Finite Group Databasebeta

← #29598337

Subgroups — #29598337

Order 15616.

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#21450805C211yesmaximal, characteristic
2C2×#16839561C211yesmaximal, characteristic
3C2×#16839560C211yesmaximal, characteristic
4C2×#16839560C211yesmaximal, characteristic
5#21445813C211yesmaximal, characteristic
6#101×Dic61C211yesmaximal, characteristic
7C2×C61×#356C211yesmaximal, characteristic
8C2×#14519775C411yescharacteristic
9C2×#14519775C2211yescharacteristic
10C2×Q8×Dic61C2211yescharacteristic
11#16839785—21no—
12C2×#14519696C2211yescharacteristic
13C2×#14519696C2211yescharacteristic
14M16×Dic61—21no—
15#16839695—21no—
16#16839695—21no—
17#16839669C411yescharacteristic
18#16839668C411yescharacteristic
19#16839657—21no—
20#16839657—21no—
21C4×#11758196C411yescharacteristic
22#16839561—22no—
23#16839560—22no—
24#16839560—22no—
25#16839530—21no—
26#16839530—21no—
27C2×C4⋊Q8×C61C2211yescharacteristic
28C2×#101×C61C2211yescharacteristic
29C2×#101×C61C2211yescharacteristic
30C61×#356—22no—
31C22×Dic122C2×C411yescharacteristic
32C2×#11758194—21no—
33C2×#11758194—21no—
34#14519775—21no—
35#14519775—21no—
36#14519775—21no—
37#14519775—21no—
38#14519775—41no—
39#14519775—41no—
40Q8×Dic61—41no—
41Q8×Dic61—41no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×C4⋊Dic61D411yescharacteristic
44C2×C4⋊Dic61D411yescharacteristic
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×#11758196—21no—
49C2×#11758196—21no—
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61C2×C411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54#14519706—41no—
55#14519706—41no—
56#14519696—21no—
57#14519696—21no—
58#14519696—21no—
59#14519696D412yes—
60#14519687—41no—
61C8×Dic61—41no—
62#14519684—21no—
63#14519684—21no—
64#14519684—21no—
65#14519684—21no—
66#14519684—21no—
67C22×Q8×C61C2×C411yescharacteristic
68C22×Q8×C61C2311yescharacteristic
69C2×M16×C61—21no—
70C2×M16×C61—21no—
71C4⋊Q8×C61—21no—
72C4⋊Q8×C61—21no—
73C4⋊Q8×C61—21no—
74C4⋊Q8×C61—21no—
75C2×C4⋊C4×C61—21no—
76C2×C4⋊C4×C61—21no—
77C2×C42×C61C2×C411yescharacteristic
78#101×C61—21no—
79#101×C61—21no—
80#101×C61—21no—
81#101×C61D412yes—
82C2×Q8×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61—41no—
85C2×Q8×C61—41no—
86C2×Q8×C61—41no—
87C2×Q8×C61—41no—
88C2×Q8×C61C2×D411yescharacteristic
89C2×Q8×C61C2×D411yescharacteristic
90C2×Q8×C61#4111yescharacteristic
91C2×Q8×C61#4111yescharacteristic
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61C22×C411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×Dic61—21no—
98C22×Dic61—21no—
99C22×Dic61C22⋊C411yescharacteristic
100C22×Dic61C22⋊C411yescharacteristic
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C22⋊C411yescharacteristic
103C2×Dic122—21no—
104C2×Dic122—21no—
105C2×Dic122—41no—
106C2×Dic122—41no—
107M16×C61—22no—
108M16×C61—41no—
109M16×C61—41no—
110M16×C61—41no—
111C2×C8×C61—41no—
112C2×C8×C61—41no—
113C4⋊C4×C61—41no—
114C4⋊C4×C61—41no—
115C4⋊C4×C61—41no—
116C4⋊C4×C61—41no—
117C42×C61—21no—
118C42×C61—21no—
119C4⋊Dic61—41no—
120C4⋊Dic61—41no—
121C4⋊Dic61—41no—
122#11758196—24no—
123#11758196—42no—
124#11758196—41no—
125#11758196—41no—
126#11758196—41no—
127#11758196—41no—
128#11758196—41no—
129#11758196—41no—
130C4×Dic61—21no—
131C4×Dic61—21no—
132C4×Dic61—21no—
133C4×Dic61—21no—
134C4×Dic61—21no—
135C4×Dic61—21no—
136C4×Dic61—21no—
137C4×Dic61—21no—
138#11758194—22no—
139#11758194—41no—
140#11758194—41no—
141#11758194—41no—
142C2×#92418—41no—
143C2×#92418—41no—
144C23×C61C2×C22⋊C411yescharacteristic
145Q8×C61—41no—
146Q8×C61—41no—
147Q8×C61—41no—
148Q8×C61—41no—
149Q8×C61—81no—
150Q8×C61—81no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—22no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61C4×D411yescharacteristic
164C2×C4×C61C4×D411yescharacteristic
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61#12411yescharacteristic
168C2×C4×C61#12711yescharacteristic
169C2×Dic61—22no—
170C2×Dic61—22no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61#9911yescharacteristic
183C2×Dic61#9911yescharacteristic
184Dic122—81no—
185Dic122—81no—
186C8×C61—42no—
187C8×C61—81no—
188#92418—42no—
189#92418—81no—
190#13227—611nomaximal, Sylow
191C22×C61—21no—
192C22×C61—21no—
193C22×C61#39011yescharacteristic
194C22×C61C2×#9911yescharacteristic
195C22×C61#41011yescharacteristic
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—42no—
203C4×C61—81no—
