Finite Group Databasebeta

← C2×#21457483 #30555179

Subgroups — C2×#21457483 #30555179

Order 15616.

2794 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519808C211yesmaximal, characteristic, complemented
2C22×#14519806C211yesmaximal, characteristic, complemented
3C2×#16840430C211yesmaximal, characteristic
4C2×Q8×C22⋊D61C211yesmaximal, characteristic, complemented
5#21457483C2116yesmaximal, direct product factor
6C2×#16840133C211yesmaximal, characteristic, complemented
7C2×#16840011C211yesmaximal, characteristic, complemented
8C2×#16840006C211yesmaximal, characteristic, complemented
9C2×#16839971C211yesmaximal, characteristic, complemented
10C2×#16839960C211yesmaximal, characteristic, complemented
11C2×#16839926C211yesmaximal, characteristic, complemented
12C2×#16839921C211yesmaximal, characteristic, complemented
13C2×#16839902C211yesmaximal, characteristic, complemented
14C2×#16839854C211yesmaximal, characteristic, complemented
15C2×#16839837C211yesmaximal, characteristic, complemented
16C2×C61×#448C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758224C2211yescharacteristic
19C22×Q8×D61C2211yescharacteristic
20C2×#14519808—28no—
21C2×#14519808C2218yescomplemented
22C2×#14519806—28no—
23C2×#14519806C2218yescomplemented
24C22×Dic244C2211yescharacteristic
25C22×#11758202C2211yescharacteristic
26C22×#11758202C2211yescharacteristic
27C22×#11758190C2211yescharacteristic
28C22×#11758200C2211yescharacteristic
29C22×#11758201C2211yescharacteristic
30C22×#11758201C2211yescharacteristic
31C22×#11758194C2211yescharacteristic
32C22×#11758189C2211yescharacteristic
33#16840430—24no—
34#16840430C2218yes—
35Q8×C22⋊D61—24no—
36Q8×C22⋊D61C2218yescomplemented
37C2×#14519775—21no—
38C2×#14519775C2211yescharacteristic
39C2×#14519773—21no—
40C2×#14519773C2211yescharacteristic
41C2×#14519756—21no—
42C2×#14519756C2211yescharacteristic
43C2×#14519753—21no—
44C2×#14519753C2211yescharacteristic
45C2×#14519752C2211yescharacteristic
46C2×#14519750—21no—
47C2×#14519749—21no—
48C2×Q8×Dic61C2211yescharacteristic
49C2×#14519742C2211yescharacteristic
50C2×C4×C22⋊D61—21no—
51C2×C4×C22⋊D61C2211yescharacteristic
52C2×#14519737—21no—
53#16840133C2218yescomplemented
54#16840011C2218yescomplemented
55#16840006C2218yescomplemented
56#16839971C2218yescomplemented
57#16839960C2218yescomplemented
58#16839926C2218yescomplemented
59#16839921C2218yescomplemented
60#16839902C2218yescomplemented
61#16839854C2218yescomplemented
62#16839837C2218yescomplemented
63C2×#14519710C2211yescharacteristic
64C2×#14519706C2211yescharacteristic
65C2×#14519702C2211yescharacteristic
66C2×#14519700C2211yescharacteristic
67C2×#14519699C2211yescharacteristic
68C2×#14519698C2211yescharacteristic
69C2×#14519689C2211yescharacteristic
70C2×C8×Dic61C2211yescharacteristic
71C23×Q8×C61C2211yescharacteristic
72C22×SD16×C61C2211yescharacteristic
73C22×SD16×C61C2211yescharacteristic
74C2×#121×C61C2211yescharacteristic
