Finite Group Databasebeta

← C2×#21455111 #30546444

Subgroups — C2×#21455111 #30546444

Order 15616.

4718 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519824C211yesmaximal, characteristic
2C22×#14519806C211yesmaximal, characteristic, complemented
3C22×Q16×D61C211yesmaximal, characteristic, complemented
4C2×#16840335C211yesmaximal, characteristic, complemented
5#21455111C2116yesmaximal, direct product factor
6C2×#16839925C211yesmaximal, characteristic, complemented
7C2×#16839924C211yesmaximal, characteristic, complemented
8C2×#16839921C211yesmaximal, characteristic, complemented
9C2×#16839920C211yesmaximal, characteristic, complemented
10C2×#16839919C211yesmaximal, characteristic, complemented
11C2×#16839917C211yesmaximal, characteristic, complemented
12C2×#16839916C211yesmaximal, characteristic, complemented
13C2×#16839769C211yesmaximal, characteristic, complemented
14C2×#16839755C211yesmaximal, characteristic, complemented
15C2×#16839727C211yesmaximal, characteristic, complemented
16C2×C61×#452C211yesmaximal, characteristic, complemented
17C2×#14519824—24no—
18C2×#14519824—28no—
19C2×#14519824—28no—
20C2×#14519824C2218yes—
21C22×#11758222—21no—
22C22×#11758222C2211yescharacteristic
23C22×#11758224—21no—
24C22×#11758224—21no—
25C22×#11758224C2211yescharacteristic
26C22×#11758224C2211yescharacteristic
27C23×Dic122—21no—
28C23×Dic122C2211yescharacteristic
29C22×Q8×D61C2211yescharacteristic
30C22×Q8×D61C2211yescharacteristic
31C22×Q8×D61C2211yescharacteristic
32C2×#14519806—28no—
33C2×#14519806C2218yescomplemented
34C22×Dic244C2211yescharacteristic
35C22×Dic244C2211yescharacteristic
36C22×#11758202C2211yescharacteristic
37C22×#11758202C2211yescharacteristic
38C22×#11758202C2211yescharacteristic
39C2×Q16×D61—28no—
40C2×Q16×D61C2218yescomplemented
41C22×#11758200C2211yescharacteristic
42C22×#11758189C2211yescharacteristic
43C22×C8×D61C2211yescharacteristic
44#16840335—24no—
45#16840335C2218yescomplemented
46C2×#14519776—21no—
47C2×#14519763—21no—
48C2×#14519762—21no—
49C2×#14519759—21no—
50C2×#14519757C2211yescharacteristic
51C2×#14519756C2211yescharacteristic
52C2×#14519753C2211yescharacteristic
53C2×#14519735C2211yescharacteristic
54#16839925C2218yescomplemented
55#16839924C2218yescomplemented
56#16839921C2218yescomplemented
57#16839920C2218yescomplemented
58#16839919C2218yescomplemented
59#16839917C2218yescomplemented
60#16839916C2218yescomplemented
61#16839769C2218yescomplemented
62#16839755C2218yescomplemented
63C2×#14519702C2211yescharacteristic
64C2×#14519702C2211yescharacteristic
65C2×#14519701C2211yescharacteristic
66C2×#14519700C2211yescharacteristic
67C2×#14519700C2211yescharacteristic
68C2×#14519698C2211yescharacteristic
69#16839727C2218yescomplemented
70C2×C22⋊#92418C2211yescharacteristic
