Finite Group Databasebeta

← C2×#21456703 #30550701

Subgroups — C2×#21456703 #30550701

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×#16840340C211yesmaximal, characteristic
2C2×#16840333C211yesmaximal, characteristic, complemented
3#21456703C2116yesmaximal, direct product factor
4C2×#16840098C211yesmaximal, characteristic, complemented
5C2×#16840104C211yesmaximal, characteristic, complemented
6C2×#16840087C211yesmaximal, characteristic, complemented
7C2×#16840093C211yesmaximal, characteristic, complemented
8C2×#16840020C211yesmaximal, characteristic, complemented
9C2×#16840008C211yesmaximal, characteristic, complemented
10C2×#16840003C211yesmaximal, characteristic, complemented
11C2×#16839991C211yesmaximal, characteristic, complemented
12C2×#16839926C211yesmaximal, characteristic, complemented
13C2×#16839926C211yesmaximal, characteristic, complemented
14C2×#16839920C211yesmaximal, characteristic, complemented
15C2×#16839903C211yesmaximal, characteristic, complemented
16C2×C61×#408C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C23×Dic122C2211yescharacteristic
19C22×Dic244C2211yescharacteristic
20C22×Dic244C2211yescharacteristic
21C22×#11758190C2211yescharacteristic
22C22×#11758190C2211yescharacteristic
23#16840340—24no—
24#16840340C2218yes—
25#16840333—24no—
26#16840333C2218yescomplemented
27C2×#14519775—21no—
28C2×#14519764—21no—
29C2×#14519758—21no—
30C2×#14519758—21no—
31C2×#14519756C2211yescharacteristic
32C2×#14519756C2211yescharacteristic
33C2×#14519756C2211yescharacteristic
34C2×#14519756C2211yescharacteristic
35C2×#14519756C2211yescharacteristic
36C2×#14519756C2211yescharacteristic
37C2×#14519753—21no—
38C2×#14519751C2211yescharacteristic
39C2×#14519751C2211yescharacteristic
40C2×#14519749—21no—
41C2×#14519749—21no—
42C2×#14519748—21no—
43C2×#14519736C2211yescharacteristic
44C22×C4⋊Dic61C2211yescharacteristic
45#16840104C2218yescomplemented
46#16840098C2218yescomplemented
47#16840093C2218yescomplemented
48#16840087C2218yescomplemented
49#16840020C2218yescomplemented
50#16840008C2218yescomplemented
51#16840003C2218yescomplemented
52#16839991C2218yescomplemented
53#16839926C2218yescomplemented
54#16839926C2218yescomplemented
55#16839920C2218yescomplemented
56#16839903C2218yescomplemented
57C2×#14519711C2211yescharacteristic
58C2×#14519711C2211yescharacteristic
59C2×#14519709C2211yescharacteristic
60C2×#14519709C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519702C2211yescharacteristic
63C2×#14519702C2211yescharacteristic
64C2×#14519702C2211yescharacteristic
65C2×#14519702C2211yescharacteristic
66C2×#14519702C2211yescharacteristic
67C2×#14519699C2211yescharacteristic
68C2×#14519699C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic
70C22×M16×C61C2211yescharacteristic
71C23×C8×C61C2211yescharacteristic
72C61×#408C2218yescomplemented
73C2×C22⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×C22⋊C8×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—42no—
