Finite Group Databasebeta

← C2×#19145263 #25966465

Subgroups — C2×#19145263 #25966465

Order 11008.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583520C211yesmaximal, characteristic
2C2×#14583511C211yesmaximal, characteristic, complemented
3#19145263C2116yesmaximal, direct product factor
4C2×#14583308C211yesmaximal, characteristic, complemented
5C2×#14583293C211yesmaximal, characteristic, complemented
6C2×#14583254C211yesmaximal, characteristic, complemented
7C2×#14583250C211yesmaximal, characteristic, complemented
8C2×#14583157C211yesmaximal, characteristic, complemented
9C2×#14583145C211yesmaximal, characteristic
10C2×#14583140C211yesmaximal, characteristic, complemented
11C2×#14583128C211yesmaximal, characteristic
12C2×#14583007C211yesmaximal, characteristic, complemented
13C2×#14583001C211yesmaximal, characteristic, complemented
14C2×C4×Dic172C211yesmaximal, characteristic, complemented
15C2×C4×#10621873C211yesmaximal, characteristic, complemented
16C2×C43×#405C211yesmaximal, characteristic, complemented
17C22×Dic172C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21#14583520—24no—
22#14583520C2218yes—
23#14583511—24no—
24#14583511C2218yescomplemented
25C2×#13063325C2211yescharacteristic
26C2×#13063325C2211yescharacteristic
27C2×#13063320—21no—
28C2×#13063318—21no—
29C2×#13063318—21no—
30C2×#13063317C2211yescharacteristic
31C2×#13063315—21no—
32C2×#13063315—21no—
33C2×#13063313C2211yescharacteristic
34C2×#13063311—21no—
35C2×#13063307—21no—
36C2×#13063304C2211yescharacteristic
37C2×#13063304C2211yescharacteristic
38C2×#13063304C2211yescharacteristic
39C2×#13063303—21no—
40C2×#13063299C2211yescharacteristic
41C2×C4×Dic86C2211yescharacteristic
42C2×C4×Dic86C2211yescharacteristic
43C2×C4×Dic86C2211yescharacteristic
44C2×C4×D172C2211yescharacteristic
45#14583308C2218yescomplemented
46#14583293C2218yescomplemented
47#14583254C2218yescomplemented
48#14583250C2218yescomplemented
49#14583157C2218yescomplemented
50#14583145C2218yes—
51#14583140C2218yescomplemented
52#14583128C2218yes—
53#14583007C2218yescomplemented
54#14583001C2218yescomplemented
55C4×Dic172C2218yescomplemented
56C4×#10621873C2218yescomplemented
57C2×#13063259C2211yescharacteristic
58C2×#13063259C2211yescharacteristic
59C2×#13063257C2211yescharacteristic
60C2×#13063257C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063250C2211yescharacteristic
65C2×#13063250C2211yescharacteristic
66C2×#13063250C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C22×M16×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic
71C2×#117×C43C2211yescharacteristic
72C43×#405C2218yescomplemented
73C2×#97×C43C2211yescharacteristic
74C2×#97×C43C2211yescharacteristic
75C2×C4×C8×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C22×Dic86C2311yescharacteristic
81C22×D172C2311yescharacteristic
82C22×C22⋊D43—21no—
83C22×C4×D43—21no—
84C2×Dic172—24no—
85C2×Dic172—24no—
86C2×Dic172C2314yes—
87C2×Dic172C2314yes—
88C2×#10621873—24no—
89C2×#10621873—24no—
90C2×#10621873C2314yes—
91C2×#10621873C2314yes—
92#13063325—22no—
93#13063325—22no—
94#13063325C2314yes—
95#13063325C2314yes—
96#13063320—28no—
