Finite Group Databasebeta

← #30603120

Subgroups — #30603120

Order 15616.

1578 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519840C212yesmaximal, complemented
2C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic
3C2×#16840704C211yesmaximal, characteristic
4C2×#16840635C212yesmaximal, complemented
5C2×C22⋊Q8×D61C211yesmaximal, characteristic
6C22×D61⋊C8C2212yes—
7C22×C4⋊#6923C2212yes—
8C22×C22⋊#6923—21no—
9C2×#14519840—24no—
10C2×#14519840—24no—
11C2×#14519840—24no—
12C2×#14519834—21no—
13D61⋊(C22⋊C8)—24no—
14C2×C22⋊#92420—21no—
15#16840704—24no—
16C2×(C2×#6923)⋊C4—21no—
17#16840635—24no—
18C22×Q8×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519757C411yescharacteristic, complemented
21C2×#14519756C411yescharacteristic, complemented
22C2×#14519755—21no—
23C2×#14519754—21no—
24C2×#14519753C411yescharacteristic, complemented
25C22⋊Q8×D61—24no—
26C22⋊Q8×D61—24no—
27C2×C4⋊C4×D61—21no—
28C2×C4⋊C4×D61C2211yescharacteristic
29C2×C22⋊C4×D61—21no—
30C2×C22⋊Q8×C61C411yescharacteristic, complemented
31C23×#6923—22no—
32C2×D61⋊C8—22no—
33C2×D61⋊C8—22no—
34C2×D61⋊C8—22no—
35C2×D61⋊C8—22no—
36C2×D61⋊C8—22no—
37C2×D61⋊C8D414yes—
38C22×#92420—22no—
39C2×C4⋊#6923—22no—
40C2×C4⋊#6923—22no—
41C2×C4⋊#6923—22no—
42C2×C4⋊#6923—22no—
43C2×C4⋊#6923—22no—
44C2×C4⋊#6923D414yes—
45C2×C22⋊#6923—24no—
46C2×C22⋊#6923—42no—
47C2×C22⋊#6923—42no—
48#14519840—216no—
49#14519834—24no—
50C22⋊#92420—24no—
51(C2×#6923)⋊C4—24no—
52C24×D61D411yescharacteristic
53C22×Dic122—21no—
54C22×Dic122C2×C411yescharacteristic
55C2×Q8×D61—22no—
56C2×Q8×D61—22no—
57C2×Q8×D61—22no—
58C2×Q8×D61—22no—
59C2×Q8×D61—22no—
60C2×Q8×D61D414yes—
61C23×Dic61D411yescharacteristic
62C22×C4×D61—21no—
63C22×C4×D61—21no—
64C22×C4×D61—22no—
65C22×C4×D61—22no—
66C22×C4×D61—22no—
67C22×C4×D61—22no—
68C22×C4×D61—22no—
69C22×C4×D61—22no—
70C22×C4×D61C2×C411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61C2311yescharacteristic
74#14519757—22no—
75#14519757—22no—
76#14519756—22no—
77#14519756—22no—
78#14519755—28no—
79#14519754—28no—
80#14519753—22no—
81#14519753—22no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61C2×C411yescharacteristic
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196—21no—
87C4⋊C4×D61—28no—
88C4⋊C4×D61—22no—
89C4⋊C4×D61D414yes—
90C2×C22⋊Dic61—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C22⋊C4×D61—28no—
94C22×Q8×C61C2×C411yescharacteristic
95C23×C4×C61C2×C411yescharacteristic
96C22⋊Q8×C61—22no—
97C22⋊Q8×C61—22no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61C2×C411yescharacteristic
100C2×C22⋊C4×C61—21no—
101C24×C61C22⋊C411yescharacteristic
102C23×D61—21no—
103C23×D61—22no—
104C23×D61—22no—
105C23×D61—21no—
106C23×D61—22no—
107C23×D61—21no—
108C23×D61—21no—
109C23×D61—22no—
110C23×D61C22⋊C411yescharacteristic
111C23×D61SD1612yes—
112C23×D61Q1612yes—
113C23×D61C2×D411yescharacteristic
114C22×#6923—24no—
115C22×#6923—42no—
116C22×#6923—42no—
117C22×#6923—42no—
118C22×#6923—42no—
119C22×#6923—42no—
120C22×#6923—42no—
121C2×Q8×C61—21no—
122C2×Q8×C61—22no—
123C2×Q8×C61—22no—
124C2×Q8×C61C22⋊C412yescomplemented
