Finite Group Databasebeta

← #190321

Subgroups — #190321

Order 512.

939 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34189C211yesmaximal, characteristic
2C4×#413C211yesmaximal, characteristic
3#17361C211yesmaximal, characteristic
4#8774C214yesmaximal, complemented
5#8773C214yesmaximal, complemented
6#8074C212yesmaximal, complemented
7#7974C212yesmaximal, complemented
8C2×C4×#41C2211yescharacteristic
9#2920C2212yes—
10C2×#413—21no—
11C2×C4×M16C2212yes—
12#2357—21no—
13#2357C412yes—
14#2356—21no—
15#2356C2212yes—
16#2353—21no—
17#2353—21no—
18#2353C412yes—
19#2353C2212yes—
20#2314—21no—
21#2314—21no—
22#2311—21no—
23#2285C411yescharacteristic
24#2283C411yescharacteristic
25#2283C411yescharacteristic
26#2283C2211yescharacteristic
27#2283C2211yescharacteristic
28C2×#382C411yescharacteristic
29#2274—21no—
30C4×#101—21no—
31C4×#101C2212yes—
32C4×#100—21no—
33C4×#100C2212yes—
34#1742—21no—
35#1467C2212yes—
36#1466C2212yes—
37#1465—21no—
38#1465—21no—
39#1458—21no—
40#1458—21no—
41#1300C2218yes—
42#1288C2218yes—
43C22×#41D411yescharacteristic
44C22×M16—22no—
45C4×#41—22no—
46C4×#41—22no—
47C4×#41—22no—
48C4×#41—22no—
49C2×C4×Q8D411yescharacteristic
50C2×C4×Q8C2311yescharacteristic
51C2×C4×D4C2×C411yescharacteristic
52C2×C4×D4C2×C411yescharacteristic
53C2×C4×D4D411yescharacteristic
54C2×C4×D4D411yescharacteristic
55C2×C4×D4D411yescharacteristic
56C2×C4×D4C2311yescharacteristic
57C2×#117—21no—
58C2×#117D411yescharacteristic
59C2×#117D411yescharacteristic
60C2×#117D411yescharacteristic
61C22×C4⋊C4—21no—
62C22×C42C2×C411yescharacteristic
63C22×C42C2×C411yescharacteristic
64C22×C42C2311yescharacteristic
65#432—22no—
66#432C2314yes—
67#431—22no—
68#431—22no—
69#423—22no—
70#413—28no—
71C2×#101—22no—
72C2×#100—22no—
73#407—22no—
74C4×M16—22no—
75C4×M16—22no—
76C4×M16—22no—
77C4×M16—22no—
78C4×M16C2314yes—
79C2×#97—22no—
80C2×C4×C8—22no—
81#391—22no—
82#390—22no—
83#388—22no—
84#388—22no—
85#388—22no—
86#388—22no—
87#387—22no—
88#387—22no—
89#387—22no—
90#387—22no—
91#386—22no—
92#386—22no—
93#384—21no—
94#383—21no—
95#383—21no—
96#383C2×C412yes—
97#383C2312yes—
98#382—21no—
99#382—21no—
100#382C2×C412yes—
101#382C2×C411yescharacteristic
102#382C2×C411yescharacteristic
103#382C2×C411yescharacteristic
104#382C2×C411yescharacteristic
105#381—21no—
106#381—21no—
107#381C2×C412yes—
108#381C2×C412yes—
109#380—21no—
110#380—21no—
111#380—21no—
112#380—21no—
113#380—21no—
114#380C2×C412yes—
115C4×C4⋊C4—22no—
116C4×C4⋊C4—22no—
117C4×C4⋊C4—21no—
118C4×C4⋊C4—21no—
119C4×C4⋊C4—21no—
120C4×C4⋊C4—21no—
121C4×C4⋊C4—21no—
122C4×C4⋊C4C2×C412yes—
123C4×C22⋊C4—21no—
124C4×C22⋊C4—21no—
125C4×C22⋊C4—22no—
126C4×C22⋊C4—22no—
127C4×C22⋊C4C2×C412yes—
128C4×C22⋊C4C2×C412yes—
129#376—21no—
130#376—21no—
131#376C2×C412yes—
132#376C2312yes—
133C2×#95—21no—
134C2×#95C2×C412yes—
135#343—22no—
136#343—22no—
137#324—22no—
138#324—22no—
139#323—22no—
140#323—22no—
141C2×#41—24no—
142C2×#41—22no—
143C2×#41—22no—
144C2×#41—42no—
