Finite Group Databasebeta

← C2×#21457391 #30555060

Subgroups — C2×#21457391 #30555060

Order 15616.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519809C211yesmaximal, characteristic, complemented
2C22×Q16×D61C211yesmaximal, characteristic, complemented
3C2×Q8×D244C211yesmaximal, characteristic, complemented
4C2×#16840424C211yesmaximal, characteristic
5#21457391C2116yesmaximal, direct product factor
6C2×#16840156C211yesmaximal, characteristic, complemented
7C2×#16840021C211yesmaximal, characteristic, complemented
8C2×#16839992C211yesmaximal, characteristic, complemented
9C2×#16839984C211yesmaximal, characteristic, complemented
10C2×#16839972C211yesmaximal, characteristic, complemented
11C2×#16839927C211yesmaximal, characteristic, complemented
12C2×#16839919C211yesmaximal, characteristic, complemented
13C2×#16839919C211yesmaximal, characteristic, complemented
14C2×#16839902C211yesmaximal, characteristic, complemented
15C2×#16839835C211yesmaximal, characteristic, complemented
16C2×C61×#441C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×Q8×D61C2211yescharacteristic
20C22×Q8×D61C2211yescharacteristic
21C2×#14519809—28no—
22C2×#14519809C2218yescomplemented
23C22×Dic244C2211yescharacteristic
24C22×Dic244C2211yescharacteristic
25C22×#11758202C2211yescharacteristic
26C22×#11758202C2211yescharacteristic
27C22×#11758202C2211yescharacteristic
28C2×Q16×D61—28no—
29C2×Q16×D61C2218yescomplemented
30C22×#11758190C2211yescharacteristic
31C22×#11758190C2211yescharacteristic
32C22×#11758201C2211yescharacteristic
33C22×#11758189C2211yescharacteristic
34C22×C8×D61C2211yescharacteristic
35Q8×D244—24no—
36Q8×D244C2218yescomplemented
37#16840424—24no—
38#16840424C2218yes—
39C2×#14519777—21no—
40C2×#14519777C2211yescharacteristic
41C2×#14519765—21no—
42C2×#14519765C2211yescharacteristic
43C2×#14519757—21no—
44C2×#14519757—21no—
45C2×#14519757—21no—
46C2×#14519757C2211yescharacteristic
47C2×#14519757C2211yescharacteristic
48C2×#14519757C2211yescharacteristic
49C2×#14519752—21no—
50C2×#14519752C2211yescharacteristic
51C2×C4×D244—21no—
52C2×C4×D244—21no—
53C2×C4×D244C2211yescharacteristic
54#16840156C2218yescomplemented
55#16840021C2218yescomplemented
56#16839992C2218yescomplemented
57#16839984C2218yescomplemented
58#16839972C2218yescomplemented
59#16839927C2218yescomplemented
60#16839919C2218yescomplemented
61#16839919C2218yescomplemented
62#16839902C2218yescomplemented
63#16839835C2218yescomplemented
64C2×C4⋊#92418C2211yescharacteristic
65C2×#14519700C2211yescharacteristic
66C2×#14519700C2211yescharacteristic
67C2×#14519700C2211yescharacteristic
68C2×#14519697C2211yescharacteristic
69C2×#14519689C2211yescharacteristic
70C2×#14519689C2211yescharacteristic
71C22×Q16×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C2×C4×Q8×C61C2211yescharacteristic
