Finite Group Databasebeta

← #29689132

Subgroups — #29689132

Order 15616.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840340C211yesmaximal, characteristic
2#21448411C211yesmaximal, characteristic, complemented
3#21446257C211yesmaximal, characteristic, complemented
4#21446252C211yesmaximal, characteristic, complemented
5#21446247C211yesmaximal, characteristic, complemented
6#21446242C211yesmaximal, characteristic, complemented
7#21446139C211yesmaximal, characteristic, complemented
8#21446134C211yesmaximal, characteristic, complemented
9#21446129C211yesmaximal, characteristic, complemented
10#21446124C211yesmaximal, characteristic, complemented
11#21445910C211yesmaximal, characteristic, complemented
12#21445906C211yesmaximal, characteristic, complemented
13#21445760C211yesmaximal, characteristic, complemented
14#21445760C211yesmaximal, characteristic, complemented
15C2×C61×#408C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17#16840340—24no—
18#16840340C418yescomplemented
19C2×#14519756C2211yescharacteristic
20C2×#14519756C2211yescharacteristic
21C2×#14519753—21no—
22C2×#14519751C2211yescharacteristic
23C2×#14519751C2211yescharacteristic
24C2×#14519749—21no—
25C2×#14519749—21no—
26C2×#14519748—21no—
27C2×#14519736C2211yescharacteristic
28C22×C4⋊Dic61C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic
30C2×#14519702C2211yescharacteristic
31C2×#14519702C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519699C2211yescharacteristic
38#16839669—21no—
39#16839665—21no—
40#16839642—21no—
41#16839642—21no—
42#16839622C2211yescharacteristic
43#16839622C2211yescharacteristic
44#16839622C2211yescharacteristic
45#16839622C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54C22×#41×C61C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C23×C8×C61C2211yescharacteristic
57C61×#408—24no—
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C2×#11758222—22no—
63C2×#11758222—41no—
64C2×#11758222—41no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C2×#11758222C2×C414yescomplemented
68C22×Dic122C2311yescharacteristic
69C22×D244C2311yescharacteristic
70C22×C22⋊D61—21no—
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C23×Dic61—21no—
74C23×Dic61—21no—
75C22×C4×D61—21no—
76#14519756—22no—
77#14519756—22no—
78#14519756C2×C414yes—
79#14519756C2×C414yescomplemented
80#14519753—28no—
81#14519751—22no—
82#14519751—22no—
83#14519751C2×C414yes—
84#14519751C2×C414yescomplemented
85#14519749—28no—
86#14519749—28no—
87#14519748—28no—
88#14519736—41no—
89#14519736—41no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—22no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61—41no—
94C2×C4⋊Dic61—41no—
95C2×C4⋊Dic61C2×C414yescomplemented
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×C4×Dic61—21no—
114#14519702—41no—
115#14519702—41no—
116#14519702—41no—
117#14519702—41no—
118#14519699—41no—
119#14519699—41no—
120#14519699—41no—
121#14519699—41no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125#14519684—21no—
126C2×#41×C61—41no—
127C2×#41×C61—41no—
128C2×#41×C61—41no—
129C2×#41×C61—41no—
130C2×#41×C61C2×C414yes—
131C2×#41×C61D414yes—
132C22×Q8×C61D411yescharacteristic
133C22×D4×C61D411yescharacteristic
134C22×D4×C61D411yescharacteristic
135C22×D4×C61D411yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C2×M16×C61—22no—
140C2×M16×C61—41no—
141C2×M16×C61—41no—
142C22×C8×C61—22no—
143C22×C8×C61—41no—
144C22×C8×C61—41no—
145C22×C8×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C22⋊C8×C61—22no—
150C22⋊C8×C61—22no—
151C22⋊C8×C61—22no—
152C22⋊C8×C61—22no—
153C24×C61C2×D411yescharacteristic
154C24×C61C2×D411yescharacteristic
155C24×C61C2×D411yescharacteristic
156C23×D61—21no—
157#41×C61—44no—
158#41×C61—44no—
