Finite Group Databasebeta

← #29695540

Subgroups — #29695540

Order 15616.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840433C211yesmaximal, characteristic
2C2×#16839764C211yesmaximal, characteristic, complemented
3C2×#16839759C211yesmaximal, characteristic, complemented
4#21448748C211yesmaximal, characteristic, complemented
5#21446745C211yesmaximal, characteristic, complemented
6#21446643C211yesmaximal, characteristic, complemented
7#21446257C211yesmaximal, characteristic, complemented
8#21446247C211yesmaximal, characteristic, complemented
9#21446139C211yesmaximal, characteristic, complemented
10#21446134C211yesmaximal, characteristic, complemented
11#21445835C211yesmaximal, characteristic, complemented
12#21445760C211yesmaximal, characteristic, complemented
13#21445760C211yesmaximal, characteristic, complemented
14#21445650C211yesmaximal, characteristic, complemented
15C2×C61×#435C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758222C2211yescharacteristic
18#16840433—24no—
19#16840433C418yescomplemented
20C2×#14519774C2211yescharacteristic
21C2×#14519773—21no—
22C2×#14519751C2211yescharacteristic
23C2×#14519751C2211yescharacteristic
24C2×#14519750—21no—
25C2×#14519750—21no—
26C2×C4×Dic122C2211yescharacteristic
27C2×#14519739—21no—
28C2×#14519736C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic
30#16839764—24no—
31#16839759—24no—
32C2×#14519702C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519702C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519699C2211yescharacteristic
38C2×#14519699C2211yescharacteristic
39C2×#14519699C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519699C2211yescharacteristic
42C2×#14519699C2211yescharacteristic
43C2×#14519699C2211yescharacteristic
44#16839655—21no—
45#16839648—21no—
46#16839642—21no—
47#16839628C2211yescharacteristic
48#16839622C2211yescharacteristic
49#16839622C2211yescharacteristic
50C4×C4⋊Dic61C2211yescharacteristic
51C22⋊C4×Dic61—21no—
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55#16839525C2211yescharacteristic
56C22×M16×C61C2211yescharacteristic
57C23×C8×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic
59C61×#435—24no—
60C2×C4⋊C8×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C2×#97×C61C2211yescharacteristic
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—22no—
69C2×#11758222—22no—
70C2×#11758222—41no—
71C2×#11758222—41no—
72C2×#11758222—41no—
73C2×#11758222—41no—
74C2×#11758222C2×C414yes—
75C2×#11758222C2×C414yescomplemented
76C22×Dic122C2311yescharacteristic
77C22×D244—21no—
78C22×D244—21no—
79C22×D244C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C23×Dic61—21no—
86C22×C4×D61—21no—
87C22×C4×D61—21no—
88#14519774—22no—
89#14519774C2×C414yescomplemented
90#14519773—28no—
91#14519751—22no—
92#14519751—22no—
93#14519751C2×C414yes—
94#14519751C2×C414yescomplemented
95#14519750—28no—
96#14519750—28no—
97C4×Dic122—22no—
98C4×Dic122C2×C414yescomplemented
99#14519739—28no—
100#14519736—22no—
101#14519736—41no—
102C2×C4⋊Dic61—22no—
103C2×C4⋊Dic61—21no—
104C2×C4⋊Dic61—41no—
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×#11758196—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×C4×Dic61—21no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61—21no—
119#14519702—22no—
120#14519702—22no—