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61C22⋊C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—22no—
137C22×Dic61—22no—
138C22×Dic61—21no—
139C22×Dic61C22⋊C411yescharacteristic
140C22×Dic61C2×D411yescharacteristic
141Q8×D61—24no—
142Q8×D61—24no—
143Q8×D61—24no—
144Q8×D61—24no—
145Q8×D61—42no—
146Q8×D61—42no—
147Q8×D61—42no—
148Q8×D61—42no—
149C2×C4×D61—21no—
150C2×C4×D61—22no—
151C2×C4×D61—24no—
152C2×C4×D61—24no—
153C2×C4×D61—22no—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—21no—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—21no—
163C2×C4×D61—41no—
164C2×C4×D61—42no—
165C2×C4×D61—41no—
166C2×C4×D61—42no—
167C2×C4×D61—41no—
168C2×C4×D61—41no—
169C2×C4×D61—42no—
170C2×C4×D61—42no—
171C2×C4×D61—42no—
172C2×C4×D61—42no—
173C2×C4×D61—42no—
174C2×C4×D61—42no—
175C2×C4×D61—42no—
176C2×C4×D61—42no—
177C2×C4×D61C2×D412yes—
178C2×C4×D61C2×D412yes—
179C2×C4×D61C2×D412yes—
180C2×C4×D61C2×D412yes—
181C2×C4×D61#4112yes—
182C2×C4×D61#4112yes—
183C2×Dic122—22no—
184C2×Dic122—22no—
185C2×Dic122—21no—
186C2×Dic122—24no—
187C2×Dic122—41no—
188C2×Dic122—42no—
189C2×Dic122—41no—
190C2×Dic122C22⋊C412yescomplemented
191C22⋊#6923—48no—
192C2×#92420—24no—
193C2×#92420—42no—
194C2×#92420—42no—
195C4⋊#6923—24no—
196C4⋊#6923—24no—
197C4⋊#6923—42no—
198C4⋊#6923—42no—
199D61⋊C8—24no—
200D61⋊C8—24no—
201D61⋊C8—42no—
202D61⋊C8—42no—
203C4⋊C4×C61—24no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61C22⋊C412yescomplemented
206C22⋊C4×C61—24no—
207C22⋊Dic61—24no—
208#11758198—24no—
209#11758198—24no—
210C4⋊Dic61—24no—
211C4⋊Dic61—21no—
212C4⋊Dic61C22⋊C412yescomplemented
213#11758196—24no—
214#11758196—24no—
215#11758196—24no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61#10312yescomplemented
223C23×C61C2×C22⋊C411yescharacteristic
224C22×D61—21no—
225C22×D61—21no—
226C22×D61—21no—
227C22×D61—21no—
228C22×D61—21no—
229C22×D61—21no—
230C22×D61—24no—
231C22×D61—22no—
232C22×D61—22no—
233C22×D61—24no—
234C22×D61—24no—
235C22×D61—24no—
236C22×D61—22no—
237C22×D61—22no—
238C22×D61—42no—
239C22×D61—42no—
240C22×D61—42no—
241C22×D61—42no—
242C22×D61—42no—
243C22×D61—42no—
244C22×D61—42no—
245C22×D61—42no—
246C22×D61#10312yescomplemented
247C22×D61#12011yescharacteristic
248C22×D61#12012yes—
249C22×D61#12112yes—
250C22×D61#12311yescharacteristic
251C22×D61C2×SD1611yescharacteristic
252C22×D61C2×Q1611yescharacteristic
253C22×D61#13512yes—
254C22×D61AGL(1,ℤ/8)11yescharacteristic
255C22×D61#13712yes—
256C22×D61#13711yescharacteristic
257C2×#6923—44no—
258C2×#6923—44no—
259C2×#6923—44no—
260C2×#6923—82no—
261C2×#6923—82no—
262C2×#6923—82no—
263C2×#6923—82no—
264Q8×C61—24no—
265Q8×C61—42no—
266C2×C4×C61—21no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—42no—
276C2×C4×C61—42no—
277C2×C4×C61C2×C22⋊C411yescharacteristic
278C2×C4×C61C2×C22⋊C411yescharacteristic
279C2×C4×C61C4×D412yes—
280C2×C4×C61C4×D412yes—
281C2×Dic61—22no—
282C2×Dic61—21no—
283C2×Dic61—22no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—42no—
291C2×Dic61—42no—
292C2×Dic61#12011yescharacteristic
293C2×Dic61#12012yes—
294C2×Dic61#12112yes—
295C2×Dic61#12311yescharacteristic
296C4×D61—42no—
297C4×D61—44no—
298C4×D61—42no—