97#13063318—28no—
98#13063318—28no—
99#13063317—22no—
100#13063317C2314yes—
101#13063315—28no—
102#13063315—28no—
103#13063313—22no—
104#13063313C2314yes—
105#13063311—28no—
106#13063307—28no—
107#13063304—22no—
108#13063304—22no—
109#13063304—22no—
110#13063304C2314yes—
111#13063304C2314yes—
112#13063304C2314yes—
113#13063303—28no—
114#13063299—22no—
115#13063299C2314yes—
116C4×Dic86—22no—
117C4×Dic86—22no—
118C4×Dic86—22no—
119C4×Dic86C2314yes—
120C4×Dic86C2314yes—
121C4×Dic86C2314yes—
122C4×D172—22no—
123C4×D172C2314yes—
124C2×C4⋊Dic43—21no—
125C2×C4⋊Dic43—21no—
126C2×C4⋊Dic43—21no—
127C2×C4⋊Dic43C2311yescharacteristic
128C2×C4⋊Dic43C2311yescharacteristic
129C2×C4⋊Dic43C2311yescharacteristic
130C2×C4⋊Dic43C2311yescharacteristic
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×C4×Dic43—21no—
147C2×C4×Dic43—21no—
148C2×C4×Dic43—21no—
149#13063259C2314yes—
150#13063259C2314yes—
151#13063257C2314yes—
152#13063257C2314yes—
153#13063250C2314yes—
154#13063250C2314yes—
155#13063250C2314yes—
156#13063250C2314yes—
157#13063250C2314yes—
158#13063250C2314yes—
159#13063247C2314yes—
160#13063247C2314yes—
161C23×C4×C43C2311yescharacteristic
162C2×M16×C43—24no—
163C2×M16×C43C2314yes—
164C22×C8×C43—24no—
165C22×C8×C43C2314yes—
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C22×C8×C43C2311yescharacteristic
170#117×C43D414yes—
171#117×C43C2314yes—
172C2×C4⋊C4×C43D411yescharacteristic
173C2×C4⋊C4×C43D411yescharacteristic
174C2×C22⋊C4×C43D411yescharacteristic
175C2×C22⋊C4×C43D411yescharacteristic
176C2×C42×C43C2311yescharacteristic
177C2×C42×C43C2311yescharacteristic
178#97×C43C2314yes—
179#97×C43C2314yes—
180C4×C8×C43C2314yes—
181C4×C8×C43C2314yes—
182C24×C43C2×D411yescharacteristic
183C23×D43—21no—
184C22×C4×C43—22no—
185C22×C4×C43—22no—
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D412yes—
192C22×C4×C43C2412yes—
193C22×C4×C43C2411yescharacteristic
194C2×C22⋊D43—24no—
195C2×C22⋊D43—82no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C2×D172—21no—
204C2×D172—22no—
205C2×D172—22no—
206C2×D172C2412yes—
207C2×C4×D43—24no—
208C2×C4×D43—82no—
209C2×Dic86—22no—
210C2×Dic86—22no—
211C2×Dic86—22no—
212C2×Dic86—22no—
213C2×Dic86—22no—
214C2×Dic86—22no—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86—21no—
218C2×Dic86—24no—
219C2×Dic86—82no—
220C2×Dic86C2412yes—
221C2×Dic86C2412yes—
222C2×Dic86C2412yes—
223M16×C43—28no—
224C2×C8×C43—22no—
225C2×C8×C43—22no—
226C2×C8×C43—28no—
227C2×C8×C43#4114yes—
228C2×C8×C43#4114yes—
229C2×C8×C43C2412yes—
230C2×C8×C43C2412yes—
231C2×C8×C43C2412yes—
232C2×C8×C43C2412yes—
233C4⋊C4×C43C2×D414yes—
234C4⋊C4×C43C2×D414yes—
235C22⋊C4×C43C2×D414yes—
236C22⋊C4×C43C2×D414yes—
237C42×C43C2×D412yes—
238C42×C43C2×D412yes—
239C42×C43C2412yes—
240C42×C43C2412yes—
241C22⋊Dic43—24no—
242C22⋊Dic43—24no—
243C22⋊Dic43—24no—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248C4⋊Dic43—24no—
249C4⋊Dic43—24no—
250C4⋊Dic43—24no—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43C2412yes—
256C4⋊Dic43C2412yes—
257C4⋊Dic43C2412yes—
258C4⋊Dic43C2412yes—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267C4×Dic43—24no—
