Finite Group Databasebeta

← #29598331

Subgroups — #29598331

Order 15616.

602 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 103 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#21450786C211yesmaximal, characteristic
2C2×#16839556C212yesmaximal, complemented
3C2×#16839554C212yesmaximal
4#21445807C211yesmaximal, characteristic, complemented
5C4×#99×C61C211yesmaximal, characteristic, complemented
6C2×#14519773C2211yescharacteristic
7C2×#14519765C411yescharacteristic, complemented
8C2×#14519764C2211yescharacteristic
9C2×#14519692C2212yes—
10#16839678—21no—
11#16839678—21no—
12#16839667C411yescharacteristic, complemented
13#16839663C411yescharacteristic, complemented
14#16839641—21no—
15#16839641—21no—
16#16839622—21no—
17C4×C4⋊Dic61C411yescharacteristic, complemented
18#16839556—24no—
19#16839554—24no—
20#16839529—21no—
21C2×C4×D4×C61C2211yescharacteristic
22C2×#99×C61C2212yes—
23C4×C22⋊C4×C61—21no—
24C61×#342—21no—
25C22×Dic122C2×C411yescharacteristic
26C22×D244C2×C411yescharacteristic
27C22×C22⋊D61—21no—
28C22×C22⋊D61—21no—
29#14519773—22no—
30#14519773—22no—
31#14519765—41no—
32#14519765—41no—
33#14519764—22no—
34#14519764—22no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—41no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—22no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×C4×Dic61C2×C411yescharacteristic
45C2×C4×Dic61C2×C411yescharacteristic
46#14519692—22no—
47#14519692—22no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—41no—
52C22×D4×C61C2311yescharacteristic
53C23×C4×C61D411yescharacteristic
54C23×C4×C61D411yescharacteristic
55C4×D4×C61—41no—
56C4×D4×C61—41no—
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61—22no—
59C2×C22⋊C4×C61D411yescharacteristic
60C2×C22⋊C4×C61D411yescharacteristic
61C2×C42×C61—41no—
62C2×C42×C61C2×C411yescharacteristic
63#99×C61—22no—
64#99×C61D414yes—
65#95×C61—41no—
66C24×C61C2×D411yescharacteristic
67C24×C61C2×D411yescharacteristic
68C23×D61—21no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C2×D4×C61C2×D412yes—
72C2×D4×C61#4112yes—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—42no—
78C22×C4×C61—81no—
79C22×C4×C61—81no—
80C22×C4×C61C22⋊C411yescharacteristic
81C22×C4×C61C22⋊C411yescharacteristic
82C22×C4×C61C22⋊C411yescharacteristic
83C22×C4×C61C22⋊C411yescharacteristic
84C22×C4×C61C22×C411yescharacteristic
85C2×C22⋊D61—42no—
86C2×C22⋊D61—42no—
87C2×C22⋊D61—42no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61—81no—
91C2×C22⋊D61—81no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61—21no—
95C22×Dic61—42no—
96C2×D244—22no—
97C2×D244—41no—
98C2×D244—41no—
99C2×Dic122—22no—
100C2×Dic122—41no—
101C2×Dic122—41no—
102C4⋊C4×C61—41no—
103C22⋊C4×C61—24no—
104C22⋊C4×C61—41no—
105C22⋊C4×C61—41no—
106C22⋊C4×C61—42no—
107C42×C61—21no—
108C42×C61—21no—
109C42×C61—82no—
110C22⋊Dic61—42no—
111C22⋊Dic61—41no—
112C22⋊Dic61—41no—
113C22⋊Dic61—42no—
114C22⋊Dic61—42no—
115#11758198—42no—
116#11758198—41no—
117#11758198—41no—
118#11758198—81no—
119#11758198—81no—
120C4⋊Dic61—42no—
121C4⋊Dic61—82no—
122C4×Dic61—22no—