71C2×#14519689C2211yescharacteristic
72C2×#14519689C2211yescharacteristic
73C22×#41×C61C2211yescharacteristic
74C22×Q16×C61C2211yescharacteristic
75C22×SD16×C61C2211yescharacteristic
76C2×C22⋊Q8×C61C2211yescharacteristic
77C61×#452C2218yescomplemented
78C2×#103×C61C2211yescharacteristic
79C2×#102×C61C2211yescharacteristic
80C2×C22⋊C8×C61C2211yescharacteristic
81#14519824—264no—
82#14519824—232no—
83#14519824—232no—
84C2×#11758222—216no—
85C2×#11758222—28no—
86C2×#11758222—24no—
87C2×#11758222—24no—
88C2×#11758222D414yes—
89C2×#11758222C2314yes—
90C2×#11758224—216no—
91C2×#11758224—216no—
92C2×#11758224—24no—
93C2×#11758224—28no—
94C2×#11758224—28no—
95C2×#11758224—22no—
96C2×#11758224—22no—
97C2×#11758224—24no—
98C2×#11758224—24no—
99C2×#11758224D418yes—
100C2×#11758224C2314yes—
101C2×#11758224C2314yes—
102C22×Dic122—216no—
103C22×Dic122—21no—
104C22×Dic122—22no—
105C22×Dic122—21no—
106C22×Dic122—21no—
107C22×Dic122—28no—
108C22×Dic122—24no—
109C22×Dic122—24no—
110C22×Dic122—21no—
111C22×Dic122D411yescharacteristic
112C22×Dic122C2311yescharacteristic
113C22×Dic122C2314yes—
114C22×Dic122C2311yescharacteristic
115C22×Dic122C2311yescharacteristic
116C2×Q8×D61—24no—
117C2×Q8×D61—24no—
118C2×Q8×D61—22no—
119C2×Q8×D61—22no—
120C2×Q8×D61—22no—
121C2×Q8×D61—24no—
122C2×Q8×D61—24no—
123C2×Q8×D61—24no—
124C2×Q8×D61D418yes—
125C2×Q8×D61C2314yes—
126C2×Q8×D61C2314yes—
127C2×Q8×D61C2314yes—
128C22×D244D411yescharacteristic
129C22×C22⋊D61—21no—
130C22×C22⋊D61—21no—
131C22×C22⋊D61D411yescharacteristic
132C22×C22⋊D61D411yescharacteristic
133C23×Dic61—21no—
134C23×Dic61—21no—
135C23×Dic61—21no—
136C22×C4×D61—21no—
137C22×C4×D61—21no—
138C22×C4×D61—21no—
139C22×C4×D61C2311yescharacteristic
140C22×C4×D61C2311yescharacteristic
141#14519806—232no—
142C2×Dic244—24no—
143C2×Dic244—24no—
144C2×Dic244C2314yes—
145C2×Dic244C2314yes—
146C2×#11758202—24no—
147C2×#11758202—24no—
148C2×#11758202—24no—
149C2×#11758202C2314yes—
150C2×#11758202C2314yes—
151C2×#11758202C2314yes—
152Q16×D61—232no—
153C2×#11758200—24no—
154C2×#11758200C2314yes—
155C2×#11758189—24no—
156C2×#11758189C2314yes—
157C22×#92418C2311yescharacteristic
158C22×#92418C2311yescharacteristic
159C2×C8×D61—24no—
160C2×C8×D61C2314yes—
161#14519776—28no—
162#14519763—28no—
163#14519762—28no—
164#14519759—28no—
165#14519757—22no—
166#14519757C2314yes—
167#14519756—22no—
168#14519756C2314yes—
169#14519753—22no—
170#14519753C2314yes—
171#14519735—22no—
172#14519735C2314yes—
173C2×C4⋊Dic61—21no—
174C2×C4⋊Dic61C2311yescharacteristic
175C2×#11758196—21no—
176C2×#11758196—21no—
177C2×C22⋊Dic61—21no—
178C2×#11758198—21no—
179C2×#11758198—21no—
180C2×#11758198—21no—
181C2×C4×Dic61—21no—
182#14519702C2314yes—
183#14519702C2314yes—
184#14519701C2314yes—
185#14519700C2314yes—
186#14519700C2314yes—
