Finite Group Databasebeta

← #222939

Subgroups — #222939

Order 512.

836 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2514C211yesmaximal, characteristic
2#22603C211yesmaximal, characteristic
3#22599C211yesmaximal, characteristic
4#9878C211yesmaximal, characteristic
5#9878C211yesmaximal, characteristic
6#9086C212yesmaximal
7#9082C212yesmaximal
8#8705C212yesmaximal
9#8558C211yesmaximal, characteristic
10C4×#324C211yesmaximal, characteristic
11#7916C212yesmaximal
12C2×#432C2212yes—
13C2×#431C2212yes—
14#2514—22no—
15#2514—22no—
16#2514—21no—
17#2514—21no—
18#2514—21no—
19#2514—21no—
20C2×#401C412yes—
21C2×#400C412yes—
22C2×#391C411yescharacteristic
23C2×#391C411yescharacteristic
24C2×#391C2211yescharacteristic
25C2×#389C411yescharacteristic
26C2×#387C2212yes—
27C2×#383C2212yes—
28C2×#382C411yescharacteristic
29C2×C4×C4⋊C4C2211yescharacteristic
30C2×C4×C4⋊C4C2211yescharacteristic
31#1939—21no—
32#1939—21no—
33#1917—22no—
34#1916—22no—
35#1817C2212yes—
36#1817C2212yes—
37#1797C2211yescharacteristic
38#1797C2211yescharacteristic
39#1770—21no—
40C8×C4⋊C4—21no—
41C4×C22⋊C8C2211yescharacteristic
42C4×C22⋊C8C2211yescharacteristic
43C2×#324C2211yescharacteristic
44C2×#324C2211yescharacteristic
45C2×#324C2212yes—
46#1280C2211yescharacteristic
47#1280C2212yes—
48#1280C2212yes—
49#1280C2212yes—
50#1280C2212yes—
51#1280C2212yes—
52#1280C2211yescharacteristic
53C23×Q8C2×C411yescharacteristic
54C22×C4⋊C4C2×C411yescharacteristic
55C22×C4⋊C4C2×C412yes—
56C22×C4⋊C4C2×C411yescharacteristic
57C22×C4⋊C4C2×C411yescharacteristic
58C22×C4⋊C4C2×C411yescharacteristic
59C22×C4⋊C4C2311yescharacteristic
60C22×C42C2×C411yescharacteristic
61C22×C42C2×C411yescharacteristic
62C22×C42C2312yes—
63C22×C42C2311yescharacteristic
64#432—24no—
65#432—42no—
66#431—24no—
67#431—42no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—22no—
71C2×C4⋊C8—22no—
72C2×C22⋊C8C2312yes—
73C2×C22⋊C8C2312yes—
74C2×C22⋊C8C2311yescharacteristic
75C2×C22⋊C8C2311yescharacteristic
76C2×C22⋊C8C2311yescharacteristic
77C2×C22⋊C8C2311yescharacteristic
78C2×#97—22no—
79C2×C4×C8—22no—
80C2×C4×C8—21no—
81C2×C4×C8—21no—
82#401—22no—
83#401—22no—
84#401—22no—
85#401—22no—
86#400—22no—
87#400—22no—
88#400—22no—
89#400—22no—
90#391—22no—
91#391—21no—
92#391—21no—
93#391—21no—
94#391—21no—
95#391—22no—
96#391—21no—
97#391—21no—
98#391—21no—
99#391—21no—
100#389—22no—
101#389—21no—
102#389—21no—
103#387—22no—
104#387—22no—
105#387—22no—
106#387—22no—
107#383—22no—
108#383—22no—
109#383—22no—
110#383—22no—
111#382—21no—
112#382—21no—
113#382—22no—
114C4×C4⋊C4—21no—
115C4×C4⋊C4—21no—
116C4×C4⋊C4—21no—
117C4×C4⋊C4—21no—
118C4×C4⋊C4D412yes—
119C4×C4⋊C4D412yes—
120C4×C4⋊C4D411yescharacteristic
121C4×C4⋊C4D411yescharacteristic
122C4×C4⋊C4D411yescharacteristic
123C4×C4⋊C4D411yescharacteristic
124C2×#95C2×C412yes—
125C2×#95C2×C412yes—
