Finite Group Databasebeta

← #25014921

Subgroups — #25014921

Order 11008.

472 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139581C211yesmaximal, characteristic
2C2×#14582698C211yesmaximal, characteristic
3C2×#14582697C211yesmaximal, characteristic
4C2×#14582697C211yesmaximal, characteristic
5#19134589C211yesmaximal, characteristic
6#101×Dic43C211yesmaximal, characteristic
7C2×C43×#356C211yesmaximal, characteristic
8C2×#13063323C411yescharacteristic
9C2×#13063323C2211yescharacteristic
10C2×Q8×Dic43C2211yescharacteristic
11#14582922—21no—
12C2×#13063244C2211yescharacteristic
13C2×#13063244C2211yescharacteristic
14M16×Dic43—21no—
15#14582832—21no—
16#14582832—21no—
17#14582806C411yescharacteristic
18#14582805C411yescharacteristic
19#14582794—21no—
20#14582794—21no—
21C4×Dic43⋊C4C411yescharacteristic
22#14582698—22no—
23#14582697—22no—
24#14582697—22no—
25#14582667—21no—
26#14582667—21no—
27C2×C4⋊Q8×C43C2211yescharacteristic
28C2×#101×C43C2211yescharacteristic
29C2×#101×C43C2211yescharacteristic
30C43×#356—22no—
31C22×Dic86C2×C411yescharacteristic
32C2×#10621877—21no—
33C2×#10621877—21no—
34#13063323—21no—
35#13063323—21no—
36#13063323—21no—
37#13063323—21no—
38#13063323—41no—
39#13063323—41no—
40Q8×Dic43—41no—
41Q8×Dic43—41no—
42C2×C4⋊Dic43C2×C411yescharacteristic
43C2×C4⋊Dic43D411yescharacteristic
44C2×C4⋊Dic43D411yescharacteristic
45C2×Dic43⋊C4—21no—
46C2×Dic43⋊C4—21no—
47C2×Dic43⋊C4—21no—
48C2×Dic43⋊C4—21no—
49C2×Dic43⋊C4—21no—
50C2×C4×Dic43C2×C411yescharacteristic
51C2×C4×Dic43C2×C411yescharacteristic
52C2×C4×Dic43D411yescharacteristic
53C2×C4×Dic43D411yescharacteristic
54Dic43⋊C8—41no—
55Dic43⋊C8—41no—
56#13063244—21no—
57#13063244—21no—
58#13063244—21no—
59#13063244D412yes—
60#13063235—41no—
61C8×Dic43—41no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C43⋊#95—21no—
65C43⋊#95—21no—
66C43⋊#95—21no—
67C22×Q8×C43C2×C411yescharacteristic
68C22×Q8×C43C2311yescharacteristic
69C2×M16×C43—21no—
70C2×M16×C43—21no—
71C4⋊Q8×C43—21no—
72C4⋊Q8×C43—21no—
73C4⋊Q8×C43—21no—
74C4⋊Q8×C43—21no—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C42×C43C2×C411yescharacteristic
78#101×C43—21no—
79#101×C43—21no—
80#101×C43—21no—
81#101×C43D412yes—
82C2×Q8×C43—21no—
83C2×Q8×C43—21no—
84C2×Q8×C43—41no—
85C2×Q8×C43—41no—
86C2×Q8×C43—41no—
87C2×Q8×C43—41no—
88C2×Q8×C43C2×D411yescharacteristic
89C2×Q8×C43C2×D411yescharacteristic
90C2×Q8×C43#4111yescharacteristic
91C2×Q8×C43#4111yescharacteristic
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43C22×C411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×Dic43—21no—
98C22×Dic43—21no—
99C22×Dic43C22⋊C411yescharacteristic
100C22×Dic43C22⋊C411yescharacteristic
101C22×Dic43C22⋊C411yescharacteristic
102C22×Dic43C22⋊C411yescharacteristic
103C2×Dic86—21no—
104C2×Dic86—21no—
105C2×Dic86—41no—
106C2×Dic86—41no—
107M16×C43—22no—
108M16×C43—41no—
109M16×C43—41no—
110M16×C43—41no—
111C2×C8×C43—41no—
112C2×C8×C43—41no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C4⋊C4×C43—41no—
116C4⋊C4×C43—41no—
