Finite Group Databasebeta

← #29689816

Subgroups — #29689816

Order 15616.

1598 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840271C211yesmaximal, characteristic
2#21448201C211yesmaximal, characteristic, complemented
3#380×D61C211yesmaximal, characteristic, complemented
4#21446802C212yesmaximal, complemented
5#21446653C212yesmaximal, complemented
6#21446271C212yesmaximal, complemented
7#21446269C212yesmaximal, complemented
8#21445807C211yesmaximal, characteristic, complemented
9#21445804C211yesmaximal, characteristic, complemented
10#21445804C211yesmaximal, characteristic, complemented
11C61×#1799C211yesmaximal, characteristic, complemented
12C22×#11758222C411yescharacteristic, complemented
13C23×C4×D61C2211yescharacteristic
14#16840271—21no—
15#16840271—21no—
16#16840271—21no—
17#16840271—21no—
18#16840271—21no—
19#16840271—21no—
20#16840271—21no—
21#16840271—21no—
22C2×#14519762C411yescharacteristic, complemented
23C2×#14519759C411yescharacteristic, complemented
24C2×#14519755C411yescharacteristic, complemented
25C2×#14519754C2211yescharacteristic
26C2×#14519750C411yescharacteristic, complemented
27C2×#14519749C2211yescharacteristic
28C2×#14519747C2211yescharacteristic
29C2×#14519745C2211yescharacteristic
30C2×C4×D244C411yescharacteristic, complemented
31C2×C4×C22⋊D61C411yescharacteristic, complemented
32C2×C4×C22⋊D61C2211yescharacteristic
33C2×#14519735—21no—
34C2×#14519734C411yescharacteristic, complemented
35C2×C4⋊C4×D61—21no—
36C2×C22⋊C4×D61C2212yes—
37C2×#14519692C2212yes—
38C2×#14519691C2212yes—
39C2×#14519691C2212yes—
40#16839624—21no—
41#16839622C2211yescharacteristic
42#16839622C2211yescharacteristic
43#16839621—21no—
44#16839620C2212yes—
45#16839619—21no—
46#16839619—21no—
47#16839617C2212yes—
48C22⋊C4×Dic61C2212yes—
49#16839609—21no—
50#95×D61—21no—
51#16839529C2212yes—
52#16839528C2212yes—
53#16839528C2212yes—
54C2×C4×D4×C61C2211yescharacteristic
55C2×#99×C61C2212yes—
56C61×#380C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#342C2212yes—
59C24×D61C2311yescharacteristic
60C2×#11758222—21no—
61C2×#11758222—21no—
62C2×#11758222—21no—
63C2×#11758222—21no—
64C2×#11758222—44no—
65C22×Dic122C2×C411yescharacteristic, complemented
66C22×D244C2×C411yescharacteristic
67C22×D244C2×C411yescharacteristic
68C22×C22⋊D61C2×C411yescharacteristic
69C22×C22⋊D61C2×C411yescharacteristic
70C22×C22⋊D61C2×C411yescharacteristic, complemented
71C22×C22⋊D61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C22×C4×D61—22no—
74C22×C4×D61—44no—
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61C2×C411yescharacteristic
77C22×C4×D61C2×C411yescharacteristic
78C22×C4×D61C2×C411yescharacteristic
79C22×C4×D61C2×C411yescharacteristic, complemented
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61D411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61D411yescharacteristic
86C22×C4×D61D411yescharacteristic
87C22×C4×D61D411yescharacteristic
88#14519762—21no—
89#14519762—21no—
90#14519762—21no—
91#14519762—21no—
92#14519759—21no—
93#14519759—21no—
94#14519759—21no—
95#14519759—21no—
96#14519755—21no—
97#14519755—21no—
98#14519755—21no—
