Finite Group Databasebeta

← C2×#72224979 #72321283

Subgroups — C2×#72224979 #72321283

Order 2048.

3136 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#151060C214yesmaximal, complemented
2C2×#151059C214yesmaximal, complemented
3C2×#512736C211yesmaximal, characteristic
4C2×#483399C211yesmaximal, characteristic
5C2×#483327C211yesmaximal, characteristic
6#72224979C2116yesmaximal, direct product factor
7C2×#151024C212yesmaximal, complemented
8C22×#7457C212yesmaximal, complemented
9C2×#33401—21no—
10C2×#33326C2211yescharacteristic
11C2×#17798—21no—
12#512736C418yes—
13#512736C2218yes—
14C2×#13643C414yes—
15C2×#13642C2214yes—
16C2×#13630C412yes—
17C2×#13556C412yes—
18C22×#1398C2212yes—
19#483399—24no—
20#483399C2218yes—
21C2×#12021C2212yes—
22C2×#12020C2212yes—
23C2×#12019—22no—
24#483327—24no—
25#483327C2218yes—
26C2×#12002—21no—
27C2×#12002C2214yes—
28C22×#1369—22no—
29C22×#1369C2212yes—
30C2×#12000—21no—
31C2×#11999C2211yescharacteristic
32C22×#1368C2211yescharacteristic
33#151060C22132yescomplemented
34#151059C22132yescomplemented
35#151024C22116yescomplemented
36C2×#7457C2214yes—
37C2×#7457C2218yes—
38C2×#7457C2214yes—
39C2×#7457C22116yescomplemented
40C2×#3407—41no—
41C22×#504C2×C411yescharacteristic
42C22×#504Q811yescharacteristic
43C2×#2989—41no—
44C2×C4×#131D411yescharacteristic
45C22×M64C2×C414yes—
46#33401—28no—
47#33401—44no—
48C2×#2153—42no—
49C2×#2153—41no—
50C22×#364—24no—
51C22×#364—22no—
52#33326C2×C414yes—
53#33326D414yes—
54#33326Q814yes—
55#33326C2314yes—
56C2×#2108C2×C412yes—
57C2×#2108C2×C411yescharacteristic
58C2×#2108Q812yes—
59C2×#2108Q811yescharacteristic
60C2×C4×M32D411yescharacteristic
61C2×C4×M32C2312yes—
62C22×#346D412yes—
63C22×#346C2311yescharacteristic
64#17798—28no—
65#17798—44no—
66C2×#1569—42no—
67C2×#1568—22no—
68C2×#1566—22no—
69C2×#1565—41no—
70C2×#1564—21no—
71C22×#334—21no—
72#13643C2×C4132yes—
73#13642C2×C4116yes—
74#13642C23116yes—
75#13630C2×C4116yes—
76C2×#1422C2×C418yes—
77#13556C2×C4116yes—
78C2×#1400C2×C418yes—
79C2×#1398C2×C414yes—
80C2×#1398C2×C418yes—
81C2×#1398C2314yes—
82C2×#1398C2318yes—
83#12021—24no—
84#12021C2318yes—
85#12020—24no—
86#12020C2318yes—
87#12019—216no—
88#12002—28no—
89#12002—28no—
90#12002C23116yes—
91C2×#1369—22no—
92C2×#1369—24no—
93C2×#1369—216no—
94C2×#1369—24no—
95C2×#1369C2314yes—
96C2×#1369C2318yes—
97#12000—28no—
98#11999—22no—
99#11999C2314yes—
100C2×#1368—21no—
101C2×#1368—21no—
102C2×#1368—22no—
103C2×#1368—22no—
104C2×#1368—22no—
105C2×#1368C2311yescharacteristic
106C2×#1368C2312yes—
107C2×#1368C2311yescharacteristic
108C2×#1368C2314yes—
109#7457C23116yes—
110#7457C23132yes—
111#7457C23116yes—
112C22×#131C4⋊C411yescharacteristic
113C22×#131SD1611yescharacteristic