74C61×#441C2218yescomplemented
75C2×#106×C61C2211yescharacteristic
76C2×#103×C61C2211yescharacteristic
77C2×#103×C61C2211yescharacteristic
78C2×#97×C61C2211yescharacteristic
79C2×#11758226—22no—
80C2×#11758226—24no—
81C2×#11758226—42no—
82C2×#11758226C2314yes—
83C22×Dic122—21no—
84C22×Dic122—21no—
85C22×Dic122—21no—
86C22×Dic122C2311yescharacteristic
87C22×Dic122C2311yescharacteristic
88C22×Dic122C2311yescharacteristic
89C2×Q8×D61—22no—
90C2×Q8×D61—22no—
91C2×Q8×D61—22no—
92C2×Q8×D61—24no—
93C2×Q8×D61—24no—
94C2×Q8×D61—24no—
95C2×Q8×D61—42no—
96C2×Q8×D61—42no—
97C2×Q8×D61—42no—
98C2×Q8×D61C2314yes—
99C2×Q8×D61C2314yes—
100C2×Q8×D61C2314yes—
101C22×D244—21no—
102C22×D244—21no—
103C22×D244D411yescharacteristic
104C22×D244C2311yescharacteristic
105C22×C4×D61—21no—
106C22×C4×D61—21no—
107C22×C4×D61—21no—
108C22×C4×D61—21no—
109C22×C4×D61C2311yescharacteristic
110C22×C4×D61C2311yescharacteristic
111#14519809—232no—
112C2×Dic244—24no—
113C2×Dic244—42no—
114C2×Dic244C2314yes—
115C2×Dic244C2314yes—
116C2×#11758202—24no—
117C2×#11758202—24no—
118C2×#11758202—24no—
119C2×#11758202C2314yes—
120C2×#11758202C2314yes—
121C2×#11758202C2314yes—
122Q16×D61—232no—
123C2×#11758190—24no—
124C2×#11758190—42no—
125C2×#11758190C2314yes—
126C2×#11758190C2314yes—
127C2×#11758201—24no—
128C2×#11758201C2314yes—
129C2×#11758189—24no—
130C2×#11758189C2314yes—
131C22×#92418C2311yescharacteristic
132C22×#92418C2311yescharacteristic
133C2×C8×D61—24no—
134C2×C8×D61C2314yes—
135#14519777—22no—
136#14519777—28no—
137#14519777C2314yes—
138#14519765—22no—
139#14519765—28no—
140#14519765C2314yes—
141#14519757—22no—
142#14519757—22no—
143#14519757—22no—
144#14519757—28no—
145#14519757—28no—
146#14519757—28no—
147#14519757C2314yes—
148#14519757C2314yes—
149#14519757C2314yes—
150#14519752—28no—
151#14519752—22no—
152#14519752C2314yes—
153C4×D244—28no—
154C4×D244—28no—
155C4×D244D414yes—
156C4×D244C2314yes—
157C2×C4⋊Dic61—21no—
158C2×C4⋊Dic61—21no—
159C2×C4⋊Dic61—21no—
160C2×C4⋊Dic61—21no—
161C2×C4⋊Dic61—21no—
162C2×C4⋊Dic61D411yescharacteristic
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×#11758198—21no—
167C2×#11758198—21no—
168C2×#11758198—21no—
169C2×#11758198D411yescharacteristic
170C2×#11758198D411yescharacteristic
171C4⋊#92418C2314yes—
172#14519700C2314yes—
173#14519700C2314yes—
174#14519700C2314yes—
175#14519697C2314yes—
176#14519689C2314yes—
177#14519689C2314yes—
178C22×Q8×C61C2311yescharacteristic
179C22×Q8×C61C2311yescharacteristic
180C2×Q16×C61D418yescomplemented
181C2×Q16×C61C2314yes—
182C22×C8×C61C2311yescharacteristic
183C22×C8×C61C2311yescharacteristic
184C4×Q8×C61—22no—
185C4×Q8×C61—22no—
186C4×Q8×C61C2314yes—
187C4×Q8×C61C2314yes—
188C2×C4⋊C4×C61—21no—
189C2×C4⋊C4×C61—21no—
190C2×C4⋊C4×C61C2311yescharacteristic