117C42×C43—21no—
118C42×C43—21no—
119C4⋊Dic43—41no—
120C4⋊Dic43—41no—
121C4⋊Dic43—41no—
122Dic43⋊C4—24no—
123Dic43⋊C4—42no—
124Dic43⋊C4—41no—
125Dic43⋊C4—41no—
126Dic43⋊C4—41no—
127Dic43⋊C4—41no—
128Dic43⋊C4—41no—
129Dic43⋊C4—41no—
130C4×Dic43—21no—
131C4×Dic43—21no—
132C4×Dic43—21no—
133C4×Dic43—21no—
134C4×Dic43—21no—
135C4×Dic43—21no—
136C4×Dic43—21no—
137C4×Dic43—21no—
138#10621877—22no—
139#10621877—41no—
140#10621877—41no—
141#10621877—41no—
142C2×C43⋊C8—41no—
143C2×C43⋊C8—41no—
144C23×C43C2×C22⋊C411yescharacteristic
145Q8×C43—41no—
146Q8×C43—41no—
147Q8×C43—41no—
148Q8×C43—41no—
149Q8×C43—81no—
150Q8×C43—81no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—22no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43C4×D411yescharacteristic
164C2×C4×C43C4×D411yescharacteristic
165C2×C4×C43#12111yescharacteristic
166C2×C4×C43#12111yescharacteristic
167C2×C4×C43#12411yescharacteristic
168C2×C4×C43#12711yescharacteristic
169C2×Dic43—22no—
170C2×Dic43—22no—
171C2×Dic43—21no—
172C2×Dic43—21no—
173C2×Dic43—21no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—41no—
178C2×Dic43—41no—
179C2×Dic43—41no—
180C2×Dic43—41no—
181C2×Dic43—41no—
182C2×Dic43#9911yescharacteristic
183C2×Dic43#9911yescharacteristic
184Dic86—81no—
185Dic86—81no—
186C8×C43—42no—
187C8×C43—81no—
188C43⋊C8—42no—
189C43⋊C8—81no—
190#13227—431nomaximal, Sylow
191C22×C43—21no—
192C22×C43—21no—
193C22×C43#39011yescharacteristic
194C22×C43C2×#9911yescharacteristic
195C22×C43#41011yescharacteristic
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—21no—
202C4×C43—42no—
203C4×C43—81no—
204Dic43—21no—
205Dic43—42no—
206Dic43—41no—
207Dic43—41no—
208Dic43—41no—
209Dic43—81no—
210Dic43#35612yescomplemented
211#2546—431no—
212C2×#356—431no—
213C2×#356—431no—
214C2×#356—431no—
215C2×#356D4311yescharacteristic
216#1801—431no—
217C4×#101—431no—
218C2×C43—21no—
219C2×C43—21no—
220C2×C43#196411yescharacteristic
221C2×C43C2×#35611yescharacteristic
222C2×C43#213511yescharacteristic
223C2×C4⋊Q8—431no—
224C2×C4⋊Q8—431no—
225C2×C4⋊Q8C2×D4311yescharacteristic
226C2×C4×Q8—431no—
227#423—861no—
228C2×#101—431no—
229C2×#101—431no—
230C2×#101C2×D4311yescharacteristic
231C2×#101C2×D4311yescharacteristic
232C4×M16—861no—
233#398—861no—
234#398—861no—
235#391—431no—
236#391—431no—
237#389—861no—
238#389—861no—
239C4×C4⋊C4—431no—
240#356—22no—
241#356—862no—
242#356—862no—
243#356—862no—
244#343—861no—
245#343—861no—
246C43#1322711yescharacteristic, complemented, Sylow
247C22×Q8—431no—
248C22×Q8C4×D4311yescharacteristic
249C22×Q8C22×D4311yescharacteristic
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—861no—
253C2×M16—861no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—861no—
259C4⋊Q8—861no—
260C4⋊Q8—861no—
261C4⋊Q8—861no—
262C4⋊Q8—1721no—
263C4⋊Q8—1721no—
264C4×Q8—1721no—
265C4×Q8—1721no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—431no—
269C2×C4⋊C4—431no—
270C2×C4⋊C4—431no—
271C2×C4⋊C4—861no—
272C2×C4⋊C4—861no—
273C2×C4⋊C4—861no—
274C2×C4⋊C4—861no—
275C2×C4⋊C4—861no—