187#14519698C2314yes—
188C22⋊#92418C2314yes—
189#14519689C2314yes—
190#14519689C2314yes—
191C2×#41×C61—24no—
192C2×#41×C61—24no—
193C2×#41×C61—22no—
194C2×#41×C61C2314yes—
195C22×Q8×C61C2311yescharacteristic
196C22×Q8×C61C2311yescharacteristic
197C22×D4×C61—21no—
198C22×D4×C61C2311yescharacteristic
199C23×C4×C61—21no—
200C23×C4×C61C2311yescharacteristic
201C2×Q16×C61—24no—
202C2×Q16×C61C2314yes—
203C2×SD16×C61—24no—
204C2×SD16×C61C2314yes—
205C22×C8×C61C2311yescharacteristic
206C22×C8×C61C2311yescharacteristic
207C22⋊Q8×C61—22no—
208C22⋊Q8×C61C2314yes—
209C2×C4⋊C4×C61—21no—
210C2×C4⋊C4×C61C2311yescharacteristic
211C2×C22⋊C4×C61—21no—
212#103×C61C2314yes—
213#102×C61C2314yes—
214C22⋊C8×C61C2314yes—
215C24×C61—21no—
216C24×C61C2×D411yescharacteristic
217C23×D61C2×D411yescharacteristic
218C23×D61C2×D411yescharacteristic
219#41×C61—216no—
220#41×C61—28no—
221#41×C61—28no—
222C2×Q8×C61—22no—
223C2×Q8×C61—21no—
224C2×Q8×C61—21no—
225C2×Q8×C61—22no—
226C2×Q8×C61—22no—
227C2×Q8×C61C2×D414yes—
228C2×Q8×C61C2412yes—
229C2×Q8×C61C2412yes—
230C2×D4×C61—28no—
231C2×D4×C61—24no—
232C2×D4×C61—21no—
233C2×D4×C61—22no—
234C2×D4×C61C2×D414yes—
235C2×D4×C61C2412yes—
236C22×C4×C61—28no—
237C22×C4×C61—21no—
238C22×C4×C61—24no—
239C22×C4×C61—22no—
240C22×C4×C61—22no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61C2×D411yescharacteristic
244C22×C4×C61C2×D412yes—
245C22×C4×C61C2412yes—
246C22×C4×C61C2411yescharacteristic
247C2×C22⋊D61—28no—
248C2×C22⋊D61—28no—
249C2×C22⋊D61—24no—
250C2×C22⋊D61—24no—
251C2×C22⋊D61—24no—
252C2×C22⋊D61—24no—
253C2×C22⋊D61C2×D414yes—
254C2×C22⋊D61C2×D414yes—
255C22×Dic61—28no—
256C22×Dic61—28no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—24no—
260C22×Dic61—28no—
261C22×Dic61—24no—
262C22×Dic61—24no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61C2×D411yescharacteristic
266C22×Dic61C2×D411yescharacteristic
267Q8×D61—216no—
268Q8×D61—28no—
269Q8×D61—216no—
270Q8×D61—28no—
271Q8×D61—28no—
272Q8×D61—28no—
273Q8×D61—28no—
274Q8×D61—48no—
275Q8×D61C2×D4116yes—
276#11758224—264no—
277#11758224—216no—
278#11758224—264no—
279#11758224—28no—
280#11758224—216no—
281#11758224—28no—
282#11758224—28no—
283#11758224C2×D4116yes—
284#11758222—264no—
285#11758222—216no—
286#11758222—28no—
287#11758222—28no—
288C2×D244—24no—
289C2×D244C2×D414yes—
290C2×C4×D61—28no—
291C2×C4×D61—28no—
292C2×C4×D61—24no—
293C2×C4×D61—24no—
294C2×C4×D61—22no—
295C2×C4×D61—22no—
296C2×C4×D61—24no—
297C2×C4×D61—44no—
298C2×C4×D61C2×D412yes—
299C2×C4×D61C2×D412yes—
300C2×C4×D61C2×D414yes—
301C2×C4×D61C2×D414yes—
302C2×C4×D61C2412yes—
303C2×C4×D61C2412yes—
304C2×Dic122—28no—
305C2×Dic122—28no—
306C2×Dic122—216no—
307C2×Dic122—264no—
308C2×Dic122—21no—
309C2×Dic122—21no—
310C2×Dic122—22no—
311C2×Dic122—22no—