159#41×C61—44no—
160#41×C61—44no—
161C2×Q8×C61—41no—
162C2×Q8×C61—41no—
163C2×Q8×C61C22⋊C414yes—
164C2×D4×C61—41no—
165C2×D4×C61—41no—
166C2×D4×C61—41no—
167C2×D4×C61—41no—
168C2×D4×C61—41no—
169C2×D4×C61—41no—
170C2×D4×C61C22⋊C414yes—
171C2×D4×C61C22⋊C414yes—
172C2×D4×C61C22⋊C414yes—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61C22×C412yes—
186C22×C4×C61C22×C412yes—
187C22×C4×C61C22×C412yes—
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D412yes—
192C22×C4×C61C2×D412yes—
193C22×C4×C61C2×D412yes—
194C22×C4×C61C2411yescharacteristic
195C2×C22⋊D61—24no—
196C2×C22⋊D61—24no—
197C2×C22⋊D61—24no—
198C2×C22⋊D61—42no—
199C2×C22⋊D61—42no—
200C2×C22⋊D61—81no—
201C2×C22⋊D61—81no—
202C2×C22⋊D61—81no—
203C2×C22⋊D61—81no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—24no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—42no—
213C22×Dic61—81no—
214C22×Dic61—81no—
215C22×Dic61—81no—
216C22×Dic61—81no—
217#11758222—44no—
218#11758222—44no—
219#11758222—44no—
220#11758222—44no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244C22×C412yes—
227C2×C4×D61—24no—
228C2×C4×D61—42no—
229C2×C4×D61—42no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122C22×C412yes—
236M16×C61—44no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—44no—
250C22⋊Dic61—24no—
251C22⋊Dic61—24no—
252C22⋊Dic61—42no—
253C22⋊Dic61—81no—
254C22⋊Dic61—81no—
255C22⋊Dic61—81no—
256C22⋊Dic61—81no—
257#11758198—24no—
258#11758198—24no—
259C4⋊Dic61—24no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61—42no—
271C4⋊Dic61C22×C412yes—
272C4⋊Dic61C22×C412yes—
273#11758196—24no—
274#11758196—24no—
275C4×Dic61—42no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61C2×C22⋊C412yes—
295C23×C61C2×C22⋊C412yes—
296C23×C61C2×C22⋊C412yes—
297C23×C61C22×D411yescharacteristic
298C22×D61—22no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305Q8×C61—44no—
306D4×C61—44no—
307D4×C61—44no—
308D4×C61—44no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61C2×C22⋊C412yes—
328C2×C4×C61C2×C22⋊C412yes—
329C2×C4×C61C2×C22⋊C412yes—
330C2×C4×C61C23×C411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61H(5,𝔽2)11yescharacteristic
333C2×C4×C61H(5,𝔽2)11yescharacteristic
334C2×C4×C61H(5,𝔽2)11yescharacteristic
335C2×C4×C61H(5,𝔽2)11yescharacteristic
336C22⋊D61—48no—
337C22⋊D61—84no—
338C22⋊D61—84no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—84no—
361C2×Dic61—84no—
362D244—22no—
363D244—22no—
364D244—41no—
365D244—41no—
366C4×D61—48no—
367Dic122—22no—
368Dic122—22no—
369Dic122—41no—
370Dic122—41no—
371C8×C61—41no—
372C8×C61—41no—
373C8×C61—41no—
374C8×C61—41no—
375#21772—611nomaximal, Sylow
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—22no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61C22×C22⋊C411yescharacteristic
398C22×C61#53411yescharacteristic
399C22×C61#53411yescharacteristic
400C22×C61#57611yescharacteristic
401C22×C61#57711yescharacteristic
402C22×C61#57711yescharacteristic
403C22×C61#57811yescharacteristic
404C2×D61—42no—
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—81no—
408C2×D61—81no—
409C2×D61—81no—
410C2×D61—81no—
411C4×C61—22no—
412C4×C61—22no—
413C4×C61—22no—
414C4×C61#51811yescharacteristic
415C4×C61#51811yescharacteristic
416C4×C61#53411yescharacteristic
417C4×C61#53411yescharacteristic
418Dic61—42no—
419Dic61—42no—
420Dic61—42no—
421Dic61—81no—
422Dic61—81no—
423Dic61—81no—
424Dic61—81no—
425C2×#537—611no—
426C2×#408D6111yescharacteristic, complemented
427#2311—611no—
428#1895—611no—
429#1894—611no—
430#1893—611no—
431#1892—611no—
432#1875—611no—
433#1874—611no—
434#1873—611no—
435#1872—611no—
436#1824—611no—
437#1823—611no—
438#1788—611no—
439#1788—611no—
440C2×C61—42no—
441C2×C61—42no—
442C2×C61—42no—
443C2×C61#230811yescharacteristic
