Finite Group Databasebeta

← #29696249

Subgroups — #29696249

Order 15616.

1258 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840467C211yesmaximal, characteristic
2C2×C8×C22⋊D61C211yesmaximal, characteristic
3C4⋊C4×C22⋊D61C211yesmaximal, characteristic
4#21446778C211yesmaximal, characteristic, complemented
5#21446765C211yesmaximal, characteristic, complemented
6#21446242C211yesmaximal, characteristic, complemented
7#21446241C211yesmaximal, characteristic, complemented
8#21446126C211yesmaximal, characteristic, complemented
9#21446125C211yesmaximal, characteristic, complemented
10#21445909C211yesmaximal, characteristic, complemented
11#21445908C211yesmaximal, characteristic, complemented
12#21445823C211yesmaximal, characteristic, complemented
13#21445638C211yesmaximal, characteristic, complemented
14#340×D61C211yesmaximal, characteristic, complemented
15C2×C61×#340C211yesmaximal, characteristic, complemented
16C22×C8×D61C2211yescharacteristic
17#16840467—24no—
18#16840467C418yescomplemented
19C2×#14519776C2211yescharacteristic
20C2×#14519767—21no—
21C2×#14519757C2211yescharacteristic
22C2×#14519756—21no—
23C2×#14519756C2211yescharacteristic
24C2×#14519755—21no—
25C2×#14519742C2211yescharacteristic
26C2×C4×C22⋊D61—21no—
27C2×C4×C22⋊D61—21no—
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31C8×C22⋊D61—24no—
32C2×#14519706C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×C8×Dic61C2211yescharacteristic
40#16839657—21no—
41#16839635—21no—
42#16839633—21no—
43#16839631C2211yescharacteristic
44#16839622C2211yescharacteristic
45#16839619C2211yescharacteristic
46C4⋊C4×Dic61C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C22×C4⋊C4×C61C2211yescharacteristic
57C22×C4⋊C4×C61C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×Dic122—21no—
63C22×Dic122C2311yescharacteristic
64C22×C22⋊D61D411yescharacteristic
65C22×C4×D61—21no—
66C22×C4×D61—21no—
67C22×C4×D61C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C2×C8×D61—22no—
71C2×C8×D61—22no—
72C2×C8×D61—41no—
73#14519776—22no—
74#14519776C2×C414yescomplemented
75#14519767—28no—
76#14519757—22no—
77#14519757C2×C414yescomplemented
78#14519756—22no—
79#14519756—28no—
80#14519756C2×C414yescomplemented
81#14519755—28no—
82#14519742—22no—
83#14519742C2×C414yescomplemented
84C4×C22⋊D61—28no—
85C4×C22⋊D61—44no—
86C4×C22⋊D61C2×C414yes—
87C4×C22⋊D61D414yes—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196D411yescharacteristic
100C4⋊C4×D61—22no—
101C4⋊C4×D61—22no—
102C4⋊C4×D61—41no—
103C4⋊C4×D61C2×C414yescomplemented
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61D411yescharacteristic
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198D411yescharacteristic
110C2×C4×Dic61—21no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61C2311yescharacteristic
113#14519706—22no—
114#14519702—22no—
115#14519702—41no—
116#14519700—22no—
117#14519700—41no—
118C22⋊#92418—22no—
119#14519689—22no—
120C8×Dic61—22no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124C23×C4×C61—21no—
125C23×C4×C61—21no—
126C23×C4×C61C2311yescharacteristic
127C22×C8×C61—22no—
128C22×C8×C61—22no—
129C22×C8×C61—41no—
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C2×C4⋊C4×C61—22no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—22no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61—41no—
137C2×C4⋊C4×C61C2×C414yescomplemented
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C4⋊C4×C61C2311yescharacteristic
142C24×C61C2×D411yescharacteristic
143C23×D61C2×D411yescharacteristic
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—24no—
152C22×C4×C61—21no—
153C22×C4×C61—42no—
154C22×C4×C61—42no—