268C4×Dic43—24no—
269C4×Dic43—24no—
270Dic172—28no—
271Dic172—28no—
272#10621873—28no—
273#10621873—28no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43C22×D412yes—
278C23×C43C22×D411yescharacteristic
279C22×D43—22no—
280C22×D43—42no—
281C22×D43—42no—
282C22×D43—42no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—24no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43C22×D412yes—
292C2×C4×C43C22×D412yes—
293C2×C4×C43C22×D412yes—
294C2×C4×C43C22×D412yes—
295C2×C4×C43C22×D412yes—
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C2×#4112yes—
298C2×C4×C43C2×#4112yes—
299C2×C4×C43C2511yescharacteristic
300C22⋊D43—84no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—42no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—42no—
315D172—22no—
316D172—22no—
317D172—42no—
318C4×D43—84no—
319Dic86—22no—
320Dic86—22no—
321Dic86—22no—
322Dic86—22no—
323Dic86—22no—
324Dic86—22no—
325Dic86—42no—
326Dic86—42no—
327Dic86—42no—
328Dic86—84no—
329C8×C43—22no—
330C8×C43—22no—
331C8×C43C2×#4114yes—
332C8×C43C2×#4114yes—
333C2×#3178—431nomaximal, Sylow
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—44no—
338C22×C43#53212yes—
339C22×C43#57712yes—
340C22×C43#57812yes—
341C22×C43C23×D411yescharacteristic
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—84no—
346C4×C43—22no—
347C4×C43—22no—
348C4×C43—22no—
349C4×C43—22no—
350C4×C43—22no—
351C4×C43#53212yes—
352C4×C43C22×#4111yescharacteristic
353C4×C43C22×#4111yescharacteristic
354Dic43—42no—
355Dic43—42no—
356Dic43—42no—
357Dic43—42no—
358Dic43—42no—
359Dic43—42no—
360Dic43—42no—
361C2×#542—431no—
362C2×#541—431no—
363#3178—4316no—
364C2×#501—431no—
365C2×#497—431no—
366C2×#488—431no—
367C2×#487—431no—
368C2×#470—431no—
369C2×#468—431no—
370C2×#467—431no—
371C2×#465—431no—
372C2×#441—431no—
373C2×#440—431no—
374C2×C4×Q16—431no—
375C2×C4×SD16—431no—
376C2×#405D4311yescharacteristic, complemented
377C2×C43—42no—
378C2×C43#317814yescomplemented
379C2×C43C2×#53211yescharacteristic
380C2×C43C2×#57711yescharacteristic
381C2×C43C2×#57811yescharacteristic
382D43—82no—
383C22×Q16—431no—
384C22×Q16—431no—
385C22×SD16—431no—
386C22×SD16—431no—
387C22×M16C2×D4311yescharacteristic
388C23×C8C2×D4311yescharacteristic
389#542—438no—
390#542—864no—
391#541—438no—
392#541—864no—
393C2×C4⋊Q8—431no—
394C2×C4⋊Q8—431no—
395C2×#126—861no—
396C2×#126—861no—
397C2×#126—861no—
398C2×#125—431no—
399C2×#125—861no—
400C2×#125—861no—
401C2×#124—431no—
402C2×#124—861no—
403C2×#123—861no—
404C2×C22⋊Q8—431no—
405C2×C22⋊Q8—431no—
406C2×C22⋊Q8—431no—
407C2×C22⋊Q8—861no—
408C2×#121—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8—431no—
411C2×C4×Q8—431no—
412C2×C4×D4—431no—
413C2×#117C2×D4311yescharacteristic
414#501—438no—
415#497—438no—
416#488—438no—
417#487—438no—
418#470—438no—
419#468—438no—
420#467—438no—
421#465—438no—
422#441—438no—
423#440—438no—
424C4×Q16—438no—
425C4×SD16—438no—
426C2×#107—431no—
427C2×#107—431no—
428C2×#106—431no—
429C2×#106—431no—
430C2×#103—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#102—431no—
437C2×#102—431no—
438#405C2×D4318yescomplemented
439C2×#97C2×D4311yescharacteristic