114C2×C4×#41SD1611yescharacteristic
115#3407—48no—
116#3407—84no—
117C2×#504—24no—
118C2×#504—24no—
119C2×#504—42no—
120C2×#504—42no—
121C2×#504—84no—
122C2×#504C4⋊C414yes—
123C2×#504C4⋊C414yes—
124C2×#504C22×C414yes—
125C2×#504C2×Q814yes—
126C22×M32—44no—
127C22×M32—42no—
128C22×M32C4⋊C411yescharacteristic
129C22×M32C4⋊C411yescharacteristic
130C22×M32C22×C412yes—
131C22×M32C2×Q812yes—
132C23×C16C4⋊C412yes—
133C23×C16C4⋊C412yes—
134C23×C16C22×C411yescharacteristic
135C23×C16C2×Q811yescharacteristic
136#2989—48no—
137#2989—84no—
138C2×#446—81no—
139C2×#436—81no—
140C2×#435—82no—
141C2×#432—42no—
142C2×#431—41no—
143C2×#423—42no—
144C22×C4⋊C8—41no—
145C4×#131C4⋊C414yes—
146C4×#131SD1614yes—
147C4×#131SD1614yes—
148C4×#131C2×D414yes—
149C2×#405C4⋊C412yes—
150C2×#405C4⋊C411yescharacteristic
151C2×#405SD1612yes—
152C2×#405SD1611yescharacteristic
153C2×C4×M16SD1611yescharacteristic
154C2×C4×M16SD1612yes—
155C22×C4×C8C2×D412yes—
156C22×C4×C8C2×D411yescharacteristic
157C2×M64—24no—
158C2×M64—28no—
159C2×M64C22×C418yes—
160C2×M64C22×C4116yes—
161C22×C32—24no—
162#2153—48no—
163#2153—416no—
164C2×#364—24no—
165C2×#364—216no—
166C2×#364—28no—
167C2×#364—44no—
168C2×#364—42no—
169C2×#364—48no—
170C2×#364—44no—
171#2108C4⋊C418yes—
172#2108C4⋊C414yes—
173#2108C4⋊C418yes—
174#2108C4⋊C414yes—
175#2108C22×C418yes—
176#2108C22×C414yes—
177#2108C2×Q818yes—
178#2108C2×Q814yes—
179C4×M32C4⋊C414yes—
180C4×M32C22×C414yes—
181C4×M32C2×D414yes—
182C4×M32C2×D414yes—
183C4×M32C2×Q814yes—
184C4×M32C2414yes—
185C2×#346C4⋊C412yes—
186C2×#346C4⋊C412yes—
187C2×#346C4⋊C418yes—
188C2×#346C22×C411yescharacteristic
189C2×#346C22×C412yes—
190C2×#346C2×D411yescharacteristic
191C2×#346C2×D412yes—
192C2×#346C2×D418yes—
193C2×#346C2×D412yes—
194C2×#346C2×Q811yescharacteristic
195C2×#346C2×Q812yes—
196C2×#346C2411yescharacteristic
197C2×#346C2412yes—
198C2×C4×C16C4⋊C412yes—
199C2×C4×C16C22×C412yes—
200C2×C4×C16C2×Q812yes—
201#1569—416no—
202#1568—28no—
203#1568—44no—
204#1566—28no—
205#1566—44no—
206#1565—48no—
207#1564—24no—
208#1564—42no—
209C2×#335—41no—
210C2×#335—42no—
211C2×#334—22no—
212C2×#334—24no—
213C2×#334—21no—
214C2×#334—21no—
215C2×#334—41no—
216C2×#334—42no—
217C2×#334—42no—
218#1422C22×C4132yes—
219#1400C22×C4132yes—
220#1398C22×C418yes—
221#1398C22×C4116yes—
222#1398C2418yes—
223#1369—28no—
224#1369—216no—
225#1369—24no—
226#1369C2418yes—
227#1368—24no—
228#1368—22no—
229#1368—24no—
230#1368—28no—
231#1368—28no—
232#1368—21no—
233#1368—21no—
234#1368C2414yes—
235#1368C2412yes—
236#1368C2412yes—
237C22×#41#10611yescharacteristic
238C2×#131—24no—
239C2×#131—24no—
240C2×#131—22no—
241C2×#131—22no—
242C2×#131—22no—
243C2×#131—22no—
244C2×#131#10614yes—
