Finite Group Databasebeta

← C2×#21456694 #30550692

Subgroups — C2×#21456694 #30550692

Order 15616.

2186 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840341C211yesmaximal, characteristic
2C2×#16840335C211yesmaximal, characteristic, complemented
3#21456694C2116yesmaximal, direct product factor
4C2×#16840096C211yesmaximal, characteristic, complemented
5C2×#16840106C211yesmaximal, characteristic, complemented
6C2×#16840084C211yesmaximal, characteristic, complemented
7C2×#16840094C211yesmaximal, characteristic, complemented
8C2×#16840018C211yesmaximal, characteristic, complemented
9C2×#16840006C211yesmaximal, characteristic, complemented
10C2×#16840003C211yesmaximal, characteristic, complemented
11C2×#16839925C211yesmaximal, characteristic, complemented
12C2×#16839921C211yesmaximal, characteristic, complemented
13C2×#16839919C211yesmaximal, characteristic, complemented
14C2×#16839899C211yesmaximal, characteristic, complemented
15C2×#16839728C211yesmaximal, characteristic, complemented
16C2×C61×#465C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758224C2211yescharacteristic
19C22×Q8×D61C2211yescharacteristic
20C22×Dic244C2211yescharacteristic
21C22×#11758202C2211yescharacteristic
22C22×#11758200C2211yescharacteristic
23C22×#11758194C2211yescharacteristic
24#16840341—24no—
25#16840341C2218yes—
26#16840335—24no—
27#16840335C2218yescomplemented
28C2×#14519776—21no—
29C2×#14519763—21no—
30C2×#14519762—21no—
31C2×#14519759—21no—
32C2×#14519757C2211yescharacteristic
33C2×#14519757C2211yescharacteristic
34C2×#14519756C2211yescharacteristic
35C2×#14519756C2211yescharacteristic
36C2×#14519754—21no—
37C2×#14519753C2211yescharacteristic
38C2×#14519750—21no—
39C2×#14519749—21no—
40C2×#14519748—21no—
41C2×#14519748C2211yescharacteristic
42C2×#14519735C2211yescharacteristic
43C2×C4⋊C4×D61C2211yescharacteristic
44#16840106C2218yescomplemented
45#16840096C2218yescomplemented
46#16840094C2218yescomplemented
47#16840084C2218yescomplemented
48#16840018C2218yescomplemented
49#16840006C2218yescomplemented
50#16840003C2218yescomplemented
51#16839925C2218yescomplemented
52#16839921C2218yescomplemented
53#16839919C2218yescomplemented
54#16839899C2218yescomplemented
55C2×#14519711C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519702C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64#16839728C2218yescomplemented
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×C22⋊Q8×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#465C2218yescomplemented
74C2×#106×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758222—42no—
78C2×#11758222—42no—
79C2×#11758222D414yes—
80C2×#11758222C2314yes—
81C2×#11758224—22no—
82C2×#11758224—42no—
83C2×#11758224—42no—
84C2×#11758224C2314yes—
85C22×Dic122—21no—
86C22×Dic122D411yescharacteristic
87C22×Dic122C2311yescharacteristic
88C22×Dic122C2311yescharacteristic
89C2×Q8×D61—22no—
90C2×Q8×D61—42no—
91C2×Q8×D61—42no—
92C2×Q8×D61C2314yes—
93C22×D244D411yescharacteristic
94C22×C22⋊D61—21no—
95C22×C22⋊D61—21no—
96C22×C22⋊D61D411yescharacteristic