204Dic61—21no—
205Dic61—42no—
206Dic61—41no—
207Dic61—41no—
208Dic61—41no—
209Dic61—81no—
210Dic61#35612yescomplemented
211#2546—611no—
212C2×#356—611no—
213C2×#356—611no—
214C2×#356—611no—
215C2×#356D6111yescharacteristic
216#1801—611no—
217C4×#101—611no—
218C2×C61—21no—
219C2×C61—21no—
220C2×C61#196411yescharacteristic
221C2×C61C2×#35611yescharacteristic
222C2×C61#213511yescharacteristic
223C2×C4⋊Q8—611no—
224C2×C4⋊Q8—611no—
225C2×C4⋊Q8C2×D6111yescharacteristic
226C2×C4×Q8—611no—
227#423—1221no—
228C2×#101—611no—
229C2×#101—611no—
230C2×#101C2×D6111yescharacteristic
231C2×#101C2×D6111yescharacteristic
232C4×M16—1221no—
233#398—1221no—
234#398—1221no—
235#391—611no—
236#391—611no—
237#389—1221no—
238#389—1221no—
239C4×C4⋊C4—611no—
240#356—22no—
241#356—1222no—
242#356—1222no—
243#356—1222no—
244#343—1221no—
245#343—1221no—
246C61#1322711yescharacteristic, complemented, Sylow
247C22×Q8—611no—
248C22×Q8C4×D6111yescharacteristic
249C22×Q8C22×D6111yescharacteristic
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—1221no—
253C2×M16—1221no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—1221no—
259C4⋊Q8—1221no—
260C4⋊Q8—1221no—
261C4⋊Q8—1221no—
262C4⋊Q8—2441no—
263C4⋊Q8—2441no—
264C4×Q8—2441no—
265C4×Q8—2441no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—611no—
269C2×C4⋊C4—611no—
270C2×C4⋊C4—611no—
271C2×C4⋊C4—1221no—
272C2×C4⋊C4—1221no—
273C2×C4⋊C4—1221no—
274C2×C4⋊C4—1221no—
275C2×C4⋊C4—1221no—
276C2×C42—611no—
277C2×C42—611no—
278C2×C42—611no—
279C2×C42—611no—
280C2×C42C4×D6111yescharacteristic
281C4⋊C8—2441no—
282C4⋊C8—2441no—
283#101—21no—
284#101—21no—
285#101—21no—
286#101—612no—
287#101—1221no—
288#101—1221no—
289#101—1221no—
290#101C22⋊D6112yes—
291#97—2441no—
292C4×C8—2441no—
293#95—1221no—
294#95—1221no—
295#95—1221no—
296#95—1221no—
297#95—1221no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—1221no—
305C2×Q8—1221no—
306C2×Q8—2441no—
307C2×Q8—2441no—
308C2×Q8#1175822211yescharacteristic
309C2×Q8D4×D6111yescharacteristic
310C2×Q8#1175822411yescharacteristic
311C2×Q8C2×C22⋊D6111yescharacteristic
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—611no—
315C22×C4—611no—
316C22×C4—611no—
317C22×C4—611no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4C2×C4×D6111yescharacteristic
321C22×C4D4×D6111yescharacteristic
322C22×C4D4×D6111yescharacteristic
323M16—22no—
324M16—41no—
325M16—41no—
326M16—41no—
327M16—1222no—
328M16—2441no—
329M16—2441no—
330M16—2441no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—2441no—
334C2×C8—2441no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—1224no—
340C4⋊C4—2441no—
341C4⋊C4—2441no—
342C4⋊C4—2441no—
343C4⋊C4—2441no—
344C4⋊C4—2441no—
345C4⋊C4—2442no—
346C4⋊C4—2441no—
347C4⋊C4—2441no—
348C4⋊C4—2441no—
349C4⋊C4—2441no—
350C42—21no—
351C42—21no—
352C42—1221no—
353C42—1221no—
354C42—1221no—
355C42—1221no—
356C42—1221no—
357C42—1221no—
358C42—1221no—
359C42—1221no—
360C23C22⋊C4×D6111yescharacteristic
361Q8—41no—
362Q8—41no—
363Q8—41no—
364Q8—41no—
365Q8—81no—
366Q8—81no—
367Q8—4881no—
368Q8—4881no—
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—611no—
382C2×C4—611no—
383C2×C4—1222no—
384C2×C4—1222no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—1221no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4#1451973711yescharacteristic
397C2×C4C4×C22⋊D6111yescharacteristic
398C2×C4#1451974911yescharacteristic
399C2×C4#1451975011yescharacteristic
400C2×C4#1451976311yescharacteristic
401C2×C4#1451977311yescharacteristic
402C8—42no—
403C8—81no—
404C8—4881no—
405C8—2442no—
406C22—21no—
407C22—21no—
408C22#1683966211yescharacteristic
409C22#99×D6111yescharacteristic
410C22#1683973411yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—42no—
418C4—81no—
419C4—612no—
420C4—1221no—
421C4—4881no—
422C4—2442no—
423C4—2441no—
424C4—2441no—
425C4—2441no—
426C2—21no—
427C2—21no—
428C2#2144665311yescharacteristic
429C2#356×D6111yescharacteristic
430C2#2144751211yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC22×Q8C22×D61
FittingC2×C61×#356C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC22×Q8×C61C23
hypercenterC2×#356D61
hypocenterC61#13227
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
210. Dic61#356semidirect
246. C61#13227semidirect

Maximal subgroups

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

subgroupindex
#214508052
C2×#168395612
C2×#168395602
#214458132
#101×Dic612
C2×C61×#3562
#1322761