312C2×Dic122—24no—
313C2×Dic122—28no—
314C2×Dic122—24no—
315C2×Dic122—24no—
316C2×Dic122—24no—
317C2×Dic122—28no—
318C2×Dic122—28no—
319C2×Dic122—22no—
320C2×Dic122—22no—
321C2×Dic122—21no—
322C2×Dic122—24no—
323C2×Dic122—44no—
324C2×Dic122C2×D414yes—
325C2×Dic122C2×D414yes—
326C2×Dic122C2×D414yes—
327C2×Dic122C2412yes—
328C2×Dic122C2412yes—
329C2×Dic122C2412yes—
330Q16×C61—28no—
331SD16×C61—28no—
332C2×C8×C61—22no—
333C2×C8×C61—22no—
334C2×C8×C61C2412yes—
335C2×C8×C61C2412yes—
336C4⋊C4×C61—24no—
337C4⋊C4×C61—21no—
338C4⋊C4×C61C2412yes—
339C22⋊C4×C61—24no—
340C22⋊Dic61—24no—
341#11758202—28no—
342#11758202—28no—
343#11758202—28no—
344#11758200—28no—
345#11758198—24no—
346#11758198—24no—
347#11758198—24no—
348C4⋊Dic61—21no—
349C4⋊Dic61—24no—
350C4⋊Dic61C2412yes—
351#11758196—24no—
352#11758196—24no—
353C4×Dic61—24no—
354C2×#92418—22no—
355C2×#92418—22no—
356C2×#92418C2412yes—
357C2×#92418C2412yes—
358Dic244—28no—
359Dic244—28no—
360#11758189—28no—
361C8×D61—28no—
362C23×C61—22no—
363C23×C61—24no—
364C23×C61—22no—
365C23×C61—22no—
366C23×C61—22no—
367C23×C61—42no—
368C23×C61—42no—
369C23×C61C22×D412yes—
370C23×C61C22×D411yescharacteristic
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—22no—
374C22×D61—22no—
375C22×D61—22no—
376C22×D61#12014yes—
377C22×D61C22×D412yes—
378C22×D61C22×D412yes—
379Q8×C61—24no—
380Q8×C61—22no—
381Q8×C61—22no—
382Q8×C61—22no—
383Q8×C61—42no—
384Q8×C61C22×D414yes—
385D4×C61—216no—
386D4×C61—24no—
387D4×C61—22no—
388D4×C61C22×D414yes—
389C2×C4×C61—216no—
390C2×C4×C61—22no—
391C2×C4×C61—24no—
392C2×C4×C61—22no—
393C2×C4×C61—24no—
394C2×C4×C61—22no—
395C2×C4×C61—22no—
396C2×C4×C61—22no—
397C2×C4×C61—22no—
398C2×C4×C61—42no—
399C2×C4×C61—42no—
400C2×C4×C61C22×D412yes—
401C2×C4×C61C22×D411yescharacteristic
402C2×C4×C61C22×D412yes—
403C2×C4×C61C22×D412yes—
404C2×C4×C61C2511yescharacteristic
405C22⋊D61—216no—
406C22⋊D61—28no—
407C22⋊D61—216no—
408C22⋊D61—28no—
409C2×Dic61—216no—
410C2×Dic61—216no—
411C2×Dic61—22no—
412C2×Dic61—24no—
413C2×Dic61—24no—
414C2×Dic61—22no—
415C2×Dic61—22no—
416C2×Dic61—216no—
417C2×Dic61—22no—
418C2×Dic61—22no—
419C2×Dic61—42no—
420C2×Dic61—42no—
421C2×Dic61#12014yes—
422C2×Dic61C22×D412yes—
423C2×Dic61C22×D412yes—
424D244—28no—
425C4×D61—216no—
426C4×D61—216no—
427C4×D61—24no—
428C4×D61—22no—
429C4×D61—22no—
430C4×D61—48no—
431C4×D61#12018yes—
432C4×D61C22×D414yes—
433C4×D61C22×D414yes—
434Dic122—216no—
435Dic122—216no—
436Dic122—24no—
437Dic122—24no—
438Dic122—22no—
439Dic122—22no—
440Dic122—28no—
441Dic122—216no—
442Dic122—22no—
443Dic122—22no—
444Dic122—42no—
445Dic122—48no—
446Dic122C22×D414yes—
447Dic122C22×D414yes—
448C8×C61—22no—
449C8×C61—22no—
450#92418—22no—
451#92418—22no—
452C2×#3011—611nomaximal, Sylow
453C22×C61—22no—
454C22×C61—24no—
455C22×C61—22no—
