Finite Group Databasebeta

← #114172

Subgroups — #114172

Order 512.

819 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60663C211yesmaximal, characteristic
2C2×#1542C211yesmaximal, characteristic
3#17486C211yesmaximal, characteristic
4#17486C211yesmaximal, characteristic
5C2×#1481C211yesmaximal, characteristic
6#10853C211yesmaximal, characteristic
7#7932C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#533C2211yescharacteristic
10#3166—22no—
11#3166—22no—
12#3165—21no—
13#3165—21no—
14#3165C412yes—
15#3165C412yes—
16#3162—22no—
17#3160—22no—
18C2×#431C2211yescharacteristic
19C2×#431C2211yescharacteristic
20#2911—22no—
21C2×#423C2211yescharacteristic
22C22×C4⋊C8C2211yescharacteristic
23C2×C4×M16C2211yescharacteristic
24C2×#341—22no—
25#1542—22no—
26#1542—22no—
27C2×#333—21no—
28C2×#332—21no—
29#1493—22no—
30#1493—22no—
31#1487—22no—
32#1487—22no—
33#1481—22no—
34#1481—22no—
35#1481—22no—
36#1481—22no—
37C2×Q8⋊C8—22no—
38#1283—22no—
39C22×M16—21no—
40C22×M16D412yes—
41C23×C8—21no—
42#533—21no—
43#533—21no—
44#533—21no—
45#533—21no—
46#533—21no—
47#533—21no—
48#533—21no—
49#533—21no—
50#533—21no—
51#533—21no—
52#533—21no—
53#533—21no—
54#533C2×C412yes—
55#533D412yes—
56#533D412yes—
57#533D412yes—
58C2×C4⋊Q8C2×C411yescharacteristic
59C2×C4⋊Q8C2×C411yescharacteristic
60C2×C4⋊Q8D411yescharacteristic
61C2×C4⋊Q8D411yescharacteristic
62C2×#125—21no—
63C2×#125—21no—
64C2×C22⋊Q8—21no—
65C2×C22⋊Q8—21no—
66C2×C22⋊Q8—21no—
67C2×C22⋊Q8—21no—
68C2×C4×Q8—21no—
69C2×C4×Q8—21no—
70C2×C4×Q8—21no—
71C2×C4×Q8—21no—
72C2×#117—21no—
73C2×#117—21no—
74C22×C42C2311yescharacteristic
75#501—24no—
76#501—24no—
77#501—24no—
78#501—24no—
79#500—22no—
80#500—22no—
81#499—28no—
82#498—22no—
83#498—22no—
84#431—21no—
85#431—21no—
86#431—21no—
87#431—21no—
88#431—21no—
89#431—21no—
90#431—21no—
91#431D412yes—
92#428—24no—
93#428—24no—
94#428—24no—
95#428—24no—
96#427—28no—
97#423—21no—
98#423—21no—
99#423—21no—
100#423D412yes—
101C2×C4⋊C8—21no—
102C2×C4⋊C8—21no—
103C2×C4⋊C8—21no—
104C2×C4⋊C8—21no—
105C2×C4⋊C8—21no—
106C2×C4⋊C8—21no—
107C2×C4⋊C8—21no—
108C2×C4⋊C8—21no—
109C2×C4⋊C8—21no—
110C2×C4⋊C8D412yes—
111C2×C22⋊C8—21no—
112C2×C22⋊C8—21no—
113C4×M16—21no—
114C4×M16—21no—
115C4×M16C2×C412yes—
116C4×M16D412yes—
117C2×#97—21no—
118C2×C4×C8—21no—
119C2×C4×C8—21no—
120C2×C4×C8D412yes—
121#341—44no—
122#333—24no—
123#332—24no—
124Q8⋊C8—28no—
125Q8⋊C8—28no—
126Q8⋊C8—28no—
127C22×Q8—21no—
128C22×Q8—21no—
129C22×Q8—21no—
130C22×Q8—21no—
131C23×C4C2×D411yescharacteristic
132C23×C4#4111yescharacteristic
133C23×C4#4111yescharacteristic
134C2×M16—22no—
135C2×M16—22no—
136C2×M16—22no—
137C2×M16—22no—
138C2×M16—41no—
139C2×M16—42no—
140C2×M16—42no—
141C2×M16C22⋊C414yes—
142C2×M16SD1614yes—
143C2×M16Q1614yes—
144C22×C8—22no—
145C22×C8—22no—
146C22×C8—22no—
147C22×C8—41no—
148C22×C8—41no—
149C22×C8—41no—
150C22×C8—41no—
151C22×C8—42no—
152C22×C8—42no—
153C4⋊Q8—21no—
154C4⋊Q8—21no—
155C4⋊Q8—21no—
156C4⋊Q8—21no—
157C4⋊Q8—21no—
158C4⋊Q8—21no—
159C4⋊Q8—21no—
