—
165#95—22no—
166#95—22no—
167#95—42no—
168#95—42no—
169#95—42no—
170#95—41no—
171#95—41no—
172#95—41no—
173#95—41no—
174C24C2×C22⋊C411yescharacteristic
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—22no—
188C22×C4—22no—
189C22×C4—21no—
190C22×C4—22no—
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—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
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×C4—41no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4C22⋊C812yes—
234C22×C4C22⋊C812yes—
235C22×C4#9912yes—
236C22×C4#10112yes—
237C22×C4#10212yes—
238C22×C4#10212yes—
239C22×C4#10312yes—
240C22×C4#10312yes—
241C22×C4#10412yes—
242C22×C4#10412yes—
243C22×C4C2×C4⋊C411yescharacteristic
244C22×C4#11711yescharacteristic
245C22×C4#12111yescharacteristic
246C22×C4#12111yescharacteristic
247C22×C4C22⋊Q811yescharacteristic
248C22×C4C22⋊Q811yescharacteristic
249C22×C4C22×C811yescharacteristic
250C22×C4C2×M1611yescharacteristic
251C22×C4C2×M1611yescharacteristic
252C22×C4C2×M1611yescharacteristic
253C22×C4C2×D811yescharacteristic
254C22×C4C2×SD1611yescharacteristic
255C22×C4C2×SD1611yescharacteristic
256C22×C4C2×Q1611yescharacteristic
257C22×C4AGL(1,ℤ/8)11yescharacteristic
258C22×C4AGL(1,ℤ/8)11yescharacteristic
259C22×C4#13711yescharacteristic
260C22×C4#13711yescharacteristic
261C2×C8—44no—
262C2×C8—44no—
263C2×C8—44no—
264C2×C8—44no—
265C2×C8—44no—
266C2×C8—44no—
267C2×C8—82no—
268C2×C8—82no—
269C2×C8—82no—
270C2×C8—82no—
271C2×C8—82no—
272C2×C8—82no—
273C2×C8—82no—
274C2×C8—82no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C4⋊C4—48no—
285C4⋊C4—42no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4C4⋊C814yescomplemented
290C42—24no—
291C42—24no—
292C42—24no—
293C42—24no—
294C42—24no—
295C42—24no—
296C42—41no—
297C42—41no—
298C42—41no—
299C42—41no—
300C42—42no—
301C42—42no—
302C42—42no—
303C42—42no—
304C42—42no—
305C42—42no—
306C42—48no—
307C42—84no—
308C23#38011yescharacteristic
309C23C2×C22⋊C811yescharacteristic
310C23#40711yescharacteristic
311C23C2×#9911yescharacteristic
312C23#41011yescharacteristic
313C23C2×#10111yescharacteristic
314C23#41311yescharacteristic
315C23C2×#10211yescharacteristic
316C23C2×#10311yescharacteristic
317C23#41711yescharacteristic
318C23#41711yescharacteristic
319C23C2×#10411yescharacteristic
320C23C2×#10411yescharacteristic
321C23#42111yescharacteristic
322C23#42111yescharacteristic
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—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—24no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4#32414yes—
409C2×C4D4⋊C814yes—
410C2×C4Q8⋊C814yes—
411C2×C4#32714yes—
412C2×C4#32814yes—
413C2×C4#33014yes—
414C2×C4#33214yes—
415C2×C4C2×C4⋊C811yescharacteristic
416C2×C4#42311yescharacteristic
417C2×C4#43111yescharacteristic
418C2×C4#43211yescharacteristic
419C2×C4#45911yescharacteristic
420C2×C4#46011yescharacteristic
421C2×C4#46111yescharacteristic
422C2×C4#46211yescharacteristic
423C2×C4#47411yescharacteristic
424C2×C4#47511yescharacteristic
425C2×C4#47611yescharacteristic
426C2×C4#47711yescharacteristic
427C8—84no—
428C8—84no—
429C22C2×#32411yescharacteristic
430C22#145811yescharacteristic
431C22#146511yescharacteristic
432C22#146711yescharacteristic
433C22C2×D4⋊C811yescharacteristic
434C22C2×Q8⋊C811yescharacteristic
435C22#147711yescharacteristic
436C22#147711yescharacteristic
437C22#148611yescharacteristic
438C22#148711yescharacteristic
439C22#148911yescharacteristic
440C22#148911yescharacteristic
441C22C2×#32711yescharacteristic
442C22C2×#32811yescharacteristic
443C22#150911yescharacteristic
444C22#150911yescharacteristic
445C22#151311yescharacteristic
446C22#151311yescharacteristic
447C22#151711yescharacteristic
448C22#151811yescharacteristic
449C22C2×#33011yescharacteristic
450C22#152911yescharacteristic
451C22#152911yescharacteristic
452C22#153711yescharacteristic
453C22C2×#33211yescharacteristic
454C22#154711yescharacteristic
455C22#155011yescharacteristic
456C22#156111yescharacteristic
457C22#179711yescharacteristic
458C22#179911yescharacteristic
459C22#180111yescharacteristic
460C22#180211yescharacteristic
461C22#180311yescharacteristic
462C22#180611yescharacteristic
463C22#180611yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—21no—
470C4—21no—
471C4—21no—
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—44no—
477C4—42no—
478C4—42no—
479C4—42no—
480C4—82no—
481C4—82no—
482C4—82no—
483C4#127118yescomplemented
484C2C2×#127111yescharacteristic
485C2#757411yescharacteristic
486C2#757711yescharacteristic
487C2#759811yescharacteristic
488C2#761611yescharacteristic
489C2#761711yescharacteristic
490C2#763611yescharacteristic
491C2#765211yescharacteristic
492C2#855811yescharacteristic
493C2#856311yescharacteristic
494C2#856411yescharacteristic
495C2#857111yescharacteristic
496C2#857211yescharacteristic
497C2#858011yescharacteristic
498C2#858611yescharacteristic
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
57. C4×C4⋊C4C8semidirect
289. C4⋊C4C4⋊C8semidirect
483. C4#1271semidirect

Maximal subgroups

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

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