75C61×#448C2218yescomplemented
76C2×#103×C61C2211yescharacteristic
77C2×#103×C61C2211yescharacteristic
78C2×C22⋊C8×C61C2211yescharacteristic
79C2×#11758222—22no—
80C2×#11758222—24no—
81C2×#11758222—42no—
82C2×#11758222C2314yes—
83C2×#11758224—22no—
84C2×#11758224—24no—
85C2×#11758224—42no—
86C2×#11758224C2314yes—
87C22×Dic122—21no—
88C22×Dic122C2311yescharacteristic
89C22×Dic122C2311yescharacteristic
90C2×Q8×D61—22no—
91C2×Q8×D61—24no—
92C2×Q8×D61—42no—
93C2×Q8×D61C2314yes—
94C22×D244—21no—
95C22×D244C2311yescharacteristic
96C22×C22⋊D61—21no—
97C22×C22⋊D61—21no—
98C22×C22⋊D61—21no—
99C22×C22⋊D61—21no—
100C22×C22⋊D61D411yescharacteristic
101C23×Dic61—21no—
102C22×C4×D61—21no—
103C22×C4×D61—21no—
104C22×C4×D61C2311yescharacteristic
105#14519808—232no—
106#14519806—232no—
107C2×Dic244—24no—
108C2×Dic244C2314yes—
109C2×#11758202—24no—
110C2×#11758202D418yescomplemented
111C2×#11758202C2314yes—
112C2×#11758202C2314yes—
113C2×#11758190—42no—
114C2×#11758190C2314yes—
115C2×#11758200—24no—
116C2×#11758200C2314yes—
117C2×#11758201—24no—
118C2×#11758201—24no—
119C2×#11758201C2314yes—
120C2×#11758201C2314yes—
121C2×#11758194—24no—
122C2×#11758194C2314yes—
123C2×#11758189—24no—
124C2×#11758189C2314yes—
125C22×#92418C2311yescharacteristic
126C22×#92418C2311yescharacteristic
127#14519775—28no—
128#14519775—22no—
129#14519775C2314yes—
130#14519773—28no—
131#14519773—22no—
132#14519773C2314yes—
133#14519756—22no—
134#14519756—28no—
135#14519756C2314yes—
136#14519753—22no—
137#14519753—28no—
138#14519753C2314yes—
139#14519752—22no—
140#14519752C2314yes—
141#14519750—28no—
142#14519749—28no—
143Q8×Dic61—22no—
144Q8×Dic61C2314yes—
145#14519742—22no—
146#14519742C2314yes—
147C4×C22⋊D61—28no—
148C4×C22⋊D61D414yes—
149C4×C22⋊D61C2314yes—
150#14519737—28no—
151C2×C4⋊Dic61—21no—
152C2×C4⋊Dic61C2311yescharacteristic
153C2×#11758196—21no—
154C2×#11758196—21no—
155C2×#11758196—21no—
156C2×#11758196—21no—
157C2×#11758196—21no—
158C2×#11758196D411yescharacteristic
159C2×C22⋊Dic61—21no—
160C2×C22⋊Dic61D411yescharacteristic
161C2×#11758198—21no—
162C2×#11758198—21no—
163C2×#11758198D411yescharacteristic
164C2×C4×Dic61—21no—
165C2×C4×Dic61—21no—
166C2×C4×Dic61C2311yescharacteristic
167#14519710C2314yes—
168#14519706C2314yes—
169#14519702C2314yes—
170#14519700C2314yes—
171#14519699C2314yes—
172#14519698C2314yes—
173#14519689C2314yes—
174C8×Dic61C2314yes—
175C22×Q8×C61—21no—
176C22×Q8×C61—22no—
177C22×Q8×C61—24no—
178C22×Q8×C61—42no—
179C22×Q8×C61C2311yescharacteristic
180C22×Q8×C61C2314yes—
181C22×Q8×C61C2311yescharacteristic
182C22×D4×C61—21no—
183C22×D4×C61C2311yescharacteristic
184C23×C4×C61—21no—
185C23×C4×C61C2311yescharacteristic
186C2×SD16×C61—24no—
187C2×SD16×C61—42no—
188C2×SD16×C61C2314yes—
189C2×SD16×C61C2314yes—
190C22×C8×C61C2311yescharacteristic
191C22×C8×C61C2311yescharacteristic
192#121×C61—22no—
193#121×C61C2314yes—
194C2×C4⋊C4×C61C2311yescharacteristic