99#14519755—21no—
100#14519754—21no—
101#14519754—21no—
102#14519754—21no—
103#14519754—21no—
104#14519750—21no—
105#14519750—21no—
106#14519750—21no—
107#14519750—21no—
108#14519749—21no—
109#14519749—21no—
110#14519749—21no—
111#14519749—21no—
112#14519747—21no—
113#14519747—21no—
114#14519747—21no—
115#14519747—21no—
116#14519745—21no—
117#14519745—21no—
118#14519745—21no—
119#14519745—21no—
120C4×D244—21no—
121C4×D244—21no—
122C4×D244—21no—
123C4×D244—21no—
124C4×C22⋊D61—21no—
125C4×C22⋊D61—21no—
126C4×C22⋊D61—21no—
127C4×C22⋊D61—21no—
128C4×C22⋊D61—21no—
129C4×C22⋊D61—21no—
130C4×C22⋊D61—21no—
131C4×C22⋊D61—21no—
132#14519735—44no—
133#14519734—21no—
134#14519734—21no—
135#14519734—21no—
136#14519734—21no—
137C2×C4⋊Dic61—21no—
138C2×C4⋊Dic61—21no—
139C2×C4⋊Dic61C2×C411yescharacteristic, complemented
140C2×#11758196—22no—
141C2×#11758196C2×C411yescharacteristic, complemented
142C2×#11758196C2×C411yescharacteristic, complemented
143C2×#11758196C2×C411yescharacteristic, complemented
144C2×#11758196C2×C411yescharacteristic, complemented
145C4⋊C4×D61—44no—
146C2×C22⋊Dic61C2×C411yescharacteristic, complemented
147C2×C22⋊Dic61C2312yes—
148C2×C22⋊Dic61C2312yes—
149C2×C22⋊Dic61C2311yescharacteristic
150C2×#11758198—22no—
151C2×#11758198—22no—
152C2×#11758198—22no—
153C2×#11758198C2×C411yescharacteristic
154C2×#11758198C2×C411yescharacteristic
155C2×#11758198C2×C411yescharacteristic
156C2×#11758198C2×C411yescharacteristic
157C2×#11758198C2×C411yescharacteristic, complemented
158C2×#11758198C2×C411yescharacteristic, complemented
159C22⋊C4×D61—42no—
160C22⋊C4×D61—42no—
161C2×C4×Dic61—22no—
162C2×C4×Dic61C2×C411yescharacteristic, complemented
163#14519692—42no—
164#14519691—42no—
165#14519691—42no—
166#14519684—21no—
167#14519684—21no—
168#14519684—22no—
169#14519684—22no—
170C22×D4×C61C2311yescharacteristic
171C23×C4×C61C2×C411yescharacteristic, complemented
172C23×C4×C61C2311yescharacteristic
173C4×D4×C61—21no—
174C4×D4×C61—21no—
175C4×D4×C61—21no—
176C4×D4×C61—21no—
177C2×C4⋊C4×C61—21no—
178C2×C4⋊C4×C61—21no—
179C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
180C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
181C2×C22⋊C4×C61C2312yes—
182C2×C22⋊C4×C61C2312yes—
183C2×C22⋊C4×C61C2311yescharacteristic
184C2×C42×C61C2×C411yescharacteristic, complemented
185#99×C61—42no—
186#95×C61—21no—
187#95×C61—21no—
188C24×C61C22×C411yescharacteristic
189C24×C61C2411yescharacteristic
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—21no—
194C23×D61—42no—
195C23×D61—42no—
196C23×D61C22×C411yescharacteristic
197C23×D61C22×C411yescharacteristic
198C23×D61C22×C411yescharacteristic
199C23×D61C2×D411yescharacteristic
200C23×D61C2×D411yescharacteristic
201C23×D61C2×D411yescharacteristic
202C23×D61C2×D411yescharacteristic
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—22no—
212C22×C4×C61—22no—
213C22×C4×C61—42no—
214C22×C4×C61—42no—
215C22×C4×C61C22×C411yescharacteristic
216C22×C4×C61C22×C411yescharacteristic
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C2×C22⋊D61—42no—
237C2×C22⋊D61—42no—
238C2×C22⋊D61—42no—
239C22×Dic61—22no—