191C2×C4⋊C4×C61C2311yescharacteristic
192C2×C42×C61—21no—
193C2×C42×C61—21no—
194C2×C42×C61C2311yescharacteristic
195#106×C61C2314yes—
196#103×C61C2314yes—
197#103×C61C2314yes—
198#97×C61C2314yes—
199C23×D61—21no—
200C23×D61C2×D411yescharacteristic
201C23×D61C2×D411yescharacteristic
202C2×Q8×C61—21no—
203C2×Q8×C61—21no—
204C2×Q8×C61—22no—
205C2×Q8×C61—22no—
206C2×Q8×C61C2×D414yes—
207C2×Q8×C61C2×D414yes—
208C2×Q8×C61C2412yes—
209C2×Q8×C61C2412yes—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2411yescharacteristic
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222#11758226—28no—
223#11758226—44no—
224#11758226—48no—
225Q8×D61—28no—
226Q8×D61—28no—
227Q8×D61—28no—
228Q8×D61—44no—
229Q8×D61—44no—
230Q8×D61—44no—
231Q8×D61—48no—
232Q8×D61—48no—
233Q8×D61—48no—
234C2×D244—24no—
235C2×D244—22no—
236C2×D244—22no—
237C2×D244—24no—
238C2×D244—24no—
239C2×D244—21no—
240C2×D244—44no—
241C2×D244—44no—
242C2×D244C2×D414yes—
243C2×D244C2412yes—
244C2×C4×D61—22no—
245C2×C4×D61—22no—
246C2×C4×D61—22no—
247C2×C4×D61—22no—
248C2×C4×D61—24no—
249C2×C4×D61—24no—
250C2×C4×D61—24no—
251C2×C4×D61—24no—
252C2×C4×D61—44no—
253C2×C4×D61—44no—
254C2×C4×D61—44no—
255C2×C4×D61—44no—
256C2×C4×D61C2×D412yes—
257C2×C4×D61C2×D412yes—
258C2×C4×D61C2412yes—
259C2×C4×D61C2412yes—
260C2×Dic122—22no—
261C2×Dic122—22no—
262C2×Dic122—22no—
263C2×Dic122—22no—
264C2×Dic122—22no—
265C2×Dic122—22no—
266C2×Dic122—21no—
267C2×Dic122—21no—
268C2×Dic122—21no—
269C2×Dic122—24no—
270C2×Dic122—24no—
271C2×Dic122—24no—
272C2×Dic122—44no—
273C2×Dic122—44no—
274C2×Dic122—44no—
275C2×Dic122C2412yes—
276C2×Dic122C2412yes—
277C2×Dic122C2412yes—
278Q16×C61C2×D4116yescomplemented
279C2×C8×C61—22no—
280C2×C8×C61C2×D414yes—
281C2×C8×C61C2412yes—
282C2×C8×C61C2412yes—
283C4⋊C4×C61—24no—
284C4⋊C4×C61—24no—
285C4⋊C4×C61—21no—
286C4⋊C4×C61—21no—
287C4⋊C4×C61C2412yes—
288C4⋊C4×C61C2412yes—
289C42×C61—24no—
290C42×C61—24no—
291C42×C61C2×D412yes—
292C42×C61C2412yes—
293#11758202—28no—
294#11758202—28no—
295#11758202—28no—
296#11758201—28no—
297#11758198—24no—
298#11758198—24no—
299#11758198—24no—
300#11758198—24no—
301#11758198—24no—
302#11758198—24no—
303#11758198C2×D414yes—
304#11758198C2×D414yes—
305C4⋊Dic61—24no—
306C4⋊Dic61—24no—
307C4⋊Dic61—24no—
308C4⋊Dic61—24no—
309C4⋊Dic61—24no—
310C4⋊Dic61C2×D414yes—
311C2×#92418—22no—
312C2×#92418—22no—
313C2×#92418C2412yes—
314C2×#92418C2412yes—
315Dic244—28no—
316Dic244—44no—
317#11758190—28no—
318#11758190—44no—
319#11758189—28no—
320C8×D61—28no—
321C23×C61C22×D411yescharacteristic
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—42no—
329C22×D61—42no—
330C22×D61—42no—
331C22×D61#13714yescomplemented
332C22×D61C22×D412yes—
333C22×D61C22×D412yes—
334Q8×C61—24no—
335Q8×C61—24no—
336Q8×C61—22no—
337Q8×C61—22no—
338Q8×C61C22×D414yes—