155C22×C4×C61—81no—
156C22×C4×C61—81no—
157C22×C4×C61—81no—
158C22×C4×C61C22×C412yes—
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D412yes—
161C22×C4×C61C2411yescharacteristic
162C2×C22⋊D61C22⋊C414yes—
163C2×C22⋊D61SD1614yes—
164C2×C22⋊D61Q1614yes—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171C22×Dic61C2×D411yescharacteristic
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—24no—
177C2×C4×D61—42no—
178C2×C4×D61—42no—
179C2×C4×D61—81no—
180C2×C4×D61—81no—
181C2×C4×D61—81no—
182C2×C4×D61C22×C412yes—
183C2×C4×D61C2×D412yes—
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—24no—
190C2×Dic122—81no—
191C2×Dic122—81no—
192C2×Dic122C22×C412yes—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—44no—
199C2×C8×C61#4112yes—
200C4⋊C4×C61—24no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—42no—
207C4⋊C4×C61C22×C412yes—
208C4⋊C4×C61C22×C412yes—
209C4⋊C4×C61#4112yes—
210C22⋊Dic61—24no—
211C22⋊Dic61—42no—
212C22⋊Dic61C22⋊C414yes—
213#11758198—24no—
214#11758198—42no—
215#11758198C22⋊C414yes—
216C4⋊Dic61—21no—
217C4⋊Dic61—24no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61C22×C412yes—
223#11758196—24no—
224#11758196—24no—
225#11758196—24no—
226#11758196—24no—
227#11758196—42no—
228#11758196—42no—
229#11758196—81no—
230#11758196C22⋊C414yes—
231C4×Dic61—24no—
232C4×Dic61—42no—
233C4×Dic61C22×C412yes—
234C4×Dic61C2×D412yes—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C8×D61—44no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61C2×C22⋊C412yes—
247C23×C61C2×SD1612yes—
248C23×C61C2×Q1612yes—
249C23×C61C22×D411yescharacteristic
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61C2×C22⋊C412yes—
255C22×D61C2×SD1612yes—
256C22×D61C2×Q1612yes—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—84no—
276C2×C4×C61—84no—
277C2×C4×C61C2×C22⋊C412yes—
278C2×C4×C61C23×C411yescharacteristic
279C2×C4×C61C22×D411yescharacteristic
280C2×C4×C61C2×#4111yescharacteristic
281C2×C4×C61C2×#4111yescharacteristic
282C2×C4×C61H(5,𝔽2)11yescharacteristic
283C2×C4×C612−1+411yescharacteristic
284C22⋊D61#103116yescomplemented
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—22no—
290C2×Dic61—22no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61C2×C22⋊C412yes—
302C2×Dic61C2×C22⋊C412yes—
303C2×Dic61C2×C22⋊C412yes—
304C2×Dic61C2×SD1612yes—
305C2×Dic61C2×Q1612yes—
306C4×D61—22no—
307C4×D61—22no—
308C4×D61—22no—
309C4×D61—22no—
310C4×D61—84no—
311C4×D61—84no—
312Dic122—22no—
313Dic122—22no—
314Dic122—41no—
315Dic122—41no—
316Dic122—84no—
317C8×C61—22no—
318C8×C61—41no—
319#92418—41no—
320#92418—41no—
321#22487—611nomaximal, Sylow
322C22×C61—22no—
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—22no—
328C22×C61C2×#10314yes—
329C22×C61C22×C22⋊C411yescharacteristic
330C22×C61#54611yescharacteristic
331C22×C61#54711yescharacteristic
332C22×C61C22×SD1611yescharacteristic
333C22×C61C22×Q1611yescharacteristic
334C22×C61#57611yescharacteristic
335C22×C61#57711yescharacteristic
336C2×D61—22no—
337C2×D61—22no—
338C2×D61—22no—
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61C2×#10314yes—
343C4×C61—22no—
344C4×C61—42no—
345C4×C61—42no—
346C4×C61—42no—
347C4×C61—81no—
348C4×C61C4×#4111yescharacteristic
349C4×C61#52011yescharacteristic
350C4×C61#54611yescharacteristic
351C4×C61#54711yescharacteristic
352Dic61—22no—
353Dic61—22no—
354Dic61—42no—
355Dic61—42no—
356Dic61—81no—
357Dic61—81no—
358Dic61C2×#10314yes—
359C2×#554—611no—
360C2×C8×D4—611no—
361D4×C4⋊C4—611no—
362#1990—611no—
363#1987—611no—
364#1892—611no—
365#1892—611no—
366#1872—611no—
367#1872—611no—
368#1824—611no—
369#1824—611no—
370#1803—611no—
371C4×#103—611no—
372C2×#340—611no—