440C2×#97C2×D4311yescharacteristic
441C2×C4×C8C2×D4311yescharacteristic
442C2×C4×C8C2×D4311yescharacteristic
443C43C2×#317811yescharacteristic, complemented, Sylow
444C22×Q8—431no—
445C22×Q8—431no—
446C22×Q8—431no—
447C22×Q8—861no—
448C22×D4—431no—
449C22×D4—861no—
450C23×C4—861no—
451C23×C4C22×D4311yescharacteristic
452C2×Q16—434no—
453C2×Q16—434no—
454C2×Q16—864no—
455C2×Q16—864no—
456C2×SD16—434no—
457C2×SD16—434no—
458C2×SD16—864no—
459C2×SD16—864no—
460C2×M16—24no—
461C2×M16C22×D4314yes—
462C22×C8—24no—
463C22×C8C22×D4311yescharacteristic
464C22×C8C22×D4314yes—
465C22×C8C22×D4311yescharacteristic
466C22×C8C22×D4311yescharacteristic
467C22×C8C22×D4311yescharacteristic
468C4⋊Q8—434no—
469C4⋊Q8—434no—
470C4⋊Q8—862no—
471C4⋊Q8—862no—
472#126—868no—
473#126—868no—
474#126—868no—
475#125—434no—
476#125—868no—
477#125—868no—
478#125—862no—
479#124—434no—
480#124—868no—
481#124—862no—
482#123—868no—
483C22⋊Q8—434no—
484C22⋊Q8—434no—
485C22⋊Q8—434no—
486C22⋊Q8—862no—
487C22⋊Q8—862no—
488C22⋊Q8—862no—
489C22⋊Q8—868no—
490#121—434no—
491#121—862no—
492C4×Q8—434no—
493C4×Q8—434no—
494C4×Q8—434no—
495C4×Q8—862no—
496C4×Q8—862no—
497C4×Q8—862no—
498C4×D4—434no—
499C4×D4—862no—
500#117D17214yes—
501#117C22×D4314yes—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4D17211yescharacteristic
518C2×C4⋊C4D17211yescharacteristic
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4D17211yescharacteristic
527C2×C22⋊C4D17211yescharacteristic
528C2×C42—861no—
529C2×C42—861no—
530C2×C42—861no—
531C2×C42C22×D4311yescharacteristic
532C2×C42C22×D4311yescharacteristic
533#107—434no—
534#107—434no—
535#106—434no—
536#106—434no—
537#103—434no—
538#103—434no—
539#103—434no—
540#103—434no—
541#103—434no—
542#103—434no—
543#102—434no—
544#102—434no—
545#97C22×D4314yes—
546#97C22×D4314yes—
547C4×C8C22×D4314yes—
548C4×C8C22×D4314yes—
549C24—861no—
550C24C2×D17211yescharacteristic
551C2×Q8—432no—
552C2×Q8—432no—
553C2×Q8—432no—
554C2×Q8—864no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×Q8—862no—
559C2×Q8—862no—
560C2×Q8—862no—
561C2×Q8—862no—
562C2×Q8—862no—
563C2×Q8—862no—
564C2×Q8—3442no—
565C2×D4—432no—
566C2×D4—864no—
567C2×D4—861no—
568C2×D4—862no—
569C2×D4—862no—
570C2×D4—3442no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—864no—
581C22×C4—3442no—
582C22×C4C2×D17212yes—
583C22×C4C2×D17211yescharacteristic
584C22×C4C2×D17211yescharacteristic
585C22×C4C2×D17211yescharacteristic
586C22×C4C2×D17211yescharacteristic
587C22×C4C2×D17211yescharacteristic
588C22×C4C23×D4312yes—
589C22×C4C23×D4311yescharacteristic
590Q16—868no—
591Q16—868no—
592SD16—868no—
593SD16—868no—
594M16—28no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—28no—
598C2×C8#1062189814yes—
599C2×C8#1062189814yes—
600C2×C8C23×D4312yes—
601C2×C8C23×D4312yes—
602C2×C8C23×D4312yes—
603C2×C8C23×D4312yes—
604C4⋊C4—432no—
605C4⋊C4—432no—
606C4⋊C4—432no—
607C4⋊C4—432no—
608C4⋊C4—861no—
609C4⋊C4—861no—
610C4⋊C4—861no—
611C4⋊C4—861no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4—864no—
615C4⋊C4—864no—
616C4⋊C4—864no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—864no—