299C4×D61—44no—
300C4×D61—44no—
301C4×D61—44no—
302C4×D61—42no—
303C4×D61—42no—
304C4×D61—42no—
305C4×D61—42no—
306C4×D61#12012yes—
307C4×D61#12112yes—
308C4×D61#12112yes—
309C4×D61#12112yes—
310C4×D61#12112yes—
311C4×D61#12312yes—
312C4×D61#12412yes—
313C4×D61#12712yes—
314Dic122—24no—
315Dic122—42no—
316Dic122—44no—
317Dic122—44no—
318#92420—44no—
319#10970—611nomaximal, Sylow
320C22×C61—22no—
321C22×C61—22no—
322C22×C61—22no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61—41no—
326C22×C61—41no—
327C22×C61#37911yescharacteristic
328C22×C61#38611yescharacteristic
329C22×C61#38611yescharacteristic
330C22×C61C2×#10311yescharacteristic
331C22×C61#41611yescharacteristic
332C22×C61#41711yescharacteristic
333C22×C61#41911yescharacteristic
334C2×D61—22no—
335C2×D61—22no—
336C2×D61—22no—
337C2×D61—41no—
338C2×D61—41no—
339C2×D61—41no—
340C2×D61—41no—
341C2×D61—44no—
342C2×D61—44no—
343C2×D61—44no—
344C2×D61—44no—
345C2×D61#39212yes—
346C2×D61#39412yes—
347C2×D61#44812yes—
348C2×D61#44912yes—
349C2×D61#45011yescharacteristic
350C2×D61#45111yescharacteristic
351C2×D61#45112yes—
352C2×D61#45212yes—
353C2×D61#45212yes—
354C2×D61#46512yes—
355C2×D61#46712yes—
356C2×D61#46812yes—
357C2×D61#47012yes—
358C2×D61#48311yescharacteristic
359C2×D61#48411yescharacteristic
360C2×D61#48512yes—
361#6923—84no—
362C4×C61—42no—
363C4×C61—41no—
364C4×C61—42no—
365C4×C61#38612yes—
366C4×C61#39012yes—
367Dic61—42no—
368Dic61—41no—
369Dic61—42no—
370Dic61#39212yes—
371Dic61#39412yes—
372C22×C22⋊Q8—611no—
373C22×#103—612no—
374C22×C22⋊C8—611no—
375C2×#380—611no—
376C2×#340—612no—
377C2×C61—42no—
378C2×C61#143811yescharacteristic
379C2×C61#178711yescharacteristic
380C2×C61#178811yescharacteristic
381C2×C61#187211yescharacteristic
382C2×C61#187311yescharacteristic
383C2×C61#189211yescharacteristic
384C2×C61#189411yescharacteristic
385D61—42no—
386D61#200012yes—
387D61#200112yes—
388D61#203512yes—
389D61#203612yes—
390C23×Q8—611no—
391C24×C4—611no—
392C23×C8—612no—
393C2×C22⋊Q8—611no—
394C2×C22⋊Q8—611no—
395C2×C22⋊Q8—611no—
396C2×C22⋊Q8—1221no—
397C2×C22⋊Q8—1221no—
398C2×C22⋊Q8—1224no—
399C2×C22⋊Q8—1224no—
400C2×C22⋊Q8#692311yescharacteristic, complemented
401C22×C4⋊C4—611no—
402C22×C4⋊C4—612no—
403C22×C4⋊C4—1221no—
404C22×C22⋊C4—1221no—
405C22×C22⋊C4—1221no—
406C2×#103—1224no—
407C2×#103—1224no—
408C2×#103—1224no—
409C2×C22⋊C8—1224no—
410C2×C22⋊C8—1221no—
411C2×C22⋊C8—1221no—
412#380—1224no—
413C2×#95—1221no—
414#340—1224no—
415C61#1097011yescharacteristic, complemented, Sylow
416C25—611no—
417C22×Q8—614no—
418C22×Q8—611no—
419C22×Q8—1221no—
420C22×Q8—1222no—
421C22×Q8—1222no—
422C22×Q8—1222no—
423C22×Q8—1222no—
424C22×Q8—1222no—
425C22×Q8C2×#692311yescharacteristic
426C23×C4—611no—
427C23×C4—611no—
428C23×C4—611no—
429C23×C4—611no—
430C23×C4—611no—
431C23×C4—1222no—
432C23×C4—1222no—
433C23×C4—1222no—
434C23×C4—1222no—
435C23×C4—1222no—
436C23×C4—1222no—
437C23×C4—1221no—
438C23×C4—1221no—
439C23×C4—1222no—
440C23×C4C2×#692311yescharacteristic
441C22×C8—614no—
442C22×C8—1222no—
443C22×C8—1222no—
444C22×C8—1222no—
445C22×C8—1222no—
446C22×C8—1222no—
447C22×C8—1222no—