195C2×C22⋊C4×C61—21no—
196#103×C61C2314yes—
197#103×C61C2314yes—
198C22⋊C8×C61C2314yes—
199C24×C61—21no—
200C24×C61C2×D411yescharacteristic
201C23×D61—21no—
202C23×D61C2×D411yescharacteristic
203C2×Q8×C61—21no—
204C2×Q8×C61—24no—
205C2×Q8×C61—21no—
206C2×Q8×C61—22no—
207C2×Q8×C61—28no—
208C2×Q8×C61—22no—
209C2×Q8×C61—22no—
210C2×Q8×C61—44no—
211C2×Q8×C61—44no—
212C2×Q8×C61—48no—
213C2×Q8×C61C2×D414yes—
214C2×Q8×C61C2412yes—
215C2×Q8×C61C2412yes—
216C2×D4×C61—24no—
217C2×D4×C61—22no—
218C2×D4×C61—21no—
219C2×D4×C61—22no—
220C2×D4×C61—82no—
221C2×D4×C61C2412yes—
222C22×C4×C61—21no—
223C22×C4×C61—22no—
224C22×C4×C61—22no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—24no—
228C22×C4×C61—44no—
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D412yes—
231C22×C4×C61C2412yes—
232C22×C4×C61C2411yescharacteristic
233C2×C22⋊D61—24no—
234C2×C22⋊D61—24no—
235C2×C22⋊D61—24no—
236C2×C22⋊D61—24no—
237C2×C22⋊D61—24no—
238C2×C22⋊D61—44no—
239C2×C22⋊D61—44no—
240C2×C22⋊D61—44no—
241C2×C22⋊D61—82no—
242C2×C22⋊D61C2×D414yes—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—24no—
247C22×Dic61—44no—
248C22×Dic61C2×D411yescharacteristic
249C22×Dic61C2×D411yescharacteristic
250C22×Dic61C2×D411yescharacteristic
251Q8×D61—28no—
252Q8×D61—44no—
253Q8×D61—48no—
254#11758224—28no—
255#11758224—44no—
256#11758224—48no—
257#11758222—28no—
258#11758222—44no—
259#11758222—48no—
260C2×D244—22no—
261C2×D244—22no—
262C2×D244—21no—
263C2×D244—24no—
264C2×D244—82no—
265C2×D244C2412yes—
266C2×C4×D61—22no—
267C2×C4×D61—22no—
268C2×C4×D61—24no—
269C2×C4×D61—24no—
270C2×C4×D61—44no—
271C2×C4×D61—44no—
272C2×C4×D61C2×D412yes—
273C2×C4×D61C2412yes—
274C2×Dic122—21no—
275C2×Dic122—22no—
276C2×Dic122—22no—
277C2×Dic122—22no—
278C2×Dic122—21no—
279C2×Dic122—24no—
280C2×Dic122—44no—
281C2×Dic122C2×D414yes—
282C2×Dic122C2412yes—
283C2×Dic122C2412yes—
284SD16×C61—28no—
285SD16×C61—44no—
286C2×C8×C61—22no—
287C2×C8×C61—22no—
288C2×C8×C61C2412yes—
289C2×C8×C61C2412yes—
290C4⋊C4×C61—21no—
291C4⋊C4×C61C2412yes—
292C22⋊C4×C61—24no—
293C22⋊Dic61—24no—
294C22⋊Dic61C2×D414yes—
295#11758202—28no—
296#11758202C2×D4116yescomplemented
297#11758201—28no—
298#11758201—28no—
299#11758200—28no—
300#11758198—24no—
301#11758198—24no—
302#11758198C2×D414yes—
303C4⋊Dic61—21no—
304C4⋊Dic61—24no—
305C4⋊Dic61C2412yes—
306#11758196—24no—
307#11758196—24no—
308#11758196—24no—
309#11758196—24no—
310#11758196—24no—
311#11758196C2×D414yes—
312C4×Dic61—24no—
313C4×Dic61—24no—
314C4×Dic61C2×D412yes—
315C4×Dic61C2412yes—
316#11758194—28no—
317C2×#92418—22no—
318C2×#92418C2×D414yes—
319C2×#92418C2412yes—
320C2×#92418C2412yes—
321Dic244—28no—
322#11758190—44no—
323#11758189—28no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—42no—
329C23×C61—42no—
330C23×C61—42no—
331C23×C61C22×D412yes—
332C23×C61C22×D411yescharacteristic
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—42no—
338C22×D61—42no—
339C22×D61—42no—