339Q8×C61C22×D414yes—
340C2×C4×C61—24no—
341C2×C4×C61—24no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—42no—
349C2×C4×C61—42no—
350C2×C4×C61C22×D412yes—
351C2×C4×C61C22×D412yes—
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C22×D412yes—
354C2×C4×C61H(5,𝔽2)12yes—
355C2×C4×C61C2511yescharacteristic
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—42no—
362C2×Dic61—42no—
363C2×Dic61—42no—
364C2×Dic61C22×D412yes—
365C2×Dic61C22×D412yes—
366D244—28no—
367D244—22no—
368D244—22no—
369D244—48no—
370D244—48no—
371D244—42no—
372C4×D61—24no—
373C4×D61—24no—
374C4×D61—22no—
375C4×D61—22no—
376C4×D61—22no—
377C4×D61—22no—
378C4×D61—48no—
379C4×D61—48no—
380C4×D61—48no—
381C4×D61—48no—
382Dic122—22no—
383Dic122—22no—
384Dic122—22no—
385Dic122—22no—
386Dic122—22no—
387Dic122—22no—
388Dic122—48no—
389Dic122—48no—
390Dic122—48no—
391Dic122—42no—
392Dic122—42no—
393Dic122—42no—
394C8×C61—22no—
395C8×C61C22×D414yes—
396#92418—22no—
397#92418—22no—
398C2×#3270—611nomaximal, Sylow
399C22×C61D4212yes—
400C22×C61C2×#13712yes—
401C22×C61#57812yes—
402C22×C61C23×D411yescharacteristic
403C2×D61—22no—
404C2×D61—28no—
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—44no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—42no—
413C2×D61—84no—
414C2×D61C2×#13714yescomplemented
415C4×C61—24no—
416C4×C61—24no—
417C4×C61—22no—
418C4×C61—22no—
419C4×C61—42no—
420C4×C61—42no—
421C4×C61D4212yes—
422C4×C61C23×D411yescharacteristic
423C4×C61C2×H(5,𝔽2)11yescharacteristic
424Dic61—22no—
425Dic61—22no—
426Dic61—42no—
427Dic61—42no—
428Dic61—42no—
429C22×#137—611no—
430C23×Q16—611no—
431C2×D4×Q8—611no—
432C2×#548—611no—
433#3270—6116no—
434C2×#497—611no—
435C2×#470—611no—
436C2×#465—611no—
437C2×#464—611no—
438C2×#462—611no—
439C2×#452—611no—
440C2×#451—611no—
441C2×#451—611no—
442C2×#448—611no—
443C2×#441D6111yescharacteristic, complemented
444C2×#435—611no—
445C2×C61#327014yescomplemented
446C2×C61C2×D4211yescharacteristic
447C2×C61C22×#13711yescharacteristic
448C2×C61C2×#57811yescharacteristic
449D61—24no—
450D61—42no—
451D61—82no—
452C22×#41—611no—
453C23×Q8—611no—
454C23×Q8—611no—
455C23×Q8—611no—
456C2×#137—618no—
457C2×#137—1228no—
458C22×Q16—611no—
459C22×Q16—611no—
460C22×Q16—611no—
461C22×Q16—618no—
462C22×Q16—611no—
463C22×Q16—611no—
464C22×Q16—1228no—
465C22×Q16C2×D6111yescharacteristic
466C22×SD16—611no—
467C22×SD16—611no—
468C22×SD16—611no—
469C22×M16—611no—
470C23×C8—611no—
471D4×Q8—618no—
472D4×Q8—1224no—
473#548—618no—
474#548—1224no—
475C2×C4⋊Q8—611no—
476C2×C4⋊Q8—1221no—
477C2×#124—611no—
478C2×#124—1221no—
479C2×C22⋊Q8—611no—
480C2×C22⋊Q8—611no—
481C2×C22⋊Q8—611no—
482C2×C22⋊Q8—1221no—
483C2×C22⋊Q8—1221no—
484C2×C22⋊Q8—1221no—
485C2×#121—611no—
486C2×#121—1221no—
487C2×C4×Q8C2×D6111yescharacteristic