240C22×Dic61—22no—
241C22×Dic61—42no—
242C22×Dic61C22×C411yescharacteristic
243C22×Dic61C22×C411yescharacteristic
244C22×Dic61C22×C411yescharacteristic
245C22×Dic61C22×C411yescharacteristic
246C22×Dic61C22×C411yescharacteristic
247C22×Dic61C2×D411yescharacteristic
248C22×Dic61C2×D411yescharacteristic
249C22×Dic61C2×D411yescharacteristic
250C22×Dic61C2×D411yescharacteristic
251#11758222—44no—
252#11758222—44no—
253#11758222—44no—
254#11758222—44no—
255C2×D244—21no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244—21no—
259C2×D244—42no—
260C2×D244—42no—
261C2×C4×D61—24no—
262C2×C4×D61—24no—
263C2×C4×D61—24no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—42no—
267C2×C4×D61—42no—
268C2×C4×D61—42no—
269C2×C4×D61—42no—
270C2×C4×D61—42no—
271C2×C4×D61—42no—
272C2×C4×D61—42no—
273C2×C4×D61—42no—
274C2×C4×D61—42no—
275C2×C4×D61—42no—
276C2×C4×D61—44no—
277C2×C4×D61—44no—
278C2×C4×D61—44no—
279C2×C4×D61C22⋊C411yescharacteristic
280C2×C4×D61C22⋊C411yescharacteristic
281C2×C4×D61C22⋊C411yescharacteristic
282C2×C4×D61C22⋊C411yescharacteristic
283C2×C4×D61C22⋊C411yescharacteristic
284C2×C4×D61C22⋊C411yescharacteristic
285C2×C4×D61C22⋊C411yescharacteristic
286C2×C4×D61C22⋊C411yescharacteristic
287C2×C4×D61C22⋊C411yescharacteristic
288C2×C4×D61C22⋊C411yescharacteristic
289C2×C4×D61C22⋊C411yescharacteristic
290C2×C4×D61C22⋊C411yescharacteristic
291C2×C4×D61C22⋊C411yescharacteristic
292C2×C4×D61C22⋊C411yescharacteristic
293C2×C4×D61C22⋊C411yescharacteristic
294C2×C4×D61C22⋊C411yescharacteristic
295C2×Dic122—21no—
296C2×Dic122—21no—
297C2×Dic122—42no—
298C4⋊C4×C61—21no—
299C4⋊C4×C61—21no—
300C4⋊C4×C61—42no—
301C4⋊C4×C61—42no—
302C22⋊C4×C61—21no—
303C22⋊C4×C61—21no—
304C22⋊C4×C61—21no—
305C22⋊C4×C61—21no—
306C22⋊C4×C61—22no—
307C22⋊C4×C61—22no—
308C22⋊C4×C61—22no—
309C22⋊C4×C61—22no—
310C42×C61—21no—
311C42×C61—21no—
312C22⋊Dic61—21no—
313C22⋊Dic61—21no—
314C22⋊Dic61—21no—
315C22⋊Dic61—21no—
316C22⋊Dic61—22no—
317C22⋊Dic61—22no—
318C22⋊Dic61—22no—
319C22⋊Dic61—22no—
320#11758198—21no—
321#11758198—21no—
322#11758198—21no—
323#11758198—21no—
324#11758198—21no—
325#11758198—21no—
326#11758198—21no—
327#11758198—21no—
328#11758198—21no—
329#11758198—21no—
330#11758198—21no—
331#11758198—21no—
332#11758198—44no—
333#11758198—44no—
334#11758198—44no—
335C4⋊Dic61—21no—
336C4⋊Dic61—21no—
337C4⋊Dic61—42no—
338C4⋊Dic61—42no—
339#11758196—21no—
340#11758196—21no—
341#11758196—21no—
342#11758196—21no—
343#11758196—21no—
344#11758196—21no—
345#11758196—21no—
346#11758196—21no—
347#11758196—44no—
348C4×Dic61—21no—
349C4×Dic61—21no—
350C4×Dic61—44no—
351C23×C61—21no—
352C23×C61—21no—
353C23×C61—21no—
354C23×C61—41no—
355C23×C61—41no—
356C23×C61—41no—
357C23×C61—41no—
358C23×C61C23×C411yescharacteristic
359C23×C61C22×D411yescharacteristic
360C23×C61C22×D411yescharacteristic
361C23×C61H(5,𝔽2)11yescharacteristic
362C23×C61H(5,𝔽2)11yescharacteristic
363C23×C612−1+411yescharacteristic
364C23×C612−1+411yescharacteristic
365C22×D61—21no—
366C22×D61—21no—
367C22×D61—22no—
368C22×D61—22no—
369C22×D61—21no—
370C22×D61—21no—
371C22×D61—21no—
372C22×D61—21no—