79C2×#11758222—42no—
80C2×#11758222C2314yes—
81C22×Dic122—21no—
82C22×Dic122—22no—
83C22×Dic122—42no—
84C22×Dic122—42no—
85C22×Dic122C2311yescharacteristic
86C22×Dic122C2311yescharacteristic
87C22×Dic122C2311yescharacteristic
88C22×Dic122C2314yes—
89C22×D244C2311yescharacteristic
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C23×Dic61—21no—
94C23×Dic61—21no—
95C22×C4×D61—21no—
96C2×Dic244—42no—
97C2×Dic244—42no—
98C2×Dic244C2314yes—
99C2×Dic244C2314yes—
100C2×#11758190—42no—
101C2×#11758190—42no—
102C2×#11758190C2314yes—
103C2×#11758190C2314yes—
104#14519775—28no—
105#14519764—28no—
106#14519758—28no—
107#14519758—28no—
108#14519756—22no—
109#14519756—22no—
110#14519756—22no—
111#14519756—22no—
112#14519756—22no—
113#14519756—22no—
114#14519756C2314yes—
115#14519756C2314yes—
116#14519756C2314yes—
117#14519756C2314yes—
118#14519756C2314yes—
119#14519756C2314yes—
120#14519753—28no—
121#14519751—22no—
122#14519751—22no—
123#14519751C2314yes—
124#14519751C2314yes—
125#14519749—28no—
126#14519749—28no—
127#14519748—28no—
128#14519736—22no—
129#14519736C2314yes—
130C2×C4⋊Dic61—21no—
131C2×C4⋊Dic61—22no—
132C2×C4⋊Dic61C2311yescharacteristic
133C2×C4⋊Dic61C2311yescharacteristic
134C2×C4⋊Dic61C2314yes—
135C2×C4⋊Dic61C2311yescharacteristic
136C2×C4⋊Dic61C2311yescharacteristic
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196—21no—
141C2×#11758196—21no—
142C2×#11758196—21no—
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61—21no—
145C2×C22⋊Dic61—21no—
146C2×C22⋊Dic61—21no—
147C2×C22⋊Dic61—21no—
148C2×C22⋊Dic61—21no—
149C2×C22⋊Dic61—21no—
150C2×#11758198—21no—
151C2×#11758198—21no—
152C2×C4×Dic61—21no—
153#14519711C2314yes—
154#14519711C2314yes—
155#14519709C2314yes—
156#14519709C2314yes—
157#14519702C2314yes—
158#14519702C2314yes—
159#14519702C2314yes—
160#14519702C2314yes—
161#14519702C2314yes—
162#14519702C2314yes—
163#14519699C2314yes—
164#14519699C2314yes—
165C2×#41×C61—42no—
166C2×#41×C61—42no—
167C2×#41×C61D414yes—
168C2×#41×C61C2314yes—
169C22×Q8×C61D411yescharacteristic
170C22×D4×C61D411yescharacteristic
171C22×D4×C61D411yescharacteristic
172C22×D4×C61D411yescharacteristic
173C23×C4×C61C2311yescharacteristic
174C23×C4×C61C2311yescharacteristic
175C23×C4×C61C2311yescharacteristic
176C2×M16×C61—42no—
177C2×M16×C61C2314yes—
178C22×C8×C61—42no—
179C22×C8×C61C2311yescharacteristic
180C22×C8×C61C2311yescharacteristic
181C22×C8×C61C2311yescharacteristic
182C22×C8×C61C2311yescharacteristic
183C22×C8×C61C2314yes—
184C22⋊C8×C61C2314yes—
185C22⋊C8×C61C2314yes—
186C22⋊C8×C61C2314yes—
187C22⋊C8×C61C2314yes—
188C24×C61C2×D411yescharacteristic
189C24×C61C2×D411yescharacteristic
190C24×C61C2×D411yescharacteristic
191C23×D61—21no—
192#41×C61—48no—
193#41×C61—44no—
194#41×C61—44no—
195C2×Q8×C61—42no—
196C2×Q8×C61C2×D414yes—
197C2×D4×C61—42no—
198C2×D4×C61—42no—
199C2×D4×C61—42no—
200C2×D4×C61C2×D414yes—
201C2×D4×C61C2×D414yes—