340C22×D61C22×D412yes—
341Q8×C61—24no—
342Q8×C61—22no—
343Q8×C61—22no—
344Q8×C61—22no—
345Q8×C61—48no—
346Q8×C61—42no—
347Q8×C61C22×D414yes—
348D4×C61—22no—
349D4×C61—22no—
350D4×C61—42no—
351D4×C61—84no—
352C2×C4×C61—24no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—24no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—48no—
361C2×C4×C61—42no—
362C2×C4×C61—42no—
363C2×C4×C61C22×D412yes—
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C22×D412yes—
366C2×C4×C61H(5,𝔽2)12yes—
367C2×C4×C61C2511yescharacteristic
368C22⋊D61—28no—
369C22⋊D61—48no—
370C22⋊D61—48no—
371C22⋊D61—48no—
372C22⋊D61—84no—
373C2×Dic61—24no—
374C2×Dic61—22no—
375C2×Dic61—22no—
376C2×Dic61—22no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—48no—
380C2×Dic61—42no—
381C2×Dic61—42no—
382C2×Dic61#13714yescomplemented
383C2×Dic61C22×D412yes—
384C2×Dic61C22×D412yes—
385C2×Dic61C22×D412yes—
386D244—22no—
387D244—22no—
388D244—42no—
389D244—84no—
390C4×D61—24no—
391C4×D61—22no—
392C4×D61—22no—
393C4×D61—48no—
394C4×D61—48no—
395Dic122—24no—
396Dic122—22no—
397Dic122—22no—
398Dic122—22no—
399Dic122—48no—
400Dic122—42no—
401Dic122C22×D414yes—
402C8×C61—22no—
403C8×C61—22no—
404#92418—22no—
405#92418C22×D414yes—
406C2×#3278—611nomaximal, Sylow
407C22×C61—22no—
408C22×C61—22no—
409C22×C61—22no—
410C22×C61—44no—
411C22×C61—42no—
412C22×C61—42no—
413C22×C61—42no—
414C22×C61—84no—
415C22×C61D4212yes—
416C22×C61C2×#13712yes—
417C22×C61#57712yes—
418C22×C61C23×D411yescharacteristic
419C2×D61—22no—
420C2×D61—22no—
421C2×D61—22no—
422C2×D61—44no—
423C2×D61—42no—
424C2×D61—42no—
425C2×D61—42no—
426C2×D61—84no—
427C4×C61—24no—
428C4×C61—22no—
429C4×C61—42no—
430C4×C61—42no—
431C4×C61D4212yes—
432C4×C61C23×D411yescharacteristic
433C4×C61C2×H(5,𝔽2)11yescharacteristic
434Dic61—24no—
435Dic61—22no—
436Dic61—22no—
437Dic61—42no—
438Dic61—42no—
439Dic61C2×#13714yescomplemented
440C22×#137—611no—
441C22×#137—611no—
442C2×#550—611no—
443C2×D4×Q8—611no—
444#3278—6116no—
445C2×#492—611no—
446C2×#468—611no—
447C2×#468—611no—
448C2×#462—611no—
449C2×#460—611no—
450C2×#452—611no—
451C2×#452—611no—
452C2×#448—611no—
453C2×#448D6111yescharacteristic, complemented
454C2×C4×Q16—611no—
455C2×#436—611no—
456C2×C61—42no—
457C2×C61—82no—
458C2×C61#327814yescomplemented
459C2×C61C2×D4211yescharacteristic
460C2×C61C22×#13711yescharacteristic
461C2×C61C2×#57711yescharacteristic
462D61—42no—
463D61—82no—
464C22×#41—611no—
465C22×#41—611no—
466C23×Q8—611no—
467C23×Q8C2×D6111yescharacteristic
468C2×#137—618no—
469C2×#137—618no—
470C2×#137—1228no—
471C2×#137—1228no—
472C22×Q16—611no—
473C22×Q16—611no—
474C22×Q16—611no—
475C22×SD16—611no—
476C22×SD16—611no—
477C22×SD16—611no—
478C22×SD16—611no—
479C22×SD16C2×D6111yescharacteristic
480C22×SD16C2×D6111yescharacteristic
481C22×M16—611no—
482C22×M16—611no—
483#550—618no—
484#550—1224no—
485D4×Q8—618no—
486D4×Q8—1224no—
487C2×C4⋊Q8—611no—
488C2×C4⋊Q8—1221no—