373C22×D61—21no—
374C22×D61—21no—
375C22×D61—21no—
376C22×D61—21no—
377C22×D61—21no—
378C22×D61—21no—
379C22×D61—22no—
380C22×D61—22no—
381C22×D61—22no—
382C22×D61—22no—
383C22×D61—21no—
384C22×D61—21no—
385C22×D61—21no—
386C22×D61—41no—
387C22×D61—41no—
388C22×D61—41no—
389C22×D61—41no—
390C22×D61—41no—
391C22×D61—41no—
392C22×D61—44no—
393C22×D61—44no—
394C22×D61—44no—
395C22×D61—44no—
396C22×D61—41no—
397C22×D61—41no—
398C22×D61C2×C22⋊C411yescharacteristic
399C22×D61C2×C22⋊C411yescharacteristic
400C22×D61C2×C22⋊C411yescharacteristic
401C22×D61C2×C22⋊C411yescharacteristic
402D4×C61—41no—
403D4×C61—41no—
404D4×C61—41no—
405D4×C61—41no—
406C2×C4×C61—22no—
407C2×C4×C61—22no—
408C2×C4×C61—22no—
409C2×C4×C61—21no—
410C2×C4×C61—21no—
411C2×C4×C61—21no—
412C2×C4×C61—21no—
413C2×C4×C61—21no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—42no—
418C2×C4×C61—42no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—42no—
422C2×C4×C61—42no—
423C2×C4×C61—42no—
424C2×C4×C61—42no—
425C2×C4×C61—42no—
426C2×C4×C61—42no—
427C2×C4×C61C2×C22⋊C411yescharacteristic
428C2×C4×C61C2×C22⋊C411yescharacteristic
429C2×C4×C61C2×C22⋊C411yescharacteristic
430C2×C4×C61C2×C22⋊C411yescharacteristic
431C22⋊D61—42no—
432C22⋊D61—42no—
433C22⋊D61—42no—
434C22⋊D61—41no—
435C22⋊D61—41no—
436C22⋊D61—41no—
437C22⋊D61—41no—
438C22⋊D61—42no—
439C22⋊D61—42no—
440C22⋊D61—42no—
441C2×Dic61—22no—
442C2×Dic61—22no—
443C2×Dic61—22no—
444C2×Dic61—21no—
445C2×Dic61—21no—
446C2×Dic61—21no—
447C2×Dic61—21no—
448C2×Dic61—21no—
449C2×Dic61—41no—
450C2×Dic61—41no—
451C2×Dic61—41no—
452C2×Dic61—41no—
453C2×Dic61—41no—
454C2×Dic61—42no—
455C2×Dic61—42no—
456C2×Dic61—42no—
457C2×Dic61—42no—
458C2×Dic61—42no—
459C2×Dic61—42no—
460C2×Dic61C2×C22⋊C411yescharacteristic
461C2×Dic61C2×C22⋊C411yescharacteristic
462C2×Dic61C2×C22⋊C411yescharacteristic
463C2×Dic61C2×C22⋊C411yescharacteristic
464D244—42no—
465D244—42no—
466D244—42no—
467D244—42no—
468C4×D61—22no—
469C4×D61—22no—
470C4×D61—22no—
471C4×D61—22no—
472C4×D61—22no—
473C4×D61—22no—
474C4×D61—22no—
475C4×D61—22no—
476C4×D61—22no—
477C4×D61—41no—
478C4×D61—41no—
479C4×D61—41no—
480C4×D61—41no—
481C4×D61—41no—
482C4×D61—41no—
483C4×D61—42no—
484C4×D61—42no—
485C4×D61—88no—
486C4×D61#9914yescomplemented
487Dic122—42no—
488Dic122—42no—
489#21874—611nomaximal, Sylow
490C22×C61—21no—
491C22×C61—21no—
492C22×C61—21no—
493C22×C61—21no—
494C22×C61—21no—
495C22×C61—21no—
496C22×C61—41no—
497C22×C61—41no—
498C22×C61—41no—
499C22×C61—41no—
500C22×C61—41no—
501C22×C61—41no—
502C22×C61—41no—
503C22×C61—81no—
504C22×C61—81no—
505C22×C61C22×C22⋊C411yescharacteristic
506C22×C61#52011yescharacteristic
507C22×C61#52011yescharacteristic
508C22×C61#53511yescharacteristic
509C22×C61#53611yescharacteristic
510C22×C61#53711yescharacteristic
511C22×C61#53711yescharacteristic
512C2×D61—24no—
513C2×D61—24no—
514C2×D61—21no—
515C2×D61—21no—
516C2×D61—21no—
517C2×D61—21no—
518C2×D61—21no—
519C2×D61—21no—
520C2×D61—21no—
521C2×D61—21no—
522C2×D61—21no—
523C2×D61—21no—
524C2×D61—42no—
525C2×D61—42no—
526C2×D61—42no—
527C2×D61—42no—
528C2×D61—42no—
529C2×D61—42no—
530C2×D61—42no—
