Finite Group Databasebeta

← C2×#20256420 #27097247

Subgroups — C2×#20256420 #27097247

Order 12032.

1906 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689851C211yesmaximal, characteristic, complemented
2C2×#15689845C211yesmaximal, characteristic
3#20256420C2116yesmaximal, direct product factor
4C2×#15689517C211yesmaximal, characteristic
5C2×#15689516C211yesmaximal, characteristic
6C2×#15689501C211yesmaximal, characteristic, complemented
7C2×#15689348C211yesmaximal, characteristic
8C2×#15689345C211yesmaximal, characteristic
9C2×#15689333C211yesmaximal, characteristic, complemented
10C2×#15689332C211yesmaximal, characteristic, complemented
11C2×#15689332C211yesmaximal, characteristic, complemented
12C2×#15689327C211yesmaximal, characteristic
13C2×#15689251C211yesmaximal, characteristic, complemented
14C2×#15689229C211yesmaximal, characteristic, complemented
15C2×#15689210C211yesmaximal, characteristic
16C2×C47×#441C211yesmaximal, characteristic, complemented
17C22×Dic188C2211yescharacteristic
18C22×Dic188C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625337C2211yescharacteristic
21C22×#10625337C2211yescharacteristic
22C22×#10625325C2211yescharacteristic
23C22×#10625325C2211yescharacteristic
24C22×#10625336C2211yescharacteristic
25#15689851—24no—
26#15689851C2218yescomplemented
27#15689845—24no—
28#15689845C2218yes—
29C2×#13094024C2211yescharacteristic
30C2×#13094022C2211yescharacteristic
31C2×#13094022C2211yescharacteristic
32C2×#13094022C2211yescharacteristic
33C2×#13094019—21no—
34C2×#13094018—21no—
35C2×#13094016—21no—
36C2×#13094014—21no—
37C2×#13094014—21no—
38C2×#13094013C2211yescharacteristic
39C2×#13094012C2211yescharacteristic
40C2×#13094002—21no—
41C2×C4×Dic94—21no—
42C2×C4×Dic94C2211yescharacteristic
43C2×#13093989C2211yescharacteristic
44C2×#13093989C2211yescharacteristic
45C2×#13093989C2211yescharacteristic
46C2×#13093986C2211yescharacteristic
47C2×#13093981—21no—
48#15689517C2218yes—
49#15689516C2218yes—
50#15689501C2218yescomplemented
51#15689348C2218yes—
52#15689345C2218yes—
53#15689333C2218yescomplemented
54#15689332C2218yescomplemented
55#15689332C2218yescomplemented
56#15689327C2218yes—
57#15689251C2218yescomplemented
58#15689229C2218yescomplemented
59#15689210C2218yes—
60C2×C4⋊(C47⋊C8)C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093947C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C2×C4×Q8×C47C2211yescharacteristic
72C47×#441C2218yescomplemented
73C2×#106×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C22×Dic94D411yescharacteristic
78C22×Dic94C2311yescharacteristic
79C22×Dic94C2311yescharacteristic
80C22×Dic94C2311yescharacteristic
81C22×D188C2311yescharacteristic
82C22×C4×D47—21no—
83C2×Dic188—24no—
84C2×Dic188—42no—
85C2×Dic188C2314yes—
86C2×Dic188C2314yes—
87C2×#10625337—42no—
88C2×#10625337—42no—
89C2×#10625337—42no—
90C2×#10625337C2314yes—
91C2×#10625337C2314yes—
92C2×#10625337C2314yes—
93C2×#10625325—24no—
94C2×#10625325—42no—
95C2×#10625325C2314yes—
96C2×#10625325C2314yes—
97C2×#10625336—42no—
98C2×#10625336C2314yes—
99C22×C47⋊C8C2311yescharacteristic
100C22×C47⋊C8C2311yescharacteristic
101#13094024—22no—
102#13094024C2314yes—