126C2×#95C2×C412yes—
127C2×#95C2×C412yes—
128C2×#95C2×C411yescharacteristic
129C2×#95C2×C412yes—
130C2×#95C2×C412yes—
131C2×#95C2×C412yes—
132C2×#95C2×C412yes—
133C2×#95C2×C412yes—
134C2×#95C2311yescharacteristic
135C2×#95C2312yes—
136#336—21no—
137#336—21no—
138#336—22no—
139#336—22no—
140#336—22no—
141#336—22no—
142#336—21no—
143#336—21no—
144#324—22no—
145#324—22no—
146#324—42no—
147C22×Q8—21no—
148C22×Q8—21no—
149C22×Q8—22no—
150C22×Q8—22no—
151C22×Q8—42no—
152C22×Q8—42no—
153C23×C4C22×C412yes—
154C23×C4C22×C411yescharacteristic
155C23×C4C22×C411yescharacteristic
156C23×C4C22×C412yes—
157C23×C4C22×C411yescharacteristic
158C23×C4C22×C411yescharacteristic
159C23×C4C22×C412yes—
160C23×C4C22×C411yescharacteristic
161C23×C4C22×C412yes—
162C23×C4C22×C411yescharacteristic
163C23×C4C2411yescharacteristic
164C22×C8—21no—
165C22×C8—21no—
166C22×C8—21no—
167C22×C8—21no—
168C22×C8—22no—
169C22×C8—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—24no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—42no—
187C2×C4⋊C4—42no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4—42no—
190C2×C4⋊C4C22⋊C411yescharacteristic
191C2×C4⋊C4C22⋊C411yescharacteristic
192C2×C4⋊C4C22⋊C412yes—
193C2×C4⋊C4C22⋊C411yescharacteristic
194C2×C4⋊C4C22⋊C411yescharacteristic
195C2×C4⋊C4C22⋊C412yes—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42—21no—
201C2×C42—21no—
202C2×C42—21no—
203C2×C42—21no—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42—42no—
207C2×C42—42no—
208C2×C42C2×D412yes—
209C2×C42C2×D412yes—
210C2×C42C2×D412yes—
211C2×C42C2×D412yes—
212C2×C42C2×D411yescharacteristic
213C2×C42C2×D411yescharacteristic
214C2×C42C2×D411yescharacteristic
215C2×C42C2×D411yescharacteristic
216C4⋊C8—44no—
217C4⋊C8—44no—
218C4⋊C8—42no—
219C4⋊C8—42no—
220C22⋊C8—21no—
221C22⋊C8—21no—
222C22⋊C8—21no—
223C22⋊C8—21no—
224C22⋊C8—22no—
225C22⋊C8—22no—
226C22⋊C8—22no—
227C22⋊C8—22no—
228C22⋊C8—21no—
229C22⋊C8—21no—
230C22⋊C8#4112yes—
231C22⋊C8#4112yes—
232#97—44no—
233C4×C8—44no—
234C4×C8—42no—
235C4×C8—42no—
236#95—21no—
237#95—21no—
238#95—22no—
239#95—22no—
240#95—22no—
241#95—22no—
242#95—22no—
243#95—22no—
244#95—22no—
245#95—22no—
246#95—22no—
247#95—22no—
248#95—22no—
249#95—22no—
250#95—22no—
251#95—22no—
252#95—22no—
253#95—22no—
254#95—21no—
255#95—21no—
256#95—22no—
257#95—22no—
258#95C22⋊C412yes—
259#95C22⋊C412yes—
260#95C22⋊C412yes—
261#95C22⋊C412yes—
262C24C23×C411yescharacteristic
263C2×Q8—42no—
264C2×Q8—42no—
265C2×Q8—42no—
266C2×Q8—42no—
267C2×Q8—42no—
268C2×Q8—42no—
269C2×Q8—84no—
270C2×Q8—84no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—22no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—42no—
308C22×C4—41no—
309C22×C4—42no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4C2×C22⋊C412yes—
321C22×C4C2×C22⋊C412yes—
322C22×C4C2×C22⋊C411yescharacteristic
323C22×C4C2×C22⋊C411yescharacteristic