160C4⋊Q8—21no—
161C4⋊Q8—21no—
162C4⋊Q8—21no—
163C4⋊Q8—21no—
164C4⋊Q8—21no—
165C4⋊Q8C22⋊C412yes—
166C4⋊Q8C22⋊C412yes—
167C4⋊Q8C22⋊C412yes—
168C4⋊Q8C22⋊C412yes—
169#125—22no—
170#125—22no—
171#125—22no—
172#125—22no—
173#125—41no—
174#125—41no—
175#125—41no—
176#125—41no—
177C22⋊Q8—22no—
178C22⋊Q8—22no—
179C22⋊Q8—22no—
180C22⋊Q8—22no—
181C22⋊Q8—22no—
182C22⋊Q8—22no—
183C22⋊Q8—22no—
184C22⋊Q8—22no—
185C22⋊Q8—41no—
186C22⋊Q8—41no—
187C22⋊Q8—41no—
188C22⋊Q8—41no—
189C22⋊Q8—41no—
190C22⋊Q8—41no—
191C22⋊Q8—41no—
192C22⋊Q8—41no—
193C4×Q8—22no—
194C4×Q8—22no—
195C4×Q8—22no—
196C4×Q8—22no—
197C4×Q8—22no—
198C4×Q8—22no—
199C4×Q8—22no—
200C4×Q8—22no—
201C4×Q8—41no—
202C4×Q8—41no—
203C4×Q8—41no—
204C4×Q8—41no—
205C4×Q8—41no—
206C4×Q8—41no—
207C4×Q8—41no—
208C4×Q8—41no—
209#117—22no—
210#117—22no—
211#117—22no—
212#117—22no—
213#117—41no—
214#117—41no—
215#117—41no—
216#117—41no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—41no—
226C2×C4⋊C4—41no—
227C2×C4⋊C4—41no—
228C2×C4⋊C4—41no—
229C2×C22⋊C4—41no—
230C2×C22⋊C4—41no—
231C2×C42—41no—
232C2×C42—41no—
233C2×C42C22×C411yescharacteristic
234C2×C42C2×D411yescharacteristic
235C2×C42C2×D411yescharacteristic
236C2×C42C2×D411yescharacteristic
237C2×C42C2×D411yescharacteristic
238C2×C42C2×D411yescharacteristic
239C2×C42C2×D411yescharacteristic
240C2×C42C2×D411yescharacteristic
241C2×C42C2×D411yescharacteristic
242C2×C42C2×D411yescharacteristic
243C2×C42#4111yescharacteristic
244C2×C42#4111yescharacteristic
245#107—28no—
246#107—28no—
247#106—28no—
248#106—28no—
249C4⋊C8—22no—
250C4⋊C8—22no—
251C4⋊C8—22no—
252C4⋊C8—22no—
253C4⋊C8—22no—
254C4⋊C8—41no—
255C4⋊C8—41no—
256C4⋊C8—41no—
257C4⋊C8—41no—
258C4⋊C8—41no—
259C4⋊C8—41no—
260C4⋊C8—41no—
261C22⋊C8—22no—
262C22⋊C8—41no—
263C22⋊C8—41no—
264C22⋊C8—41no—
265#97—22no—
266#97—22no—
267C4×C8—22no—
268C4×C8—22no—
269C4×C8—22no—
270C4×C8—22no—
271C4×C8—22no—
272C4×C8—41no—
273C24#12411yescharacteristic
274C2×Q8—22no—
275C2×Q8—22no—
276C2×Q8—22no—
277C2×Q8—22no—
278C2×Q8—44no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—82no—
284C2×Q8—82no—
285C2×Q8—82no—
286C22×C4—42no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—81no—
292C22×C4C2×C22⋊C411yescharacteristic
293C22×C4C4×D411yescharacteristic
294C22×C4C4×D411yescharacteristic
295C22×C4#12011yescharacteristic
296C22×C4#12011yescharacteristic
297C22×C4#12111yescharacteristic
298C22×C4#12111yescharacteristic
299C22×C4#12111yescharacteristic
300C22×C4#12111yescharacteristic
301C22×C4#12111yescharacteristic
302C22×C4#12111yescharacteristic
303C22×C4#12111yescharacteristic
304C22×C4#12111yescharacteristic
305C22×C4#12311yescharacteristic
306C22×C4#12311yescharacteristic
307C22×C4#12311yescharacteristic
308C22×C4#12311yescharacteristic
309C22×C4#12711yescharacteristic
310C22×C4C2×SD1612yes—
311C22×C4C2×Q1612yes—
312C22×C4#13712yes—
313C22×C4#13712yes—
314M16—24no—
315M16—24no—
316M16—24no—
317M16—44no—
318M16—81no—
319M16—81no—
320M16#10318yes—
321C2×C8—24no—
322C2×C8—24no—