123C4×Dic61—22no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61C2×C22⋊C411yescharacteristic
133C23×C61#12112yes—
134C23×C61#12411yescharacteristic
135C23×C61#12711yescharacteristic
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—41no—
143D4×C61—42no—
144D4×C61—42no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—41no—
151C2×C4×C61—42no—
152C2×C4×C61—42no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—44no—
157C2×C4×C61—81no—
158C2×C4×C61—81no—
159C2×C4×C61—82no—
160C2×C4×C61—82no—
161C2×C4×C61#9911yescharacteristic
162C2×C4×C61#9911yescharacteristic
163C2×C4×C61C4×D412yes—
164C22⋊D61—84no—
165C22⋊D61—82no—
166C22⋊D61—82no—
167C2×Dic61—22no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—82no—
177C2×Dic61—82no—
178C2×Dic61—82no—
179D244—82no—
180Dic122—82no—
181#13225—611nomaximal, Sylow
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—22no—
186C22×C61—21no—
187C22×C61—42no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—41no—
192C22×C61—41no—
193C22×C61—41no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61#39011yescharacteristic
197C22×C61C2×#9911yescharacteristic
198C22×C61#41011yescharacteristic
199C2×D61—81no—
200C2×D61—81no—
201C2×D61—81no—
202C2×D61—81no—
203C2×D61—81no—
204C2×D61—81no—
205C2×D61—81no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—22no—
209C4×C61—41no—
210C4×C61—41no—
211C4×C61—41no—
212C4×C61—84no—
213Dic61—42no—
214Dic61—81no—
215Dic61—81no—
216Dic61—162no—
217#2544—611no—
218C2×#354—612no—
219C2×#353—612no—
220#1799—611no—
221C4×#99D6111yescharacteristic, complemented
222C2×C61—21no—
223C2×C61—21no—
224C2×C61—41no—
225C2×C61—42no—
226C2×C61—41no—
227C2×C61#196411yescharacteristic
228C2×C61#212611yescharacteristic
229C2×C61#212711yescharacteristic
230D61—161no—
231C2×#127—611no—
232C2×#124—611no—
233C2×#124—611no—
234C2×C4×D4C2×D6111yescharacteristic
235C2×#99—612no—
236C2×#99C2×D6112yes—
237#394—1221no—
238#394—1221no—
239#391—611no—
240#390—611no—
241#386—1221no—
242#386—1221no—
243#380—1221no—
244C4×C4⋊C4—611no—
245C4×C22⋊C4—21no—
246#354—1224no—
247#353—1224no—
248#342—21no—
249#342—1221no—
250C61#1322511yescharacteristic, complemented, Sylow
251C22×Q8—611no—
252C22×D4—611no—
253C22×D4—1221no—
254C22×D4—1221no—
255C22×D4C22×D6111yescharacteristic
256C23×C4D24411yescharacteristic
257C23×C4C22⋊D6111yescharacteristic
258#127—1222no—
259#127—1222no—
260#124—1222no—
261#124—1222no—
262#124—2441no—
263#124—2441no—
264C4×D4—41no—
265C4×D4—41no—
266C2×C4⋊C4—1221no—
267C2×C4⋊C4—2441no—
268C2×C4⋊C4C4×D6111yescharacteristic
269C2×C22⋊C4—22no—
270C2×C22⋊C4—1221no—
271C2×C22⋊C4—1221no—
272C2×C22⋊C4—1221no—
273C2×C22⋊C4—1221no—
274C2×C22⋊C4—1221no—
275C2×C22⋊C4—1221no—
276C2×C22⋊C4—1222no—
277C2×C22⋊C4D24411yescharacteristic
278C2×C22⋊C4C22⋊D6111yescharacteristic
279C2×C42—41no—
280C2×C42—611no—
281C2×C42—611no—
282C2×C42C4×D6111yescharacteristic
283#99—22no—
284#99—1222no—
285#99—1222no—
286#99D24414yes—
287#95—41no—
288#95—1221no—
289#95—1221no—
290#95—1221no—
291#95—2441no—
292C24—1221no—
293C24C2×D24411yescharacteristic
294C24C2×C22⋊D6111yescharacteristic