121#14519702—22no—
122#14519702D414yescomplemented
123#14519699—22no—
124#14519699—22no—
125#14519699—22no—
126#14519699—22no—
127#14519699—41no—
128#14519699—41no—
129#14519699—41no—
130#14519699—41no—
131#14519684—21no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136C22×D4×C61D411yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C2×M16×C61—22no—
140C2×M16×C61—22no—
141C2×M16×C61—41no—
142C22×C8×C61—22no—
143C22×C8×C61—22no—
144C22×C8×C61—41no—
145C22×C8×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C4×D4×C61C2×C414yes—
150C4×D4×C61D414yes—
151C2×C4⋊C4×C61D411yescharacteristic
152C2×C22⋊C4×C61D411yescharacteristic
153C2×C22⋊C4×C61D411yescharacteristic
154C2×C42×C61C2311yescharacteristic
155C4⋊C8×C61—22no—
156C22⋊C8×C61—22no—
157C22⋊C8×C61—22no—
158#97×C61—22no—
159C24×C61C2×D411yescharacteristic
160C24×C61C2×D411yescharacteristic
161C23×D61—21no—
162C23×D61—21no—
163C2×D4×C61—41no—
164C2×D4×C61—41no—
165C2×D4×C61C22⋊C414yes—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61C22×C412yes—
175C22×C4×C61C22×C412yes—
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D412yes—
181C22×C4×C61C2×D412yes—
182C22×C4×C61C2411yescharacteristic
183C2×C22⋊D61—24no—
184C2×C22⋊D61—24no—
185C2×C22⋊D61—24no—
186C2×C22⋊D61—24no—
187C2×C22⋊D61—42no—
188C2×C22⋊D61—42no—
189C2×C22⋊D61—42no—
190C2×C22⋊D61—42no—
191C2×C22⋊D61—81no—
192C2×C22⋊D61—81no—
193C2×C22⋊D61—81no—
194C2×C22⋊D61—81no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—42no—
202C22×Dic61—42no—
203C22×Dic61—81no—
204#11758222—28no—
205#11758222—28no—
206#11758222—44no—
207#11758222—44no—
208#11758222—44no—
209#11758222—44no—
210#11758222—44no—
211#11758222—44no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—24no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—24no—
224C2×D244—42no—
225C2×D244—42no—
226C2×D244—81no—
227C2×D244—81no—
228C2×D244C22×C412yes—
229C2×D244C22×C412yes—
230C2×C4×D61—24no—
231C2×C4×D61—24no—
232C2×C4×D61—42no—
233C2×C4×D61—42no—
234C2×C4×D61—42no—
235C2×C4×D61—42no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122C22×C412yes—
240C2×Dic122C2×D412yes—
241C2×Dic122#4112yes—
242M16×C61—44no—
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—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C2×C8×C61—21no—
254C2×C8×C61—44no—
255C2×C8×C61C2×D412yes—
256C4⋊C4×C61C22⋊C414yes—
257C22⋊C4×C61C22⋊C414yes—
258C22⋊C4×C61C22⋊C414yes—
259C42×C61C22×C412yes—
260C42×C61C2×D412yes—
261C22⋊Dic61—42no—
262C22⋊Dic61—42no—
263C22⋊Dic61—81no—
264#11758198—24no—
265#11758198—24no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—42no—
275C4⋊Dic61C22×C412yes—
276C4⋊Dic61C2×D412yes—
277#11758196—24no—
278C4×Dic61—24no—
279C4×Dic61—42no—
280C4×Dic61—81no—
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×C61C2×C22⋊C412yes—
294C23×C61C2×C22⋊C412yes—
295C23×C61C22×D411yescharacteristic
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310D4×C61—44no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
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×C61C2×C22⋊C412yes—
331C2×C4×C61C23×C411yescharacteristic
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C2×#4111yescharacteristic
335C2×C4×C61H(5,𝔽2)11yescharacteristic
336C2×C4×C61H(5,𝔽2)11yescharacteristic
337C22⋊D61—48no—
338C22⋊D61—48no—