145C22×Q8C2×D411yescharacteristic
146C22×D4C22⋊C411yescharacteristic
147C22×D4C22⋊C411yescharacteristic
148C22×D4C2×D411yescharacteristic
149C23×C4—22no—
150C23×C4C22⋊C411yescharacteristic
151C23×C4C22⋊C411yescharacteristic
152C23×C4C22⋊C411yescharacteristic
153C23×C4C22⋊C411yescharacteristic
154C23×C4C22×C411yescharacteristic
155C23×C4C22×C411yescharacteristic
156C23×C4C22×C411yescharacteristic
157C23×C4C2×D411yescharacteristic
158C23×C4C2×D411yescharacteristic
159C2×M16—28no—
160C2×M16—24no—
161C2×M16—44no—
162C2×M16—42no—
163C2×M16—42no—
164C22×C8—42no—
165C4×Q8—22no—
166C4×Q8—22no—
167C4×Q8—22no—
168C4×Q8—22no—
169C4×D4—22no—
170C4×D4—22no—
171C4×D4—22no—
172C4×D4—22no—
173C4×D4—22no—
174C4×D4—22no—
175C4×D4—22no—
176C4×D4—22no—
177C4×D4—22no—
178C4×D4—22no—
179C4×D4—22no—
180C4×D4—22no—
181#117—22no—
182#117—22no—
183#117—22no—
184#117—22no—
185#117—22no—
186#117—22no—
187#117—44no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—44no—
196C2×C4⋊C4C22⋊C411yescharacteristic
197C2×C4⋊C4C22⋊C411yescharacteristic
198C2×C4⋊C4C2×D411yescharacteristic
199C2×C4⋊C4C2×D411yescharacteristic
200C2×C4⋊C4C2×D411yescharacteristic
201C2×C4⋊C4C2×D411yescharacteristic
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—22no—
207C2×C22⋊C4C22⋊C411yescharacteristic
208C2×C22⋊C4C22⋊C411yescharacteristic
209C2×C22⋊C4C22⋊C411yescharacteristic
210C2×C22⋊C4C22⋊C411yescharacteristic
211C2×C22⋊C4C2×D411yescharacteristic
212C2×C22⋊C4C2×D411yescharacteristic
213C2×C42—21no—
214C2×C42—21no—
215C2×C42—21no—
216C2×C42—21no—
217C2×C42—21no—
218C2×C42—21no—
219C2×C42—21no—
220C2×C42—21no—
221C2×C42—22no—
222C2×C42—22no—
223C2×C42—22no—
224C2×C42—22no—
225C2×C42—22no—
226C2×C42C22⋊C411yescharacteristic
227C2×C42C22⋊C411yescharacteristic
228C2×C42C22⋊C411yescharacteristic
229C2×C42C22⋊C411yescharacteristic
230C2×C42C22×C411yescharacteristic
231C2×C42C22×C411yescharacteristic
232C2×C42C22×C411yescharacteristic
233C2×C42C2×D411yescharacteristic
234C2×C42C2×D411yescharacteristic
235C2×C42#4112yes—
236C2×C42#4112yes—
237C2×C42#4112yes—
238C2×C42#4112yes—
239C2×C42C2411yescharacteristic
240C4⋊C8—24no—
241C4⋊C8—42no—
242#101—28no—
243#100—28no—
244C22⋊C8—24no—
245C22⋊C8—42no—
246#97—24no—
247#97—24no—
248#97—42no—
249C4×C8—24no—
250C4×C8—42no—
251C4×C8—42no—
252#95—21no—
253#95—21no—
254#95—22no—
255#95—22no—
256#95—21no—
257#95—22no—
258#95—22no—
259#95—21no—
260#95—22no—
261#95—22no—
262#95—22no—
263#95—22no—
264#95—22no—
265#95—22no—
266#95C22×C412yes—
267#95C22×C412yes—
268#95C22×C412yes—
269#95C22×C412yes—
270C24C2×C22⋊C411yescharacteristic
271C24C2×C22⋊C411yescharacteristic
272C24C2×C22⋊C411yescharacteristic
273#41—48no—
274#41—48no—
275C2×Q8—22no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—22no—
281C2×D4—22no—
282C2×D4—22no—
283C2×D4—22no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—44no—
309C22×C4—81no—
310C22×C4—81no—
311C22×C4—81no—
312C22×C4—81no—
313C22×C4—81no—
314C22×C4—81no—
315C22×C4—82no—
316C22×C4—82no—
