Finite Group Databasebeta

← C2×#19147112 #25975210

Subgroups — C2×#19147112 #25975210

Order 11008.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583614C211yesmaximal, characteristic
2C2×#14583589C211yesmaximal, characteristic, complemented
3#19147112C2116yesmaximal, direct product factor
4C2×#14583308C211yesmaximal, characteristic, complemented
5C2×#14583218C211yesmaximal, characteristic, complemented
6C2×#14583241C211yesmaximal, characteristic, complemented
7C2×#14583241C211yesmaximal, characteristic, complemented
8C2×#14583224C211yesmaximal, characteristic, complemented
9C2×#14583185C211yesmaximal, characteristic, complemented
10C2×#14583200C211yesmaximal, characteristic, complemented
11C2×#14583145C211yesmaximal, characteristic, complemented
12C2×#14583128C211yesmaximal, characteristic, complemented
13C2×#14583001C211yesmaximal, characteristic, complemented
14C2×#14582941C211yesmaximal, characteristic, complemented
15C2×#14582937C211yesmaximal, characteristic, complemented
16C2×C43×#435C211yesmaximal, characteristic, complemented
17C22×#10621873C2211yescharacteristic
18#14583614—24no—
19#14583614C2218yes—
20#14583589—24no—
21#14583589C2218yescomplemented
22C2×#13063325C2211yescharacteristic
23C2×#13063318—21no—
24C2×#13063317C2211yescharacteristic
25C2×#13063315—21no—
26C2×#13063311—21no—
27C2×#13063311—21no—
28C2×#13063306—21no—
29C2×#13063304C2211yescharacteristic
30C2×#13063304C2211yescharacteristic
31C2×#13063299C2211yescharacteristic
32C2×#13063299C2211yescharacteristic
33C2×#13063296—21no—
34C2×C4×Dic86C2211yescharacteristic
35C2×C4×D172C2211yescharacteristic
36C2×#13063284C2211yescharacteristic
37C2×#13063284C2211yescharacteristic
38C2×#13063284C2211yescharacteristic
39C2×#13063283—21no—
40C2×#13063281—21no—
41C22×C4⋊Dic43C2211yescharacteristic
42#14583308C2218yescomplemented
43#14583241C2218yescomplemented
44#14583241C2218yescomplemented
45#14583224C2218yescomplemented
46#14583218C2218yescomplemented
47#14583200C2218yescomplemented
48#14583185C2218yescomplemented
49#14583145C2218yescomplemented
50#14583128C2218yescomplemented
51#14583001C2218yescomplemented
52#14582941C2218yescomplemented
53#14582937C2218yescomplemented
54C2×#13063259C2211yescharacteristic
55C2×#13063259C2211yescharacteristic
56C2×#13063259C2211yescharacteristic
57C2×#13063259C2211yescharacteristic
58C2×#13063257C2211yescharacteristic
59C2×#13063257C2211yescharacteristic
60C2×#13063257C2211yescharacteristic
61C2×#13063257C2211yescharacteristic
62C2×#13063257C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063250C2211yescharacteristic
65C2×#13063250C2211yescharacteristic
66C2×#13063247C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C22×M16×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C43×#435C2218yescomplemented
73C2×C4⋊C8×C43C2211yescharacteristic
74C2×C22⋊C8×C43C2211yescharacteristic
75C2×C22⋊C8×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×D172C2311yescharacteristic
80C22×C22⋊D43—21no—
81C22×C22⋊D43—21no—
82C23×Dic43—21no—
83C22×C4×D43—21no—
84C2×#10621873—24no—
85C2×#10621873C2314yes—
86#13063325—22no—
87#13063325C2314yes—
88#13063318—28no—
89#13063317—22no—
90#13063317C2314yes—
91#13063315—28no—
92#13063311—28no—
93#13063311—28no—
94#13063306—28no—
95#13063304—22no—
96#13063304—22no—
97#13063304C2314yes—
98#13063304C2314yes—
99#13063299—22no—
100#13063299—22no—
101#13063299C2314yes—
102#13063299C2314yes—
103#13063296—28no—
104C4×Dic86—22no—
105C4×Dic86C2314yes—
106C4×D172—22no—
107C4×D172C2314yes—
108#13063284—22no—
109#13063284—22no—
110#13063284—22no—
111#13063284C2314yes—
112#13063284C2314yes—
113#13063284C2314yes—
114#13063283—28no—
115#13063281—28no—
116C2×C4⋊Dic43—22no—
117C2×C4⋊Dic43—21no—
118C2×C4⋊Dic43—21no—
119C2×C4⋊Dic43C2314yes—