456C22×C61—22no—
457C22×C61—44no—
458C22×C61—48no—
459C22×C61—42no—
460C22×C61—42no—
461C22×C61C2×#12012yes—
462C22×C61#57812yes—
463C22×C61#57812yes—
464C22×C61C23×D411yescharacteristic
465C2×D61—28no—
466C2×D61—22no—
467C2×D61—22no—
468C2×D61—22no—
469C2×D61—22no—
470C2×D61—22no—
471C2×D61—44no—
472C2×D61C2×#12014yes—
473C4×C61—22no—
474C4×C61—24no—
475C4×C61—42no—
476C4×C61—42no—
477C4×C61C2×#12012yes—
478C4×C61C23×D411yescharacteristic
479C4×C61C23×D411yescharacteristic
480Dic61—22no—
481Dic61—24no—
482Dic61—24no—
483Dic61—42no—
484Dic61—42no—
485Dic61C2×#12014yes—
486C22×2−1+4—611no—
487C22×#137—611no—
488C23×Q16—611no—
489C2×#536—611no—
490#3011—6116no—
491C2×#452—611no—
492C2×#452—611no—
493C2×#452—611no—
494C2×#452D6111yescharacteristic, complemented
495C2×#451—611no—
496C2×#451—611no—
497C2×#451—611no—
498C2×#451—611no—
499C2×#419—611no—
500C2×#416—611no—
501C2×#408—611no—
502C2×C61—42no—
503C2×C61—44no—
504C2×C61#301114yescomplemented
505C2×C61C22×#12011yescharacteristic
506C2×C61C2×#57811yescharacteristic
507C2×C61C2×#57811yescharacteristic
508D61—24no—
509D61—42no—
510C2×2−1+4—618no—
511C2×2−1+4—1228no—
512C2×2−1+4—1228no—
513C2×2−1+4—1224no—
514C22×#41—611no—
515C22×#41—611no—
516C22×#41—611no—
517C22×#41—1221no—
518C22×#41—1221no—
519C22×#41—1221no—
520C22×#41C2×D6111yescharacteristic
521C23×Q8—611no—
522C23×Q8—611no—
523C23×Q8—611no—
524C23×Q8—611no—
525C23×Q8—1221no—
526C2×#137—618no—
527C2×#137—1228no—
528C22×Q16—611no—
529C22×Q16—611no—
530C22×Q16—611no—
531C22×Q16—618no—
532C22×Q16—611no—
533C22×Q16—611no—
534C22×Q16—1228no—
535C22×Q16C2×D6111yescharacteristic
536C22×SD16—611no—
537C22×SD16C2×D6111yescharacteristic
538C22×M16—611no—
539C23×C8—611no—
540#536—618no—
541#536—1224no—
542C2×C4⋊Q8—1221no—
543C2×#124—1221no—
544C2×#123—1221no—
545C2×#123—1221no—
546C2×C22⋊Q8—611no—
547C2×C22⋊Q8—611no—
548C2×C22⋊Q8—611no—
549C2×C22⋊Q8C2×D6111yescharacteristic
550C2×#117—611no—
551#452—618no—
552#452—618no—
553#452—618no—
554#452C2×D6118yescomplemented
555#451—618no—
556#451—618no—
557#451—618no—
558#451—618no—
559#419—618no—
560#416—618no—
561C2×#103—611no—
562C2×#103—611no—
563C2×#103—611no—
564C2×#103—611no—
565C2×#103—611no—
566C2×#103C2×D6111yescharacteristic
567C2×#102—611no—
568C2×#102C2×D6111yescharacteristic
569#408—618no—
570C2×C22⋊C8—611no—
571C2×C22⋊C8—611no—
572C2×C22⋊C8—611no—
573C2×C22⋊C8C2×D6111yescharacteristic
574C61C2×#301111yescharacteristic, complemented, Sylow
5752−1+4—12232no—
5762−1+4—12232no—
5772−1+4—12264no—
578C2×#41—24no—
579C2×#41—24no—
580C2×#41—22no—
581C2×#41—614no—
582C2×#41—614no—
583C2×#41—618no—
584C2×#41—614no—
585C2×#41—614no—
586C2×#41—1224no—
587C2×#41—1224no—
588C2×#41—1228no—
589C2×#41—12216no—
590C2×#41—1222no—
591C2×#41—1224no—
592C2×#41—1222no—