245C2×#131#10614yes—
246C2×#131C2×C4⋊C414yes—
247C2×#131C2×SD1614yes—
248C22×M16—82no—
249C22×M16#10612yes—
250C22×M16#10612yes—
251C22×M16#10611yescharacteristic
252C22×M16#10611yescharacteristic
253C23×C8—81no—
254C23×C8C2×C4⋊C412yes—
255C23×C8C2×C4⋊C411yescharacteristic
256C23×C8C2×SD1612yes—
257C23×C8C2×SD1611yescharacteristic
258C4×#41—24no—
259C4×#41#10614yes—
260C4×#41C2×SD1614yes—
261C2×C4×Q8—21no—
262C2×C4×D4—22no—
263C2×C4×D4—21no—
264C2×#117#10612yes—
265C2×#117#10611yescharacteristic
266C22×C42C2×SD1612yes—
267C22×C42C2×SD1611yescharacteristic
268#504—216no—
269#504—216no—
270#504—48no—
271#504—48no—
272#504—832no—
273C2×M32—22no—
274C2×M32—22no—
275C2×M32—22no—
276C2×M32—22no—
277C2×M32—24no—
278C2×M32—24no—
279C2×M32—42no—
280C2×M32—42no—
281C2×M32—44no—
282C2×M32—416no—
283C2×M32—48no—
284C2×M32—82no—
285C2×M32—84no—
286C2×M32—84no—
287C2×M32—88no—
288C2×M32C2×C4⋊C414yes—
289C2×M32C2×C4⋊C414yes—
290C2×M32C2×C4⋊C414yes—
291C2×M32C2×C4⋊C414yes—
292C2×M32C23×C414yes—
293C2×M32C22×Q814yes—
294C22×C16—22no—
295C22×C16—22no—
296C22×C16—24no—
297C22×C16—24no—
298C22×C16—42no—
299C22×C16—42no—
300C22×C16—82no—
301C22×C16—84no—
302C22×C16C2×C4⋊C412yes—
303C22×C16C2×C4⋊C412yes—
304C22×C16C2×C4⋊C411yescharacteristic
305C22×C16C2×C4⋊C418yes—
306C22×C16C2×C4⋊C412yes—
307C22×C16C2×C4⋊C418yes—
308C22×C16C2×C4⋊C411yescharacteristic
309C22×C16C2×C4⋊C412yes—
310C22×C16#13114yes—
311C22×C16#13114yes—
312C22×C16C23×C411yescharacteristic
313C22×C16C23×C412yes—
314C22×C16C22×Q811yescharacteristic
315C22×C16C22×Q812yes—
316#446—88no—
317#436—88no—
318#435—816no—
319#432—48no—
320#432—84no—
321#431—44no—
322#431—82no—
323#423—48no—
324#423—84no—
325C2×C4⋊C8—42no—
326C2×C4⋊C8—41no—
327C2×C4⋊C8—44no—
328C2×C4⋊C8—41no—
329C2×C4⋊C8—81no—
330C2×C4⋊C8—82no—
331C2×C4⋊C8—82no—
332C2×C22⋊C8—81no—
333C2×C22⋊C8—82no—
334#405#10618yes—
335#405#10614yes—
336#405#10614yes—
337#405#10618yes—
338#405C2×C4⋊C418yes—
339#405C2×C4⋊C414yes—
340#405C2×SD1614yes—
341#405C2×SD1618yes—
342C4×M16#10618yes—
343C4×M16#10614yes—
344C4×M16C2×SD1614yes—
345C4×M16C2×SD1618yes—
346C2×#97—82no—
347C2×#97#10612yes—
348C2×#97#10612yes—
349C2×#97#10612yes—
350C2×C4×C8—81no—
351C2×C4×C8C2×C4⋊C411yescharacteristic
352C2×C4×C8C2×C4⋊C412yes—
353C2×C4×C8C2×C4⋊C414yes—
354C2×C4×C8C2×C4⋊C412yes—
355C2×C4×C8C2×SD1612yes—
356C2×C4×C8C2×SD1611yescharacteristic
357C2×C4×C8C2×SD1612yes—
358C2×C4×C8C2×SD1614yes—
359C2×C4×C8C2×SD1612yes—
360C2×C4×C8C2×SD1611yescharacteristic
361C2×C4×C8C2×SD1614yes—
362C2×C4×C8C2×SD1612yes—
363C2×C4×C8C22×D411yescharacteristic
364C2×C4×C8C22×D412yes—
365C2×C4×C8C22×D414yes—
366M64—216no—
367M64—28no—
368M64C23×C4116yes—
369C2×C32—28no—
370C2×C32—216no—
371#364—28no—