120C2×C4⋊Dic43C2311yescharacteristic
121C2×C4⋊Dic43C2311yescharacteristic
122C2×C4⋊Dic43C2311yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
124C2×C4⋊Dic43C2311yescharacteristic
125C2×C4⋊Dic43C2311yescharacteristic
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×C22⋊Dic43—21no—
132C2×C22⋊Dic43—21no—
133C2×C22⋊Dic43—21no—
134C2×C22⋊Dic43—21no—
135C2×C22⋊Dic43—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43—21no—
142C2×C4×Dic43—21no—
143#13063259C2314yes—
144#13063259C2314yes—
145#13063259C2314yes—
146#13063259C2314yes—
147#13063257C2314yes—
148#13063257C2314yes—
149#13063257C2314yes—
150#13063257C2314yes—
151#13063257C2314yes—
152#13063250C2314yes—
153#13063250C2314yes—
154#13063250C2314yes—
155#13063247C2314yes—
156#13063247C2314yes—
157#13063247C2314yes—
158C22×D4×C43D411yescharacteristic
159C23×C4×C43C2311yescharacteristic
160C23×C4×C43C2311yescharacteristic
161C2×M16×C43—24no—
162C2×M16×C43C2314yes—
163C22×C8×C43—24no—
164C22×C8×C43C2314yes—
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C4×D4×C43D414yes—
170C4×D4×C43C2314yes—
171C2×C4⋊C4×C43D411yescharacteristic
172C2×C22⋊C4×C43D411yescharacteristic
173C2×C22⋊C4×C43D411yescharacteristic
174C2×C42×C43C2311yescharacteristic
175C4⋊C8×C43C2314yes—
176C22⋊C8×C43C2314yes—
177C22⋊C8×C43C2314yes—
178#97×C43C2314yes—
179C24×C43C2×D411yescharacteristic
180C24×C43C2×D411yescharacteristic
181C23×D43—21no—
182C2×D4×C43—42no—
183C2×D4×C43C2×D414yes—
184C22×C4×C43—22no—
185C22×C4×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43—22no—
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D412yes—
193C22×C4×C43C2×D412yes—
194C22×C4×C43C2412yes—
195C22×C4×C43C2412yes—
196C22×C4×C43C2411yescharacteristic
197C2×C22⋊D43—24no—
198C2×C22⋊D43—24no—
199C2×C22⋊D43—82no—
200C2×C22⋊D43—82no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—24no—
209C22×Dic43—44no—
210C2×D172—21no—
211C2×D172—22no—
212C2×D172—22no—
213C2×D172C2412yes—
214C2×C4×D43—24no—
215C2×C4×D43—44no—
216C2×Dic86—22no—
217C2×Dic86—22no—
218C2×Dic86—21no—
219C2×Dic86—24no—
220C2×Dic86—82no—
221C2×Dic86C2412yes—
222M16×C43—28no—
223C2×C8×C43—22no—
224C2×C8×C43—22no—
225C2×C8×C43—22no—
226C2×C8×C43—28no—
227C2×C8×C43#4114yes—
228C2×C8×C43C2412yes—
229C2×C8×C43C2412yes—
230C2×C8×C43C2412yes—
231C2×C8×C43C2412yes—
232C4⋊C4×C43C2×D414yes—
233C22⋊C4×C43C2×D414yes—
234C22⋊C4×C43C2×D414yes—
235C42×C43C2×D412yes—
236C42×C43C2412yes—
237C22⋊Dic43—24no—
238C22⋊Dic43—24no—
239C22⋊Dic43—24no—
240C22⋊Dic43—24no—
241C22⋊Dic43—24no—
242(C2×D43)⋊C4—24no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4—24no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—24no—
248C4⋊Dic43—24no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43C2412yes—
254C4⋊Dic43C2412yes—
255C4⋊Dic43C2412yes—
256C4⋊Dic43C2412yes—
257C4⋊Dic43C2412yes—
258C4⋊Dic43C2412yes—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264C4×Dic43—24no—
265C4×Dic43—24no—
266C4×Dic43—24no—
267C4×Dic43—24no—
268#10621873—28no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43C22×D412yes—
276C23×C43C22×D412yes—
277C23×C43C22×D411yescharacteristic
278C22×D43—22no—
279C22×D43—42no—
280C22×D43—42no—
281C22×D43—42no—
282D4×C43—44no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—24no—
288C2×C4×C43—24no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43C22×D412yes—
294C2×C4×C43C22×D412yes—
295C2×C4×C43C22×D412yes—
296C2×C4×C43C22×D412yes—
297C2×C4×C43C22×D411yescharacteristic
298C2×C4×C43C2×#4112yes—
299C2×C4×C432−1+412yes—
300C2×C4×C43C2511yescharacteristic
301C22⋊D43—84no—
302C22⋊D43—84no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—48no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318D172—22no—
319D172—22no—
320D172—42no—
321C4×D43—48no—
322Dic86—22no—
323Dic86—22no—
324Dic86—42no—