317C22×C4#10414yes—
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×C4C2×C22⋊C411yescharacteristic
325C22×C4C2×C22⋊C411yescharacteristic
326C22×C4C2×C22⋊C411yescharacteristic
327C22×C4#11712yes—
328C22×C4#11712yes—
329C22×C4#12312yes—
330C22×C4#12312yes—
331C22×C4#12312yes—
332C22×C4#12312yes—
333C22×C4C23×C411yescharacteristic
334C22×C4C22×D411yescharacteristic
335C22×C4C22×D411yescharacteristic
336M16—28no—
337M16—44no—
338M16—48no—
339M16—84no—
340C2×C8—48no—
341C2×C8—44no—
342C2×C8—44no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—44no—
350C4⋊C4—42no—
351C4⋊C4—42no—
352C4⋊C4—42no—
353C4⋊C4—42no—
354C4⋊C4—82no—
355C4⋊C4—82no—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—22no—
359C22⋊C4—22no—
360C22⋊C4—22no—
361C22⋊C4—22no—
362C22⋊C4—44no—
363C22⋊C4—82no—
364C22⋊C4—82no—
365C22⋊C4—82no—
366C22⋊C4—82no—
367C42—21no—
368C42—21no—
369C42—21no—
370C42—21no—
371C42—21no—
372C42—21no—
373C42—21no—
374C42—21no—
375C42—21no—
376C42—21no—
377C42—21no—
378C42—21no—
379C42—44no—
380C42—82no—
381C42—82no—
382C42—82no—
383C42—82no—
384C42#11711yescharacteristic
385C42#11711yescharacteristic
386C42#11711yescharacteristic
387C42#11711yescharacteristic
388C42#12312yes—
389C42#12312yes—
390C42#12312yes—
391C42#12312yes—
392C42C2×#4112yes—
393C42C2×#4112yes—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23#38112yes—
408C23C2×#10412yes—
409C23C22×C22⋊C411yescharacteristic
410Q8—44no—
411D4—44no—
412D4—44no—
413D4—44no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
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—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—81no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4—81no—
463C2×C4—164no—
464C2×C4#38111yescharacteristic
465C2×C4#38111yescharacteristic
466C2×C4#38112yes—
467C2×C4#38111yescharacteristic
468C2×C4#38111yescharacteristic
469C2×C4C2×#10412yes—
470C2×C4C2×#10412yes—
471C2×C4#42112yes—
472C2×C4C2×#11711yescharacteristic
473C2×C4C2×#11711yescharacteristic
474C2×C4C2×#12312yes—
475C2×C4C2×#12312yes—
476C8—48no—
477C8—84no—
478C22—21no—
479C22—21no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—42no—
485C22—42no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22C2×#38111yescharacteristic
496C22C22×#10411yescharacteristic
497C22C2×#42111yescharacteristic
498C4—22no—
499C4—22no—
500C4—22no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—21no—
505C4—22no—
506C4—41no—
507C4—41no—
508C4—41no—
509C4—41no—
510C4—41no—
511C4—82no—
512C4—82no—
513C4—82no—
514C4—82no—
515C4#182612yes—
516C4#182612yes—
517C2—21no—
518C2—21no—
519C2—42no—
520C2—42no—
521C2—81no—
522C2C2×#182611yescharacteristic
523C2#2070811yescharacteristic
524C2#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. #8774C2semidirect
5. #8773C2semidirect
6. #8074C2semidirect
7. #7974C2semidirect

Maximal subgroups

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

subgroupindex
#341892
C4×#4132
#173612
#87742
#87732
#80742
#79742