593C2×#41—1228no—
594C2×#41—1228no—
595C2×#41—1224no—
596C2×#41—12216no—
597C2×#41—12216no—
598C2×#41—1224no—
599C2×#41C22×D6114yes—
600C22×Q8—611no—
601C22×Q8—618no—
602C22×Q8—614no—
603C22×Q8—614no—
604C22×Q8—614no—
605C22×Q8—611no—
606C22×Q8—611no—
607C22×Q8—611no—
608C22×Q8—614no—
609C22×Q8—1221no—
610C22×Q8—1221no—
611C22×Q8—1221no—
612C22×Q8—1224no—
613C22×Q8—1224no—
614C22×Q8—1228no—
615C22×Q8—12216no—
616C22×Q8—1222no—
617C22×Q8—1224no—
618C22×Q8—1222no—
619C22×Q8—1222no—
620C22×Q8—1224no—
621C22×Q8—1224no—
622C22×Q8—1224no—
623C22×Q8—1224no—
624C22×Q8—1221no—
625C22×Q8—1222no—
626C22×Q8C22×D6111yescharacteristic
627C22×Q8C22×D6111yescharacteristic
628C22×D4—21no—
629C22×D4—611no—
630C22×D4—611no—
631C22×D4—611no—
632C22×D4—1221no—
633C22×D4—1221no—
634C22×D4C22×D6111yescharacteristic
635C23×C4—21no—
636C23×C4—611no—
637C23×C4—611no—
638C23×C4—1221no—
639C23×C4—1221no—
640C23×C4—1221no—
641C23×C4—1221no—
642C23×C4—1221no—
643C23×C4—1221no—
644C23×C4C22×D6111yescharacteristic
645#137—12232no—
646C2×Q16—24no—
647C2×Q16—614no—
648C2×Q16—614no—
649C2×Q16—614no—
650C2×Q16—614no—
651C2×Q16—614no—
652C2×Q16—1224no—
653C2×Q16—1224no—
654C2×Q16—12232no—
655C2×Q16—1224no—
656C2×Q16—1224no—
657C2×Q16—1224no—
658C2×Q16C22×D6114yes—
659C2×SD16—24no—
660C2×SD16—614no—
661C2×SD16—1224no—
662C2×SD16C22×D6114yes—
663C2×M16—614no—
664C2×M16—1224no—
665C22×C8—611no—
666C22×C8—611no—
667C22×C8—614no—
668C22×C8—1224no—
669C22×C8C22×D6111yescharacteristic
670C22×C8C22×D6111yescharacteristic
671C4⋊Q8—1228no—
672#124—1228no—
673#123—1228no—
674#123—1228no—
675C22⋊Q8—22no—
676C22⋊Q8—614no—
677C22⋊Q8—614no—
678C22⋊Q8—614no—
679C22⋊Q8—1222no—
680C22⋊Q8—1222no—
681C22⋊Q8—1222no—
682C22⋊Q8C22×D6114yes—
683#117—614no—
684#117—1222no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—611no—
687C2×C4⋊C4—1221no—
688C2×C4⋊C4—1221no—
689C2×C4⋊C4—1221no—
690C2×C4⋊C4C22×D6111yescharacteristic
691C2×C22⋊C4—21no—
692C2×C22⋊C4—1221no—
693C2×C22⋊C4—1221no—
694C2×C22⋊C4—1221no—
695C2×C22⋊C4—1221no—
696C2×C42—1221no—
697#103—614no—
698#103—614no—
699#103—614no—
700#103—614no—
701#103—614no—
702#103C22×D6114yes—
703#102—614no—
704#102C22×D6114yes—
705C22⋊C8—614no—
706C22⋊C8—614no—
707C22⋊C8—614no—
708C22⋊C8C22×D6114yes—
709C24—21no—
710C24—611no—
711C24—611no—
712C24D4×D6111yescharacteristic
713#41—216no—
714#41—28no—
715#41—28no—
716#41—6116no—
717#41—12216no—
718#41—1228no—
719#41—1228no—
720#41—12264no—
721#41—12216no—
722#41—1228no—
723#41—1228no—
724#41—12264no—
725#41—12264no—
726#41—12216no—
727#41—1228no—
728C2×Q8—22no—
729C2×Q8—21no—
730C2×Q8—21no—
731C2×Q8—22no—
732C2×Q8—22no—
733C2×Q8—614no—
734C2×Q8—6116no—
735C2×Q8—614no—
736C2×Q8—614no—
737C2×Q8—612no—
738C2×Q8—612no—
739C2×Q8—612no—
740C2×Q8—1224no—
741C2×Q8—1228no—
742C2×Q8—1224no—