202C2×D4×C61C2×D414yes—
203C22×C4×C61—22no—
204C22×C4×C61—22no—
205C22×C4×C61—22no—
206C22×C4×C61—22no—
207C22×C4×C61—22no—
208C22×C4×C61—22no—
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D412yes—
212C22×C4×C61C2×D412yes—
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D412yes—
215C22×C4×C61C2412yes—
216C22×C4×C61C2412yes—
217C22×C4×C61C2412yes—
218C22×C4×C61C2411yescharacteristic
219C2×C22⋊D61—24no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—24no—
222C2×C22⋊D61—44no—
223C2×C22⋊D61—82no—
224C2×C22⋊D61—82no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—24no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—24no—
234C22×Dic61—44no—
235C22×Dic61—82no—
236#11758222—44no—
237#11758222—44no—
238#11758222—48no—
239C2×D244—22no—
240C2×D244—22no—
241C2×D244—21no—
242C2×D244C2412yes—
243C2×C4×D61—24no—
244C2×C4×D61—44no—
245C2×Dic122—22no—
246C2×Dic122—22no—
247C2×Dic122—22no—
248C2×Dic122—22no—
249C2×Dic122—22no—
250C2×Dic122—22no—
251C2×Dic122—21no—
252C2×Dic122—21no—
253C2×Dic122—24no—
254C2×Dic122—21no—
255C2×Dic122—44no—
256C2×Dic122—44no—
257C2×Dic122—44no—
258C2×Dic122—48no—
259C2×Dic122C2412yes—
260C2×Dic122C2412yes—
261C2×Dic122C2412yes—
262M16×C61—44no—
263C2×C8×C61—22no—
264C2×C8×C61—22no—
265C2×C8×C61—22no—
266C2×C8×C61—22no—
267C2×C8×C61—44no—
268C2×C8×C61C2412yes—
269C2×C8×C61C2412yes—
270C2×C8×C61C2412yes—
271C2×C8×C61C2412yes—
272C22⋊Dic61—24no—
273C22⋊Dic61—24no—
274C22⋊Dic61—24no—
275C22⋊Dic61—24no—
276C22⋊Dic61—24no—
277C22⋊Dic61—24no—
278C22⋊Dic61—24no—
279#11758198—24no—
280#11758198—24no—
281C4⋊Dic61—24no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61C2412yes—
287C4⋊Dic61C2412yes—
288C4⋊Dic61C2412yes—
289C4⋊Dic61C2412yes—
290#11758196—24no—
291#11758196—24no—
292#11758196—24no—
293#11758196—24no—
294#11758196—24no—
295#11758196—24no—
296C4×Dic61—24no—
297Dic244—44no—
298Dic244—44no—
299#11758190—44no—
300#11758190—44no—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61C22×D412yes—
311C23×C61C22×D412yes—
312C23×C61C22×D412yes—
313C23×C61C22×D411yescharacteristic
314C22×D61—22no—
315C22×D61—42no—
316C22×D61—42no—
317C22×D61—42no—
318Q8×C61—44no—
319D4×C61—44no—
320D4×C61—44no—
321D4×C61—44no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—24no—
326C2×C4×C61—24no—
327C2×C4×C61—24no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61C22×D412yes—
335C2×C4×C61C22×D412yes—
336C2×C4×C61C22×D412yes—
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61H(5,𝔽2)12yes—
339C2×C4×C61H(5,𝔽2)12yes—
340C2×C4×C61C2511yescharacteristic
341C22⋊D61—48no—
342C22⋊D61—84no—
343C22⋊D61—84no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—48no—
352C2×Dic61—42no—
353C2×Dic61—42no—
354C2×Dic61—42no—
355C2×Dic61—42no—
356C2×Dic61—42no—
357C2×Dic61—42no—
358C2×Dic61—42no—
359C2×Dic61—84no—
360D244—22no—
361D244—22no—
362D244—42no—
363C4×D61—48no—
364Dic122—22no—
365Dic122—22no—
366Dic122—22no—
367Dic122—22no—