372#364—44no—
373#364—416no—
374#364—48no—
375#346C2×C4⋊C412yes—
376#346C2×C4⋊C414yes—
377#346C2×C4⋊C418yes—
378#346C2×C4⋊C418yes—
379#346C2×C4⋊C412yes—
380#346C2×C4⋊C412yes—
381#346C23×C411yescharacteristic
382#346C23×C412yes—
383#346C22×D412yes—
384#346C22×D414yes—
385#346C22×D411yescharacteristic
386#346C22×Q811yescharacteristic
387#346C22×Q812yes—
388#346C2511yescharacteristic
389C4×C16C2×C4⋊C418yes—
390C4×C16C2×C4⋊C414yes—
391C4×C16C2×C4⋊C414yes—
392C4×C16C23×C414yes—
393C4×C16C22×Q814yes—
394#335—44no—
395#335—48no—
396#334—24no—
397#334—22no—
398#334—22no—
399#334—42no—
400#334—44no—
401#334—41no—
402#334—41no—
403#334—48no—
404C2×#41—22no—
405C2×#41—22no—
406C2×#41—22no—
407C2×#41—22no—
408C2×#41#36514yes—
409C2×#41C2×#10614yes—
410C22×Q8#36511yescharacteristic
411C22×D4#36512yes—
412C22×D4#36511yescharacteristic
413C23×C4—21no—
414C23×C4—22no—
415C23×C4C2×#10612yes—
416C23×C4C2×#10611yescharacteristic
417#131—216no—
418#131—216no—
419#131—28no—
420#131—28no—
421#131—28no—
422#131—28no—
423C2×M16—22no—
424C2×M16—22no—
425C2×M16—24no—
426C2×M16—24no—
427C2×M16—24no—
428C2×M16—24no—
429C2×M16—88no—
430C2×M16—324no—
431C2×M16#36514yes—
432C2×M16#36514yes—
433C2×M16C2×#10614yes—
434C2×M16C2×#10618yes—
435C2×M16C2×#10618yes—
436C2×M16C2×#10614yes—
437C22×C8—22no—
438C22×C8—22no—
439C22×C8—22no—
440C22×C8—22no—
441C22×C8—22no—
442C22×C8—22no—
443C22×C8—24no—
444C22×C8—24no—
445C22×C8—82no—
446C22×C8—81no—
447C22×C8—81no—
448C22×C8—84no—
449C22×C8—322no—
450C22×C8#42412yes—
451C22×C8#42412yes—
452C22×C8C2×#10612yes—
453C22×C8C2×#10614yes—
454C22×C8C2×#10611yescharacteristic
455C22×C8C2×#10612yes—
456C22×C8C2×#10614yes—
457C22×C8C2×#10611yescharacteristic
458C22×C8C2×#10612yes—
459C22×C8C2×#10612yes—
460C22×C8#43012yes—
461C22×C8#43012yes—
462C22×C8C22×C4⋊C414yes—
463C22×C8C22×C4⋊C411yescharacteristic
464C22×C8C22×C4⋊C412yes—
465C22×C8C22×SD1611yescharacteristic
466C22×C8C22×SD1612yes—
467C22×C8C22×SD1614yes—
468C4×Q8—24no—
469C4×Q8—24no—
470C4×D4—28no—
471C4×D4—24no—
472C4×D4—28no—
473C4×D4—24no—
474#117—24no—
475#117—22no—
476#117C2×#10618yes—
477#117C2×#10614yes—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—21no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—21no—
482C2×C42—21no—
483C2×C42—22no—
484C2×C42—22no—
485C2×C42—24no—
486C2×C42C2×#10611yescharacteristic
487C2×C42C2×#10612yes—
488C2×C42C2×#10614yes—
489C2×C42C2×#10612yes—
490C2×C42C22×SD1612yes—
491C2×C42C22×SD1614yes—
492C2×C42C22×SD1611yescharacteristic
493M32—28no—
494M32—28no—
495M32—28no—
496M32—28no—
497M32—44no—
498M32—44no—
499M32—48no—
500M32—84no—
501M32—88no—
502M32—816no—
503C2×C16—22no—
504C2×C16—22no—
505C2×C16—21no—
506C2×C16—21no—
507C2×C16—24no—