103#13094022—22no—
104#13094022—22no—
105#13094022—22no—
106#13094022C2314yes—
107#13094022C2314yes—
108#13094022C2314yes—
109#13094019—28no—
110#13094018—28no—
111#13094016—28no—
112#13094014—28no—
113#13094014—28no—
114#13094013—22no—
115#13094013C2314yes—
116#13094012—22no—
117#13094012C2314yes—
118#13094002—28no—
119C4×Dic94—28no—
120C4×Dic94D414yes—
121C4×Dic94C2314yes—
122#13093989—22no—
123#13093989—22no—
124#13093989—22no—
125#13093989C2314yes—
126#13093989C2314yes—
127#13093989C2314yes—
128#13093986—22no—
129#13093986C2314yes—
130#13093981—28no—
131C2×C4⋊Dic47—21no—
132C2×C4⋊Dic47—21no—
133C2×C4⋊Dic47D411yescharacteristic
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4—21no—
140C2×Dic47⋊C4—21no—
141C2×Dic47⋊C4—21no—
142C2×Dic47⋊C4—21no—
143C2×Dic47⋊C4D411yescharacteristic
144C2×Dic47⋊C4D411yescharacteristic
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4—21no—
149C2×(C2×D47)⋊C4—21no—
150C2×C4×Dic47—21no—
151C2×C4×Dic47—21no—
152C2×C4×Dic47—21no—
153C2×C4×Dic47C2311yescharacteristic
154C2×C4×Dic47C2311yescharacteristic
155C4⋊(C47⋊C8)C2314yes—
156Dic47⋊C8C2314yes—
157Dic47⋊C8C2314yes—
158#13093947C2314yes—
159#13093947C2314yes—
160#13093947C2314yes—
161#13093944C2314yes—
162#13093934C2314yes—
163C8×Dic47C2314yes—
164C22×Q8×C47C2311yescharacteristic
165C22×Q8×C47C2311yescharacteristic
166C2×Q16×C47—24no—
167C2×Q16×C47C2314yes—
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2311yescharacteristic
170C4×Q8×C47—22no—
171C4×Q8×C47—22no—
172C4×Q8×C47C2314yes—
173C4×Q8×C47C2314yes—
174C2×C4⋊C4×C47—21no—
175C2×C4⋊C4×C47—21no—
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C42×C47—21no—
179C2×C42×C47—21no—
180C2×C42×C47C2311yescharacteristic
181#106×C47C2314yes—
182#103×C47C2314yes—
183#103×C47C2314yes—
184#97×C47C2314yes—
185C23×D47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47—21no—
188C2×Q8×C47—22no—
189C2×Q8×C47—22no—
190C2×Q8×C47—22no—
191C2×Q8×C47—22no—
192C2×Q8×C47C2412yes—
193C2×Q8×C47C2412yes—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2411yescharacteristic
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47C2×D411yescharacteristic
205C22×Dic47C2×D411yescharacteristic
206C22×Dic47C2×D411yescharacteristic
207C22×Dic47C2×D411yescharacteristic
208C2×D188—22no—
209C2×D188—22no—
210C2×D188—21no—
211C2×D188C2412yes—
212C2×C4×D47—24no—
213C2×C4×D47—44no—
214C2×Dic94—24no—
215C2×Dic94—22no—
216C2×Dic94—22no—
217C2×Dic94—22no—
218C2×Dic94—22no—
219C2×Dic94—22no—
220C2×Dic94—22no—
221C2×Dic94—21no—
222C2×Dic94—21no—
223C2×Dic94—21no—
224C2×Dic94C2×D414yes—
225C2×Dic94C2412yes—
226C2×Dic94C2412yes—
227C2×Dic94C2412yes—
228Q16×C47—28no—
229C2×C8×C47—22no—
230C2×C8×C47#4114yes—
231C2×C8×C47C2412yes—
232C2×C8×C47C2412yes—
233C4⋊C4×C47—24no—
234C4⋊C4×C47—24no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47C2412yes—
238C4⋊C4×C47C2412yes—
239C42×C47—24no—
240C42×C47—24no—
241C42×C47C2×D412yes—
242C42×C47C2412yes—
243#10625337—44no—
244#10625337—44no—
245#10625337—44no—
246#10625336—44no—
247(C2×D47)⋊C4—24no—
248(C2×D47)⋊C4—24no—
249(C2×D47)⋊C4—24no—
250(C2×D47)⋊C4—24no—
251(C2×D47)⋊C4—24no—
252C4⋊Dic47—24no—
253C4⋊Dic47—24no—