339C22⋊D61—84no—
340C22⋊D61—84no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
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—84no—
360D244—22no—
361D244—22no—
362D244—22no—
363D244—22no—
364D244—48no—
365D244—41no—
366D244—41no—
367D244—41no—
368D244—41no—
369D244—84no—
370C4×D61—48no—
371C4×D61—48no—
372Dic122—22no—
373Dic122—22no—
374Dic122—22no—
375Dic122C4×D414yes—
376C8×C61—22no—
377C8×C61—41no—
378C8×C61—41no—
379C8×C61—41no—
380#22422—611nomaximal, Sylow
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—22no—
385C22×C61—22no—
386C22×C61—22no—
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×C61C22×C22⋊C411yescharacteristic
396C22×C61D4211yescharacteristic
397C22×C61#54611yescharacteristic
398C22×C61#57511yescharacteristic
399C22×C61#57511yescharacteristic
400C22×C61#57611yescharacteristic
401C22×C61#57711yescharacteristic
402C2×D61—42no—
403C2×D61—42no—
404C2×D61—42no—
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—42no—
408C2×D61—81no—
409C2×D61—81no—
410C2×D61—81no—
411C2×D61—81no—
412C2×D61—81no—
413C2×D61—81no—
414C2×D61—81no—
415C2×D61—81no—
416C4×C61—22no—
417C4×C61—22no—
418C4×C61—22no—
419C4×C61—22no—
420C4×C61C2×C4×D411yescharacteristic
421C4×C61#51811yescharacteristic
422C4×C61D4211yescharacteristic
423C4×C61#54611yescharacteristic
424Dic61—24no—
425Dic61—42no—
426Dic61—42no—
427Dic61—81no—
428Dic61—81no—
429Dic61—81no—
430C2×#550—611no—
431C2×#435D6111yescharacteristic, complemented
432C2×#417—611no—
433C2×#416—611no—
434#2352—611no—
435#1982—611no—
436#1961—611no—
437#1895—611no—
438#1893—611no—
439#1875—611no—
440#1874—611no—
441#1805—611no—
442#1788—611no—
443#1788—611no—
444#1763—611no—
445C2×C61—42no—
446C2×C61—42no—
447C2×C61D4×C22⋊C411yescharacteristic
448C2×C61#289611yescharacteristic
449C2×C61#289711yescharacteristic
450C2×C61#326811yescharacteristic
451C2×C61#327111yescharacteristic
452C2×C61#330911yescharacteristic
453C2×C61#331711yescharacteristic
454D61—82no—
455D61—82no—
456C22×#41—611no—
457C22×#41—611no—
458C22×M16C2×D6111yescharacteristic
459C23×C8C2×D6111yescharacteristic
460#550—618no—
461#550—1224no—
462C2×#127—611no—
463C2×#127—1221no—
464C2×#121—611no—
465C2×#121—611no—
466C2×#121—1221no—
467C2×#121—1221no—
468C2×C4×Q8—611no—
469C2×C4×D4—1221no—
470C2×C4×D4C2×D6111yescharacteristic
471C2×#117—611no—
472C22×C4⋊C4—611no—
473#435—24no—
474C2×C4⋊C8C2×D6111yescharacteristic
475#417—1224no—
476#416—1224no—
477C2×#103—611no—
478C2×#103—611no—
479C2×#103—611no—
480C2×#103—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×#102—611no—
484C2×#102—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×C22⋊C8C2×D6111yescharacteristic
490C2×C22⋊C8C2×D6111yescharacteristic
491C2×#97C2×D6111yescharacteristic
492#388—1221no—
493#387—1221no—
494#386—1221no—
495#382—611no—
496#380—611no—
497#380—611no—
498C4×C4⋊C4—611no—
499C4×C22⋊C4—1221no—
500#340—611no—
501#340—611no—
502#340—611no—
503#340—611no—
504C61#2242211yescharacteristic, complemented, Sylow
505C2×#41—614no—
506C2×#41—614no—
507C2×#41—1222no—
508C2×#41—1222no—
509C2×#41—1222no—
510C2×#41—1222no—
511C2×#41—1222no—
512C2×#41—1222no—
513C2×#41—2441no—
514C2×#41—2441no—
515C2×#41—2441no—
516C2×#41—2441no—
517C22×Q8—611no—
518C22×D4—611no—
519C22×D4—611no—
520C22×D4—1221no—
521C22×D4—1221no—
522C22×D4—1221no—