368Dic122—22no—
369Dic122—22no—
370Dic122—48no—
371Dic122—42no—
372Dic122—42no—
373Dic122—42no—
374C8×C61—22no—
375C8×C61—22no—
376C8×C61—22no—
377C8×C61—22no—
378C2×#3201—611nomaximal, Sylow
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—22no—
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—44no—
389C22×C61—44no—
390C22×C61—44no—
391C22×C61#53412yes—
392C22×C61#57712yes—
393C22×C61#57812yes—
394C22×C61C23×D411yescharacteristic
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—84no—
399C4×C61—22no—
400C4×C61—22no—
401C4×C61—22no—
402C4×C61#53412yes—
403C4×C61C2×H(5,𝔽2)11yescharacteristic
404C4×C61C2×H(5,𝔽2)11yescharacteristic
405Dic61—42no—
406Dic61—42no—
407Dic61—42no—
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×#465—611no—
423C2×#452—611no—
424C2×#452—611no—
425C2×#451—611no—
426C2×#448—611no—
427C2×#408D6111yescharacteristic, complemented
428C2×C61—42no—
429C2×C61—42no—
430C2×C61—42no—
431C2×C61#320114yescomplemented
432C2×C61C2×#53411yescharacteristic
433C2×C61C2×#57711yescharacteristic
434C2×C61C2×#57811yescharacteristic
435D61—82no—
436C22×#41—611no—
437C22×#41C2×D6111yescharacteristic
438C23×Q8—611no—
439C22×Q16—611no—
440C22×Q16—611no—
441C22×SD16—611no—
442C22×SD16—611no—
443C22×M16C2×D6111yescharacteristic
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—611no—
459C2×C22⋊Q8—1221no—
460C2×#121—611no—
461C2×#121—611no—
462C2×#121—1221no—
463C2×#121—1221no—
464C2×#121—1221no—
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#465—618no—
475#452—618no—
476#452—618no—
477#451—618no—
478#448—618no—
479C2×#107—611no—
480C2×#107—611no—
481C2×#106—611no—
482C2×#106—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#103—611no—
486C2×#103—611no—
487C2×#103—611no—
488C2×#103—611no—
489C2×#102—611no—
490C2×#102—611no—
491#408C2×D6118yescomplemented
492C2×C22⋊C8C2×D6111yescharacteristic
493C2×C22⋊C8C2×D6111yescharacteristic
494C2×C22⋊C8C2×D6111yescharacteristic
495C2×C22⋊C8C2×D6111yescharacteristic
496C61C2×#320111yescharacteristic, complemented, Sylow
497C2×#41—42no—
498C2×#41—42no—
499C2×#41—614no—
500C2×#41—1222no—
501C2×#41—2442no—
502C2×#41—2442no—
503C2×#41D24414yes—
504C2×#41C22×D6114yes—
505C22×Q8—611no—
506C22×Q8—611no—
507C22×Q8—611no—
508C22×Q8—614no—
509C22×Q8—1221no—
510C22×Q8—1222no—
511C22×Q8—2442no—
512C22×Q8—2442no—
513C22×Q8D24411yescharacteristic
514C22×D4—611no—
515C22×D4—1221no—
516C22×D4—1221no—
517C22×D4—1221no—
518C22×D4D24411yescharacteristic
519C22×D4D24411yescharacteristic
520C22×D4D24411yescharacteristic
521C23×C4—1221no—
522C23×C4—1221no—
523C23×C4—1221no—
524C23×C4C22×D6111yescharacteristic
525C23×C4C22×D6111yescharacteristic
526C23×C4C22×D6111yescharacteristic
527C2×Q16—614no—
528C2×Q16—614no—
529C2×Q16—2442no—
530C2×Q16—2442no—
531C2×SD16—614no—
532C2×SD16—614no—
533C2×SD16—2442no—
534C2×SD16—2442no—
535C2×M16—42no—
536C2×M16C22×D6114yes—
537C22×C8—42no—
538C22×C8C22×D6111yescharacteristic
