Finite Group Databasebeta

← #190337

Subgroups — #190337

Order 512.

871 conjugacy classes of subgroups.

The subgroup lattice has 521 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34189C211yesmaximal, characteristic
2#20728C211yesmaximal, characteristic
3#17363C211yesmaximal, characteristic
4#8775C214yesmaximal, complemented
5#8773C214yesmaximal, complemented
6#8069C212yesmaximal, complemented
7#7978C212yesmaximal, complemented
8C2×C4×#41C2211yescharacteristic
9#2920C2212yes—
10C2×#432C2212yes—
11#2357—21no—
12#2357C412yes—
13#2356—21no—
14#2356C2212yes—
15#2353—21no—
16#2353—21no—
17#2353C412yes—
18#2353C2212yes—
19#2314—21no—
20#2314—21no—
21#2311—21no—
22#2285C411yescharacteristic
23#2283C411yescharacteristic
24#2283C411yescharacteristic
25#2283C2211yescharacteristic
26#2283C2211yescharacteristic
27C2×#382C411yescharacteristic
28#2274—21no—
29#1822—21no—
30#1801—21no—
31#1800—21no—
32#1785—21no—
33C4×#101C2212yes—
34C4×#100C2212yes—
35#1467C2212yes—
36#1466C2212yes—
37#1464—21no—
38#1464—21no—
39#1459—21no—
40#1459—21no—
41#1300C2218yes—
42#1288C2218yes—
43C22×#41D411yescharacteristic
44C4×#41—22no—
45C4×#41—22no—
46C4×#41—22no—
47C4×#41—22no—
48C2×C4×Q8D411yescharacteristic
49C2×C4×Q8C2311yescharacteristic
50C2×C4×D4C2×C411yescharacteristic
51C2×C4×D4C2×C411yescharacteristic
52C2×C4×D4D411yescharacteristic
53C2×C4×D4D411yescharacteristic
54C2×C4×D4D411yescharacteristic
55C2×C4×D4C2311yescharacteristic
56C2×#117—21no—
57C2×#117D411yescharacteristic
58C2×#117D411yescharacteristic
59C2×#117D411yescharacteristic
60C22×C4⋊C4—21no—
61C22×C42C2×C411yescharacteristic
62C22×C42C2×C411yescharacteristic
63C22×C42C2311yescharacteristic
64#432—22no—
65#432—22no—
66#432—22no—
67#432—22no—
68#432—22no—
69#432C2314yes—
70#431—22no—
71#431—22no—
72#423—22no—
73C2×C4⋊C8—22no—
74C2×#101—22no—
75C2×#100—22no—
76#407—22no—
77C2×C22⋊C8—22no—
78C4×M16C2314yes—
79C2×#97—22no—
80#391—22no—
81#390—22no—
82#388—22no—
83#388—22no—
84#388—22no—
85#388—22no—
86#387—22no—
87#387—22no—
88#387—22no—
89#387—22no—
90#386—22no—
91#386—22no—
92#384—21no—
93#383—21no—
94#383—21no—
95#383C2×C412yes—
96#383C2312yes—
97#382—21no—
98#382—21no—
99#382C2×C412yes—
100#382C2×C411yescharacteristic
101#382C2×C411yescharacteristic
102#382C2×C411yescharacteristic
103#382C2×C411yescharacteristic
104#381—21no—
105#381—21no—
106#381C2×C412yes—
107#381C2×C412yes—
108#380—21no—
109#380—21no—
110#380—21no—
111#380—21no—
112#380—21no—
113#380C2×C412yes—
114C4×C4⋊C4—22no—
115C4×C4⋊C4—22no—
116C4×C4⋊C4—21no—
117C4×C4⋊C4—21no—
118C4×C4⋊C4—21no—
119C4×C4⋊C4—21no—
120C4×C4⋊C4—21no—
121C4×C4⋊C4C2×C412yes—
122C4×C22⋊C4—21no—
123C4×C22⋊C4—21no—
124C4×C22⋊C4—22no—
125C4×C22⋊C4—22no—
126C4×C22⋊C4C2×C412yes—
127C4×C22⋊C4C2×C412yes—
128#376—21no—
129#376—21no—
130#376C2×C412yes—
131#376C2312yes—
132C2×#95—21no—
133C2×#95C2×C412yes—
134#343—22no—
135#343—22no—
136#324—22no—
137#324—22no—
138#323—22no—
139#323—22no—
140C2×#41—22no—
141C2×#41—22no—
142C2×#41—42no—
143C2×#41—42no—