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450C22⋊Q8—1228no—
451C22⋊Q8—1222no—
452C22⋊Q8—1228no—
453C22⋊Q8—1222no—
454C22⋊Q8—1222no—
455C22⋊Q8—1222no—
456C22⋊Q8—1222no—
457C22⋊Q8—1222no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—614no—
461C2×C4⋊C4—614no—
462C2×C4⋊C4—1222no—
463C2×C4⋊C4—1228no—
464C2×C4⋊C4—1221no—
465C2×C4⋊C4—1221no—
466C2×C4⋊C4—1221no—
467C2×C4⋊C4—1221no—
468C2×C4⋊C4—1222no—
469C2×C4⋊C4—1222no—
470C2×C4⋊C4—1222no—
471C2×C4⋊C4—1222no—
472C2×C4⋊C4—1222no—
473C2×C4⋊C4C2×#692311yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—1228no—
476C2×C22⋊C4—1221no—
477C2×C22⋊C4—1221no—
478C2×C22⋊C4—1221no—
479C2×C22⋊C4—1224no—
480C2×C22⋊C4—2442no—
481C2×C22⋊C4—2442no—
482#103—12216no—
483C22⋊C8—1224no—
484C22⋊C8—1224no—
485#95—1224no—
486C24—611no—
487C24—612no—
488C24—612no—
489C24—611no—
490C24—1221no—
491C24—1222no—
492C24—1221no—
493C24—1222no—
494C24—1221no—
495C24—1222no—
496C24—1221no—
497C24—1222no—
498C24C22⋊#692311yescharacteristic
499C2×Q8—21no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—612no—
503C2×Q8—1224no—
504C2×Q8—1224no—
505C2×Q8—1224no—
506C2×Q8—1224no—
507C2×Q8—1224no—
508C2×Q8—1221no—
509C2×Q8—1222no—
510C2×Q8—1222no—
511C2×Q8—2441no—
512C2×Q8—2442no—
513C2×Q8—2441no—
514C2×Q8—2442no—
515C2×Q8—2442no—
516C2×Q8—2442no—
517C2×Q8—2442no—
518C2×Q8C22⋊#692312yescomplemented
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—611no—
526C22×C4—612no—
527C22×C4—612no—
528C22×C4—612no—
529C22×C4—612no—
530C22×C4—612no—
531C22×C4—612no—
532C22×C4—611no—
533C22×C4—1221no—
534C22×C4—1222no—
535C22×C4—1222no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—1224no—
539C22×C4—1224no—
540C22×C4—1222no—
541C22×C4—1222no—
542C22×C4—1221no—
543C22×C4—1221no—
544C22×C4—1222no—
545C22×C4—1222no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1222no—
552C22×C4—1222no—
553C22×C4—1224no—
554C22×C4—2442no—
555C22×C4—2442no—
556C22×C4—2442no—
557C22×C4—2442no—
558C22×C4—2442no—
559C22×C4—2442no—
560C22×C4—2442no—
561C22×C4—2442no—
562C22×C4—2441no—
563C22×C4—2442no—
564C22×C4—2441no—
565C22×C4—2442no—
566C22×C4—2441no—
567C22×C4—2441no—
568C22×C4—2442no—
569C22×C4—2442no—
570C22×C4—2442no—
571C22×C4—2442no—
572C22×C4—2442no—
573C22×C4—2442no—
574C22×C4C22⋊#692311yescharacteristic
575C22×C4C22×#692311yescharacteristic
576C2×C8—1224no—
577C2×C8—1224no—
578C2×C8—1224no—
579C2×C8—2442no—
580C2×C8—2442no—
581C2×C8—2442no—
582C2×C8—2442no—
583C4⋊C4—24no—
584C4⋊C4—21no—
585C4⋊C4—612no—
586C4⋊C4—1224no—
587C4⋊C4—1224no—
588C4⋊C4—1224no—
589C4⋊C4—1224no—
590C4⋊C4—1224no—
591C4⋊C4—1224no—
592C4⋊C4—1221no—
593C4⋊C4—2442no—
594C4⋊C4—2442no—
595C4⋊C4C22⋊#692312yescomplemented
596C22⋊C4—24no—
597C22⋊C4—1224no—
598C22⋊C4—1224no—
599C22⋊C4—1224no—
600C22⋊C4—2448no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—611no—
608C23—612no—
609C23—611no—
610C23—611no—
611C23—611no—
612C23—612no—
613C23—611no—
614C23—611no—
615C23—612no—
616C23—612no—
617C23—612no—
618C23—1222no—
619C23—1222no—
620C23—1222no—
621C23—1222no—
622C23—1224no—
623C23—1224no—
624C23—1224no—
625C23—1224no—
626C23—1221no—
627C23—1221no—
628C23—1221no—
629C23—1221no—
