Finite Group Databasebeta

← #24996897

Subgroups — #24996897

Order 11008.

610 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C2×#14583232C211yesmaximal, characteristic
2#19140410C211yesmaximal, characteristic
3C2×#14582839C211yesmaximal, characteristic
4#19134686C211yesmaximal, characteristic
5C2×#14582624C211yesmaximal, characteristic
6#19132474C211yesmaximal, characteristic
7C2×C43×#328C211yesmaximal, characteristic
8C22×C4⋊Dic43C2211yescharacteristic
9C22×Dic43⋊C4C2211yescharacteristic
10#14583232—22no—
11#14583232—22no—
12C2×#13063258—21no—
13C2×#13063249—21no—
14C2×C22⋊(C43⋊C8)C2211yescharacteristic
15#14582839—22no—
16#14582839—22no—
17#14582837—21no—
18#14582832—22no—
19#14582818—21no—
20#14582771—21no—
21#14582760—21no—
22#14582759C2211yescharacteristic
23C2×C43⋊#95—21no—
24C2×C43⋊#95—21no—
25#14582662—22no—
26#14582624—22no—
27C2×C22⋊Q8×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×#95×C43C2211yescharacteristic
30C43×#328—22no—
31C23×Dic43—21no—
32C23×Dic43D411yescharacteristic
33C23×Dic43D411yescharacteristic
34C22×C43⋊C8—21no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43D412yes—
41C2×C4⋊Dic43D412yes—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4—21no—
45C2×Dic43⋊C4—21no—
46C2×Dic43⋊C4—21no—
47C2×Dic43⋊C4—21no—
48C2×Dic43⋊C4—22no—
49C2×C22⋊Dic43—21no—
50#13063258—24no—
51#13063249—24no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)D412yes—
54C43⋊#95—22no—
55C43⋊#95—22no—
56C43⋊#95—22no—
57C43⋊#95—24no—
58C43⋊#95—24no—
59C43⋊#95—21no—
60C22×Q8×C43D411yescharacteristic
61C23×C4×C43—21no—
62C23×C4×C43C2311yescharacteristic
63C22×C8×C43—21no—
64C22⋊Q8×C43—21no—
65C22⋊Q8×C43—21no—
66C22⋊Q8×C43—21no—
67C22⋊Q8×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43D411yescharacteristic
70C2×C22⋊C4×C43—21no—
71C22⋊C8×C43—21no—
72C22⋊C8×C43—21no—
73#95×C43—21no—
74#95×C43D412yes—
75C24×C43C2×D411yescharacteristic
76C2×Q8×C43—21no—
77C2×Q8×C43—21no—
78C2×Q8×C43—42no—
79C22×C4×C43—22no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—42no—
83C22×C4×C43—42no—
84C22×C4×C43—42no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C22×Dic43—21no—
94C22×Dic43—21no—
95C22×Dic43—22no—
96C22×Dic43—21no—
97C22×Dic43—22no—
98C22×Dic43—21no—
99C22×Dic43—21no—
100C22×Dic43—21no—
101C22×Dic43—21no—
102C22×Dic43—21no—
103C22×Dic43—21no—
104C22×Dic43—42no—
105C22×Dic43—44no—
106C22×Dic43—41no—
107C22×Dic43—41no—
108C22×Dic43Q1612yes—
109C2×C8×C43—42no—
110C2×C8×C43—41no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C22⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C22⋊Dic43—41no—
118C22⋊Dic43—41no—
119C4⋊Dic43—22no—
120C4⋊Dic43—22no—
121C4⋊Dic43—41no—
122C4⋊Dic43—41no—
123C4⋊Dic43—42no—
124Dic43⋊C4—41no—
125Dic43⋊C4—41no—
126Dic43⋊C4—41no—
127Dic43⋊C4—41no—
128Dic43⋊C4—82no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—42no—
131C23×C43—22no—
132C23×C43—22no—
133C23×C43#12011yescharacteristic
134C23×C43#12011yescharacteristic
135C23×C43#12111yescharacteristic
136C23×C43C2×Q1611yescharacteristic
