Finite Group Databasebeta

← #30602783

Subgroups — #30602783

Order 15616.

1338 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840704C211yesmaximal, characteristic
2C2×C4×C22⋊#6923C211yesmaximal, characteristic
3C2×#16840640C214yesmaximal
4C2×#16839621C211yesmaximal, characteristic
5C22×C4⋊#6923—21no—
6C22×C22⋊#6923C2212yes—
7C22×C22⋊#6923C2212yes—
8C22×C4×#6923—21no—
9#16840704—22no—
10#16840704C414yescomplemented
11C4×C22⋊#6923—22no—
12C4×C22⋊#6923C414yescomplemented
13C2×(C2×#6923)⋊C4—21no—
14C2×(C2×#6923)⋊C4—21no—
15#16840640—28no—
16C23×C4×D61C2211yescharacteristic
17C22×#11758196C412yescomplemented
18C22×#11758198C2212yes—
19#16839621—21no—
20#16839621—21no—
21#16839621—21no—
22#16839621—21no—
23C2×#14519684C411yescharacteristic, complemented
24C2×#95×C61C411yescharacteristic, complemented
25C23×#6923—22no—
26C23×#6923—22no—
27C2×C4⋊#6923—24no—
28C2×C4⋊#6923—44no—
29C2×C22⋊#6923—22no—
30C2×C22⋊#6923—22no—
31C2×C22⋊#6923—22no—
32C2×C22⋊#6923—24no—
33C2×C22⋊#6923—24no—
34C2×C22⋊#6923—22no—
35C2×C22⋊#6923C2×C414yes—
36C2×C22⋊#6923C2×C414yes—
37C2×C22⋊#6923D414yes—
38C2×C22⋊#6923Q814yes—
39C2×C4×#6923—24no—
40C2×C4×#6923—44no—
41(C2×#6923)⋊C4—24no—
42(C2×#6923)⋊C4—24no—
43C24×D61C2311yescharacteristic
44C23×Dic61C2×C411yescharacteristic
45C23×Dic61C2×C412yes—
46C22×C4×D61—44no—
47C22×C4×D61C2×C412yes—
48C22×C4×D61C2×C412yes—
49C22×C4×D61D411yescharacteristic
50C22×C4×D61D411yescharacteristic
51C22×C4×D61D412yes—
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61Q812yes—
55C2×#11758196—22no—
56C2×#11758196—22no—
57C2×#11758196—44no—
58C2×#11758198—24no—
59C2×#11758198—22no—
60C2×#11758198—22no—
61C2×#11758198—24no—
62#14519684—21no—
63#14519684—21no—
64C23×C4×C61C2×C412yes—
65C23×C4×C61C2×C411yescharacteristic
66#95×C61—21no—
67#95×C61—21no—
68C24×C61C22×C411yescharacteristic
69C23×D61—42no—
70C23×D61—42no—
71C23×D61C22×C411yescharacteristic
72C23×D61C22×C411yescharacteristic
73C23×D61C2×D411yescharacteristic
74C23×D61C2×D411yescharacteristic
75C23×D61C2×D411yescharacteristic
76C23×D61C2×D412yes—
77C23×D61C2×Q811yescharacteristic
78C23×D61C2×Q812yes—
79C23×D61#4112yes—
80C23×D61#4112yes—
81C22×#6923—24no—
82C22×#6923—24no—
83C22×#6923—24no—
84C22×#6923—24no—
85C22×#6923—44no—
86C22×#6923—44no—
87C22×#6923—44no—
88C22×#6923—44no—
89C22×#6923—42no—
90C22×#6923—42no—
91C22×C4×C61—22no—
92C22×C4×C61—24no—
93C22×C4×C61—42no—
94C22×C4×C61—42no—
95C22×C4×C61—42no—
96C22×C4×C61C4212yes—
97C22×C4×C61C22⋊C411yescharacteristic
98C22×C4×C61C22⋊C411yescharacteristic
99C22×C4×C61C4⋊C412yes—
100C22×Dic61—24no—
101C22×Dic61—22no—
102C22×Dic61—24no—
103C22×Dic61—42no—
104C22×Dic61—42no—
105C22×Dic61C4212yes—
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C22⋊C411yescharacteristic
108C22×Dic61C4⋊C412yes—
109C2×C4×D61—24no—
110C2×C4×D61—24no—
111C2×C4×D61—44no—
112C2×C4×D61—44no—
113C2×C4×D61—44no—
114C2×C4×D61—44no—
115C2×C4×D61—42no—
116C2×C4×D61—42no—
117C2×C4×D61C22⋊C412yes—