630C23—1221no—
631C23—1221no—
632C23—2442no—
633C23—2442no—
634C23—2442no—
635C23—2442no—
636C23—2442no—
637C23—2442no—
638C23—2442no—
639C23—2442no—
640C23#1451984012yescomplemented
641C23C2×C22⋊#692311yescharacteristic
642Q8—24no—
643Q8—42no—
644Q8—1224no—
645Q8—2444no—
646Q8—2444no—
647Q8—2442no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—611no—
660C2×C4—612no—
661C2×C4—611no—
662C2×C4—612no—
663C2×C4—612no—
664C2×C4—612no—
665C2×C4—612no—
666C2×C4—612no—
667C2×C4—612no—
668C2×C4—612no—
669C2×C4—612no—
670C2×C4—612no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1221no—
676C2×C4—4882no—
677C2×C4—4882no—
678C2×C4—4882no—
679C2×C4—4882no—
680C2×C4—2442no—
681C2×C4—2442no—
682C2×C4—2442no—
683C2×C4—2442no—
684C2×C4—2444no—
685C2×C4—2444no—
686C2×C4—2444no—
687C2×C4—2444no—
688C2×C4—2442no—
689C2×C4—2442no—
690C2×C4—2444no—
691C2×C4—2444no—
692C2×C4—2444no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2442no—
698C2×C4—2442no—
699C2×C4C2×C22⋊#692311yescharacteristic
700C2×C4C2×C22⋊#692311yescharacteristic
701C2×C4D4×#692312yes—
702C2×C4D4×#692312yes—
703C8—2444no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—612no—
712C22—612no—
713C22—611no—
714C22—611no—
715C22—611no—
716C22—611no—
717C22—612no—
718C22—612no—
719C22—612no—
720C22—612no—
721C22—612no—
722C22—612no—
723C22—612no—
724C22—612no—
725C22—612no—
726C22—612no—
727C22—1222no—
728C22—1222no—
729C22—1222no—
730C22—2444no—
731C22—2444no—
732C22—2444no—
733C22—2444no—
734C22—2441no—
735C22—2441no—
736C22—2441no—
737C22—2441no—
738C22#1684070311yescharacteristic
739C22#1684071011yescharacteristic
740C22#1684071011yescharacteristic
741C22C2×#1451984011yescharacteristic
742C22#1684075211yescharacteristic
743C22#1684075311yescharacteristic
744C22#1684075511yescharacteristic
745C4—41no—
746C4—42no—
747C4—42no—
748C4—612no—
749C4—612no—
750C4—4884no—
751C4—2441no—
752C4—2442no—
753C4—2442no—
754C4#1684071012yes—
755C4#1684071412yes—
756C2—42no—
757C2—612no—
758C2—612no—
759C2—612no—
760C2—612no—
761C2—2442no—
762C2#2146100111yescharacteristic
763C2#2146165811yescharacteristic
764C2#2146165911yescharacteristic
765C2#2146180411yescharacteristic
766C2#2146180511yescharacteristic
767C2#2146183211yescharacteristic
768C2#2146183411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C22⋊Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenterC2×C22⋊Q8#6923
hypocenterC61#10970
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14519840C2semidirect
4. C2×#16840635C2semidirect
20. C2×#14519757C4semidirect
21. C2×#14519756C4semidirect
24. C2×#14519753C4semidirect
30. C2×C22⋊Q8×C61C4semidirect
124. C2×Q8×C61C22⋊C4semidirect
190. C2×Dic122C22⋊C4semidirect
205. C4⋊C4×C61C22⋊C4semidirect
212. C4⋊Dic61C22⋊C4semidirect
222. C23×C61#103semidirect
246. C22×D61#103semidirect
400. C2×C22⋊Q8#6923semidirect
415. C61#10970semidirect
518. C2×Q8C22⋊#6923semidirect
595. C4⋊C4C22⋊#6923semidirect
640. C23#14519840semidirect

Maximal subgroups

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

subgroupindex
C22×#145198402
C2×D61⋊(C22⋊C8)2
C2×#168407042
C2×#168406352
C2×C22⋊Q8×D612
#1097061