539C22×C8C22×D6111yescharacteristic
540C22×C8C22×D6111yescharacteristic
541C22×C8C22×D6111yescharacteristic
542C22×C8C22×D6114yes—
543C4⋊Q8—1228no—
544#124—1228no—
545#123—1228no—
546#123—1228no—
547C22⋊Q8—614no—
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⋊Q8—1222no—
560#121—614no—
561#121—614no—
562#121—1228no—
563#121—1228no—
564#121—1228no—
565#121—1222no—
566#121—1222no—
567#117—614no—
568#117—1222no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—611no—
571C2×C4⋊C4—614no—
572C2×C4⋊C4—611no—
573C2×C4⋊C4—611no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4—1222no—
576C2×C4⋊C4—1221no—
577C2×C4⋊C4—1221no—
578C2×C4⋊C4—1221no—
579C2×C4⋊C4—1221no—
580C2×C4⋊C4—1221no—
581C2×C4⋊C4—1221no—
582C2×C22⋊C4—1221no—
583C2×C22⋊C4—1221no—
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#106—614no—
596#103—614no—
597#103—614no—
598#103—614no—
599#103—614no—
600#103—614no—
601#103—614no—
602#102—614no—
603#102—614no—
604C22⋊C8C22×D6114yes—
605C22⋊C8C22×D6114yes—
606C22⋊C8C22×D6114yes—
607C22⋊C8C22×D6114yes—
608C24—1221no—
609C24C2×D24411yescharacteristic
610C24C2×D24411yescharacteristic
611C24C2×D24411yescharacteristic
612#41—48no—
613#41—44no—
614#41—44no—
615#41—2444no—
616#41—2444no—
617#41—2448no—
618C2×Q8—42no—
619C2×Q8—612no—
620C2×Q8—612no—
621C2×Q8—612no—
622C2×Q8—1221no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×Q8—1224no—
626C2×Q8—1222no—
627C2×Q8—1222no—
628C2×Q8—1222no—
629C2×Q8—1222no—
630C2×Q8—1222no—
631C2×Q8—1222no—
632C2×Q8—2444no—
633C2×Q8—2444no—
634C2×Q8—2444no—
635C2×Q8—2448no—
636C2×Q8C2×D24414yes—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—612no—
641C2×D4—1224no—
642C2×D4—1224no—
643C2×D4—1224no—
644C2×D4—1221no—
645C2×D4—1222no—
646C2×D4—1222no—
647C2×D4—4882no—
648C2×D4—4882no—
649C2×D4—2444no—
650C2×D4C2×D24414yes—
651C2×D4C2×D24414yes—
652C2×D4C2×D24414yes—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—1224no—
660C22×C4—1224no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1224no—
669C22×C4—4882no—
670C22×C4—2444no—
671C22×C4—2444no—
672C22×C4C2×D24412yes—
673C22×C4C2×D24412yes—
674C22×C4C2×D24412yes—
675C22×C4C2×D24411yescharacteristic
676C22×C4C2×D24411yescharacteristic
677C22×C4C2×D24411yescharacteristic
678C22×C4C23×D6112yes—
679C22×C4C23×D6112yes—
680C22×C4C23×D6112yes—
681C22×C4C23×D6111yescharacteristic
682Q16—2444no—
683Q16—2444no—
684SD16—2444no—
685SD16—2444no—
686M16—44no—
687C2×C8—22no—
688C2×C8—22no—
689C2×C8—22no—
690C2×C8—22no—
691C2×C8—44no—
692C2×C8C23×D6112yes—
693C2×C8C23×D6112yes—
694C2×C8C23×D6112yes—
695C2×C8C23×D6112yes—
696C4⋊C4—612no—
697C4⋊C4—612no—
698C4⋊C4—612no—
699C4⋊C4—612no—
700C4⋊C4—1224no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1224no—
706C4⋊C4—1224no—
707C4⋊C4—1224no—
708C4⋊C4—1224no—
709C4⋊C4—1224no—
710C4⋊C4—1224no—
711C22⋊C4—1224no—
712C22⋊C4—1224no—
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—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—1222no—