531C2×D61—42no—
532C2×D61—42no—
533C2×D61—42no—
534C2×D61—41no—
535C2×D61—41no—
536C2×D61—41no—
537C2×D61—81no—
538C2×D61—81no—
539C2×D61C2×#9912yes—
540C2×D61#41012yes—
541C4×C61—21no—
542C4×C61—21no—
543C4×C61—21no—
544C4×C61—41no—
545C4×C61—41no—
546C4×C61—41no—
547C4×C61—82no—
548C4×C61—82no—
549C4×C61C2×#9912yes—
550Dic61—21no—
551Dic61—21no—
552Dic61—21no—
553Dic61—41no—
554Dic61—41no—
555Dic61—41no—
556Dic61—82no—
557Dic61—82no—
558Dic61C2×#9912yes—
559C2×#525—611no—
560#2280—611no—
561C2×#380—611no—
562#1996—612no—
563#1964—612no—
564#1898—612no—
565#1898—612no—
566#1799—611no—
567#1799—611no—
568#1799—611no—
569#1799D6111yescharacteristic, complemented
570C2×C61—21no—
571C2×C61—21no—
572C2×C61—21no—
573C2×C61—21no—
574C2×C61—21no—
575C2×C61—21no—
576C2×C61—81no—
577C2×C61#231111yescharacteristic
578C2×C61C22×#9911yescharacteristic
579C2×C61C2×#41011yescharacteristic
580D61—22no—
581D61—22no—
582D61—41no—
583D61—41no—
584D61—81no—
585C22×#41—611no—
586C24×C4—611no—
587#525—1221no—
588#525—1221no—
589#525—1221no—
590#525—1221no—
591#525—1221no—
592#525—1221no—
593#525—1221no—
594#525—1221no—
595C2×#123—611no—
596C2×#123—611no—
597C2×C22⋊Q8—611no—
598C2×C22⋊Q8—611no—
599C2×#121—611no—
600C2×#121—611no—
601C2×#120—611no—
602C2×#120—611no—
603C2×C4×D4—611no—
604C2×C4×D4—611no—
605C2×C4×D4—611no—
606C2×C4×D4C2×D6111yescharacteristic
607C2×#117—611no—
608C2×#117—1221no—
609C22×C4⋊C4—1221no—
610C22×C22⋊C4—612no—
611C2×#99—612no—
612C2×#99—612no—
613C2×#99—612no—
614C2×#99C2×D6112yes—
615#381—1221no—
616#380—611no—
617#380—611no—
618#380—612no—
619#380—1221no—
620#380—1221no—
621#380—1221no—
622#380C2×D6111yescharacteristic
623#380C2×D6111yescharacteristic
624#379—612no—
625C4×C22⋊C4—612no—
626C4×C22⋊C4—1221no—
627C2×#95—1221no—
628#342—612no—
629#342—612no—
630#342—612no—
631#342C2×D6112yes—
632C61#2187411yescharacteristic, complemented, Sylow
633C25—611no—
634C2×#41—1221no—
635C2×#41—1221no—
636C2×#41—1221no—
637C2×#41—1221no—
638C2×#41—2444no—
639C22×Q8—611no—
640C22×D4—611no—
641C22×D4—611no—
642C22×D4—611no—
643C22×D4—611no—
644C22×D4—611no—
645C22×D4—611no—
646C22×D4C22×D6111yescharacteristic
647C23×C4—611no—
648C23×C4—611no—
649C23×C4—611no—
650C23×C4—611no—
651C23×C4—611no—
652C23×C4—611no—
653C23×C4—611no—
654C23×C4—611no—
655C23×C4—611no—
656C23×C4—611no—
657C23×C4—611no—
658C23×C4—611no—
659C23×C4—611no—
660C23×C4—611no—
661C23×C4—1222no—
662C23×C4—2444no—
663C23×C4C4×D6111yescharacteristic, complemented
664C23×C4C22×D6111yescharacteristic
665#123—1221no—
666#123—1221no—
667#123—1221no—
668#123—1221no—
669#123—1221no—
670#123—1221no—
671#123—1221no—
672#123—1221no—
673C22⋊Q8—1221no—
674C22⋊Q8—1221no—
675C22⋊Q8—1221no—
676C22⋊Q8—1221no—
677C22⋊Q8—1221no—
678C22⋊Q8—1221no—
679C22⋊Q8—1221no—
680C22⋊Q8—1221no—
681#121—1221no—
682#121—1221no—
683#121—1221no—
684#121—1221no—
685#121—1221no—
686#121—1221no—
687#121—1221no—
688#121—1221no—
689#120—1221no—
690#120—1221no—
691#120—1221no—
692#120—1221no—
693#120—1221no—
694#120—1221no—
695#120—1221no—
696#120—1221no—
697C4×D4—21no—
698C4×D4—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—1221no—