295C2×Q8—1222no—
296C2×Q8—2441no—
297C2×Q8—2441no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—1222no—
301C2×D4—4881no—
302C2×D4—4881no—
303C2×D4—2441no—
304C2×D4—2441no—
305C2×D4—2442no—
306C2×D4—2442no—
307C2×D4—2442no—
308C2×D4—2441no—
309C2×D4—2441no—
310C2×D4C2×D24412yes—
311C2×D4#1175822212yes—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—42no—
317C22×C4—81no—
318C22×C4—81no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4—1221no—
322C22×C4—2442no—
323C22×C4#1175819811yescharacteristic
324C22×C4#1175819811yescharacteristic
325C22×C4#1175819811yescharacteristic
326C22×C4#1175819811yescharacteristic
327C22×C4C2×C4×D6111yescharacteristic
328C4⋊C4—41no—
329C4⋊C4—4882no—
330C4⋊C4—2442no—
331C22⋊C4—24no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—42no—
335C22⋊C4—4881no—
336C22⋊C4—4881no—
337C22⋊C4—2442no—
338C22⋊C4—2442no—
339C22⋊C4—2442no—
340C22⋊C4—2442no—
341C22⋊C4—2441no—
342C22⋊C4—2441no—
343C22⋊C4—2441no—
344C22⋊C4—2441no—
345C42—21no—
346C42—21no—
347C42—82no—
348C42—1222no—
349C42—1222no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—2441no—
359C23—2441no—
360C23—2441no—
361C23—2441no—
362C23—2441no—
363C23—2441no—
364C23—2441no—
365C23C2×#1175819811yescharacteristic
366C23#1451975112yes—
367C23#1451976511yescharacteristic
368C23#1451977411yescharacteristic
369Q8—4882no—
370D4—42no—
371D4—42no—
372D4—4882no—
373D4—4884no—
374D4—4882no—
375D4—4882no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—44no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—1222no—
393C2×C4—4882no—
394C2×C4—4882no—
395C2×C4—4882no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4#1451969111yescharacteristic
405C2×C4#1451969111yescharacteristic
406C2×C4C4×D24412yes—
407C22—21no—
408C22—21no—
409C22—22no—
410C22—21no—
411C22—21no—
412C22—42no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—81no—
420C22—81no—
421C22—4881no—
422C22—4881no—
423C22—4881no—
424C22—4881no—
425C22—4881no—
426C22—4881no—
427C22—4881no—
428C22#1683966411yescharacteristic
429C22C2×#1451969111yescharacteristic
430C22#1683973511yescharacteristic
431C4—21no—
432C4—21no—
433C4—22no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—84no—
438C4—9762no—
439C4—4881no—
440C4—4881no—
441C4—2442no—
442C2—21no—
443C2—21no—
444C2—42no—
445C2—41no—
446C2—41no—
447C2—9761no—
448C2#2144665511yescharacteristic
449C2#2144748211yescharacteristic
450C2#2144748611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC22×D4C22×D61
FittingC4×#99×C61C2
socleC22×C61C2×#99
prime radicalC2×#14519773C22
cosocleC22×D4×C61C23
hypercenterC4×#99D61
hypocenterC61#13225
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. C2×#16839556C2semidirect
4. #21445807C2semidirect
5. C4×#99×C61C2semidirect
7. C2×#14519765C4semidirect
12. #16839667C4semidirect
13. #16839663C4semidirect
17. C4×C4⋊Dic61C4semidirect
221. C4×#99D61semidirect
250. C61#13225semidirect

Maximal subgroups

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

subgroupindex
#214507862
C2×#168395562
C2×#168395542
#214458072
C4×#99×C612
#1322561