97C22×C22⋊D61D411yescharacteristic
98C23×Dic61—21no—
99C22×C4×D61—21no—
100C22×C4×D61—21no—
101C22×C4×D61C2311yescharacteristic
102C22×C4×D61C2311yescharacteristic
103C2×Dic244—42no—
104C2×Dic244C2314yes—
105C2×#11758202—42no—
106C2×#11758202C2314yes—
107C2×#11758200—42no—
108C2×#11758200C2314yes—
109C2×#11758194—42no—
110C2×#11758194C2314yes—
111C22×#92418C2311yescharacteristic
112C22×#92418C2311yescharacteristic
113#14519776—28no—
114#14519763—28no—
115#14519762—28no—
116#14519759—28no—
117#14519757—22no—
118#14519757—22no—
119#14519757C2314yes—
120#14519757C2314yes—
121#14519756—22no—
122#14519756—22no—
123#14519756C2314yes—
124#14519756C2314yes—
125#14519754—28no—
126#14519753—22no—
127#14519753C2314yes—
128#14519750—28no—
129#14519749—28no—
130#14519748—28no—
131#14519748—22no—
132#14519748C2314yes—
133#14519735—22no—
134#14519735C2314yes—
135C2×C4⋊Dic61—21no—
136C2×C4⋊Dic61—21no—
137C2×C4⋊Dic61C2311yescharacteristic
138C2×C4⋊Dic61C2311yescharacteristic
139C2×#11758196—21no—
140C2×#11758196—21no—
141C2×#11758196—21no—
142C2×#11758196—21no—
143C4⋊C4×D61—22no—
144C4⋊C4×D61C2314yes—
145C2×C22⋊Dic61—21no—
146C2×C22⋊Dic61—21no—
147C2×C22⋊Dic61—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×#11758198—21no—
152C2×C4×Dic61—21no—
153#14519711C2314yes—
154#14519710C2314yes—
155#14519708C2314yes—
156#14519702C2314yes—
157#14519702C2314yes—
158#14519701C2314yes—
159#14519700C2314yes—
160#14519700C2314yes—
161#14519698C2314yes—
162#14519689C2314yes—
163#14519689C2314yes—
164#14519689C2314yes—
165#14519689C2314yes—
166C22×Q8×C61C2311yescharacteristic
167C22×D4×C61—21no—
168C22×D4×C61C2311yescharacteristic
169C23×C4×C61C2311yescharacteristic
170C2×SD16×C61—42no—
171C2×SD16×C61C2314yes—
172C22×C8×C61—42no—
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2311yescharacteristic
175C22×C8×C61C2314yes—
176C22⋊Q8×C61—22no—
177C22⋊Q8×C61C2314yes—
178#121×C61—22no—
179#121×C61C2314yes—
180C2×C4⋊C4×C61—21no—
181C2×C4⋊C4×C61C2311yescharacteristic
182C2×C4⋊C4×C61C2311yescharacteristic
183C2×C22⋊C4×C61—21no—
184C2×C22⋊C4×C61—21no—
185#106×C61C2314yes—
186#103×C61C2314yes—
187#102×C61C2314yes—
188C24×C61—21no—
189C24×C61C2×D411yescharacteristic
190C23×D61C2×D411yescharacteristic
191C23×D61C2×D411yescharacteristic
192C2×Q8×C61—21no—
193C2×Q8×C61—22no—
194C2×Q8×C61—22no—
195C2×Q8×C61C2412yes—
196C2×D4×C61—24no—
197C2×D4×C61—21no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61—82no—
201C2×D4×C61C2412yes—
202C22×C4×C61—22no—
203C22×C4×C61—22no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D412yes—
209C22×C4×C61C2412yes—
210C22×C4×C61C2411yescharacteristic
211C2×C22⋊D61—24no—
212C2×C22⋊D61—24no—
213C2×C22⋊D61—42no—
214C2×C22⋊D61—42no—
215C2×C22⋊D61—44no—
216C2×C22⋊D61—82no—
217C2×C22⋊D61C2×D414yes—
218C2×C22⋊D61C2×D414yes—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—24no—
224C22×Dic61—44no—
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227Q8×D61—44no—
228Q8×D61—44no—
229Q8×D61—48no—
230#11758224—44no—
231#11758224—44no—
232#11758224—48no—