489C2×#127—611no—
490C2×#127—1221no—
491C2×C22⋊Q8—611no—
492C2×C22⋊Q8—611no—
493C2×C22⋊Q8—1221no—
494C2×C22⋊Q8—1221no—
495C2×#121—611no—
496C2×#121—1221no—
497C2×#121—1221no—
498C2×#121C2×D6111yescharacteristic
499C2×C4×Q8—611no—
500C2×C4×Q8—611no—
501C2×C4×D4—611no—
502C2×C4×D4—1221no—
503C2×C4×D4—1221no—
504#492—618no—
505#468—618no—
506#468—618no—
507#462—618no—
508#460—618no—
509#452—618no—
510#452—618no—
511#448—618no—
512#448C2×D6118yescomplemented
513C4×Q16—618no—
514#436—618no—
515C2×#107—611no—
516C2×C4⋊C8—611no—
517C2×#103—611no—
518C2×#103—611no—
519C2×#103C2×D6111yescharacteristic
520C2×#103C2×D6111yescharacteristic
521C2×#102—611no—
522C2×#102—611no—
523C2×C22⋊C8—611no—
524C2×C22⋊C8C2×D6111yescharacteristic
525C2×C4×C8—611no—
526C61C2×#327811yescharacteristic, complemented, Sylow
527C2×#41—614no—
528C2×#41—614no—
529C2×#41—1224no—
530C2×#41—1222no—
531C2×#41—1222no—
532C2×#41—1224no—
533C2×#41—2442no—
534C2×#41—2442no—
535C22×Q8—21no—
536C22×Q8—22no—
537C22×Q8—24no—
538C22×Q8—42no—
539C22×Q8—614no—
540C22×Q8—611no—
541C22×Q8—611no—
542C22×Q8—1221no—
543C22×Q8—1222no—
544C22×Q8—1224no—
545C22×Q8—2442no—
546C22×Q8C22×D6111yescharacteristic
547C22×Q8C22×D6114yes—
548C22×Q8C22×D6111yescharacteristic
549C22×D4—21no—
550C22×D4—611no—
551C22×D4—611no—
552C22×D4—1221no—
553C22×D4—1221no—
554C22×D4—1221no—
555C22×D4—1221no—
556C22×D4—1221no—
557C22×D4C22×D6111yescharacteristic
558C23×C4—21no—
559C23×C4—611no—
560C23×C4—1221no—
561C23×C4—1221no—
562C23×C4—1221no—
563C23×C4C22×D6111yescharacteristic
564#137—12232no—
565#137—12232no—
566C2×Q16—618no—
567C2×Q16—614no—
568C2×Q16—614no—
569C2×Q16—614no—
570C2×Q16—1224no—
571C2×Q16—1224no—
572C2×SD16—24no—
573C2×SD16—42no—
574C2×SD16—614no—
575C2×SD16—614no—
576C2×SD16—614no—
577C2×SD16—614no—
578C2×SD16—1224no—
579C2×SD16—1224no—
580C2×SD16—1224no—
581C2×SD16—2442no—
582C2×SD16C22×D6114yes—
583C2×SD16C22×D6114yes—
584C2×M16—614no—
585C2×M16—614no—
586C2×M16—1224no—
587C2×M16—1224no—
588C22×C8—611no—
589C22×C8—611no—
590C22×C8C22×D6111yescharacteristic
591C22×C8C22×D6111yescharacteristic
592C4⋊Q8—614no—
593C4⋊Q8—1222no—
594C4⋊Q8—1228no—
595#127—614no—
596#127—1222no—
597#127—1228no—
598C22⋊Q8—614no—
599C22⋊Q8—614no—
600C22⋊Q8—1228no—
601C22⋊Q8—1228no—
602C22⋊Q8—1222no—
603C22⋊Q8—1222no—
604#121—22no—
605#121—614no—
606#121—1228no—
607#121—1228no—
608#121—1222no—
609#121C22×D6114yes—
610C4×Q8—614no—
611C4×Q8—614no—
612C4×Q8—1222no—
613C4×Q8—1222no—
614C4×D4—614no—
615C4×D4—614no—
616C4×D4—1228no—
617C4×D4—1228no—
618C2×C4⋊C4—611no—
619C2×C4⋊C4—611no—
620C2×C4⋊C4—1221no—
621C2×C4⋊C4—1221no—
622C2×C4⋊C4—1221no—
623C2×C4⋊C4—1221no—
624C2×C4⋊C4—1221no—
625C2×C4⋊C4—1221no—
626C2×C4⋊C4C22×D6111yescharacteristic
627C2×C22⋊C4—21no—
628C2×C22⋊C4—611no—
629C2×C22⋊C4—611no—
630C2×C22⋊C4—1221no—
631C2×C22⋊C4—1221no—
632C2×C22⋊C4—1221no—
633C2×C42—611no—
634C2×C42—1221no—
635C2×C42—1221no—
636#107—614no—
637C4⋊C8—614no—