743C2×Q8—1224no—
744C2×Q8—1224no—
745C2×Q8—1228no—
746C2×Q8—1228no—
747C2×Q8—1228no—
748C2×Q8—1228no—
749C2×Q8—12264no—
750C2×Q8—12216no—
751C2×Q8—12216no—
752C2×Q8—1228no—
753C2×Q8—1228no—
754C2×Q8—1228no—
755C2×Q8—1228no—
756C2×Q8—12216no—
757C2×Q8—1228no—
758C2×Q8—1222no—
759C2×Q8—1222no—
760C2×Q8—1224no—
761C2×Q8—1221no—
762C2×Q8—1221no—
763C2×Q8—1221no—
764C2×Q8—1222no—
765C2×Q8—1222no—
766C2×Q8—2444no—
767C2×Q8—2448no—
768C2×Q8D4×D6114yes—
769C2×Q8C23×D6112yes—
770C2×Q8C23×D6112yes—
771C2×D4—28no—
772C2×D4—24no—
773C2×D4—21no—
774C2×D4—22no—
775C2×D4—614no—
776C2×D4—614no—
777C2×D4—614no—
778C2×D4—1224no—
779C2×D4—1224no—
780C2×D4—1224no—
781C2×D4—1228no—
782C2×D4—1224no—
783C2×D4—1224no—
784C2×D4—1228no—
785C2×D4D4×D6114yes—
786C2×D4C23×D6112yes—
787C22×C4—28no—
788C22×C4—21no—
789C22×C4—24no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—611no—
795C22×C4—612no—
796C22×C4—614no—
797C22×C4—614no—
798C22×C4—612no—
799C22×C4—611no—
800C22×C4—612no—
801C22×C4—612no—
802C22×C4—1228no—
803C22×C4—1224no—
804C22×C4—1224no—
805C22×C4—1228no—
806C22×C4—1224no—
807C22×C4—1228no—
808C22×C4—1224no—
809C22×C4—1224no—
810C22×C4—1228no—
811C22×C4—1228no—
812C22×C4—1224no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1222no—
816C22×C4—1222no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—2444no—
820C22×C4D4×D6112yes—
821C22×C4D4×D6111yescharacteristic
822C22×C4C23×D6112yes—
823C22×C4C23×D6111yescharacteristic
824Q16—28no—
825Q16—1228no—
826Q16—1228no—
827Q16—1228no—
828Q16—1228no—
829Q16—1228no—
830SD16—28no—
831SD16—1228no—
832M16—1228no—
833C2×C8—22no—
834C2×C8—22no—
835C2×C8—612no—
836C2×C8—612no—
837C2×C8—1228no—
838C2×C8—1222no—
839C2×C8—1222no—
840C2×C8C23×D6112yes—
841C2×C8C23×D6112yes—
842C4⋊C4—24no—
843C4⋊C4—21no—
844C4⋊C4—612no—
845C4⋊C4—1224no—
846C4⋊C4—1224no—
847C4⋊C4—1221no—
848C4⋊C4—1224no—
849C4⋊C4C23×D6112yes—
850C22⋊C4—24no—
851C22⋊C4—1224no—
852C22⋊C4—1224no—
853C22⋊C4—1224no—
854C22⋊C4—1224no—
855C42—1224no—
856C23—22no—
857C23—24no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—42no—
862C23—42no—
863C23—614no—
864C23—612no—
865C23—612no—
866C23—1222no—
867C23—1222no—
868C23—1222no—
869C23—1222no—
870C23—1222no—
871C23C2×D4×D6112yes—
872C23C2×D4×D6111yescharacteristic
873Q8—24no—
874Q8—22no—
875Q8—22no—
876Q8—22no—
877Q8—42no—
878Q8—614no—
879Q8—614no—
880Q8—1228no—
881Q8—12216no—
882Q8—12216no—
883Q8—12216no—
884Q8—1224no—
885Q8—1224no—
886Q8—1222no—
887Q8—1222no—
888Q8—1222no—
889Q8—1222no—
890Q8—2448no—
891Q8—2442no—
892Q8C2×D4×D6114yes—
893D4—216no—
894D4—24no—
895D4—22no—
896D4—1228no—
897D4—1228no—
898D4—1228no—
899D4—12216no—
900D4—12216no—
901D4C2×D4×D6114yes—
902C2×C4—216no—
903C2×C4—22no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—24no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—614no—