373C2×#340D6111yescharacteristic, complemented
374C2×C61—24no—
375C2×C61#233911yescharacteristic
376C2×C61C22×#10311yescharacteristic
377C2×C61#289711yescharacteristic
378C2×C61#329511yescharacteristic
379C2×C61#329911yescharacteristic
380C2×C61#333511yescharacteristic
381C2×C61#333811yescharacteristic
382D61—24no—
383C23×C8—611no—
384C23×C8C2×D6111yescharacteristic
385#554—618no—
386#554—1224no—
387C2×C4⋊Q8—611no—
388C2×#125—1221no—
389C2×C22⋊Q8—611no—
390C2×C22⋊Q8—611no—
391C2×C22⋊Q8—1221no—
392C2×C22⋊Q8—1221no—
393C2×C4×Q8—611no—
394C2×C4×D4—611no—
395C2×C4×D4—1221no—
396C2×C4×D4—1221no—
397C22×C4⋊C4—611no—
398C22×C4⋊C4—611no—
399C22×C4⋊C4C2×D6111yescharacteristic
400C22×C4⋊C4C2×D6111yescharacteristic
401C8×D4—1224no—
402C2×C4⋊C8—611no—
403C2×#103—611no—
404C2×#103—611no—
405C2×#103—611no—
406C2×#103—611no—
407C2×C22⋊C8—611no—
408C2×C22⋊C8—611no—
409C2×C4×C8—611no—
410#389—1221no—
411#385—1221no—
412#385—1221no—
413#384—611no—
414#380—611no—
415#380—611no—
416C4×C4⋊C4—611no—
417#340—611no—
418#340—611no—
419#340—611no—
420#340—611no—
421#340—611no—
422#340—611no—
423#340—611no—
424#340—611no—
425#340C2×D6111yescharacteristic
426#340C2×D6111yescharacteristic
427#340C2×D6111yescharacteristic
428#340C2×D6111yescharacteristic
429C61#2248711yescharacteristic, complemented, Sylow
430C22×Q8—611no—
431C22×Q8—1221no—
432C22×D4—611no—
433C23×C4—21no—
434C23×C4—21no—
435C23×C4—611no—
436C23×C4—1221no—
437C23×C4—1221no—
438C23×C4C22×D6111yescharacteristic
439C22×C8—22no—
440C22×C8—22no—
441C22×C8—41no—
442C22×C8—611no—
443C22×C8—611no—
444C22×C8—1222no—
445C22×C8—1222no—
446C22×C8—2441no—
447C22×C8C22×D6111yescharacteristic
448C22×C8C22×D6111yescharacteristic
449C4⋊Q8—614no—
450C4⋊Q8—1222no—
451#125—1228no—
452C22⋊Q8—614no—
453C22⋊Q8—614no—
454C22⋊Q8—1228no—
455C22⋊Q8—1228no—
456C22⋊Q8—1222no—
457C22⋊Q8—1222no—
458C4×Q8—614no—
459C4×Q8—1222no—
460C4×D4—614no—
461C4×D4—614no—
462C4×D4—1228no—
463C4×D4—2444no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—41no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—614no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—1222no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1222no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—2441no—
485C2×C4⋊C4C4×D6114yescomplemented
486C2×C4⋊C4C22×D6111yescharacteristic
487C2×C4⋊C4C22×D6111yescharacteristic
488C2×C4⋊C4C22×D6111yescharacteristic
489C2×C4⋊C4C22×D6111yescharacteristic
490C2×C22⋊C4—611no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C42—611no—
497C2×C42—1221no—
498C2×C42—1221no—
499C4⋊C8—1222no—
500#103—1222no—
501#103—1222no—
502#103—2441no—
503#103—2441no—
504C22⋊C8—1222no—
505C22⋊C8—1222no—
506C4×C8—1222no—
507#95—1221no—
508#95—1221no—
509#95—1221no—
510C24—611no—
511C24D4×D6111yescharacteristic
512C2×Q8—612no—
513C2×Q8—1224no—
514C2×Q8—1221no—
515C2×Q8—1221no—
516C2×Q8—1221no—
517C2×Q8—1221no—
518C2×Q8—1221no—
519C2×Q8—4881no—
520C2×Q8—4881no—
521C2×D4—614no—
522C2×D4—614no—
523C2×D4—614no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—81no—
536C22×C4—81no—
537C22×C4—81no—
538C22×C4—611no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—612no—
542C22×C4—612no—
543C22×C4—1224no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—4881no—
553C22×C4—4881no—
554C22×C4—4881no—
555C22×C4—2442no—
556C22×C4—2442no—
557C22×C4C2×C4×D6112yes—
558C22×C4D4×D6112yes—
559C22×C4D4×D6111yescharacteristic
560C22×C4C23×D6111yescharacteristic
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—44no—
567C2×C8—1221no—
568C2×C8—1221no—
569C2×C8—1221no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—2444no—