118C2×C4×D61C22⋊C412yes—
119C2×C4×D61C22⋊C412yes—
120C2×C4×D61C22⋊C412yes—
121C2×C4×D61C4⋊C412yes—
122C2×C4×D61C4⋊C412yes—
123C2×C4×D61C4⋊C412yes—
124C2×C4×D61C4⋊C412yes—
125C22⋊#6923—24no—
126C22⋊#6923—24no—
127C22⋊#6923—24no—
128C22⋊#6923—28no—
129C22⋊#6923—44no—
130C22⋊#6923C4⋊C418yescomplemented
131C4⋊#6923—48no—
132C4×#6923—48no—
133#11758198—44no—
134#11758198—42no—
135#11758198—42no—
136#11758196—44no—
137#11758196—44no—
138C23×C61—22no—
139C23×C61—22no—
140C23×C61C2×C4211yescharacteristic
141C23×C61C2×C22⋊C411yescharacteristic
142C23×C61C2×C4⋊C411yescharacteristic
143C23×C61C4×D412yes—
144C23×C61C4×Q812yes—
145C22×D61—22no—
146C22×D61—22no—
147C22×D61—22no—
148C22×D61—22no—
149C22×D61—41no—
150C22×D61—41no—
151C22×D61—41no—
152C22×D61—41no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—44no—
156C22×D61—41no—
157C22×D61—41no—
158C22×D61—44no—
159C22×D61—44no—
160C22×D61—44no—
161C22×D61C2×C22⋊C411yescharacteristic
162C22×D61C2×C22⋊C411yescharacteristic
163C22×D61C2×C4⋊C411yescharacteristic
164C22×D61C2×C4⋊C411yescharacteristic
165C22×D61C2×C4⋊C412yes—
166C22×D61#11712yes—
167C22×D61C4×D412yes—
168C22×D61C4×Q812yes—
169C22×D61#12112yes—
170C22×D61#12112yes—
171C22×D61C22⋊Q812yes—
172C22×D61C22⋊Q812yes—
173C22×D61#12411yescharacteristic
174C22×D61#12411yescharacteristic
175C22×D61#12512yes—
176C22×D61#12711yescharacteristic
177C22×D61C4⋊Q811yescharacteristic
178C22×D61C4⋊Q812yes—
179C2×#6923—28no—
180C2×#6923—44no—
181C2×#6923—48no—
182C2×#6923—44no—
183C2×#6923—48no—
184C2×#6923—44no—
185C2×#6923—44no—
186C2×#6923—44no—
187C2×#6923—84no—
188C2×#6923—84no—
189C2×C4×C61—22no—
190C2×C4×C61—22no—
191C2×C4×C61—42no—
192C2×C4×C61—42no—
193C2×C4×C61—42no—
194C2×C4×C61—42no—
195C2×C4×C61—42no—
196C2×C4×C61—84no—
197C2×C4×C61#9512yes—
198C2×C4×C61#9512yes—
199C2×Dic61—22no—
200C2×Dic61—24no—
201C2×Dic61—24no—
202C2×Dic61—42no—
203C2×Dic61—42no—
204C2×Dic61—42no—
205C2×Dic61—84no—
206C2×Dic61#9512yes—
207C2×Dic61#9512yes—
208C2×Dic61#9914yes—
209C4×D61—24no—
210C4×D61—24no—
211C4×D61—24no—
212C4×D61—24no—
213C4×D61—42no—
214C4×D61—42no—
215C4×D61—42no—
216C4×D61—42no—
217#10854—611nomaximal, Sylow
218C22×C61—24no—
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—24no—
224C22×C61C2×#9511yescharacteristic
225C22×C61C4×C4⋊C412yes—
226C22×C61#38912yes—
227C22×C61#39011yescharacteristic
228C22×C61#39111yescharacteristic
229C22×C61C2×#9912yes—
230C22×C61#41012yes—
231C2×D61—24no—
232C2×D61—22no—
233C2×D61—22no—
234C2×D61—21no—
235C2×D61—21no—
236C2×D61—21no—
237C2×D61—21no—
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—21no—
241C2×D61—21no—
242C2×D61—24no—
243C2×D61—22no—
244C2×D61—22no—
245C2×D61—42no—
246C2×D61—42no—
247C2×D61—42no—
248C2×D61—42no—
249C2×D61—42no—
250C2×D61—42no—
251C2×D61—42no—
252C2×D61—42no—
253C2×D61#38012yes—
254C2×D61#38211yescharacteristic
255C2×D61#38411yescharacteristic
256C2×D61#38912yes—
257C2×D61#39011yescharacteristic
258C2×D61#39111yescharacteristic
259#6923—48no—