276C2×C42—431no—
277C2×C42—431no—
278C2×C42—431no—
279C2×C42—431no—
280C2×C42C4×D4311yescharacteristic
281C4⋊C8—1721no—
282C4⋊C8—1721no—
283#101—21no—
284#101—21no—
285#101—21no—
286#101—432no—
287#101—861no—
288#101—861no—
289#101—861no—
290#101C22⋊D4312yes—
291#97—1721no—
292C4×C8—1721no—
293#95—861no—
294#95—861no—
295#95—861no—
296#95—861no—
297#95—861no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—861no—
305C2×Q8—861no—
306C2×Q8—1721no—
307C2×Q8—1721no—
308C2×Q8#1062189811yescharacteristic
309C2×Q8D4×D4311yescharacteristic
310C2×Q8#1062190011yescharacteristic
311C2×Q8C2×C22⋊D4311yescharacteristic
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—431no—
315C22×C4—431no—
316C22×C4—431no—
317C22×C4—431no—
318C22×C4—861no—
319C22×C4—861no—
320C22×C4C2×C4×D4311yescharacteristic
321C22×C4D4×D4311yescharacteristic
322C22×C4D4×D4311yescharacteristic
323M16—22no—
324M16—41no—
325M16—41no—
326M16—41no—
327M16—862no—
328M16—1721no—
329M16—1721no—
330M16—1721no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—1721no—
334C2×C8—1721no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—864no—
340C4⋊C4—1721no—
341C4⋊C4—1721no—
342C4⋊C4—1721no—
343C4⋊C4—1721no—
344C4⋊C4—1721no—
345C4⋊C4—1722no—
346C4⋊C4—1721no—
347C4⋊C4—1721no—
348C4⋊C4—1721no—
349C4⋊C4—1721no—
350C42—21no—
351C42—21no—
352C42—861no—
353C42—861no—
354C42—861no—
355C42—861no—
356C42—861no—
357C42—861no—
358C42—861no—
359C42—861no—
360C23C22⋊C4×D4311yescharacteristic
361Q8—41no—
362Q8—41no—
363Q8—41no—
364Q8—41no—
365Q8—81no—
366Q8—81no—
367Q8—3441no—
368Q8—3441no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—431no—
382C2×C4—431no—
383C2×C4—862no—
384C2×C4—862no—
385C2×C4—861no—
386C2×C4—861no—
387C2×C4—861no—
388C2×C4—1721no—
389C2×C4—1721no—
390C2×C4—1721no—
391C2×C4—1721no—
392C2×C4—1721no—
393C2×C4—1721no—
394C2×C4—1721no—
395C2×C4—1721no—
396C2×C4(C22⋊D43)⋊C411yescharacteristic
397C2×C4C4×C22⋊D4311yescharacteristic
398C2×C4#1306329711yescharacteristic
399C2×C4#1306329811yescharacteristic
400C2×C4#1306331111yescharacteristic
401C2×C4#1306332111yescharacteristic
402C8—42no—
403C8—81no—
404C8—3441no—
405C8—1722no—
406C22—21no—
407C22—21no—
408C22#1458279911yescharacteristic
409C22#99×D4311yescharacteristic
410C22#1458287111yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—42no—
418C4—81no—
419C4—432no—
420C4—861no—
421C4—3441no—
422C4—1722no—
423C4—1721no—
424C4—1721no—
425C4—1721no—
426C2—21no—
427C2—21no—
428C2#1913542911yescharacteristic
429C2#356×D4311yescharacteristic
430C2#1913628811yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC22×Q8C22×D43
FittingC2×C43×#356C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC22×Q8×C43C23
hypercenterC2×#356D43
hypocenterC43#13227
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
210. Dic43#356semidirect
246. C43#13227semidirect

Maximal subgroups

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

subgroupindex
#191395812
C2×#145826982
C2×#145826972
#191345892
#101×Dic432
C2×C43×#3562
#1322743