488C2×C4×Q8C2×D6111yescharacteristic
489C2×C4×D4—611no—
490C2×C4×D4—1221no—
491C2×C4×D4—1221no—
492#497—618no—
493#470—618no—
494#465—618no—
495#464—618no—
496#462—618no—
497#452—618no—
498#451—618no—
499#451—618no—
500#448—618no—
501#441C2×D6118yescomplemented
502#435—618no—
503C2×#106C2×D6111yescharacteristic
504C2×C4⋊C8—611no—
505C2×#103—611no—
506C2×#103—611no—
507C2×#103—611no—
508C2×#103C2×D6111yescharacteristic
509C2×#103C2×D6111yescharacteristic
510C2×#102—611no—
511C2×C22⋊C8—611no—
512C2×C22⋊C8—611no—
513C2×#97C2×D6111yescharacteristic
514C61C2×#327011yescharacteristic, complemented, Sylow
515C2×#41—614no—
516C2×#41—1222no—
517C2×#41—1224no—
518C2×#41—2442no—
519C22×Q8—614no—
520C22×Q8—614no—
521C22×Q8—614no—
522C22×Q8—611no—
523C22×Q8—611no—
524C22×Q8—611no—
525C22×Q8—1221no—
526C22×Q8—1221no—
527C22×Q8—1221no—
528C22×Q8—1222no—
529C22×Q8—1222no—
530C22×Q8—1222no—
531C22×Q8—1224no—
532C22×Q8—1224no—
533C22×Q8—1224no—
534C22×Q8—2442no—
535C22×Q8—2442no—
536C22×Q8—2442no—
537C22×Q8C22×D6111yescharacteristic
538C22×Q8C22×D6111yescharacteristic
539C22×D4—611no—
540C22×D4—611no—
541C22×D4—1221no—
542C22×D4—1221no—
543C23×C4—611no—
544C23×C4—611no—
545C23×C4—1221no—
546C23×C4—1221no—
547C23×C4—1221no—
548C23×C4—1221no—
549#137—12232no—
550C2×Q16—614no—
551C2×Q16—614no—
552C2×Q16—614no—
553C2×Q16—614no—
554C2×Q16—614no—
555C2×Q16—1224no—
556C2×Q16—1224no—
557C2×Q16—1224no—
558C2×Q16—12232no—
559C2×Q16—1224no—
560C2×Q16—2442no—
561C2×Q16D24418yescomplemented
562C2×Q16C22×D6114yes—
563C2×SD16—614no—
564C2×SD16—614no—
565C2×SD16—614no—
566C2×SD16—1224no—
567C2×SD16—1224no—
568C2×SD16—2442no—
569C2×M16—614no—
570C2×M16—1224no—
571C22×C8—611no—
572C22×C8—611no—
573C22×C8—614no—
574C22×C8—1224no—
575C22×C8C22×D6111yescharacteristic
576C22×C8C22×D6111yescharacteristic
577C4⋊Q8—614no—
578C4⋊Q8—1228no—
579C4⋊Q8—1222no—
580#124—614no—
581#124—1228no—
582#124—1222no—
583C22⋊Q8—614no—
584C22⋊Q8—614no—
585C22⋊Q8—614no—
586C22⋊Q8—1228no—
587C22⋊Q8—1228no—
588C22⋊Q8—1228no—
589C22⋊Q8—1222no—
590C22⋊Q8—1222no—
591C22⋊Q8—1222no—
592#121—614no—
593#121—1222no—
594#121—1228no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8C22×D6114yes—
598C4×Q8C22×D6114yes—
599C4×D4—614no—
600C4×D4—614no—
601C4×D4—1228no—
602C4×D4—1228no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—611no—
606C2×C4⋊C4—1221no—
607C2×C4⋊C4—1221no—
608C2×C4⋊C4—1221no—
609C2×C4⋊C4—1221no—
610C2×C4⋊C4—1221no—
611C2×C4⋊C4C22×D6111yescharacteristic
612C2×C4⋊C4C22×D6111yescharacteristic
613C2×C22⋊C4—611no—
614C2×C22⋊C4—611no—
615C2×C22⋊C4—1221no—
616C2×C22⋊C4—1221no—
617C2×C22⋊C4—1221no—
618C2×C22⋊C4—1221no—
619C2×C22⋊C4—1221no—
620C2×C22⋊C4—1221no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42C22×D6111yescharacteristic
624#106C22×D6114yes—
625C4⋊C8—614no—
626#103—614no—