621C4⋊C4—864no—
622C4⋊C4—864no—
623C4⋊C4C2×D17214yes—
624C4⋊C4C2×D17214yes—
625C22⋊C4—864no—
626C22⋊C4—864no—
627C22⋊C4—864no—
628C22⋊C4—864no—
629C22⋊C4—864no—
630C22⋊C4—864no—
631C22⋊C4—864no—
632C22⋊C4C2×D17214yes—
633C22⋊C4C2×D17214yes—
634C42—864no—
635C42—864no—
636C42—864no—
637C42C2×D17212yes—
638C42C2×D17212yes—
639C42C23×D4312yes—
640C42C23×D4312yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—862no—
645C23—1722no—
646C23—1722no—
647C23—1722no—
648C23C22×D17212yes—
649C23C22×D17211yescharacteristic
650Q8—862no—
651Q8—862no—
652Q8—862no—
653Q8—862no—
654Q8—862no—
655Q8—862no—
656Q8—3444no—
657Q8—1722no—
658Q8—1722no—
659Q8—1722no—
660D4—862no—
661D4—862no—
662D4—3444no—
663D4—1722no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—3444no—
680C2×C4—1722no—
681C2×C4—1722no—
682C2×C4—1722no—
683C2×C4—1722no—
684C2×C4—1722no—
685C2×C4—1722no—
686C2×C4—1722no—
687C2×C4C22×D17212yes—
688C2×C4C22×D17212yes—
689C2×C4C22×D17212yes—
690C2×C4C22×D17212yes—
691C2×C4C22×D17212yes—
692C2×C4C22×D17211yescharacteristic
693C2×C4C2×#1062189812yes—
694C2×C4C2×#1062189812yes—
695C2×C4C24×D4311yescharacteristic
696C8—22no—
697C8—22no—
698C8C2×#1062189814yes—
699C8C2×#1062189814yes—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—3444no—
705C22—1722no—
706C22—1722no—
707C22—1722no—
708C22#1458344912yes—
709C22#1458371112yes—
710C22#1458371612yes—
711C22C23×D17211yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—1722no—
718C4—1722no—
719C4—1722no—
720C4—1722no—
721C4—1722no—
722C4—1722no—
723C4—1722no—
724C4#1458344912yes—
725C4C22×#1062189811yescharacteristic
726C4C22×#1062189811yescharacteristic
727C2—42no—
728C2—3442no—
729C2#1914526314yesdirect product factor
730C2C2×#1458344911yescharacteristic
731C2C2×#1458371111yescharacteristic
732C2C2×#1458371611yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#405C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenterC2×#405D43
hypocenterC43C2×#3178
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
2. C2×#14583511C2semidirect
3. #19145263C2direct (N × H)
4. C2×#14583308C2semidirect
5. C2×#14583293C2semidirect
6. C2×#14583254C2semidirect
7. C2×#14583250C2semidirect
8. C2×#14583157C2semidirect
10. C2×#14583140C2semidirect
12. C2×#14583007C2semidirect
13. C2×#14583001C2semidirect
14. C2×C4×Dic172C2semidirect
15. C2×C4×#10621873C2semidirect
16. C2×C43×#405C2semidirect
24. #14583511C22semidirect
45. #14583308C22semidirect
46. #14583293C22semidirect
47. #14583254C22semidirect
48. #14583250C22semidirect
49. #14583157C22semidirect
51. #14583140C22semidirect
53. #14583007C22semidirect
54. #14583001C22semidirect
55. C4×Dic172C22semidirect
56. C4×#10621873C22semidirect
72. C43×#405C22semidirect
376. C2×#405D43semidirect
378. C2×C43#3178semidirect
438. #405C2×D43semidirect
443. C43C2×#3178semidirect
729. C2#19145263direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835202
C2×#145835112
#191452632
C2×#145833082
C2×#145832932
C2×#145832542
C2×#145832502
C2×#145831572
C2×#145831452
C2×#145831402
C2×#145831282
C2×#145830072
C2×#145830012
C2×C4×Dic1722
C2×C4×#106218732
C2×C43×#4052
C2×#317843