233#11758222—48no—
234#11758222—44no—
235#11758222—44no—
236C2×D244—42no—
237C2×D244C2×D414yes—
238C2×C4×D61—22no—
239C2×C4×D61—22no—
240C2×C4×D61—22no—
241C2×C4×D61—22no—
242C2×C4×D61—24no—
243C2×C4×D61—24no—
244C2×C4×D61—44no—
245C2×C4×D61—82no—
246C2×C4×D61C2×D412yes—
247C2×C4×D61C2×D412yes—
248C2×C4×D61C2412yes—
249C2×C4×D61C2412yes—
250C2×Dic122—22no—
251C2×Dic122—22no—
252C2×Dic122—22no—
253C2×Dic122—22no—
254C2×Dic122—21no—
255C2×Dic122—21no—
256C2×Dic122—24no—
257C2×Dic122—42no—
258C2×Dic122—44no—
259C2×Dic122C2×D414yes—
260C2×Dic122C2412yes—
261C2×Dic122C2412yes—
262SD16×C61—44no—
263C2×C8×C61—22no—
264C2×C8×C61—22no—
265C2×C8×C61—44no—
266C2×C8×C61C2412yes—
267C2×C8×C61C2412yes—
268C4⋊C4×C61—24no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61C2412yes—
272C4⋊C4×C61C2412yes—
273C22⋊C4×C61—24no—
274C22⋊C4×C61—24no—
275C22⋊Dic61—24no—
276C22⋊Dic61—24no—
277C22⋊Dic61—24no—
278#11758202—44no—
279#11758200—44no—
280#11758198—24no—
281#11758198—24no—
282#11758198—24no—
283#11758198—24no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—24no—
287C4⋊Dic61—24no—
288C4⋊Dic61C2412yes—
289C4⋊Dic61C2412yes—
290#11758196—24no—
291#11758196—24no—
292#11758196—24no—
293#11758196—24no—
294C4×Dic61—24no—
295#11758194—44no—
296C2×#92418—22no—
297C2×#92418—22no—
298C2×#92418C2412yes—
299C2×#92418C2412yes—
300Dic244—44no—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—42no—
306C23×C61—42no—
307C23×C61—42no—
308C23×C61C22×D412yes—
309C23×C61C22×D411yescharacteristic
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61C22×D412yes—
317C22×D61C22×D412yes—
318Q8×C61—22no—
319Q8×C61—22no—
320Q8×C61—42no—
321D4×C61—22no—
322D4×C61—22no—
323D4×C61—42no—
324D4×C61—84no—
325C2×C4×C61—22no—
326C2×C4×C61—24no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—42no—
333C2×C4×C61—42no—
334C2×C4×C61—42no—
335C2×C4×C61C22×D412yes—
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61H(5,𝔽2)12yes—
338C2×C4×C61H(5,𝔽2)12yes—
339C2×C4×C61C2511yescharacteristic
340C22⋊D61—44no—
341C22⋊D61—44no—
342C22⋊D61—48no—
343C22⋊D61—84no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—48no—
351C2×Dic61—42no—
352C2×Dic61—42no—
353C2×Dic61—42no—
354C2×Dic61—42no—
355C2×Dic61C22×D412yes—
356C2×Dic61C22×D412yes—
357D244—44no—
358C4×D61—24no—
359C4×D61—24no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—22no—
364C4×D61—48no—
365C4×D61—84no—
366Dic122—22no—
367Dic122—22no—
368Dic122—22no—
369Dic122—22no—
370Dic122—44no—
371Dic122—48no—
372Dic122—42no—
373Dic122—42no—
374C8×C61—22no—
375C8×C61—22no—
376#92418—22no—
377#92418—22no—
378C2×#3201—611nomaximal, Sylow
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—44no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—84no—
387C22×C61#53412yes—
388C22×C61#57712yes—
389C22×C61#57812yes—
390C22×C61C23×D411yescharacteristic
391C2×D61—22no—
392C2×D61—22no—
393C2×D61—22no—
394C2×D61—22no—
395C2×D61—22no—
396C2×D61—22no—
397C2×D61—44no—
398C2×D61—44no—
399C4×C61—22no—
400C4×C61—42no—
401C4×C61—42no—
402C4×C61—42no—