638#103—614no—
639#103—614no—
640#103C22×D6114yes—
641#103C22×D6114yes—
642#102—614no—
643#102—614no—
644C22⋊C8—614no—
645C22⋊C8C22×D6114yes—
646C4×C8—614no—
647C24—21no—
648C24—611no—
649C24—1221no—
650C24D4×D6111yescharacteristic
651#41—1228no—
652#41—1228no—
653#41—2444no—
654#41—2448no—
655#41—2444no—
656#41—2448no—
657C2×Q8—21no—
658C2×Q8—24no—
659C2×Q8—21no—
660C2×Q8—22no—
661C2×Q8—28no—
662C2×Q8—22no—
663C2×Q8—22no—
664C2×Q8—44no—
665C2×Q8—44no—
666C2×Q8—48no—
667C2×Q8—614no—
668C2×Q8—612no—
669C2×Q8—612no—
670C2×Q8—1224no—
671C2×Q8—1221no—
672C2×Q8—1221no—
673C2×Q8—1222no—
674C2×Q8—1228no—
675C2×Q8—1222no—
676C2×Q8—1222no—
677C2×Q8—2444no—
678C2×Q8—2444no—
679C2×Q8—2448no—
680C2×Q8D4×D6114yes—
681C2×Q8C23×D6112yes—
682C2×Q8C23×D6112yes—
683C2×D4—24no—
684C2×D4—22no—
685C2×D4—21no—
686C2×D4—22no—
687C2×D4—82no—
688C2×D4—614no—
689C2×D4—612no—
690C2×D4—1224no—
691C2×D4—1224no—
692C2×D4—1224no—
693C2×D4—1224no—
694C2×D4—1224no—
695C2×D4—1224no—
696C2×D4—1222no—
697C2×D4—1221no—
698C2×D4—1222no—
699C2×D4—4882no—
700C2×D4—4882no—
701C2×D4—2444no—
702C2×D4—2444no—
703C2×D4—2444no—
704C2×D4C23×D6112yes—
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—24no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—44no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—612no—
716C22×C4—612no—
717C22×C4—1224no—
718C22×C4—1224no—
719C22×C4—1221no—
720C22×C4—1222no—
721C22×C4—1222no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1224no—
725C22×C4—2444no—
726C22×C4—2444no—
727C22×C4—2444no—
728C22×C4D4×D6112yes—
729C22×C4D4×D6111yescharacteristic
730C22×C4C23×D6112yes—
731C22×C4C23×D6111yescharacteristic
732Q16—6116no—
733Q16—1228no—
734Q16—1228no—
735SD16—28no—
736SD16—44no—
737SD16—1228no—
738SD16—1228no—
739SD16—1228no—
740SD16—2444no—
741M16—1228no—
742M16—1228no—
743C2×C8—22no—
744C2×C8—22no—
745C2×C8—614no—
746C2×C8—612no—
747C2×C8—612no—
748C2×C8—1222no—
749C2×C8C23×D6112yes—
750C2×C8C23×D6112yes—
751C4⋊C4—21no—
752C4⋊C4—614no—
753C4⋊C4—612no—
754C4⋊C4—1224no—
755C4⋊C4—1224no—
756C4⋊C4—1224no—
757C4⋊C4—1224no—
758C4⋊C4—1224no—
759C4⋊C4—1221no—
760C4⋊C4—1224no—
761C4⋊C4C23×D6112yes—
762C22⋊C4—24no—
763C22⋊C4—614no—
764C22⋊C4—614no—
765C22⋊C4—1224no—
766C22⋊C4—1224no—
767C22⋊C4—1224no—
768C42—612no—
769C42—612no—
770C42—1224no—
771C42—1224no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—612no—
780C23—1222no—
781C23—1222no—
782C23—1222no—
783C23—1222no—
784C23—2442no—
785C23—2442no—
786C23—2442no—
787C23C2×D4×D6112yes—
788C23C2×D4×D6111yescharacteristic
789Q8—22no—
790Q8—24no—
791Q8—22no—
792Q8—22no—
793Q8—48no—
794Q8—42no—
795Q8—614no—
796Q8—1222no—
797Q8—1224no—
798Q8—1222no—
799Q8—1222no—
800Q8—2448no—
801Q8—2442no—
802Q8C2×D4×D6114yes—
803D4—22no—
804D4—22no—
805D4—42no—
806D4—84no—
807D4—1228no—
808D4—1222no—
809D4—1222no—
810D4—4884no—
811D4—4884no—
812D4—2448no—
813D4—2448no—
814D4—2448no—