260#6923—84no—
261C4×C61—22no—
262C4×C61—22no—
263C4×C61—82no—
264Dic61—22no—
265Dic61—82no—
266Dic61#34214yescomplemented
267C2×#380—611no—
268C2×#380—611no—
269C2×C4×C22⋊C4—611no—
270C2×#342—614no—
271C2×C61—22no—
272C2×C61—22no—
273C2×C61C4⋊#9511yescharacteristic
274C2×C61C2×#34211yescharacteristic
275C2×C61#174011yescharacteristic
276C2×C61#196412yes—
277C2×C61#199612yes—
278D61—22no—
279D61—21no—
280D61—21no—
281D61—21no—
282D61—22no—
283D61—21no—
284C24×C4—611no—
285C22×C4⋊C4—612no—
286C22×C4⋊C4—1221no—
287C22×C22⋊C4—612no—
288C22×C22⋊C4—612no—
289C22×C22⋊C4—612no—
290C22×C42—1221no—
291#380—614no—
292#380—1221no—
293#380—1221no—
294#380—1221no—
295#380—1221no—
296#380—1222no—
297C4×C22⋊C4—614no—
298C4×C22⋊C4—1222no—
299C2×#95—611no—
300C2×#95—1221no—
301C2×#95—1221no—
302C2×#95#692311yescharacteristic, complemented
303#342—1228no—
304C61#1085411yescharacteristic, complemented, Sylow
305C25—611no—
306C23×C4—611no—
307C23×C4—611no—
308C23×C4—611no—
309C23×C4—612no—
310C23×C4—612no—
311C23×C4—612no—
312C23×C4—612no—
313C23×C4—611no—
314C23×C4—611no—
315C23×C4—612no—
316C23×C4—1222no—
317C23×C4—1222no—
318C23×C4—2444no—
319C23×C4C2×#692312yes—
320C23×C4C2×#692311yescharacteristic
321C2×C4⋊C4—1222no—
322C2×C4⋊C4—1222no—
323C2×C4⋊C4—1224no—
324C2×C4⋊C4—2444no—
325C2×C4⋊C4—2444no—
326C2×C22⋊C4—614no—
327C2×C22⋊C4—614no—
328C2×C22⋊C4—614no—
329C2×C22⋊C4—614no—
330C2×C22⋊C4—1222no—
331C2×C22⋊C4—1222no—
332C2×C22⋊C4—1222no—
333C2×C22⋊C4—1224no—
334C2×C22⋊C4—1224no—
335C2×C22⋊C4—1224no—
336C2×C22⋊C4—1222no—
337C2×C22⋊C4—1222no—
338C2×C22⋊C4—1224no—
339C2×C22⋊C4—1222no—
340C2×C42—1224no—
341C2×C42—2444no—
342#95—21no—
343#95—21no—
344#95—1224no—
345#95—1224no—
346#95—1221no—
347#95—1221no—
348C24—611no—
349C24—611no—
350C24—611no—
351C24—611no—
352C24—611no—
353C24—611no—
354C24—612no—
355C24—612no—
356C24—612no—
357C24—612no—
358C24—2442no—
359C24—2442no—
360C24C22×#692311yescharacteristic
361C22×C4—22no—
362C22×C4—24no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—611no—
367C22×C4—612no—
368C22×C4—611no—
369C22×C4—612no—
370C22×C4—612no—
371C22×C4—612no—
372C22×C4—612no—
373C22×C4—612no—
374C22×C4—612no—
375C22×C4—612no—
376C22×C4—612no—
377C22×C4—612no—
378C22×C4—1224no—
379C22×C4—1224no—
380C22×C4—1224no—
381C22×C4—1224no—
382C22×C4—1224no—
383C22×C4—1224no—
384C22×C4—1224no—
385C22×C4—1224no—
386C22×C4—1222no—
387C22×C4—2442no—
388C22×C4—2442no—
389C22×C4—2444no—
390C22×C4—2444no—
391C22×C4—2444no—
392C22×C4—2444no—
393C22×C4—2442no—
394C22×C4—2442no—
395C22×C4—2444no—
396C22×C4—2444no—
397C22×C4—2442no—
398C22×C4—2442no—
399C22×C4—2444no—
400C22×C4—2444no—
401C22×C4C4×#692312yes—
402C22×C4C4⋊#692312yes—
403C22×C4C22⋊#692311yescharacteristic
404C22×C4C22⋊#692311yescharacteristic
405C4⋊C4—2444no—
406C4⋊C4—2444no—
407C4⋊C4—2448no—
408C22⋊C4—618no—
409C22⋊C4—1224no—
410C22⋊C4—1224no—
411C22⋊C4—1224no—
412C22⋊C4—1228no—
413C22⋊C4—2444no—
414C22⋊C4—2442no—
415C22⋊C4—2442no—
416C22⋊C4—2444no—