137C23×C43#13511yescharacteristic
138C23×C43#13711yescharacteristic
139C23×C43#13711yescharacteristic
140Q8×C43—42no—
141Q8×C43—81no—
142C2×C4×C43—22no—
143C2×C4×C43—22no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—42no—
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43—82no—
156C2×C4×C43—82no—
157C2×C4×C43#12011yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C2×C4×C43#12111yescharacteristic
160C2×C4×C43#12711yescharacteristic
161C2×Dic43—22no—
162C2×Dic43—22no—
163C2×Dic43—22no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—44no—
169C2×Dic43—42no—
170C2×Dic43—41no—
171C2×Dic43—42no—
172C2×Dic43—42no—
173C2×Dic43—42no—
174C2×Dic43—42no—
175C2×Dic43—42no—
176C2×Dic43—82no—
177C2×Dic43—82no—
178C2×Dic43—81no—
179C8×C43—81no—
180C43⋊C8—42no—
181#9929—431nomaximal, Sylow
182C22×C43—22no—
183C22×C43—22no—
184C22×C43—22no—
185C22×C43—22no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43#39211yescharacteristic
191C22×C43#45111yescharacteristic
192C22×C43#45111yescharacteristic
193C22×C43#45211yescharacteristic
194C22×C43#45211yescharacteristic
195C22×C43#45412yes—
196C22×C43#45812yes—
197C22×C43#46711yescharacteristic
198C22×C43#47011yescharacteristic
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—21no—
202C4×C43—21no—
203C4×C43—82no—
204C4×C43—81no—
205C4×C43—81no—
206Dic43—42no—
207Dic43—82no—
208Dic43—82no—
209Dic43—81no—
210C2×#484—431no—
211#2627—431no—
212C2×#400—431no—
213#1824—431no—
214C2×#328D4311yescharacteristic
215C2×#324—431no—
216#1294—431no—
217C2×C43—21no—
218C2×C43—21no—
219C2×C43—21no—
220C2×C43—21no—
221C2×C43#161512yes—
222C2×C43#161712yes—
223C2×C43#200111yescharacteristic
224C2×C43#200311yescharacteristic
225C2×C43#202211yescharacteristic
226C2×C22⋊Q8C2×D4311yescharacteristic
227C22×C4⋊C4—431no—
228C22×C4⋊C4—431no—
229#484—862no—
230#484—862no—
231C2×#107—861no—
232C2×#103—861no—
233C2×C22⋊C8—431no—
234C2×C22⋊C8C2×D4311yescharacteristic
235#400—862no—
236#400—861no—
237#400—862no—
238#398—862no—
239#395—861no—
240#385—861no—
241#381—861no—
242#380—431no—
243C2×#95—861no—
244C2×#95—861no—
245C2×#95C2×D4311yescharacteristic
246#340—862no—
247#328—22no—
248#324—862no—
249C43#992911yescharacteristic, complemented, Sylow
250C22×Q8D17211yescharacteristic
251C23×C4—21no—
252C23×C4—431no—
253C23×C4—431no—
254C23×C4—861no—
255C23×C4C22×D4311yescharacteristic
256C22×C8—21no—
257C22×C8—861no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C22⋊Q8—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—432no—
264C2×C4⋊C4—432no—
265C2×C4⋊C4—861no—
266C2×C4⋊C4—861no—
267C2×C4⋊C4—861no—
268C2×C4⋊C4—861no—
269C2×C4⋊C4—862no—
270C2×C4⋊C4—861no—
271C2×C4⋊C4—861no—
272C2×C4⋊C4—861no—
273C2×C4⋊C4—861no—
274C2×C4⋊C4—861no—
275C2×C4⋊C4—861no—
276C2×C4⋊C4—861no—
277C2×C4⋊C4D17211yescharacteristic
278C2×C22⋊C4—21no—
279C2×C22⋊C4—861no—
280#107—864no—
281#103—864no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—432no—
285C22⋊C8—861no—
286#95—21no—
287#95—864no—
288#95—864no—