627#103—614no—
628#103—614no—
629#103C22×D6114yes—
630#103C22×D6114yes—
631#102—614no—
632C22⋊C8—614no—
633C22⋊C8—614no—
634#97C22×D6114yes—
635C24—611no—
636C24—611no—
637C24—1221no—
638#41—1228no—
639#41—2444no—
640#41—2448no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—22no—
644C2×Q8—22no—
645C2×Q8—612no—
646C2×Q8—612no—
647C2×Q8—612no—
648C2×Q8—1224no—
649C2×Q8—1224no—
650C2×Q8—1224no—
651C2×Q8—1221no—
652C2×Q8—1221no—
653C2×Q8—1221no—
654C2×Q8—1228no—
655C2×Q8—1228no—
656C2×Q8—1228no—
657C2×Q8—1222no—
658C2×Q8—1222no—
659C2×Q8—1222no—
660C2×Q8—1222no—
661C2×Q8—1222no—
662C2×Q8—1222no—
663C2×Q8—2444no—
664C2×Q8—2444no—
665C2×Q8—2444no—
666C2×Q8—2444no—
667C2×Q8—2444no—
668C2×Q8—2444no—
669C2×Q8—2448no—
670C2×Q8—2448no—
671C2×Q8—2448no—
672C2×Q8C2×D24414yes—
673C2×Q8C2×D24414yes—
674C2×Q8C23×D6112yes—
675C2×Q8C23×D6112yes—
676C2×D4—614no—
677C2×D4—612no—
678C2×D4—1224no—
679C2×D4—1224no—
680C2×D4—1224no—
681C2×D4—1221no—
682C2×D4—1222no—
683C2×D4—1222no—
684C2×D4—2444no—
685C2×D4—2444no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—612no—
693C22×C4—612no—
694C22×C4—612no—
695C22×C4—612no—
696C22×C4—1224no—
697C22×C4—1224no—
698C22×C4—1224no—
699C22×C4—1224no—
700C22×C4—1222no—
701C22×C4—1222no—
702C22×C4—1222no—
703C22×C4—1222no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—2444no—
708C22×C4—2444no—
709C22×C4—2444no—
710C22×C4—2444no—
711C22×C4D4×D6111yescharacteristic
712C22×C4D4×D6111yescharacteristic
713C22×C4C23×D6111yescharacteristic
714Q16—1228no—
715Q16—1228no—
716Q16—1228no—
717Q16—1228no—
718Q16—2444no—
719Q16C2×D244116yescomplemented
720SD16—1228no—
721SD16—1228no—
722SD16—2444no—
723M16—1228no—
724C2×C8—22no—
725C2×C8—612no—
726C2×C8—612no—
727C2×C8—1222no—
728C2×C8—1222no—
729C2×C8—1228no—
730C2×C8C2×D24414yes—
731C2×C8C23×D6112yes—
732C2×C8C23×D6112yes—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—614no—
738C4⋊C4—1224no—
739C4⋊C4—1224no—
740C4⋊C4—1224no—
741C4⋊C4—1224no—
742C4⋊C4—1224no—
743C4⋊C4C23×D6112yes—
744C4⋊C4C23×D6112yes—
745C22⋊C4—614no—
746C22⋊C4—614no—
747C22⋊C4—1224no—
748C22⋊C4—1224no—
749C22⋊C4—1224no—
750C22⋊C4—1224no—
751C22⋊C4—1224no—
752C22⋊C4—1224no—
753C42—24no—
754C42—24no—
755C42D4×D6112yes—
756C42C23×D6112yes—
757C23—614no—
758C23—612no—
759C23—612no—
760C23—1222no—
761C23—1222no—
762C23—1222no—
763C23—1222no—
764C23—1222no—
765C23—1222no—
766C23—2442no—
767C23—2442no—
768C23—2442no—
769C23C2×D4×D6111yescharacteristic
770Q8—22no—
771Q8—22no—
772Q8—24no—
773Q8—24no—
774Q8—1222no—
775Q8—1222no—
776Q8—1222no—
777Q8—1222no—
778Q8—1222no—
779Q8—1222no—
780Q8—2448no—
781Q8—2448no—
782Q8—2448no—
783Q8—2442no—
784Q8—2442no—
785Q8—2442no—
786Q8C22×D24414yes—
787Q8C22×D24414yes—
788D4—1228no—
789D4—1222no—
790D4—1222no—
791D4—2448no—
792D4—2448no—