508C2×C16—21no—
509C2×C16—21no—
510C2×C16—24no—
511C2×C16—22no—
512C2×C16—22no—
513C2×C16—216no—
514C2×C16—48no—
515C2×C16—84no—
516C2×C16—88no—
517C2×C16—816no—
518C2×C16#42412yes—
519C2×C16#42412yes—
520C2×C16#42418yes—
521C2×C16C22×C4⋊C411yescharacteristic
522C2×C16C22×C4⋊C414yes—
523C2×C16C22×C4⋊C414yes—
524C2×C16C22×C4⋊C412yes—
525C2×C16C22×C4⋊C411yescharacteristic
526C2×C16C22×C4⋊C412yes—
527C2×C16C2×#13112yes—
528C2×C16C2×#13118yes—
529C2×C16C2×#13112yes—
530C2×C16C24×C411yescharacteristic
531C2×C16C23×Q811yescharacteristic
532C4⋊C8—44no—
533C4⋊C8—42no—
534C4⋊C8—42no—
535C4⋊C8—82no—
536C4⋊C8—84no—
537C4⋊C8—81no—
538C4⋊C8—81no—
539C4⋊C8—88no—
540C22⋊C8—84no—
541C22⋊C8—88no—
542#97—88no—
543#97C2×#10618yes—
544#97C2×#10618yes—
545#97C2×#10618yes—
546C4×C8—84no—
547C4×C8C2×#10612yes—
548C4×C8C2×#10614yes—
549C4×C8C2×#10614yes—
550C4×C8C2×#10612yes—
551C4×C8C2×#10612yes—
552C4×C8C2×#10614yes—
553C4×C8C22×C4⋊C412yes—
554C4×C8C22×C4⋊C414yes—
555C4×C8C22×C4⋊C411yescharacteristic
556C4×C8C22×SD1611yescharacteristic
557C4×C8C22×SD1614yes—
558C4×C8C22×SD1612yes—
559C4×C8C22×SD1611yescharacteristic
560C4×C8C22×SD1612yes—
561C4×C8C22×SD1614yes—
562C4×C8C23×D411yescharacteristic
563C32—216no—
564C24C2×#36512yes—
565C24C2×#36511yescharacteristic
566#41—28no—
567#41—28no—
568#41—28no—
569#41—28no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8C2×#36514yes—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4C2×#36518yes—
578C2×D4C2×#36514yes—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—82no—
591C22×C4—84no—
592C22×C4#157012yes—
593C22×C4#157012yes—
594C22×C4C2×#36512yes—
595C22×C4C2×#36514yes—
596C22×C4C2×#36512yes—
597C22×C4C2×#36512yes—
598C22×C4C2×#36511yescharacteristic
599C22×C4C2×#36512yes—
600C22×C4C22×#10614yes—
601C22×C4C22×#10611yescharacteristic
602C22×C4C22×#10612yes—
603M16—28no—
604M16—216no—
605M16—216no—
606M16—328no—
607M16C2×#365116yes—
608C2×C8—21no—
609C2×C8—24no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—24no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—28no—
617C2×C8—28no—
618C2×C8—24no—
619C2×C8—24no—
620C2×C8—24no—
621C2×C8—24no—
622C2×C8—82no—
623C2×C8—82no—
624C2×C8—84no—
625C2×C8—162no—
626C2×C8—164no—
627C2×C8—162no—
628C2×C8—324no—
629C2×C8#157012yes—
630C2×C8#157012yes—
631C2×C8#157014yes—
632C2×C8#157014yes—
633C2×C8C2×#36514yes—
634C2×C8C2×#36514yes—
635C2×C8C2×#42411yescharacteristic
636C2×C8C2×#42411yescharacteristic
637C2×C8C2×#42414yes—
638C2×C8C22×#10611yescharacteristic
639C2×C8C22×#10612yes—
640C2×C8C22×#10614yes—
641C2×C8C22×#10614yes—
642C2×C8C22×#10611yescharacteristic
643C2×C8C22×#10612yes—
644C2×C8C2×#43011yescharacteristic
645C2×C8C2×#43011yescharacteristic