323C2×C8—24no—
324C2×C8—42no—
325C2×C8—42no—
326C2×C8—42no—
327C2×C8—42no—
328C2×C8—44no—
329C2×C8—82no—
330C2×C8—82no—
331C2×C8—82no—
332C2×C8—81no—
333C2×C8—81no—
334C2×C8—82no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—42no—
346C4⋊C4—42no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—42no—
353C4⋊C4—42no—
354C4⋊C4—42no—
355C4⋊C4—41no—
356C4⋊C4—42no—
357C4⋊C4—42no—
358C4⋊C4—42no—
359C22⋊C4—42no—
360C22⋊C4—42no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C42—42no—
364C42—42no—
365C42—42no—
366C42—42no—
367C42C2×C22⋊C411yescharacteristic
368C42C2×C22⋊C411yescharacteristic
369C42C4×D411yescharacteristic
370C42C4×D411yescharacteristic
371C42#12011yescharacteristic
372C42#12011yescharacteristic
373C42#12011yescharacteristic
374C42#12011yescharacteristic
375C42#12011yescharacteristic
376C42#12011yescharacteristic
377C42#12111yescharacteristic
378C42#12111yescharacteristic
379C42#12111yescharacteristic
380C42#12111yescharacteristic
381C42#12411yescharacteristic
382C42#12711yescharacteristic
383C23—41no—
384C23—41no—
385C23#39011yescharacteristic
386C23#39411yescharacteristic
387C23#39411yescharacteristic
388C23#48712yes—
389C23#49112yes—
390Q8—44no—
391Q8—44no—
392Q8—44no—
393Q8—82no—
394Q8—82no—
395Q8—82no—
396Q8—82no—
397Q8—82no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—82no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—82no—
418C2×C4#37911yescharacteristic
419C2×C4#38611yescharacteristic
420C2×C4#38611yescharacteristic
421C2×C4#38611yescharacteristic
422C2×C4#38611yescharacteristic
423C2×C4#39011yescharacteristic
424C2×C4#39211yescharacteristic
425C2×C4#39211yescharacteristic
426C2×C4#39211yescharacteristic
427C2×C4#39211yescharacteristic
428C2×C4#39411yescharacteristic
429C2×C4#39411yescharacteristic
430C2×C4C2×#10312yes—
431C2×C4#41912yes—
432C2×C4#44812yes—
433C2×C4#44812yes—
434C2×C4#45112yes—
435C2×C4#45112yes—
436C2×C4#46112yes—
437C2×C4#46112yes—
438C2×C4#46212yes—
439C2×C4#46212yes—
440C2×C4#49211yescharacteristic
441C2×C4#49411yescharacteristic
442C2×C4#49711yescharacteristic
443C2×C4#49711yescharacteristic
444C8—28no—
445C8—82no—
446C8—82no—
447C8—82no—
448C8—82no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—42no—
456C22—42no—
457C22#143811yescharacteristic
458C22#195611yescharacteristic
459C22#196011yescharacteristic
460C22#204312yes—
461C22#204312yes—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—82no—
470C4—82no—
471C4—82no—
472C4—82no—
473C4#178712yes—
474C4#188112yes—
475C4#198112yes—
476C4#201311yescharacteristic
477C4#201311yescharacteristic
478C4#201611yescharacteristic
479C4#201611yescharacteristic
480C2—21no—
481C2—21no—
482C2—22no—
483C2—22no—
484C2#1101011yescharacteristic
485C2#1101811yescharacteristic
486C2#1103211yescharacteristic
subgroupG/H
centerC2×C4#392
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC22#1438
prime radicalC24#124
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#606632
C2×#15422
#174862
C2×#14812
#108532
#79322