417C42—2448no—
418C23—22no—
419C23—22no—
420C23—612no—
421C23—611no—
422C23—611no—
423C23—612no—
424C23—611no—
425C23—611no—
426C23—611no—
427C23—611no—
428C23—611no—
429C23—611no—
430C23—612no—
431C23—612no—
432C23—612no—
433C23—612no—
434C23—612no—
435C23—612no—
436C23—612no—
437C23—612no—
438C23—1222no—
439C23—1222no—
440C23—1222no—
441C23—1222no—
442C23—2441no—
443C23—2441no—
444C23—2441no—
445C23—2441no—
446C23—2441no—
447C23—2441no—
448C23—2441no—
449C23—2441no—
450C23—2444no—
451C23—2444no—
452C23—2444no—
453C23—2444no—
454C23C2×C4×#692311yescharacteristic
455C23C2×C22⋊#692311yescharacteristic
456C23C2×C4⋊#692311yescharacteristic
457C23D4×#692312yes—
458C23Q8×#692312yes—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—84no—
467C2×C4—614no—
468C2×C4—612no—
469C2×C4—612no—
470C2×C4—1224no—
471C2×C4—1224no—
472C2×C4—1224no—
473C2×C4—1224no—
474C2×C4—1224no—
475C2×C4—1224no—
476C2×C4—1222no—
477C2×C4—1228no—
478C2×C4—4884no—
479C2×C4—4884no—
480C2×C4—4884no—
481C2×C4—2442no—
482C2×C4—2442no—
483C2×C4—2442no—
484C2×C4—2442no—
485C2×C4—2444no—
486C2×C4—2444no—
487C2×C4—2444no—
488C2×C4—2442no—
489C2×C4—2442no—
490C2×C4—2442no—
491C2×C4—2444no—
492C2×C4—2444no—
493C2×C4—2448no—
494C2×C4—2448no—
495C2×C4(C2×#6923)⋊C412yes—
496C2×C4(C2×#6923)⋊C412yes—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—24no—
502C22—24no—
503C22—612no—
504C22—611no—
505C22—611no—
506C22—611no—
507C22—612no—
508C22—611no—
509C22—1221no—
510C22—1221no—
511C22—1221no—
512C22—1221no—
513C22—1221no—
514C22—1221no—
515C22—1221no—
516C22—1221no—
517C22—1222no—
518C22—1224no—
519C22—1222no—
520C22—1222no—
521C22—1224no—
522C22—1222no—
523C22—2442no—
524C22—2442no—
525C22—2442no—
526C22—2442no—
527C22—2442no—
528C22—2442no—
529C22—2442no—
530C22—2442no—
531C22C2×(C2×#6923)⋊C411yescharacteristic
532C22C4⋊C4×#692312yes—
533C22#1684071312yes—
534C22#1684071411yescharacteristic
535C22(C2×#6923)⋊Q811yescharacteristic
536C22D61⋊#9912yes—
537C22#1684074112yes—
538C4—22no—
539C4—22no—
540C4—82no—
541C4—614no—
542C4—1222no—
543C4—4884no—
544C4—4882no—
545C4—2448no—
546C2—22no—
547C2—22no—
548C2—1221no—
549C2—1222no—
550C2—1221no—
551C2—1221no—
552C2—1222no—
553C2—1221no—
554C2#2146099611yescharacteristic
555C2#2146151611yescharacteristic
556C2#2146151811yescharacteristic
557C2#2146196012yes—
558C2#2146201012yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC2×#95×C61C4
socleC23×C61C2×C22⋊C4
prime radical, cosocleC24×D61C23
hypercenterC2×#95#6923
hypocenterC61#10854
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
10. #16840704C4semidirect
12. C4×C22⋊#6923C4semidirect
17. C22×#11758196C4semidirect
23. C2×#14519684C4semidirect
24. C2×#95×C61C4semidirect
130. C22⋊#6923C4⋊C4semidirect
266. Dic61#342semidirect
302. C2×#95#6923semidirect
304. C61#10854semidirect

Maximal subgroups

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

subgroupindex
C2×#168407042
C2×C4×C22⋊#69232
C2×#168406402
C2×#168396212
#1085461