646C2×C8C2×#43014yes—
647C2×C8C23×C4⋊C411yescharacteristic
648C2×C8C23×SD1611yescharacteristic
649C4⋊C4—28no—
650C4⋊C4—24no—
651C22⋊C4—28no—
652C22⋊C4—24no—
653C42—22no—
654C42—24no—
655C42—21no—
656C42—21no—
657C42—22no—
658C42—24no—
659C42—22no—
660C42C22×#10611yescharacteristic
661C42C22×#10612yes—
662C42C22×#10614yes—
663C42C23×SD1611yescharacteristic
664C16—24no—
665C16—22no—
666C16—21no—
667C16—21no—
668C16—24no—
669C16—88no—
670C16C2×#42414yes—
671C16C2×#42412yes—
672C16C22×#13112yes—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—44no—
677C23#1203012yes—
678C23#1203012yes—
679C23C22×#36511yescharacteristic
680C23C22×#36514yes—
681C23C22×#36512yes—
682Q8—28no—
683D4—216no—
684D4—28no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—44no—
698C2×C4—82no—
699C2×C4—84no—
700C2×C4—82no—
701C2×C4—84no—
702C2×C4#1203012yes—
703C2×C4#1203014yes—
704C2×C4#1203014yes—
705C2×C4#1203012yes—
706C2×C4C2×#157011yescharacteristic
707C2×C4C2×#157014yes—
708C2×C4C2×#157011yescharacteristic
709C2×C4C22×#36514yes—
710C2×C4C22×#36511yescharacteristic
711C2×C4C22×#36512yes—
712C2×C4C22×#36511yescharacteristic
713C2×C4C22×#36514yes—
714C2×C4C22×#36511yescharacteristic
715C2×C4C23×#10611yescharacteristic
716C8—21no—
717C8—21no—
718C8—22no—
719C8—24no—
720C8—162no—
721C8—164no—
722C8—162no—
723C8C2×#157011yescharacteristic
724C8C2×#157011yescharacteristic
725C8C2×#157014yes—
726C8C22×#36518yes—
727C8C22×#42411yescharacteristic
728C8C22×#43011yescharacteristic
729C22—22no—
730C22—24no—
731C22—24no—
732C22—42no—
733C22—42no—
734C22—44no—
735C22—44no—
736C22—82no—
737C22C2×#1203011yescharacteristic
738C22C2×#1203014yes—
739C22C2×#1203011yescharacteristic
740C22C23×#36511yescharacteristic
741C4—24no—
742C4—41no—
743C4—42no—
744C4—44no—
745C4—41no—
746C4C2×#1203011yescharacteristic
747C4C2×#1203011yescharacteristic
748C4C2×#1203014yes—
749C4C22×#157011yescharacteristic
750C4C23×#36511yescharacteristic
751C2—21no—
752C2—21no—
753C2—24no—
754C2—44no—
755C2#7222497912yesdirect product factor
756C2C22×#1203011yescharacteristic
subgroupG/H
center, socleC22C2×#12030
commutatorC2×C16C24×C4
Frattini, cosocle#346C25
prime radicalC22×#41#106
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C4×#131 ◁ C2×#33326 ◁ G
LECSG ▷ #346 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#151060C2semidirect
2. C2×#151059C2semidirect
6. #72224979C2direct (N × H)
7. C2×#151024C2semidirect
8. C22×#7457C2semidirect
33. #151060C22semidirect
34. #151059C22semidirect
35. #151024C22semidirect
39. C2×#7457C22semidirect
755. C2#72224979direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#1510602
C2×#1510592
C2×#5127362
C2×#4833992
C2×#4833272
#722249792
C2×#1510242
C22×#74572