444C2×C61#289711yescharacteristic
445C2×C61#289811yescharacteristic
446C2×C61#319811yescharacteristic
447C2×C61#320111yescharacteristic
448C2×C61#320311yescharacteristic
449C2×C61#320411yescharacteristic
450D61—82no—
451C22×#41—611no—
452C22×#41C2×D6111yescharacteristic
453C22×M16C2×D6111yescharacteristic
454C23×C8C2×D6111yescharacteristic
455#537—618no—
456#537—1224no—
457C2×C22⋊Q8—611no—
458C2×C22⋊Q8—611no—
459C2×C22⋊Q8—1221no—
460C2×#121—611no—
461C2×#121—611no—
462C2×#121—1221no—
463C2×#121—1221no—
464C2×#121—1221no—
465C2×#117—611no—
466C22×C4⋊C4—611no—
467C22×C4⋊C4—611no—
468C2×#103—611no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#102—611no—
473C2×#102—611no—
474C2×#102—611no—
475C2×#102—611no—
476#408—24no—
477C2×C22⋊C8C2×D6111yescharacteristic
478C2×C22⋊C8C2×D6111yescharacteristic
479C2×C22⋊C8C2×D6111yescharacteristic
480C2×C22⋊C8C2×D6111yescharacteristic
481#391—1221no—
482#390—1221no—
483#386—1221no—
484#386—1221no—
485#380—611no—
486#380—611no—
487#380—611no—
488#380—611no—
489#340—611no—
490#340—611no—
491#340—611no—
492#340—611no—
493#340—611no—
494#340—611no—
495#340—611no—
496#340—611no—
497C61#2177211yescharacteristic, complemented, Sylow
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—614no—
503C2×#41—1222no—
504C2×#41—2441no—
505C2×#41—2441no—
506C2×#41—2441no—
507C2×#41—2441no—
508C2×#41C4×D6114yes—
509C2×#41C22⋊D6114yes—
510C22×Q8—611no—
511C22×Q8D24411yescharacteristic
512C22×D4—611no—
513C22×D4—1221no—
514C22×D4—1221no—
515C22×D4—1221no—
516C22×D4D24411yescharacteristic
517C22×D4D24411yescharacteristic
518C22×D4D24411yescharacteristic
519C23×C4—1221no—
520C23×C4—1221no—
521C23×C4—1221no—
522C23×C4C22×D6111yescharacteristic
523C23×C4C22×D6111yescharacteristic
524C23×C4C22×D6111yescharacteristic
525C2×M16—22no—
526C2×M16—41no—
527C2×M16—41no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C22×D6111yescharacteristic
532C22×C8C22×D6111yescharacteristic
533C22×C8C22×D6111yescharacteristic
534C22×C8C22×D6111yescharacteristic
535C22⋊Q8—614no—
536C22⋊Q8—614no—
537C22⋊Q8—1228no—
538C22⋊Q8—1222no—
539C22⋊Q8—1222no—
540#121—614no—
541#121—614no—
542#121—1228no—
543#121—1228no—
544#121—1228no—
545#121—1222no—
546#121—1222no—
547#117—2441no—
548#117—2441no—
549C2×C4⋊C4—614no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1222no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—2441no—
562C2×C4⋊C4—2441no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C42—1221no—
573#103—2441no—
574#103—2441no—
575#103—2441no—
576#103—2441no—
577#102—2441no—
578#102—2441no—
579#102—2441no—
580#102—2441no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—22no—
584C22⋊C8—22no—
585#95—1221no—
586#95—1221no—
587#95—1221no—
588#95—1221no—
589C24—1221no—
590C24C2×D24411yescharacteristic
591C24C2×D24411yescharacteristic
592C24C2×D24411yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—2444no—
598#41—2444no—
599#41—2444no—
600#41—2444no—
601C2×Q8—41no—
602C2×Q8—41no—
603C2×Q8—612no—
604C2×Q8—1221no—
605C2×Q8—1221no—
606C2×Q8—1221no—
607C2×Q8—1221no—
608C2×Q8—1221no—
609C2×Q8#1175819814yes—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—41no—
616C2×D4—612no—
617C2×D4—1224no—
618C2×D4—1224no—
619C2×D4—1224no—
620C2×D4—1221no—
621C2×D4—1221no—
622C2×D4—1221no—
623C2×D4—1221no—
624C2×D4—1221no—
625C2×D4—4881no—
626C2×D4—4881no—
627C2×D4—4881no—
628C2×D4—4881no—
629C2×D4—2442no—
630C2×D4—2442no—
631C2×D4#1175819814yes—
632C2×D4#1175819814yes—
633C2×D4#1175819814yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—1224no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1224no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—4881no—
656C22×C4—4881no—
657C22×C4—4881no—
658C22×C4—4881no—