914C2×C4—612no—
915C2×C4—618no—
916C2×C4—614no—
917C2×C4—614no—
918C2×C4—612no—
919C2×C4—12216no—
920C2×C4—12216no—
921C2×C4—12216no—
922C2×C4—12216no—
923C2×C4—12216no—
924C2×C4—1222no—
925C2×C4—1224no—
926C2×C4—1224no—
927C2×C4—1222no—
928C2×C4—1222no—
929C2×C4—1224no—
930C2×C4—1222no—
931C2×C4—1222no—
932C2×C4—1222no—
933C2×C4—1222no—
934C2×C4—2448no—
935C2×C4—2442no—
936C2×C4—2442no—
937C2×C4C2×D4×D6112yes—
938C2×C4C2×D4×D6111yescharacteristic
939C2×C4C2×D4×D6112yes—
940C2×C4C2×D4×D6112yes—
941C2×C4C24×D6111yescharacteristic
942C8—22no—
943C8—22no—
944C8—1222no—
945C8—1222no—
946C22—22no—
947C22—24no—
948C22—22no—
949C22—22no—
950C22—44no—
951C22—48no—
952C22—42no—
953C22—42no—
954C22—614no—
955C22—1228no—
956C22—1222no—
957C22—1222no—
958C22—1222no—
959C22—1222no—
960C22—1222no—
961C22—2444no—
962C22#120×D6112yes—
963C22#1684057612yes—
964C22#1684057812yes—
965C22C22×D4×D6111yescharacteristic
966C4—22no—
967C4—24no—
968C4—42no—
969C4—42no—
970C4—614no—
971C4—1222no—
972C4—1224no—
973C4—1224no—
974C4—2442no—
975C4—2442no—
976C4#120×D6112yes—
977C4C22×D4×D6111yescharacteristic
978C4C22×D4×D6111yescharacteristic
979C2—42no—
980C2—44no—
981C2—1224no—
982C2—2442no—
983C2#2145511114yesdirect product factor
984C2C2×#120×D6111yescharacteristic
985C2C2×#1684057611yescharacteristic
986C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#452C2
socleC23×C61C22×D4
prime radicalC22×#14519824C2
hypercenterC2×#452D61
hypocenterC61C2×#3011
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C22×#14519806C2semidirect
3. C22×Q16×D61C2semidirect
4. C2×#16840335C2semidirect
5. #21455111C2direct (N × H)
6. C2×#16839925C2semidirect
7. C2×#16839924C2semidirect
8. C2×#16839921C2semidirect
9. C2×#16839920C2semidirect
10. C2×#16839919C2semidirect
11. C2×#16839917C2semidirect
12. C2×#16839916C2semidirect
13. C2×#16839769C2semidirect
14. C2×#16839755C2semidirect
15. C2×#16839727C2semidirect
16. C2×C61×#452C2semidirect
33. C2×#14519806C22semidirect
40. C2×Q16×D61C22semidirect
45. #16840335C22semidirect
54. #16839925C22semidirect
55. #16839924C22semidirect
56. #16839921C22semidirect
57. #16839920C22semidirect
58. #16839919C22semidirect
59. #16839917C22semidirect
60. #16839916C22semidirect
61. #16839769C22semidirect
62. #16839755C22semidirect
69. #16839727C22semidirect
77. C61×#452C22semidirect
494. C2×#452D61semidirect
504. C2×C61#3011semidirect
554. #452C2×D61semidirect
574. C61C2×#3011semidirect
983. C2#21455111direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198242
C22×#145198062
C22×Q16×D612
C2×#168403352
#214551112
C2×#168399252
C2×#168399242
C2×#168399212
C2×#168399202
C2×#168399192
C2×#168399172
C2×#168399162
C2×#168397692
C2×#168397552
C2×#168397272
C2×C61×#4522
C2×#301161