289#95—862no—
290#95—862no—
291#95—862no—
292#95—861no—
293#95C22⋊D4312yes—
294C24D4×D4311yescharacteristic
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—42no—
298C22×C4—22no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—432no—
307C22×C4—861no—
308C22×C4—861no—
309C22×C4—861no—
310C22×C4—861no—
311C22×C4—861no—
312C22×C4—861no—
313C22×C4—861no—
314C22×C4—862no—
315C22×C4—861no—
316C22×C4—862no—
317C22×C4—861no—
318C22×C4—1724no—
319C22×C4—1721no—
320C22×C4—1721no—
321C22×C4—1722no—
322C22×C4C2×D17211yescharacteristic
323C22×C4#1062189811yescharacteristic
324C22×C4D4×D4311yescharacteristic
325C22×C4D4×D4311yescharacteristic
326C22×C4D4×D4311yescharacteristic
327C22×C4C2×C22⋊D4311yescharacteristic
328C2×C8—42no—
329C2×C8—41no—
330C2×C8—862no—
331C2×C8—1722no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—862no—
337C4⋊C4—862no—
338C4⋊C4—3442no—
339C4⋊C4—1722no—
340C4⋊C4—1721no—
341C4⋊C4—1721no—
342C4⋊C4—1721no—
343C4⋊C4—1721no—
344C4⋊C4—1721no—
345C4⋊C4—1721no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—1721no—
349C22⋊C4—1721no—
350C23—22no—
351C23—22no—
352C23#1306329311yescharacteristic
353C23#1306329511yescharacteristic
354C23#1306329811yescharacteristic
355C23Q16×D4311yescharacteristic
356C23#1306334611yescharacteristic
357C23#1306335411yescharacteristic
358C23#1306335711yescharacteristic
359Q8—42no—
360Q8—81no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4—862no—
377C2×C4—862no—
378C2×C4—862no—
379C2×C4—3442no—
380C2×C4—3442no—
381C2×C4—3441no—
382C2×C4—1724no—
383C2×C4—1722no—
384C2×C4—1722no—
385C2×C4—1721no—
386C2×C4—1722no—
387C2×C4—1722no—
388C2×C4—1722no—
389C2×C4—1722no—
390C2×C4—1721no—
391C2×C4—1721no—
392C2×C4—1721no—
393C2×C4—1721no—
394C2×C4#1306329511yescharacteristic
395C2×C4#1306329811yescharacteristic
396C2×C4#1306329911yescharacteristic
397C2×C4#1306332111yescharacteristic
398C8—81no—
399C8—1722no—
400C22—21no—
401C22—21no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—21no—
407C22—21no—
408C22#1458280811yescharacteristic
409C22#1458305311yescharacteristic
410C22#1458305611yescharacteristic
411C22#1458305811yescharacteristic
412C22#1458306411yescharacteristic
413C22#1458307312yes—
414C22#1458309012yes—
415C22#1458313911yescharacteristic
416C22#1458315611yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—82no—
422C4—81no—
423C4—81no—
424C4—3442no—
425C4—3442no—
426C4—3441no—
427C4—1722no—
428C2—21no—
429C2—21no—
430C2—21no—
431C2—21no—
432C2#1913362912yes—
433C2#1913363812yes—
434C2#1913560411yescharacteristic
435C2#1913561611yescharacteristic
436C2#1913572511yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC2×C43×#328C2
socleC23×C43#120
prime radicalC24×C43C2×D4
hypercenterC2×#328D43
hypocenterC43#9929
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
249. C43#9929semidirect

Maximal subgroups

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

subgroupindex
C2×#145832322
#191404102
C2×#145828392
#191346862
C2×#145826242
#191324742
C2×C43×#3282
#992943