Finite Group Databasebeta

← #24995609

Subgroups — #24995609

Order 11008.

526 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142968C211yesmaximal, characteristic
2#19134449C211yesmaximal, characteristic, complemented
3#97×Dic43C211yesmaximal, characteristic, complemented
4C2×#14582641C211yesmaximal, characteristic, complemented
5C2×#14582638C211yesmaximal, characteristic
6C2×#14582638C211yesmaximal, characteristic
7C2×C43×#330C211yesmaximal, characteristic, complemented
8C2×#13063313C2211yescharacteristic
9C2×Dic43⋊C8—21no—
10C2×#13063236C2211yescharacteristic
11C2×#13063236C2211yescharacteristic
12C2×#13063235—21no—
13C2×C8×Dic43—21no—
14#14582804C411yescharacteristic
15#14582804C411yescharacteristic
16#14582800C411yescharacteristic
17#14582800C411yescharacteristic
18#14582789—21no—
19#14582789—21no—
20#14582789—21no—
21#14582789—21no—
22C42×Dic43C2211yescharacteristic
23#14582653—21no—
24#14582641—22no—
25#14582638—22no—
26#14582638—22no—
27C2×#125×C43C2211yescharacteristic
28C2×#97×C43C2211yescharacteristic
29C2×#97×C43C2211yescharacteristic
30C43×#330—22no—
31C22×Dic86C2×C411yescharacteristic
32C22×D172C2×C411yescharacteristic
33C22×C43⋊C8—21no—
34C22×C43⋊C8—21no—
35#13063313—21no—
36#13063313—21no—
37#13063313—21no—
38#13063313—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×C4×Dic43C2×C411yescharacteristic
46C2×C4×Dic43C2×C411yescharacteristic
47C2×C4×Dic43D411yescharacteristic
48C2×C4×Dic43D411yescharacteristic
49C2×C4×Dic43D411yescharacteristic
50C2×C4×Dic43D411yescharacteristic
51Dic43⋊C8—24no—
52#13063236—21no—
53#13063236—21no—
54#13063236—21no—
55#13063236D412yes—
56#13063235—24no—
57C8×Dic43—24no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C22×C8×C43—21no—
63C22×C8×C43—21no—
64#125×C43—21no—
65#125×C43—21no—
66#125×C43—21no—
67#125×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43C2×C411yescharacteristic
71C2×C4⋊C4×C43C2×C411yescharacteristic
72C2×C42×C43C2311yescharacteristic
73#97×C43—21no—
74#97×C43—21no—
75#97×C43—21no—
76#97×C43D412yes—
77C23×D43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43C22×C411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×Dic43—21no—
84C22×Dic43C22⋊C411yescharacteristic
85C22×Dic43C22⋊C411yescharacteristic
86C22×Dic43C22⋊C411yescharacteristic
87C22×Dic43C22⋊C411yescharacteristic
88C2×D172—21no—
89C2×D172—21no—
90C2×D172—41no—
91C2×D172—41no—
92C2×Dic86—21no—
93C2×Dic86—21no—
94C2×Dic86—41no—
95C2×Dic86—41no—
96C2×C8×C43—22no—
97C2×C8×C43—22no—
98C2×C8×C43—22no—
99C2×C8×C43—22no—
100C2×C8×C43—41no—
101C2×C8×C43—41no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C4⋊C4×C43—41no—
109C4⋊C4×C43—41no—
110C42×C43C2×D411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43#4111yescharacteristic
113C42×C43#4111yescharacteristic
114(C2×D43)⋊C4—42no—
115(C2×D43)⋊C4—41no—
116(C2×D43)⋊C4—41no—
117(C2×D43)⋊C4—41no—
118(C2×D43)⋊C4—41no—
119(C2×D43)⋊C4—42no—
120(C2×D43)⋊C4—42no—
121(C2×D43)⋊C4—42no—
122C4×Dic43—22no—
123C4×Dic43—22no—
124C4×Dic43—22no—