403C4×C61#53412yes—
404C4×C61C2×H(5,𝔽2)11yescharacteristic
405C4×C61C2×H(5,𝔽2)11yescharacteristic
406Dic61—22no—
407Dic61—22no—
408Dic61—42no—
409Dic61—42no—
410Dic61—42no—
411Dic61—42no—
412C2×#537—611no—
413C2×#536—611no—
414#3201—6116no—
415C2×#484—611no—
416C2×#485—611no—
417C2×#482—611no—
418C2×#483—611no—
419C2×#470—611no—
420C2×#468—611no—
421C2×#467—611no—
422C2×#465D6111yescharacteristic, complemented
423C2×#452—611no—
424C2×#452—611no—
425C2×#451—611no—
426C2×#448—611no—
427C2×#408—611no—
428C2×C61—42no—
429C2×C61—82no—
430C2×C61#320114yescomplemented
431C2×C61C2×#53411yescharacteristic
432C2×C61C2×#57711yescharacteristic
433C2×C61C2×#57811yescharacteristic
434D61—42no—
435D61—42no—
436C22×#41—611no—
437C22×#41—611no—
438C23×Q8—611no—
439C22×Q16—611no—
440C22×Q16—611no—
441C22×SD16—611no—
442C22×SD16C2×D6111yescharacteristic
443C22×M16—611no—
444C23×C8C2×D6111yescharacteristic
445#537—618no—
446#537—1224no—
447#536—618no—
448#536—1224no—
449C2×C4⋊Q8—1221no—
450C2×#124—1221no—
451C2×#123—1221no—
452C2×#123—1221no—
453C2×C22⋊Q8—611no—
454C2×C22⋊Q8—611no—
455C2×C22⋊Q8—611no—
456C2×C22⋊Q8—611no—
457C2×C22⋊Q8—611no—
458C2×C22⋊Q8—1221no—
459C2×C22⋊Q8C2×D6111yescharacteristic
460C2×#121—611no—
461C2×#121—1221no—
462C2×#121—1221no—
463C2×#121—1221no—
464C2×#121C2×D6111yescharacteristic
465C2×#117—611no—
466C22×C4⋊C4—611no—
467#485—618no—
468#484—618no—
469#483—618no—
470#482—618no—
471#470—618no—
472#468—618no—
473#467—618no—
474#465C2×D6118yescomplemented
475#452—618no—
476#452—618no—
477#451—618no—
478#448—618no—
479C2×#107—611no—
480C2×#107—611no—
481C2×#106—611no—
482C2×#106C2×D6111yescharacteristic
483C2×#103—611no—
484C2×#103—611no—
485C2×#103—611no—
486C2×#103—611no—
487C2×#103—611no—
488C2×#103C2×D6111yescharacteristic
489C2×#102—611no—
490C2×#102C2×D6111yescharacteristic
491#408—618no—
492C2×C22⋊C8—611no—
493C2×C22⋊C8—611no—
494C2×C22⋊C8—611no—
495C2×C22⋊C8—611no—
496C61C2×#320111yescharacteristic, complemented, Sylow
497C2×#41—614no—
498C2×#41—614no—
499C2×#41—614no—
500C2×#41—1222no—
501C2×#41—2442no—
502C2×#41—2442no—
503C2×#41—2442no—
504C2×#41—2442no—
505C22×Q8—611no—
506C22×Q8—614no—
507C22×Q8—611no—
508C22×Q8—611no—
509C22×Q8—1221no—
510C22×Q8—1222no—
511C22×Q8—2442no—
512C22×Q8—2442no—
513C22×Q8C22×D6111yescharacteristic
514C22×D4—21no—
515C22×D4—611no—
516C22×D4—611no—
517C22×D4—611no—
518C22×D4—1221no—
519C22×D4—1221no—
520C22×D4C22×D6111yescharacteristic
521C23×C4—611no—
522C23×C4—611no—
523C23×C4—1221no—
524C23×C4—1221no—
525C23×C4—1221no—
526C23×C4C22×D6111yescharacteristic
527C2×Q16—614no—
528C2×Q16—614no—
529C2×Q16—2442no—
530C2×Q16—2442no—
531C2×SD16—42no—
532C2×SD16—614no—
533C2×SD16—2442no—
534C2×SD16C22×D6114yes—
535C2×M16—614no—
536C2×M16—2442no—
537C22×C8—42no—
538C22×C8—611no—
539C22×C8—611no—
540C22×C8C22×D6111yescharacteristic
541C22×C8C22×D6111yescharacteristic
542C22×C8C22×D6114yes—
543C4⋊Q8—1228no—
544#124—1228no—
545#123—1228no—
546#123—1228no—
547C22⋊Q8—22no—
548C22⋊Q8—614no—
549C22⋊Q8—614no—
550C22⋊Q8—614no—
551C22⋊Q8—614no—