254C4⋊Dic47C2×D414yes—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264Dic47⋊C4C2×D414yes—
265Dic47⋊C4C2×D414yes—
266C4×Dic47—24no—
267C4×Dic47—24no—
268C4×Dic47—24no—
269C4×Dic47C2×D412yes—
270C4×Dic47C2×D412yes—
271C4×Dic47C2412yes—
272C4×Dic47C2412yes—
273C2×C47⋊C8—22no—
274C2×C47⋊C8—22no—
275C2×C47⋊C8C2412yes—
276C2×C47⋊C8C2412yes—
277Dic188—28no—
278Dic188—44no—
279#10625325—28no—
280#10625325—44no—
281C23×C47C22×D411yescharacteristic
282C22×D47—22no—
283C22×D47—42no—
284C22×D47—42no—
285C22×D47—42no—
286Q8×C47—22no—
287Q8×C47—22no—
288Q8×C47—22no—
289Q8×C47—22no—
290Q8×C47—42no—
291Q8×C47—42no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—42no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47C22×D412yes—
303C2×C4×C47C22×D412yes—
304C2×C4×C47C22×D411yescharacteristic
305C2×C4×C47C2×#4112yes—
306C2×C4×C47H(5,𝔽2)12yes—
307C2×C4×C47C2511yescharacteristic
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47#13714yes—
318C2×Dic47C22×D412yes—
319C2×Dic47C22×D412yes—
320C2×Dic47C22×D412yes—
321C2×Dic47C22×D412yes—
322D188—22no—
323D188—22no—
324D188—42no—
325C4×D47—48no—
326Dic94—28no—
327Dic94—22no—
328Dic94—22no—
329Dic94—22no—
330Dic94—22no—
331Dic94—22no—
332Dic94—22no—
333Dic94—42no—
334Dic94—42no—
335Dic94—42no—
336C8×C47—22no—
337C8×C47C2×#4114yes—
338C47⋊C8—22no—
339C47⋊C8—22no—
340C2×#3398—471nomaximal, Sylow
341C22×C47#55012yes—
342C22×C47C2×#13712yes—
343C22×C47#57812yes—
344C22×C47C23×D411yescharacteristic
345C2×D47—42no—
346C2×D47—42no—
347C2×D47—42no—
348C2×D47—84no—
349C4×C47—22no—
350C4×C47—22no—
351C4×C47—42no—
352C4×C47—42no—
353C4×C47—42no—
354C4×C47—42no—
355C4×C47#55012yes—
356C4×C47C22×#4111yescharacteristic
357C4×C47C2×H(5,𝔽2)11yescharacteristic
358Dic47—22no—
359Dic47—22no—
360Dic47—22no—
361Dic47—42no—
362Dic47—42no—
363Dic47—42no—
364Dic47C2×#13714yes—
365C2×#557—471no—
366C2×#556—471no—
367#3398—4716no—
368C2×#497—471no—
369C2×#497—471no—
370C2×#494—471no—
371C2×#464—471no—
372C2×#464—471no—
373C2×#462—471no—
374C2×#462—471no—
375C2×#462—471no—
376C2×#461—471no—
377C2×#446—471no—
378C2×#441—471no—
379C2×#441D4711yescharacteristic, complemented
380C2×C4×SD16—471no—
381C2×C47#339814yescomplemented
382C2×C47C2×#55011yescharacteristic
383C2×C47C22×#13711yescharacteristic
384C2×C47C2×#57811yescharacteristic
385D47—82no—
386C22×Q16—471no—
387C22×Q16—471no—
388C22×Q16—471no—
389C22×Q16—471no—
390C22×Q16—471no—
391C22×Q16C2×D4711yescharacteristic
392C22×SD16—471no—
393C22×SD16—471no—
394C22×SD16—471no—
395#557—478no—
396#557—944no—
397#556—478no—
398#556—944no—
399C2×C4⋊Q8—471no—
400C2×C4⋊Q8—471no—
401C2×C4⋊Q8—471no—
402C2×C4⋊Q8—471no—
403C2×#126—941no—
404C2×#126—941no—
405C2×#125—941no—
406C2×#125—941no—
407C2×#125—941no—
408C2×#124—471no—
409C2×#124—471no—
410C2×C22⋊Q8—941no—
411C2×C4×Q8—471no—
412C2×C4×Q8—471no—
413C2×C4×Q8—471no—
414C2×C4×Q8—471no—
415C2×C4×Q8—941no—
416C2×C4×Q8C2×D4711yescharacteristic
417C2×C4×Q8C2×D4711yescharacteristic
418C2×C4×D4—471no—
419C2×#117—941no—
420#497—478no—
421#497—478no—
422#494—478no—
423#464—478no—
424#464—478no—
425#462—478no—
426#462—478no—
427#462—478no—
428#461—478no—
429#446—478no—
430#441—478no—
431#441C2×D4718yescomplemented