125C4×Dic43—41no—
126C4×Dic43—41no—
127C4×Dic43—41no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—41no—
133C2×C43⋊C8—41no—
134C23×C43C2×C22⋊C411yescharacteristic
135C22×D43—41no—
136C22×D43—41no—
137C22×D43—41no—
138C22×D43—41no—
139C22×D43—41no—
140C22×D43—41no—
141C22×D43—41no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43C4×D411yescharacteristic
155C2×C4×C43C4×D411yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12411yescharacteristic
159C2×C4×C43#12711yescharacteristic
160C2×Dic43—21no—
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43#10412yes—
173C2×Dic43#10412yes—
174C2×Dic43#10412yes—
175D172—81no—
176D172—81no—
177Dic86—81no—
178Dic86—81no—
179C8×C43—24no—
180C8×C43—42no—
181C43⋊C8—24no—
182C43⋊C8—42no—
183#9687—431nomaximal, Sylow
184C22×C43#39011yescharacteristic
185C22×C43#41311yescharacteristic
186C22×C43#41311yescharacteristic
187C22×C43C2×#10411yescharacteristic
188C22×C43C2×#10411yescharacteristic
189C22×C43C2×#10411yescharacteristic
190C22×C43#42111yescharacteristic
191C2×D43—81no—
192C2×D43—81no—
193C2×D43—81no—
194C2×D43—81no—
195C2×D43—81no—
196C2×D43—81no—
197C2×D43—81no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—21no—
202C4×C43—21no—
203C4×C43—21no—
204C4×C43—81no—
205C4×C43—81no—
206Dic43—22no—
207Dic43—22no—
208Dic43—22no—
209Dic43—41no—
210Dic43—81no—
211#2861—431no—
212#1767—431no—
213C4×#97—431no—
214C2×#330—431no—
215C2×#330D4311yescharacteristic, complemented
216C2×#329—431no—
217C2×#329—431no—
218C2×C43#152411yescharacteristic
219C2×C43#152411yescharacteristic
220C2×C43#152911yescharacteristic
221C2×C43#153211yescharacteristic
222C2×C43#196211yescharacteristic
223C2×C43#196711yescharacteristic
224C2×C43#198011yescharacteristic
225D43—161no—
226C2×#125C2×D4311yescharacteristic
227C2×#124—431no—
228C2×C4⋊C8—861no—
229C2×#97—431no—
230C2×#97—431no—
231C2×#97—861no—
232C2×#97C2×D4311yescharacteristic
233C2×#97C2×D4311yescharacteristic
234C2×C4×C8—861no—
235#391—431no—
236#391—431no—
237#390—431no—
238#390—431no—
239#388—861no—
240#388—861no—
241#388—861no—
242#388—861no—
243C43—431no—
244#336—861no—
245#330—22no—
246#330—862no—
247#329—862no—
248#329—862no—
249C43#968711yescharacteristic, complemented, Sylow
250C22×Q8—431no—
251C22×D4—431no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—861no—
255C22×C8—861no—
256#125—21no—
257#125—21no—
258#125—21no—
259#125—21no—
260#124—861no—
261#124—861no—
262#124—861no—
263#124—861no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4C4×D4311yescharacteristic
267C2×C4⋊C4C4×D4311yescharacteristic
268C2×C22⋊C4—861no—
269C2×C22⋊C4—861no—
270C2×C22⋊C4—861no—
271C2×C22⋊C4—861no—
272C2×C22⋊C4—861no—
273C2×C22⋊C4—861no—
274C2×C42—431no—
275C2×C42—431no—
276C2×C42—431no—
277C2×C42—431no—
278C2×C42—431no—
279C2×C42—431no—
280C2×C42C22×D4311yescharacteristic
281C4⋊C8—864no—
282#97—21no—
283#97—21no—
284#97—21no—
285#97—432no—
286#97—864no—
287#97—861no—
288#97—861no—
289#97—861no—
290#97C22⋊D4312yes—
291C4×C8—864no—
292#95—861no—
293#95—861no—