523C22×D4—1221no—
524C22×D4—1221no—
525C22×D4—1221no—
526C22×D4D24411yescharacteristic
527C23×C4—1221no—
528C23×C4—1221no—
529C23×C4—1221no—
530C23×C4C22×D6111yescharacteristic
531C23×C4C22×D6111yescharacteristic
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—41no—
535C22×C8—22no—
536C22×C8—22no—
537C22×C8—41no—
538C22×C8C22×D6111yescharacteristic
539C22×C8C22×D6111yescharacteristic
540C22×C8C22×D6111yescharacteristic
541C22×C8C22×D6111yescharacteristic
542#127—614no—
543#127—1228no—
544#127—1222no—
545#121—614no—
546#121—614no—
547#121—1222no—
548#121—1222no—
549#121—1228no—
550#121—1228no—
551C4×Q8—614no—
552C4×Q8—1222no—
553C4×D4—1228no—
554C4×D4C4×D6114yes—
555C4×D4C22⋊D6114yes—
556#117—1222no—
557#117—2441no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—1222no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—2441no—
567C2×C4⋊C4D24411yescharacteristic
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4D24411yescharacteristic
574C2×C22⋊C4D24411yescharacteristic
575C2×C42—1221no—
576C2×C42—1221no—
577C2×C42—1221no—
578C2×C42C22×D6111yescharacteristic
579C4⋊C8—22no—
580#103—614no—
581#103—1222no—
582#103—1222no—
583#103—1222no—
584#102—1222no—
585#102—1222no—
586#102—1222no—
587#102—1222no—
588#102—2441no—
589#102—2441no—
590#102—2441no—
591#102—2441no—
592C22⋊C8—22no—
593C22⋊C8—22no—
594#97—22no—
595#95—1221no—
596#95—1221no—
597#95—1221no—
598#95—1221no—
599#95—1221no—
600C24—1221no—
601C24—1221no—
602C24C2×D24411yescharacteristic
603C24C2×D24411yescharacteristic
604#41—1228no—
605#41—1228no—
606#41—2444no—
607#41—2444no—
608#41—2444no—
609#41—2444no—
610#41—2444no—
611#41—2444no—
612C2×Q8—612no—
613C2×Q8—612no—
614C2×Q8—612no—
615C2×Q8—1221no—
616C2×Q8—1221no—
617C2×Q8—1221no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—612no—
621C2×D4—612no—
622C2×D4—1224no—
623C2×D4—1224no—
624C2×D4—1224no—
625C2×D4—1224no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4—1221no—
631C2×D4—1221no—
632C2×D4—1221no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1224no—
637C2×D4—1224no—
638C2×D4—4881no—
639C2×D4—4881no—
640C2×D4—4881no—
641C2×D4—4881no—
642C2×D4—4881no—
643C2×D4—4881no—
644C2×D4—2442no—
645C2×D4—2442no—
646C2×D4—2442no—
647C2×D4—2442no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4#1175819814yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1224no—
663C22×C4—1224no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—4881no—
668C22×C4—2442no—
669C22×C4—2442no—
670C22×C4—2442no—
671C22×C4—2442no—
672C22×C4—2442no—
673C22×C4—2442no—
674C22×C4C2×C4×D6112yes—
675C22×C4C2×C4×D6112yes—
676C22×C4C2×D24411yescharacteristic
677C22×C4C2×D24411yescharacteristic
678C22×C4C2×D24411yescharacteristic
679C22×C4C2×D24411yescharacteristic
680C22×C4C2×C22⋊D6112yes—
681C22×C4C2×C22⋊D6112yes—
682C22×C4C23×D6111yescharacteristic
683M16—44no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—44no—
696C2×C8D4×D6112yes—
697C4⋊C4—612no—
698C4⋊C4—612no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1224no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—2442no—
709C4⋊C4#1175819814yes—
710C22⋊C4—1224no—
711C22⋊C4—1224no—
712C22⋊C4—4881no—
713C22⋊C4—2442no—
714C22⋊C4—2442no—
715C22⋊C4#1175819814yes—
716C22⋊C4#1175819814yes—
717C42—1224no—
718C42—4881no—
719C42—2442no—