552C22⋊Q8—614no—
553C22⋊Q8—1228no—
554C22⋊Q8—1222no—
555C22⋊Q8—1222no—
556C22⋊Q8—1222no—
557C22⋊Q8—1222no—
558C22⋊Q8—1222no—
559C22⋊Q8C22×D6114yes—
560#121—22no—
561#121—614no—
562#121—1228no—
563#121—1222no—
564#121—1228no—
565#121—1228no—
566#121C22×D6114yes—
567#117—614no—
568#117—1222no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—611no—
571C2×C4⋊C4—611no—
572C2×C4⋊C4—614no—
573C2×C4⋊C4—1222no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4—1221no—
576C2×C4⋊C4—1221no—
577C2×C4⋊C4—1221no—
578C2×C4⋊C4—1221no—
579C2×C4⋊C4—1221no—
580C2×C4⋊C4C22×D6111yescharacteristic
581C2×C4⋊C4C22×D6111yescharacteristic
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—1221no—
585C2×C22⋊C4—1221no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C42—1221no—
592#107—614no—
593#107—614no—
594#106—614no—
595#106C22×D6114yes—
596#103—614no—
597#103—614no—
598#103—614no—
599#103—614no—
600#103—614no—
601#103C22×D6114yes—
602#102—614no—
603#102C22×D6114yes—
604C22⋊C8—614no—
605C22⋊C8—614no—
606C22⋊C8—614no—
607C22⋊C8—614no—
608C24—21no—
609C24—611no—
610C24—611no—
611C24D4×D6111yescharacteristic
612#41—2448no—
613#41—2444no—
614#41—2444no—
615#41—2444no—
616#41—2444no—
617#41—2448no—
618C2×Q8—21no—
619C2×Q8—22no—
620C2×Q8—22no—
621C2×Q8—614no—
622C2×Q8—612no—
623C2×Q8—612no—
624C2×Q8—1224no—
625C2×Q8—1221no—
626C2×Q8—1221no—
627C2×Q8—1222no—
628C2×Q8—1222no—
629C2×Q8—1222no—
630C2×Q8—1222no—
631C2×Q8—2442no—
632C2×Q8—2444no—
633C2×Q8—2444no—
634C2×Q8—2444no—
635C2×Q8—2448no—
636C2×Q8C23×D6112yes—
637C2×D4—24no—
638C2×D4—21no—
639C2×D4—22no—
640C2×D4—22no—
641C2×D4—82no—
642C2×D4—614no—
643C2×D4—614no—
644C2×D4—614no—
645C2×D4—1224no—
646C2×D4—1224no—
647C2×D4—4882no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4—2442no—
651C2×D4—2444no—
652C2×D4C23×D6112yes—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—612no—
661C22×C4—612no—
662C22×C4—612no—
663C22×C4—612no—
664C22×C4—1224no—
665C22×C4—1224no—
666C22×C4—1224no—
667C22×C4—1222no—
668C22×C4—1222no—
669C22×C4—1222no—
670C22×C4—1222no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—4882no—
676C22×C4—2444no—
677C22×C4—2444no—
678C22×C4D4×D6112yes—
679C22×C4D4×D6111yescharacteristic
680C22×C4C23×D6112yes—
681C22×C4C23×D6111yescharacteristic
682Q16—2444no—
683Q16—2444no—
684SD16—44no—
685SD16—2444no—
686M16—2444no—
687C2×C8—22no—
688C2×C8—22no—
689C2×C8—44no—
690C2×C8—612no—
691C2×C8—612no—
692C2×C8—1222no—
693C2×C8—1222no—
694C2×C8C23×D6112yes—
695C2×C8C23×D6112yes—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—612no—
700C4⋊C4—612no—
701C4⋊C4—1224no—
702C4⋊C4—1224no—
703C4⋊C4—1224no—
704C4⋊C4—1224no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1224no—
708C4⋊C4—1224no—
709C4⋊C4C23×D6112yes—
710C4⋊C4C23×D6112yes—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—1224no—
714C22⋊C4—1224no—
715C22⋊C4—1224no—
716C22⋊C4—1224no—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C22⋊C4—1224no—
720C42—1224no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—612no—
729C23—612no—