659C22×C4—2442no—
660C22×C4—2442no—
661C22×C4—2442no—
662C22×C4C2×C4×D6112yes—
663C22×C4C2×C4×D6112yes—
664C22×C4C2×C4×D6112yes—
665C22×C4C2×D24411yescharacteristic
666C22×C4C2×D24411yescharacteristic
667C22×C4C2×D24411yescharacteristic
668C22×C4C2×C22⋊D6112yes—
669C22×C4C2×C22⋊D6112yes—
670C22×C4C2×C22⋊D6112yes—
671C22×C4C23×D6111yescharacteristic
672M16—44no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—44no—
686C4⋊C4—612no—
687C4⋊C4—612no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1224no—
691C4⋊C4—1224no—
692C4⋊C4—1224no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—2442no—
702C22⋊C4—1224no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1224no—
706C22⋊C4—4881no—
707C22⋊C4—4881no—
708C22⋊C4—4881no—
709C22⋊C4—4881no—
710C22⋊C4—2442no—
711C42—2442no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—1222no—
731C23—2441no—
732C23—2441no—
733C23—2441no—
734C23—2441no—
735C23—2441no—
736C23—2441no—
737C23C2×#1175819812yes—
738C23C2×#1175819812yes—
739C23C2×#1175819812yes—
740C23C22×D24411yescharacteristic
741Q8—44no—
742Q8—1222no—
743Q8—1222no—
744Q8—2441no—
745Q8—2441no—
746D4—44no—
747D4—44no—
748D4—44no—
749D4—1222no—
750D4—1222no—
751D4—4884no—
752D4—4884no—
753D4—2448no—
754D4—2441no—
755D4—2441no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—4884no—
778C2×C4—4884no—
779C2×C4—2448no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4C2×#1175819812yes—
799C2×C4C2×#1175819812yes—
800C2×C4C2×#1175819812yes—
801C2×C4C22×C4×D6111yescharacteristic
802C2×C4C22×C22⋊D6111yescharacteristic
803C2×C4#1451982211yescharacteristic
804C2×C4#1451982211yescharacteristic
805C2×C4#1451982211yescharacteristic
806C2×C4#1451982211yescharacteristic
807C8—41no—
808C8—41no—
809C8—41no—
810C8—41no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—4881no—
833C22—4881no—
834C22—4881no—
835C22—4881no—
836C22—2442no—
837C22—2442no—
838C22—2442no—
839C22C22×#1175819811yescharacteristic
840C22#1684032411yescharacteristic
841C22#1684032411yescharacteristic
842C22#1684056711yescharacteristic
843C22#1684057411yescharacteristic
844C22#1684057411yescharacteristic
845C22#1684057911yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—4881no—
850C4—4881no—
851C4—4881no—
852C4—4881no—
853C4—2442no—
854C4—2442no—
855C4—2442no—
856C4#1684023511yescharacteristic
857C4#1684023511yescharacteristic
858C4#1684032111yescharacteristic
859C4#1684032111yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—4882no—
864C2#2144839411yescharacteristic
865C2#2145434611yescharacteristic
866C2#2145435311yescharacteristic
867C2#2145667311yescharacteristic
868C2#2145670311yescharacteristic
869C2#2145672111yescharacteristic
870C2#2145673111yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#408C2
socleC23×C61C22×D4
prime radicalC2×#16840340C2
cosocleC22×C4×C61C24
hypercenterC2×#408D61
hypocenterC61#21772
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. #21448411C2semidirect
3. #21446257C2semidirect
4. #21446252C2semidirect
5. #21446247C2semidirect
6. #21446242C2semidirect
7. #21446139C2semidirect
8. #21446134C2semidirect
9. #21446129C2semidirect
10. #21446124C2semidirect
11. #21445910C2semidirect
12. #21445906C2semidirect
13. #21445760C2semidirect
14. #21445760C2semidirect
15. C2×C61×#408C2semidirect
18. #16840340C4semidirect
67. C2×#11758222C2×C4semidirect
79. #14519756C2×C4semidirect
84. #14519751C2×C4semidirect
95. C2×C4⋊Dic61C2×C4semidirect
426. C2×#408D61semidirect
497. C61#21772semidirect

Maximal subgroups

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

subgroupindex
C2×#168403402
#214484112
#214462572
#214462522
#214462472
#214462422
#214461392
#214461342
#214461292
#214461242
#214459102
#214459062
#214457602
C2×C61×#4082
#2177261