793D4—2442no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—612no—
805C2×C4—612no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1224no—
813C2×C4—1224no—
814C2×C4—1222no—
815C2×C4—1222no—
816C2×C4—1222no—
817C2×C4—2448no—
818C2×C4—2448no—
819C2×C4—2448no—
820C2×C4—2448no—
821C2×C4—2442no—
822C2×C4—2442no—
823C2×C4—2442no—
824C2×C4C2×D4×D6112yes—
825C2×C4C2×D4×D6112yes—
826C2×C4C2×D4×D6111yescharacteristic
827C2×C4C22×D24412yes—
828C2×C4#1451982312yes—
829C2×C4C24×D6111yescharacteristic
830C8—22no—
831C8—1222no—
832C8—1222no—
833C8C22×D24414yes—
834C22—614no—
835C22—1222no—
836C22—1222no—
837C22—1228no—
838C22—1222no—
839C22—1222no—
840C22—1222no—
841C22—4884no—
842C22—2442no—
843C22—2442no—
844C22—2442no—
845C22—2444no—
846C22D4×D24412yes—
847C22#137×D6112yes—
848C22#1684057812yes—
849C22C22×D4×D6111yescharacteristic
850C4—24no—
851C4—24no—
852C4—22no—
853C4—22no—
854C4—42no—
855C4—42no—
856C4—1222no—
857C4—1222no—
858C4—2442no—
859C4—2442no—
860C4—2442no—
861C4D4×D24412yes—
862C4C23×D24411yescharacteristic
863C4C2×#1451982311yescharacteristic
864C2—1224no—
865C2—4882no—
866C2—2442no—
867C2#2145739114yesdirect product factor
868C2C2×D4×D24411yescharacteristic
869C2C2×#137×D6111yescharacteristic
870C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#441C2
socleC23×C61C22×D4
prime radicalC2×#16840424C2
hypercenterC2×#441D61
hypocenterC61C2×#3270
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
1. C22×#14519809C2semidirect
2. C22×Q16×D61C2semidirect
3. C2×Q8×D244C2semidirect
5. #21457391C2direct (N × H)
6. C2×#16840156C2semidirect
7. C2×#16840021C2semidirect
8. C2×#16839992C2semidirect
9. C2×#16839984C2semidirect
10. C2×#16839972C2semidirect
11. C2×#16839927C2semidirect
12. C2×#16839919C2semidirect
13. C2×#16839919C2semidirect
14. C2×#16839902C2semidirect
15. C2×#16839835C2semidirect
16. C2×C61×#441C2semidirect
22. C2×#14519809C22semidirect
29. C2×Q16×D61C22semidirect
36. Q8×D244C22semidirect
54. #16840156C22semidirect
55. #16840021C22semidirect
56. #16839992C22semidirect
57. #16839984C22semidirect
58. #16839972C22semidirect
59. #16839927C22semidirect
60. #16839919C22semidirect
61. #16839919C22semidirect
62. #16839902C22semidirect
63. #16839835C22semidirect
74. C61×#441C22semidirect
180. C2×Q16×C61D4semidirect
278. Q16×C61C2×D4semidirect
331. C22×D61#137semidirect
414. C2×D61C2×#137semidirect
443. C2×#441D61semidirect
445. C2×C61#3270semidirect
501. #441C2×D61semidirect
514. C61C2×#3270semidirect
561. C2×Q16D244semidirect
719. Q16C2×D244semidirect
867. C2#21457391direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198092
C22×Q16×D612
C2×Q8×D2442
C2×#168404242
#214573912
C2×#168401562
C2×#168400212
C2×#168399922
C2×#168399842
C2×#168399722
C2×#168399272
C2×#168399192
C2×#168399022
C2×#168398352
C2×C61×#4412
C2×#327061