294#95—861no—
295#95—861no—
296C24—861no—
297C2×Q8—861no—
298C2×Q8—861no—
299C2×Q8—1721no—
300C2×Q8—1721no—
301C2×D4—861no—
302C2×D4—861no—
303C2×D4—1721no—
304C2×D4—1721no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—431no—
308C22×C4—431no—
309C22×C4—431no—
310C22×C4—431no—
311C22×C4—861no—
312C22×C4C2×C4×D4311yescharacteristic
313C22×C4D4×D4311yescharacteristic
314C22×C4D4×D4311yescharacteristic
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—862no—
322C2×C8—862no—
323C2×C8—862no—
324C2×C8—862no—
325C2×C8—1721no—
326C2×C8—1721no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C22⋊C4—1722no—
336C22⋊C4—1722no—
337C22⋊C4—1722no—
338C22⋊C4—1722no—
339C22⋊C4—1721no—
340C22⋊C4—1721no—
341C22⋊C4—1721no—
342C22⋊C4—1721no—
343C42—862no—
344C42—862no—
345C42—862no—
346C42—1721no—
347C42—1721no—
348C42—1721no—
349C42#1062189811yescharacteristic
350C42D4×D4311yescharacteristic
351C42#1062190011yescharacteristic
352C42C2×C22⋊D4311yescharacteristic
353C23—1721no—
354C23—1721no—
355C23—1721no—
356C23—1721no—
357C23—1721no—
358C23—1721no—
359C23—1721no—
360C23C22⋊C4×D4311yescharacteristic
361Q8—3441no—
362Q8—3441no—
363D4—3441no—
364D4—3441no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—432no—
378C2×C4—432no—
379C2×C4—432no—
380C2×C4—861no—
381C2×C4—861no—
382C2×C4—861no—
383C2×C4—861no—
384C2×C4—861no—
385C2×C4—861no—
386C2×C4—861no—
387C2×C4—861no—
388C2×C4—861no—
389C2×C4—1721no—
390C2×C4—1721no—
391C2×C4—1721no—
392C2×C4(C22⋊D43)⋊C411yescharacteristic
393C2×C4C4×C22⋊D4311yescharacteristic
394C2×C4#1306329711yescharacteristic
395C2×C4#1306329811yescharacteristic
396C2×C4#1306331111yescharacteristic
397C2×C4#1306332111yescharacteristic
398C8—24no—
399C8—42no—
400C8—864no—
401C8—1722no—
402C22—3441no—
403C22—3441no—
404C22—3441no—
405C22—3441no—
406C22—3441no—
407C22—3441no—
408C22—3441no—
409C22#1458279911yescharacteristic
410C22#1458288211yescharacteristic
411C22#1458288211yescharacteristic
412C22#104×D4311yescharacteristic
413C22#104×D4311yescharacteristic
414C22#104×D4311yescharacteristic
415C22#1458291411yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—81no—
423C4—81no—
424C4—862no—
425C4—862no—
426C4—862no—
427C4—3441no—
428C4—1721no—
429C2—6881no—
430C2#1913318211yescharacteristic
431C2#1913318211yescharacteristic
432C2#1913320111yescharacteristic
433C2#1913321411yescharacteristic
434C2#1913542111yescharacteristic
435C2#1913544311yescharacteristic
436C2#1913551211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#330C2
socleC23×C43C2×C22⋊C4
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenterC2×#330D43
hypocenterC43#9687
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
2. #19134449C2semidirect
3. #97×Dic43C2semidirect
4. C2×#14582641C2semidirect
7. C2×C43×#330C2semidirect
215. C2×#330D43semidirect
249. C43#9687semidirect

Maximal subgroups

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

subgroupindex
#191429682
#191344492
#97×Dic432
C2×#145826412
C2×#145826382
C2×C43×#3302
#968743