720C42C2×C4×D6112yes—
721C42C2×C22⋊D6112yes—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—1222no—
735C23—1222no—
736C23—2441no—
737C23—2441no—
738C23—2441no—
739C23—2441no—
740C23—2441no—
741C23—2441no—
742C23—2441no—
743C23—2441no—
744C23—2441no—
745C23—2441no—
746C23—2441no—
747C23—2441no—
748C23C2×#1175819812yes—
749C23C2×#1175819812yes—
750C23C22×D24411yescharacteristic
751Q8—614no—
752Q8—1222no—
753Q8—1222no—
754Q8—1222no—
755D4—44no—
756D4—1222no—
757D4—1222no—
758D4—1222no—
759D4—1222no—
760D4—4884no—
761D4—4884no—
762D4—4884no—
763D4—2448no—
764D4—2448no—
765D4—2448no—
766D4—2441no—
767D4—2441no—
768D4—2441no—
769D4—2441no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1222no—
791C2×C4—4884no—
792C2×C4—2448no—
793C2×C4—2448no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4C2×#1175819812yes—
808C2×C4C2×#1175819812yes—
809C2×C4C2×#1175819812yes—
810C2×C4C2×#1175819812yes—
811C2×C4C22×C4×D6111yescharacteristic
812C2×C4C2×D4×D6111yescharacteristic
813C2×C4C22×C22⋊D6111yescharacteristic
814C2×C4#41×D6111yescharacteristic
815C2×C4#1451982211yescharacteristic
816C2×C4#1451982311yescharacteristic
817C8—22no—
818C8—41no—
819C8—41no—
820C8—41no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—4881no—
836C22—4881no—
837C22—4881no—
838C22—4881no—
839C22—4881no—
840C22—4881no—
841C22—4881no—
842C22—4881no—
843C22—2442no—
844C22—2442no—
845C22—2442no—
846C22—2442no—
847C22—2442no—
848C22—2442no—
849C22C22×#1175819811yescharacteristic
850C22D4×D24411yescharacteristic
851C22#1684040711yescharacteristic
852C22#1684056211yescharacteristic
853C22#1684056211yescharacteristic
854C22#1684056711yescharacteristic
855C22#1684057411yescharacteristic
856C4—22no—
857C4—22no—
858C4—22no—
859C4—22no—
860C4—1224no—
861C4—4881no—
862C4—4881no—
863C4—4881no—
864C4—2442no—
865C4—2442no—
866C4C4×D4×D6111yescharacteristic
867C4#1684023411yescharacteristic
868C4D4×C22⋊D6111yescharacteristic
869C4#1684040011yescharacteristic
870C2—42no—
871C2—42no—
872C2—4882no—
873C2—4882no—
874C2D4×#1175819811yescharacteristic
875C2#2145433911yescharacteristic
876C2#2145434611yescharacteristic
877C2#2145736411yescharacteristic
878C2#2145740911yescharacteristic
879C2#2145782711yescharacteristic
880C2#2145794711yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
prime radicalC2×#16840433C2
cosocleC22×C4×C61C24
hypercenterC2×#435D61
hypocenterC61#22422
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#16839764C2semidirect
3. C2×#16839759C2semidirect
4. #21448748C2semidirect
5. #21446745C2semidirect
6. #21446643C2semidirect
7. #21446257C2semidirect
8. #21446247C2semidirect
9. #21446139C2semidirect
10. #21446134C2semidirect
11. #21445835C2semidirect
12. #21445760C2semidirect
13. #21445760C2semidirect
14. #21445650C2semidirect
15. C2×C61×#435C2semidirect
19. #16840433C4semidirect
75. C2×#11758222C2×C4semidirect
89. #14519774C2×C4semidirect
94. #14519751C2×C4semidirect
98. C4×Dic122C2×C4semidirect
122. #14519702D4semidirect
431. C2×#435D61semidirect
504. C61#22422semidirect

Maximal subgroups

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

subgroupindex
C2×#168404332
C2×#168397642
C2×#168397592
#214487482
#214467452
#214466432
#214462572
#214462472
#214461392
#214461342
#214458352
#214457602
#214456502
C2×C61×#4352
#2242261