815D4—2442no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—24no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—48no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—614no—
828C2×C4—612no—
829C2×C4—612no—
830C2×C4—612no—
831C2×C4—1222no—
832C2×C4—1222no—
833C2×C4—1222no—
834C2×C4—1224no—
835C2×C4—1222no—
836C2×C4—1222no—
837C2×C4—1224no—
838C2×C4—1222no—
839C2×C4—1222no—
840C2×C4—2448no—
841C2×C4—2448no—
842C2×C4—2448no—
843C2×C4—2442no—
844C2×C4—2442no—
845C2×C4C2×D4×D6112yes—
846C2×C4C2×D4×D6112yes—
847C2×C4C2×D4×D6111yescharacteristic
848C2×C4#1451982212yes—
849C2×C4C24×D6111yescharacteristic
850C8—22no—
851C8—22no—
852C8—614no—
853C8—1222no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—44no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—84no—
862C22—1222no—
863C22—1222no—
864C22—1222no—
865C22—4884no—
866C22—2442no—
867C22—2442no—
868C22—2442no—
869C22—2444no—
870C22#1684039412yes—
871C22#137×D6112yes—
872C22#1684056812yes—
873C22C22×D4×D6111yescharacteristic
874C4—22no—
875C4—24no—
876C4—42no—
877C4—42no—
878C4—614no—
879C4—1222no—
880C4—1224no—
881C4—1222no—
882C4—2442no—
883C4—2442no—
884C4#1684039412yes—
885C4C22×D4×D6111yescharacteristic
886C4C2×#1451982211yescharacteristic
887C2—42no—
888C2—82no—
889C2—4882no—
890C2—2442no—
891C2#2145748314yesdirect product factor
892C2C2×#1684039411yescharacteristic
893C2C2×#137×D6111yescharacteristic
894C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#448C2
socleC23×C61C22×D4
prime radicalC2×#16840430C2
hypercenterC2×#448D61
hypocenterC61C2×#3278
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C22×#14519808C2semidirect
2. C22×#14519806C2semidirect
4. C2×Q8×C22⋊D61C2semidirect
5. #21457483C2direct (N × H)
6. C2×#16840133C2semidirect
7. C2×#16840011C2semidirect
8. C2×#16840006C2semidirect
9. C2×#16839971C2semidirect
10. C2×#16839960C2semidirect
11. C2×#16839926C2semidirect
12. C2×#16839921C2semidirect
13. C2×#16839902C2semidirect
14. C2×#16839854C2semidirect
15. C2×#16839837C2semidirect
16. C2×C61×#448C2semidirect
21. C2×#14519808C22semidirect
23. C2×#14519806C22semidirect
36. Q8×C22⋊D61C22semidirect
53. #16840133C22semidirect
54. #16840011C22semidirect
55. #16840006C22semidirect
56. #16839971C22semidirect
57. #16839960C22semidirect
58. #16839926C22semidirect
59. #16839921C22semidirect
60. #16839902C22semidirect
61. #16839854C22semidirect
62. #16839837C22semidirect
75. C61×#448C22semidirect
110. C2×#11758202D4semidirect
296. #11758202C2×D4semidirect
382. C2×Dic61#137semidirect
439. Dic61C2×#137semidirect
453. C2×#448D61semidirect
458. C2×C61#3278semidirect
512. #448C2×D61semidirect
526. C61C2×#3278semidirect
891. C2#21457483direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198082
C22×#145198062
C2×#168404302
C2×Q8×C22⋊D612
#214574832
C2×#168401332
C2×#168400112
C2×#168400062
C2×#168399712
C2×#168399602
C2×#168399262
C2×#168399212
C2×#168399022
C2×#168398542
C2×#168398372
C2×C61×#4482
C2×#327861