144C22×Q8C2×D411yescharacteristic
145C22×D4C22⋊C411yescharacteristic
146C22×D4C22⋊C411yescharacteristic
147C22×D4C2×D411yescharacteristic
148C23×C4—22no—
149C23×C4C22⋊C411yescharacteristic
150C23×C4C22⋊C411yescharacteristic
151C23×C4C22⋊C411yescharacteristic
152C23×C4C22⋊C411yescharacteristic
153C23×C4C22×C411yescharacteristic
154C23×C4C22×C411yescharacteristic
155C23×C4C22×C411yescharacteristic
156C23×C4C2×D411yescharacteristic
157C23×C4C2×D411yescharacteristic
158C2×M16—24no—
159C22×C8—42no—
160C4×Q8—22no—
161C4×Q8—22no—
162C4×Q8—22no—
163C4×Q8—22no—
164C4×D4—22no—
165C4×D4—22no—
166C4×D4—22no—
167C4×D4—22no—
168C4×D4—22no—
169C4×D4—22no—
170C4×D4—22no—
171C4×D4—22no—
172C4×D4—22no—
173C4×D4—22no—
174C4×D4—22no—
175C4×D4—22no—
176#117—22no—
177#117—22no—
178#117—22no—
179#117—22no—
180#117—22no—
181#117—22no—
182#117—44no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—44no—
191C2×C4⋊C4C22⋊C411yescharacteristic
192C2×C4⋊C4C22⋊C411yescharacteristic
193C2×C4⋊C4C2×D411yescharacteristic
194C2×C4⋊C4C2×D411yescharacteristic
195C2×C4⋊C4C2×D411yescharacteristic
196C2×C4⋊C4C2×D411yescharacteristic
197C2×C22⋊C4—22no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4C22⋊C411yescharacteristic
203C2×C22⋊C4C22⋊C411yescharacteristic
204C2×C22⋊C4C22⋊C411yescharacteristic
205C2×C22⋊C4C22⋊C411yescharacteristic
206C2×C22⋊C4C2×D411yescharacteristic
207C2×C22⋊C4C2×D411yescharacteristic
208C2×C42—21no—
209C2×C42—21no—
210C2×C42—21no—
211C2×C42—21no—
212C2×C42—21no—
213C2×C42—21no—
214C2×C42—21no—
215C2×C42—21no—
216C2×C42—22no—
217C2×C42—22no—
218C2×C42—22no—
219C2×C42—22no—
220C2×C42—22no—
221C2×C42C22⋊C411yescharacteristic
222C2×C42C22⋊C411yescharacteristic
223C2×C42C22⋊C411yescharacteristic
224C2×C42C22⋊C411yescharacteristic
225C2×C42C22×C411yescharacteristic
226C2×C42C22×C411yescharacteristic
227C2×C42C22×C411yescharacteristic
228C2×C42C2×D411yescharacteristic
229C2×C42C2×D411yescharacteristic
230C2×C42#4112yes—
231C2×C42#4112yes—
232C2×C42#4112yes—
233C2×C42#4112yes—
234C2×C42C2411yescharacteristic
235C4⋊C8—24no—
236C4⋊C8—42no—
237C4⋊C8—42no—
238C4⋊C8—42no—
239#101—44no—
240#100—44no—
241C22⋊C8—24no—
242C22⋊C8—42no—
243C22⋊C8—42no—
244C22⋊C8—42no—
245#97—24no—
246#97—24no—
247#97—42no—
248C4×C8—24no—
249#95—21no—
250#95—21no—
251#95—22no—
252#95—22no—
253#95—21no—
254#95—22no—
255#95—22no—
256#95—21no—
257#95—22no—
258#95—22no—
259#95—22no—
260#95—22no—
261#95—22no—
262#95—22no—
263#95C22×C412yes—
264#95C22×C412yes—
265#95C22×C412yes—
266#95C22×C412yes—
267C24C2×C22⋊C411yescharacteristic
268C24C2×C22⋊C411yescharacteristic
269C24C2×C22⋊C411yescharacteristic
270#41—48no—
271#41—48no—
272C2×Q8—22no—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—22no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C22×C4—22no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—44no—
307C22×C4—81no—
308C22×C4—81no—
309C22×C4—81no—
310C22×C4—81no—
311C22×C4—81no—
312C22×C4—81no—
313C22×C4—82no—
314C22×C4—82no—
315C22×C4C2×C22⋊C411yescharacteristic