730C23—1222no—
731C23—1222no—
732C23—1222no—
733C23—1222no—
734C23—1222no—
735C23—1222no—
736C23C2×D4×D6112yes—
737C23C2×D4×D6111yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—42no—
741Q8—1222no—
742Q8—1222no—
743Q8—1222no—
744Q8—1222no—
745Q8—2444no—
746Q8—2448no—
747Q8—2442no—
748Q8—2442no—
749D4—22no—
750D4—22no—
751D4—42no—
752D4—84no—
753D4—4884no—
754D4—2444no—
755D4—2444no—
756D4—2444no—
757D4—2448no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—612no—
769C2×C4—612no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1224no—
773C2×C4—1224no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—4884no—
783C2×C4—2448no—
784C2×C4—2448no—
785C2×C4—2442no—
786C2×C4—2442no—
787C2×C4—2442no—
788C2×C4—2442no—
789C2×C4C2×D4×D6112yes—
790C2×C4C2×D4×D6111yescharacteristic
791C2×C4#1451982212yes—
792C2×C4#1451982312yes—
793C2×C4C24×D6111yescharacteristic
794C8—22no—
795C8—22no—
796C8—1222no—
797C8—1222no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—84no—
806C22—1222no—
807C22—1222no—
808C22—1222no—
809C22—1222no—
810C22—1222no—
811C22—1222no—
812C22—2444no—
813C22—2444no—
814C22#1684032012yes—
815C22#1684056812yes—
816C22#1684057612yes—
817C22C22×D4×D6111yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—1222no—
823C4—1222no—
824C4—2442no—
825C4—2442no—
826C4—2442no—
827C4—2442no—
828C4#1684032012yes—
829C4C2×#1451982211yescharacteristic
830C4C2×#1451982311yescharacteristic
831C2—42no—
832C2—82no—
833C2—2442no—
834C2—2442no—
835C2#2145669414yesdirect product factor
836C2C2×#1684032011yescharacteristic
837C2C2×#1684056811yescharacteristic
838C2C2×#1684057611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#465C2
socleC23×C61C22×D4
prime radicalC2×#16840341C2
hypercenterC2×#465D61
hypocenterC61C2×#3201
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
2. C2×#16840335C2semidirect
3. #21456694C2direct (N × H)
4. C2×#16840096C2semidirect
5. C2×#16840106C2semidirect
6. C2×#16840084C2semidirect
7. C2×#16840094C2semidirect
8. C2×#16840018C2semidirect
9. C2×#16840006C2semidirect
10. C2×#16840003C2semidirect
11. C2×#16839925C2semidirect
12. C2×#16839921C2semidirect
13. C2×#16839919C2semidirect
14. C2×#16839899C2semidirect
15. C2×#16839728C2semidirect
16. C2×C61×#465C2semidirect
27. #16840335C22semidirect
44. #16840106C22semidirect
45. #16840096C22semidirect
46. #16840094C22semidirect
47. #16840084C22semidirect
48. #16840018C22semidirect
49. #16840006C22semidirect
50. #16840003C22semidirect
51. #16839925C22semidirect
52. #16839921C22semidirect
53. #16839919C22semidirect
54. #16839899C22semidirect
64. #16839728C22semidirect
73. C61×#465C22semidirect
422. C2×#465D61semidirect
430. C2×C61#3201semidirect
474. #465C2×D61semidirect
496. C61C2×#3201semidirect
835. C2#21456694direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403412
C2×#168403352
#214566942
C2×#168400962
C2×#168401062
C2×#168400842
C2×#168400942
C2×#168400182
C2×#168400062
C2×#168400032
C2×#168399252
C2×#168399212
C2×#168399192
C2×#168398992
C2×#168397282
C2×C61×#4652
C2×#320161