574C2×C8#1175822212yes—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—24no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—42no—
582C4⋊C4—614no—
583C4⋊C4—612no—
584C4⋊C4—1224no—
585C4⋊C4—1224no—
586C4⋊C4—1224no—
587C4⋊C4—1224no—
588C4⋊C4—1221no—
589C4⋊C4—1224no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—4881no—
595C4⋊C4—2442no—
596C4⋊C4—2442no—
597C4⋊C4C2×C4×D6112yes—
598C4⋊C4C2×C4×D6112yes—
599C4⋊C4#1175822212yes—
600C22⋊C4—614no—
601C22⋊C4—614no—
602C22⋊C4—1224no—
603C22⋊C4—1224no—
604C22⋊C4—2442no—
605C22⋊C4—2442no—
606C42—612no—
607C42—612no—
608C42—1224no—
609C42—2442no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—612no—
615C23—612no—
616C23—612no—
617C23—1221no—
618C23—1221no—
619C23—1221no—
620C23—1221no—
621C23C22⋊C4×D6112yes—
622C23SD16×D6112yes—
623C23Q16×D6112yes—
624C23C2×D4×D6111yescharacteristic
625Q8—1222no—
626Q8—1222no—
627Q8—4884no—
628Q8—2441no—
629Q8—2441no—
630D4—6116no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—612no—
652C2×C4—612no—
653C2×C4—612no—
654C2×C4—612no—
655C2×C4—612no—
656C2×C4—1221no—
657C2×C4—1221no—
658C2×C4—1221no—
659C2×C4—1221no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—1222no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—4884no—
667C2×C4—4884no—
668C2×C4—2441no—
669C2×C4—2441no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4C22⋊C4×D6112yes—
679C2×C4C22×C4×D6111yescharacteristic
680C2×C4C2×D4×D6111yescharacteristic
681C2×C4C2×#1175822211yescharacteristic
682C2×C4C2×#1175822211yescharacteristic
683C2×C4#1451982211yescharacteristic
684C2×C4#1451982511yescharacteristic
685C8—22no—
686C8—41no—
687C8—2441no—
688C8—2441no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—614no—
696C22—1222no—
697C22—1222no—
698C22—1222no—
699C22—1222no—
700C22—1222no—
701C22—1222no—
702C22#103×D6114yes—
703C22C2×C22⋊C4×D6111yescharacteristic
704C22#1684040211yescharacteristic
705C22#1684041311yescharacteristic
706C22C2×SD16×D6111yescharacteristic
707C22C2×Q16×D6111yescharacteristic
708C22#1684056311yescharacteristic
709C22#1684056811yescharacteristic
710C4—22no—
711C4—42no—
712C4—42no—
713C4—42no—
714C4—81no—
715C4—614no—
716C4—1222no—
717C4—1222no—
718C4—4881no—
719C4—4881no—
720C4—2442no—
721C4—2442no—
722C4C4×#1175822211yescharacteristic
723C4#1684024311yescharacteristic
724C4#1684040211yescharacteristic
725C4#1684041311yescharacteristic
726C2—24no—
727C2—1224no—
728C2#2144864611yescharacteristic
729C2C2×#103×D6111yescharacteristic
730C2#2145434011yescharacteristic
731C2#2145763911yescharacteristic
732C2#2145769111yescharacteristic
733C2#2145817211yescharacteristic
734C2#2145820911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#340C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
cosocleC22×C4×C61C24
hypercenterC2×#340D61
hypocenterC61#22487
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. #21446778C2semidirect
5. #21446765C2semidirect
6. #21446242C2semidirect
7. #21446241C2semidirect
8. #21446126C2semidirect
9. #21446125C2semidirect
10. #21445909C2semidirect
11. #21445908C2semidirect
12. #21445823C2semidirect
13. #21445638C2semidirect
14. #340×D61C2semidirect
15. C2×C61×#340C2semidirect
18. #16840467C4semidirect
74. #14519776C2×C4semidirect
77. #14519757C2×C4semidirect
80. #14519756C2×C4semidirect
83. #14519742C2×C4semidirect
103. C4⋊C4×D61C2×C4semidirect
137. C2×C4⋊C4×C61C2×C4semidirect
284. C22⋊D61#103semidirect
373. C2×#340D61semidirect
429. C61#22487semidirect
485. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404672
C2×C8×C22⋊D612
C4⋊C4×C22⋊D612
#214467782
#214467652
#214462422
#214462412
#214461262
#214461252
#214459092
#214459082
#214458232
#214456382
#340×D612
C2×C61×#3402
#2248761