432C4×SD16—478no—
433C2×#106C2×D4711yescharacteristic
434C2×C4⋊C8—471no—
435C2×C4⋊C8—471no—
436C2×C4⋊C8—471no—
437C2×#103—471no—
438C2×#103—471no—
439C2×#103—471no—
440C2×#103C2×D4711yescharacteristic
441C2×#103C2×D4711yescharacteristic
442C2×#102—471no—
443C2×#97—471no—
444C2×#97C2×D4711yescharacteristic
445C2×C4×C8—471no—
446C47C2×#339811yescharacteristic, complemented, Sylow
447C22×Q8—471no—
448C22×Q8—471no—
449C22×Q8—471no—
450C22×Q8—471no—
451C22×Q8C22×D4711yescharacteristic
452C22×Q8C22×D4711yescharacteristic
453C22×D4—471no—
454C23×C4—941no—
455C2×Q16—24no—
456C2×Q16—474no—
457C2×Q16—474no—
458C2×Q16—474no—
459C2×Q16—474no—
460C2×Q16—474no—
461C2×Q16—944no—
462C2×Q16—1882no—
463C2×Q16—1882no—
464C2×Q16—1882no—
465C2×Q16—1882no—
466C2×Q16C22×D4714yes—
467C2×SD16—474no—
468C2×SD16—474no—
469C2×SD16—474no—
470C2×SD16—944no—
471C2×SD16—1882no—
472C2×SD16—1882no—
473C22×C8—471no—
474C22×C8—471no—
475C22×C8C22×D4711yescharacteristic
476C22×C8C22×D4711yescharacteristic
477C4⋊Q8—474no—
478C4⋊Q8—474no—
479C4⋊Q8—474no—
480C4⋊Q8—474no—
481C4⋊Q8—942no—
482C4⋊Q8—942no—
483C4⋊Q8—942no—
484C4⋊Q8—942no—
485#126—948no—
486#126—948no—
487#125—948no—
488#125—948no—
489#125—948no—
490#124—474no—
491#124—474no—
492#124—942no—
493#124—942no—
494C22⋊Q8—948no—
495C4×Q8—22no—
496C4×Q8—22no—
497C4×Q8—474no—
498C4×Q8—474no—
499C4×Q8—474no—
500C4×Q8—474no—
501C4×Q8—474no—
502C4×Q8—948no—
503C4×Q8—942no—
504C4×Q8—942no—
505C4×Q8—942no—
506C4×Q8C22×D4714yes—
507C4×Q8C22×D4714yes—
508C4×D4—474no—
509C4×D4—942no—
510#117—948no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—471no—
514C2×C4⋊C4—471no—
515C2×C4⋊C4—471no—
516C2×C4⋊C4—941no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4—941no—
521C2×C4⋊C4—941no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—941no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4—941no—
526C2×C4⋊C4—941no—
527C2×C4⋊C4C22×D4711yescharacteristic
528C2×C4⋊C4C22×D4711yescharacteristic
529C2×C22⋊C4—941no—
530C2×C22⋊C4—941no—
531C2×C22⋊C4—941no—
532C2×C22⋊C4—941no—
533C2×C22⋊C4—941no—
534C2×C42—21no—
535C2×C42—21no—
536C2×C42—471no—
537C2×C42—471no—
538C2×C42—941no—
539C2×C42—941no—
540C2×C42—941no—
541C2×C42C22×D4711yescharacteristic
542#106C22×D4714yes—
543C4⋊C8—474no—
544C4⋊C8—474no—
545C4⋊C8—474no—
546#103—474no—
547#103—474no—
548#103—474no—
549#103C22×D4714yes—
550#103C22×D4714yes—
551#102—474no—
552#97—474no—
553#97C22×D4714yes—
554C4×C8—474no—
555C24—941no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—474no—
563C2×Q8—472no—
564C2×Q8—472no—
565C2×Q8—472no—
566C2×Q8—944no—
567C2×Q8—941no—
568C2×Q8—941no—
569C2×Q8—941no—
570C2×Q8—942no—
571C2×Q8—942no—
572C2×Q8—942no—
573C2×Q8—942no—
574C2×Q8—942no—
575C2×Q8—942no—
576C2×Q8C23×D4712yes—
577C2×Q8C23×D4712yes—
578C2×D4—472no—
579C2×D4—941no—
580C2×D4—942no—
581C2×D4—942no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—471no—
587C22×C4—471no—
588C22×C4—471no—
589C22×C4—471no—
590C22×C4—944no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—1884no—
595C22×C4D4×D4711yescharacteristic
596C22×C4D4×D4711yescharacteristic
597C22×C4C23×D4711yescharacteristic
598Q16—28no—
599Q16—948no—
600Q16—1884no—