702C4×D4—1221no—
703C4×D4—1221no—
704C4×D4—1221no—
705C4×D4—1221no—
706C4×D4—1221no—
707C4×D4—1221no—
708C4×D4—1221no—
709C4×D4—1221no—
710C4×D4—1221no—
711C4×D4—1221no—
712C4×D4—1221no—
713#117—1221no—
714#117—1221no—
715#117—1221no—
716#117—1221no—
717#117—2444no—
718C2×C4⋊C4—21no—
719C2×C4⋊C4—21no—
720C2×C4⋊C4—611no—
721C2×C4⋊C4—611no—
722C2×C4⋊C4—611no—
723C2×C4⋊C4—611no—
724C2×C4⋊C4—611no—
725C2×C4⋊C4—1222no—
726C2×C4⋊C4—1221no—
727C2×C4⋊C4—1221no—
728C2×C4⋊C4—2444no—
729C2×C4⋊C4C4×D6111yescharacteristic, complemented
730C2×C22⋊C4—611no—
731C2×C22⋊C4—611no—
732C2×C22⋊C4—611no—
733C2×C22⋊C4—611no—
734C2×C22⋊C4—611no—
735C2×C22⋊C4—611no—
736C2×C22⋊C4—611no—
737C2×C22⋊C4—611no—
738C2×C22⋊C4—612no—
739C2×C22⋊C4—612no—
740C2×C22⋊C4—1222no—
741C2×C22⋊C4—1222no—
742C2×C22⋊C4—1222no—
743C2×C22⋊C4—2442no—
744C2×C22⋊C4—2442no—
745C2×C22⋊C4C4×D6111yescharacteristic, complemented
746C2×C22⋊C4C22×D6112yes—
747C2×C22⋊C4C22×D6112yes—
748C2×C22⋊C4C22×D6111yescharacteristic
749C2×C42—611no—
750C2×C42—1222no—
751C2×C42C4×D6111yescharacteristic, complemented
752#99—42no—
753#99—2442no—
754#99—2442no—
755#99—2442no—
756#95—21no—
757#95—21no—
758#95—1222no—
759#95—1222no—
760#95—1221no—
761#95—1221no—
762C24—611no—
763C24—611no—
764C24—611no—
765C24—611no—
766C24—611no—
767C24—611no—
768C24—611no—
769C24—1221no—
770C24—1221no—
771C24—1221no—
772C24—1221no—
773C24—2442no—
774C24—2442no—
775C24C2×C4×D6111yescharacteristic
776C24C23×D6111yescharacteristic
777#41—2444no—
778#41—2444no—
779#41—2444no—
780#41—2444no—
781C2×Q8—1221no—
782C2×Q8—1221no—
783C2×Q8—2442no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—1221no—
791C2×D4—1221no—
792C2×D4—1221no—
793C2×D4—1221no—
794C2×D4—1221no—
795C2×D4—1221no—
796C2×D4—1221no—
797C2×D4—1221no—
798C2×D4—1221no—
799C2×D4—1221no—
800C2×D4—1221no—
801C2×D4—1221no—
802C2×D4—1221no—
803C2×D4—1221no—
804C2×D4—1221no—
805C2×D4—1221no—
806C2×D4—2442no—
807C2×D4—2442no—
808C2×D4—2442no—
809C2×D4—2442no—
810C2×D4—2442no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—611no—
818C22×C4—611no—
819C22×C4—611no—
820C22×C4—611no—
821C22×C4—611no—
822C22×C4—611no—
823C22×C4—611no—
824C22×C4—611no—
825C22×C4—611no—
826C22×C4—611no—
827C22×C4—611no—
828C22×C4—611no—
829C22×C4—611no—
830C22×C4—611no—
831C22×C4—611no—
832C22×C4—611no—
833C22×C4—611no—
834C22×C4—611no—
835C22×C4—611no—
836C22×C4—611no—
837C22×C4—611no—
838C22×C4—611no—
839C22×C4—611no—
840C22×C4—611no—
841C22×C4—611no—
842C22×C4—1224no—
843C22×C4—1224no—
844C22×C4—1224no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1222no—
848C22×C4—1222no—
849C22×C4—2442no—
850C22×C4—2442no—
851C22×C4—2442no—
852C22×C4—2442no—
853C22×C4—2442no—
854C22×C4—2442no—
855C22×C4—2442no—
856C22×C4—2442no—
857C22×C4—2442no—
858C22×C4—2442no—
859C22×C4—2444no—
860C22×C4—2444no—
861C22×C4—2444no—
862C22×C4—2442no—
863C22×C4C2×C4×D6111yescharacteristic
864C22×C4C2×C4×D6111yescharacteristic
865C22×C4C2×C4×D6111yescharacteristic
866C22×C4C2×C4×D6111yescharacteristic
867C22×C4C2×C4×D6111yescharacteristic
868C22×C4D4×D6111yescharacteristic
869C22×C4D4×D6111yescharacteristic