316C22×C4C2×C22⋊C411yescharacteristic
317C22×C4C2×C22⋊C411yescharacteristic
318C22×C4C2×C22⋊C411yescharacteristic
319C22×C4C2×C22⋊C411yescharacteristic
320C22×C4C2×C22⋊C411yescharacteristic
321C22×C4C2×C22⋊C411yescharacteristic
322C22×C4C2×C22⋊C411yescharacteristic
323C22×C4C2×C22⋊C411yescharacteristic
324C22×C4#11712yes—
325C22×C4#11712yes—
326C22×C4#12312yes—
327C22×C4#12312yes—
328C22×C4#12312yes—
329C22×C4#12312yes—
330C22×C4C23×C411yescharacteristic
331C22×C4C22×D411yescharacteristic
332C22×C4C22×D411yescharacteristic
333M16—44no—
334M16—44no—
335C2×C8—44no—
336C2×C8—44no—
337C2×C8—84no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—42no—
345C4⋊C4—42no—
346C4⋊C4—42no—
347C4⋊C4—42no—
348C4⋊C4—44no—
349C4⋊C4—82no—
350C4⋊C4—82no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—22no—
356C22⋊C4—22no—
357C22⋊C4—44no—
358C22⋊C4—82no—
359C22⋊C4—82no—
360C22⋊C4—82no—
361C22⋊C4—82no—
362C42—21no—
363C42—21no—
364C42—21no—
365C42—21no—
366C42—21no—
367C42—21no—
368C42—21no—
369C42—21no—
370C42—21no—
371C42—21no—
372C42—21no—
373C42—21no—
374C42—44no—
375C42—82no—
376C42—82no—
377C42—82no—
378C42—82no—
379C42#11711yescharacteristic
380C42#11711yescharacteristic
381C42#11711yescharacteristic
382C42#11711yescharacteristic
383C42#12312yes—
384C42#12312yes—
385C42#12312yes—
386C42#12312yes—
387C42C2×#4112yes—
388C42C2×#4112yes—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23#38112yes—
403C23#42112yes—
404C23C22×C22⋊C411yescharacteristic
405Q8—44no—
406D4—44no—
407D4—44no—
408D4—44no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—81no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4—81no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—164no—
461C2×C4#38111yescharacteristic
462C2×C4#38111yescharacteristic
463C2×C4#38111yescharacteristic
464C2×C4#38111yescharacteristic
465C2×C4#38112yes—
466C2×C4#42112yes—
467C2×C4C2×#11711yescharacteristic
468C2×C4C2×#11711yescharacteristic
469C2×C4C2×#12312yes—
470C2×C4C2×#12312yes—
471C8—84no—
472C8—84no—
473C22—21no—
474C22—21no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—42no—
480C22—42no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22C2×#38111yescharacteristic
491C22C2×#42111yescharacteristic
492C22C2×#42111yescharacteristic
493C4—22no—
494C4—21no—
495C4—21no—
496C4—22no—
497C4—22no—
498C4—21no—
499C4—21no—
500C4—21no—
501C4—21no—
502C4—22no—
503C4—41no—
504C4—41no—
505C4—41no—
506C4—41no—
507C4—41no—
508C4—82no—
509C4—82no—
510C4—82no—
511C4—82no—
512C2—21no—
513C2—21no—
514C2—42no—
515C2—42no—
516C2—81no—
517C2#2070511yescharacteristic
518C2#2070811yescharacteristic
519C2#2071311yescharacteristic
subgroupG/H
center, socleC22C2×#381
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC22×#41D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #8775C2semidirect
5. #8773C2semidirect
6. #8069C2semidirect
7. #7978C2semidirect

Maximal subgroups

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

subgroupindex
#341892
#207282
#173632
#87752
#87732
#80692
#79782