731C23—2442no—
732C23—2442no—
733C23—2442no—
734C23C22×D24412yes—
735C23C22×D24412yes—
736C23C22×D24412yes—
737C23C22×D24411yescharacteristic
738Q8—44no—
739Q8—1222no—
740Q8—1222no—
741Q8—1222no—
742Q8—1222no—
743Q8—1222no—
744Q8—1222no—
745Q8—2448no—
746Q8—2442no—
747Q8—2442no—
748Q8—2442no—
749D4—44no—
750D4—44no—
751D4—44no—
752D4—1222no—
753D4—1222no—
754D4—4884no—
755D4—4884no—
756D4—2448no—
757D4—2442no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—4884no—
778C2×C4—2448no—
779C2×C4—2448no—
780C2×C4—2442no—
781C2×C4—2442no—
782C2×C4—2442no—
783C2×C4—2442no—
784C2×C4—2442no—
785C2×C4—2442no—
786C2×C4—2442no—
787C2×C4C22×D24412yes—
788C2×C4C22×D24412yes—
789C2×C4C22×D24412yes—
790C2×C4C22×D24411yescharacteristic
791C2×C4#1451982212yes—
792C2×C4#1451982212yes—
793C2×C4C24×D6111yescharacteristic
794C8—22no—
795C8—22no—
796C8—22no—
797C8—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—4884no—
811C22—2442no—
812C22—2442no—
813C22—2442no—
814C22#1684032412yes—
815C22#1684057412yes—
816C22#1684057912yes—
817C22C23×D24411yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—2442no—
822C4—2442no—
823C4—2442no—
824C4—2442no—
825C4—2442no—
826C4—2442no—
827C4—2442no—
828C4#1684032412yes—
829C4C2×#1451982211yescharacteristic
830C4C2×#1451982211yescharacteristic
831C2—42no—
832C2—42no—
833C2—42no—
834C2—4882no—
835C2#2145670314yesdirect product factor
836C2C2×#1684032411yescharacteristic
837C2C2×#1684057411yescharacteristic
838C2C2×#1684057911yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#408C2
socleC23×C61C22×D4
prime radicalC2×#16840340C2
hypercenterC2×#408D61
hypocenterC61C2×#3201
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. C2×#16840333C2semidirect
3. #21456703C2direct (N × H)
4. C2×#16840098C2semidirect
5. C2×#16840104C2semidirect
6. C2×#16840087C2semidirect
7. C2×#16840093C2semidirect
8. C2×#16840020C2semidirect
9. C2×#16840008C2semidirect
10. C2×#16840003C2semidirect
11. C2×#16839991C2semidirect
12. C2×#16839926C2semidirect
13. C2×#16839926C2semidirect
14. C2×#16839920C2semidirect
15. C2×#16839903C2semidirect
16. C2×C61×#408C2semidirect
26. #16840333C22semidirect
45. #16840104C22semidirect
46. #16840098C22semidirect
47. #16840093C22semidirect
48. #16840087C22semidirect
49. #16840020C22semidirect
50. #16840008C22semidirect
51. #16840003C22semidirect
52. #16839991C22semidirect
53. #16839926C22semidirect
54. #16839926C22semidirect
55. #16839920C22semidirect
56. #16839903C22semidirect
72. C61×#408C22semidirect
427. C2×#408D61semidirect
431. C2×C61#3201semidirect
491. #408C2×D61semidirect
496. C61C2×#3201semidirect
835. C2#21456703direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403402
C2×#168403332
#214567032
C2×#168400982
C2×#168401042
C2×#168400872
C2×#168400932
C2×#168400202
C2×#168400082
C2×#168400032
C2×#168399912
C2×#168399262
C2×#168399202
C2×#168399032
C2×C61×#4082
C2×#320161