870C22×C4D4×D6111yescharacteristic
871C22×C4D4×D6111yescharacteristic
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—1221no—
877C4⋊C4—1221no—
878C4⋊C4—1221no—
879C4⋊C4—1221no—
880C4⋊C4—1221no—
881C4⋊C4—1221no—
882C4⋊C4—1221no—
883C4⋊C4—1221no—
884C4⋊C4—1221no—
885C4⋊C4—1221no—
886C4⋊C4—2442no—
887C4⋊C4—2442no—
888C4⋊C4—2444no—
889C22⋊C4—21no—
890C22⋊C4—21no—
891C22⋊C4—21no—
892C22⋊C4—21no—
893C22⋊C4—22no—
894C22⋊C4—22no—
895C22⋊C4—22no—
896C22⋊C4—22no—
897C22⋊C4—1221no—
898C22⋊C4—1221no—
899C22⋊C4—1221no—
900C22⋊C4—1221no—
901C22⋊C4—1221no—
902C22⋊C4—1221no—
903C22⋊C4—1221no—
904C22⋊C4—1221no—
905C22⋊C4—1221no—
906C22⋊C4—1221no—
907C22⋊C4—1221no—
908C22⋊C4—1221no—
909C22⋊C4—1221no—
910C22⋊C4—1221no—
911C22⋊C4—1221no—
912C22⋊C4—1221no—
913C22⋊C4—1222no—
914C22⋊C4—1222no—
915C22⋊C4—1222no—
916C22⋊C4—1222no—
917C22⋊C4—2444no—
918C22⋊C4—2444no—
919C22⋊C4—2444no—
920C42—21no—
921C42—21no—
922C42—1221no—
923C42—1221no—
924C42—2444no—
925C23—21no—
926C23—21no—
927C23—21no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—611no—
933C23—611no—
934C23—611no—
935C23—611no—
936C23—1222no—
937C23—1222no—
938C23—1222no—
939C23—1222no—
940C23—1222no—
941C23—1222no—
942C23—1221no—
943C23—1221no—
944C23—1221no—
945C23—1221no—
946C23—1221no—
947C23—1221no—
948C23—1221no—
949C23—1221no—
950C23—1221no—
951C23—1221no—
952C23—1221no—
953C23—1221no—
954C23—1221no—
955C23—1221no—
956C23—1221no—
957C23—2441no—
958C23—2441no—
959C23—2441no—
960C23—2441no—
961C23—2441no—
962C23—2441no—
963C23—2441no—
964C23—2441no—
965C23—2444no—
966C23—2444no—
967C23—2444no—
968C23—2444no—
969C23C22×C4×D6111yescharacteristic
970C23C2×D4×D6111yescharacteristic
971C23C2×D4×D6111yescharacteristic
972C23#1451982211yescharacteristic
973C23#1451982311yescharacteristic
974C23#1451982411yescharacteristic
975C23#1451982511yescharacteristic
976Q8—2442no—
977Q8—2442no—
978D4—41no—
979D4—41no—
980D4—41no—
981D4—41no—
982D4—2442no—
983D4—2442no—
984D4—2442no—
985D4—2442no—
986D4—2442no—
987D4—2442no—
988D4—2442no—
989D4—2442no—
990D4—2442no—
991D4—2442no—
992D4—2441no—
993D4—2441no—
994D4—2441no—
995D4—2441no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—42no—
1008C2×C4—42no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—42no—
1015C2×C4—42no—
1016C2×C4—42no—
1017C2×C4—611no—
1018C2×C4—614no—
1019C2×C4—611no—
1020C2×C4—611no—
1021C2×C4—611no—
1022C2×C4—1222no—
1023C2×C4—1222no—
1024C2×C4—1222no—
1025C2×C4—1222no—
1026C2×C4—1222no—
1027C2×C4—1222no—
1028C2×C4—1222no—
1029C2×C4—1222no—
1030C2×C4—1222no—
1031C2×C4—1222no—
1032C2×C4—1222no—
1033C2×C4—1222no—
1034C2×C4—1221no—
1035C2×C4—1221no—
1036C2×C4—1221no—
1037C2×C4—1221no—
1038C2×C4—1221no—
1039C2×C4—4888no—
1040C2×C4—2441no—
1041C2×C4—2441no—
1042C2×C4—2441no—
1043C2×C4—2441no—
1044C2×C4—2441no—
1045C2×C4—2441no—
1046C2×C4—2442no—
1047C2×C4—2441no—
1048C2×C4—2441no—
1049C2×C4—2441no—
1050C2×C4—2442no—
1051C2×C4—2442no—
1052C2×C4—2442no—
1053C2×C4—2442no—
1054C2×C4—2442no—
1055C2×C4—2442no—
1056C2×C4—2442no—
1057C2×C4—2441no—
1058C2×C4—2441no—
1059C2×C4C22⋊C4×D6111yescharacteristic
1060C2×C4C22⋊C4×D6111yescharacteristic