601Q16—1884no—
602Q16—1884no—
603Q16—1884no—
604SD16—948no—
605SD16—1884no—
606SD16—1884no—
607C2×C8—22no—
608C2×C8—472no—
609C2×C8—472no—
610C2×C8—942no—
611C2×C8—942no—
612C2×C8#1062535014yes—
613C2×C8C23×D4712yes—
614C2×C8C23×D4712yes—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—474no—
620C4⋊C4—474no—
621C4⋊C4—474no—
622C4⋊C4—944no—
623C4⋊C4—944no—
624C4⋊C4—944no—
625C4⋊C4—944no—
626C4⋊C4—944no—
627C4⋊C4—944no—
628C4⋊C4—944no—
629C4⋊C4—944no—
630C4⋊C4—944no—
631C4⋊C4—944no—
632C4⋊C4—944no—
633C4⋊C4C23×D4712yes—
634C4⋊C4C23×D4712yes—
635C22⋊C4—944no—
636C22⋊C4—944no—
637C22⋊C4—944no—
638C22⋊C4—944no—
639C22⋊C4—944no—
640C42—24no—
641C42—24no—
642C42—472no—
643C42—472no—
644C42—472no—
645C42—472no—
646C42—944no—
647C42—944no—
648C42—944no—
649C42D4×D4712yes—
650C42C23×D4712yes—
651C23—942no—
652C23—1882no—
653C23—1882no—
654C23—1882no—
655C23C2×D4×D4711yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—948no—
663Q8—942no—
664Q8—942no—
665Q8—942no—
666Q8—942no—
667Q8—942no—
668Q8—942no—
669Q8—1882no—
670Q8—1882no—
671Q8—1882no—
672D4—942no—
673D4—942no—
674D4—1882no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—474no—
686C2×C4—472no—
687C2×C4—472no—
688C2×C4—472no—
689C2×C4—472no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—1888no—
697C2×C4—1882no—
698C2×C4—1882no—
699C2×C4—1882no—
700C2×C4C2×D4×D4712yes—
701C2×C4C2×D4×D4712yes—
702C2×C4C2×D4×D4711yescharacteristic
703C2×C4C2×#1062535012yes—
704C2×C4#1309407012yes—
705C2×C4C24×D4711yescharacteristic
706C8—22no—
707C8—942no—
708C8—942no—
709C8C2×#1062535014yes—
710C22—3764no—
711C22—1882no—
712C22—1882no—
713C22—1882no—
714C22#1568979412yes—
715C22#137×D4712yes—
716C22#1568993912yes—
717C22C22×D4×D4711yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—474no—
725C4—942no—
726C4—942no—
727C4—942no—
728C4—1882no—
729C4—1882no—
730C4—1882no—
731C4#1568979412yes—
732C4C22×#1062535011yescharacteristic
733C4C2×#1309407011yescharacteristic
734C2—3762no—
735C2#2025642014yesdirect product factor
736C2C2×#1568979411yescharacteristic
737C2C2×#137×D4711yescharacteristic
738C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#441C2
socleC23×C47C22×D4
prime radicalC22×D188C23
hypercenterC2×#441D47
hypocenterC47C2×#3398
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
1. C2×#15689851C2semidirect
3. #20256420C2direct (N × H)
6. C2×#15689501C2semidirect
9. C2×#15689333C2semidirect
10. C2×#15689332C2semidirect
11. C2×#15689332C2semidirect
13. C2×#15689251C2semidirect
14. C2×#15689229C2semidirect
16. C2×C47×#441C2semidirect
26. #15689851C22semidirect
50. #15689501C22semidirect
53. #15689333C22semidirect
54. #15689332C22semidirect
55. #15689332C22semidirect
57. #15689251C22semidirect
58. #15689229C22semidirect
72. C47×#441C22semidirect
379. C2×#441D47semidirect
381. C2×C47#3398semidirect
431. #441C2×D47semidirect
446. C47C2×#3398semidirect
735. C2#20256420direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898512
C2×#156898452
#202564202
C2×#156895172
C2×#156895162
C2×#156895012
C2×#156893482
C2×#156893452
C2×#156893332
C2×#156893322
C2×#156893272
C2×#156892512
C2×#156892292
C2×#156892102
C2×C47×#4412
C2×#339847