324C22×C4C2×C22⋊C412yes—
325C22×C4C2×C22⋊C412yes—
326C22×C4C2×C22⋊C411yescharacteristic
327C22×C4C2×C22⋊C411yescharacteristic
328C22×C4#13112yes—
329C22×C4#13112yes—
330C22×C4#13112yes—
331C22×C4C22×D411yescharacteristic
332C22×C4C22×D411yescharacteristic
333C22×C4C2×#4111yescharacteristic
334C22×C4C2×#4111yescharacteristic
335C22×C4H(5,𝔽2)11yescharacteristic
336C22×C42−1+411yescharacteristic
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—42no—
346C2×C8—42no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—42no—
350C2×C8—42no—
351C2×C8—42no—
352C2×C8—42no—
353C2×C8—41no—
354C2×C8—41no—
355C4⋊C4—24no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—42no—
361C4⋊C4—42no—
362C4⋊C4—42no—
363C4⋊C4—44no—
364C4⋊C4—44no—
365C4⋊C4—42no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—42no—
371C42—22no—
372C42—22no—
373C42—22no—
374C42—22no—
375C42—22no—
376C42—22no—
377C42—22no—
378C42—22no—
379C42—22no—
380C42—22no—
381C42—41no—
382C42—41no—
383C42—42no—
384C42—42no—
385C42—42no—
386C42—42no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23C22×C22⋊C411yescharacteristic
392C23C4×#4111yescharacteristic
393C23#52011yescharacteristic
394C23C2×#13111yescharacteristic
395C23C2×#13111yescharacteristic
396C23C2×#13111yescharacteristic
397C23#56811yescharacteristic
398Q8—84no—
399Q8—84no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4—82no—
463C2×C4—82no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4—82no—
469C2×C4—82no—
470C2×C4#40812yes—
471C2×C4#40812yes—
472C2×C4#41012yes—
473C2×C4#41312yes—
474C2×C4#54611yescharacteristic
475C2×C4#54611yescharacteristic
476C2×C4#54711yescharacteristic
477C2×C4#54711yescharacteristic
478C8—42no—
479C8—42no—
480C8—82no—
481C8—82no—
482C8—81no—
483C8—81no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22#233911yescharacteristic
497C22C2×#40811yescharacteristic
498C22#288011yescharacteristic
499C22C2×#41011yescharacteristic
500C22#288411yescharacteristic
501C22C2×#41311yescharacteristic
502C22#288911yescharacteristic
503C22#296611yescharacteristic
504C22#296911yescharacteristic
505C22#299311yescharacteristic
506C22#299411yescharacteristic
507C4—21no—
508C4—21no—
509C4—21no—
510C4—21no—
511C4—22no—
512C4—41no—
513C4—41no—
514C4—42no—
515C4—42no—
516C4—42no—
517C4—42no—
518C4—42no—
519C4—81no—
520C4—82no—
521C4—81no—
522C4—82no—
523C4—81no—
524C4#147314yes—
525C2—21no—
526C2—21no—
527C2—21no—
528C2—21no—
529C2C2×#147311yescharacteristic
530C2#1739111yescharacteristic
531C2#1742011yescharacteristic
532C2#1742811yescharacteristic
533C2#2247411yescharacteristic
534C2#2247811yescharacteristic
535C2#2248411yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutator, prime radicalC24C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#25142
#226032
#225992
#98782
#90862
#90822
#87052
#85582
C4×#3242
#79162