1061C2×C4C22⋊C4×D6111yescharacteristic
1062C2×C4C22⋊C4×D6111yescharacteristic
1063C22—21no—
1064C22—21no—
1065C22—21no—
1066C22—21no—
1067C22—21no—
1068C22—21no—
1069C22—41no—
1070C22—41no—
1071C22—41no—
1072C22—41no—
1073C22—41no—
1074C22—41no—
1075C22—41no—
1076C22—81no—
1077C22—81no—
1078C22—612no—
1079C22—612no—
1080C22—1224no—
1081C22—1224no—
1082C22—1221no—
1083C22—1221no—
1084C22—1221no—
1085C22—1221no—
1086C22—1221no—
1087C22—1221no—
1088C22—1221no—
1089C22—1221no—
1090C22—1221no—
1091C22—1221no—
1092C22—4881no—
1093C22—4881no—
1094C22—2442no—
1095C22—2442no—
1096C22—2442no—
1097C22—2442no—
1098C22—2442no—
1099C22—2442no—
1100C22—2442no—
1101C22—2442no—
1102C22—2442no—
1103C22—2442no—
1104C22—2441no—
1105C22—2441no—
1106C22—2441no—
1107C22C2×C22⋊C4×D6111yescharacteristic
1108C22#1684024211yescharacteristic
1109C22#1684024311yescharacteristic
1110C22#1684032811yescharacteristic
1111C22#1684033511yescharacteristic
1112C22#1684034111yescharacteristic
1113C22#1684034211yescharacteristic
1114C4—21no—
1115C4—21no—
1116C4—21no—
1117C4—41no—
1118C4—41no—
1119C4—41no—
1120C4—82no—
1121C4—82no—
1122C4—612no—
1123C4—1221no—
1124C4—1221no—
1125C4—1221no—
1126C4—4882no—
1127C4—4882no—
1128C4—2441no—
1129C4—2441no—
1130C4—2441no—
1131C4#99×D6112yes—
1132C2—21no—
1133C2—21no—
1134C2—21no—
1135C2—21no—
1136C2—21no—
1137C2—21no—
1138C2—81no—
1139C2—1222no—
1140C2—1222no—
1141C2—4881no—
1142C2—2441no—
1143C2—2441no—
1144C2#2144840811yescharacteristic
1145C2C2×#99×D6111yescharacteristic
1146C2#410×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1799C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840271C2
cosocleC24×C61C24
hypercenter#1799D61
hypocenterC61#21874
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #21448201C2semidirect
3. #380×D61C2semidirect
4. #21446802C2semidirect
5. #21446653C2semidirect
6. #21446271C2semidirect
7. #21446269C2semidirect
8. #21445807C2semidirect
9. #21445804C2semidirect
10. #21445804C2semidirect
11. C61×#1799C2semidirect
12. C22×#11758222C4semidirect
22. C2×#14519762C4semidirect
23. C2×#14519759C4semidirect
24. C2×#14519755C4semidirect
26. C2×#14519750C4semidirect
30. C2×C4×D244C4semidirect
31. C2×C4×C22⋊D61C4semidirect
34. C2×#14519734C4semidirect
65. C22×Dic122C2×C4semidirect
70. C22×C22⋊D61C2×C4semidirect
79. C22×C4×D61C2×C4semidirect
139. C2×C4⋊Dic61C2×C4semidirect
141. C2×#11758196C2×C4semidirect
142. C2×#11758196C2×C4semidirect
143. C2×#11758196C2×C4semidirect
144. C2×#11758196C2×C4semidirect
146. C2×C22⋊Dic61C2×C4semidirect
157. C2×#11758198C2×C4semidirect
158. C2×#11758198C2×C4semidirect
162. C2×C4×Dic61C2×C4semidirect
171. C23×C4×C61C2×C4semidirect
179. C2×C4⋊C4×C61C2×C4semidirect
180. C2×C22⋊C4×C61C2×C4semidirect
184. C2×C42×C61C2×C4semidirect
486. C4×D61#99semidirect
569. #1799D61semidirect
632. C61#21874semidirect
663. C23×C4C4×D61semidirect
729. C2×C4⋊C4C4×D61semidirect
745. C2×C22⋊C4C4×D61semidirect
751. C2×C42C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402712
#214482012
#380×D612
#214468022
#214466532
#214462712
#214462692
#214458072
#214458042
C61×#17992
#2187461