325Dic86—84no—
326C8×C43—22no—
327C8×C43—22no—
328C8×C43—22no—
329C8×C43C2×#4114yes—
330C2×#3348—431nomaximal, Sylow
331C22×C43—22no—
332C22×C43—22no—
333C22×C43—22no—
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—44no—
338C22×C43—44no—
339C22×C43#54712yes—
340C22×C43#57512yes—
341C22×C43#57712yes—
342C22×C43C23×D411yescharacteristic
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—42no—
346C2×D43—84no—
347C4×C43—22no—
348C4×C43—22no—
349C4×C43—22no—
350C4×C43—22no—
351C4×C43#54712yes—
352C4×C43C22×#4111yescharacteristic
353C4×C43C2×2−1+411yescharacteristic
354Dic43—42no—
355Dic43—42no—
356Dic43—42no—
357Dic43—42no—
358Dic43—42no—
359Dic43—42no—
360Dic43—42no—
361C2×#555—431no—
362C2×#552—431no—
363#3348—4316no—
364C2×#501—431no—
365C2×#481—431no—
366C2×#485—431no—
367C2×#485—431no—
368C2×#482—431no—
369C2×#475—431no—
370C2×#478—431no—
371C2×#468—431no—
372C2×#465—431no—
373C2×#440—431no—
374C2×#435D4311yescharacteristic, complemented
375C2×#428—431no—
376C2×#427—431no—
377C2×C43—42no—
378C2×C43—42no—
379C2×C43#334814yescomplemented
380C2×C43C2×#54711yescharacteristic
381C2×C43C2×#57511yescharacteristic
382C2×C43C2×#57711yescharacteristic
383D43—82no—
384C22×SD16—431no—
385C22×M16C2×D4311yescharacteristic
386C23×C8C2×D4311yescharacteristic
387#555—438no—
388#555—864no—
389#552—438no—
390#552—864no—
391C2×C4⋊Q8—431no—
392C2×#126—861no—
393C2×#125—431no—
394C2×#125—861no—
395C2×#124—861no—
396C2×#124—861no—
397C2×#123—861no—
398C2×C22⋊Q8—431no—
399C2×C22⋊Q8—431no—
400C2×#121—431no—
401C2×#121—431no—
402C2×#121—861no—
403C2×C4×Q8—431no—
404C2×C4×D4—431no—
405C2×C4×D4C2×D4311yescharacteristic
406C2×#117—431no—
407C2×#117—431no—
408C2×#117—431no—
409C2×#117—861no—
410C2×#117—861no—
411C22×C4⋊C4—431no—
412#501—438no—
413#485—438no—
414#485—438no—
415#482—438no—
416#481—438no—
417#478—438no—
418#475—438no—
419#468—438no—
420#465—438no—
421#440—438no—
422#435C2×D4318yescomplemented
423#428—438no—
424#427—438no—
425C2×#107—431no—
426C2×#107—431no—
427C2×#107—431no—
428C2×#107—431no—
429C2×#106—431no—
430C2×#106—431no—
431C2×#106—431no—
432C2×#106—431no—
433C2×#106—431no—
434C2×C4⋊C8C2×D4311yescharacteristic
435C2×#103—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#102—431no—
439C2×#102—431no—
440C2×#102—431no—
441C2×C22⋊C8C2×D4311yescharacteristic
442C2×C22⋊C8C2×D4311yescharacteristic
443C2×#97C2×D4311yescharacteristic
444C43C2×#334811yescharacteristic, complemented, Sylow
445C22×Q8—431no—
446C22×Q8—861no—
447C22×D4—431no—
448C22×D4—861no—
449C22×D4—861no—
450C22×D4D17211yescharacteristic
451C23×C4—861no—
452C23×C4—861no—
453C23×C4C22×D4311yescharacteristic
454C23×C4C22×D4311yescharacteristic
455C2×SD16—434no—
456C2×SD16—864no—
457C2×M16—24no—
458C2×M16C22×D4314yes—
459C22×C8—24no—
460C22×C8C22×D4311yescharacteristic
461C22×C8C22×D4314yes—
462C22×C8C22×D4311yescharacteristic
463C22×C8C22×D4311yescharacteristic
464C22×C8C22×D4311yescharacteristic
465C4⋊Q8—434no—
466C4⋊Q8—862no—
467#126—868no—
468#125—434no—
469#125—868no—
470#125—862no—
471#124—868no—
472#124—868no—
473#123—868no—
474C22⋊Q8—434no—
475C22⋊Q8—434no—
476C22⋊Q8—862no—
477C22⋊Q8—862no—
478#121—434no—
479#121—434no—
480#121—868no—
481#121—862no—
482#121—862no—
483C4×Q8—434no—
484C4×Q8—862no—
485C4×D4—434no—
486C4×D4—862no—
487C4×D4D17214yes—
488C4×D4C22×D4314yes—
489#117—434no—
490#117—434no—
491#117—434no—
492#117—862no—
493#117—862no—
494#117—862no—
495#117—868no—
496#117—868no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—434no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—862no—
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⋊C4D17211yescharacteristic
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4D17211yescharacteristic
522C2×C22⋊C4D17211yescharacteristic
523C2×C42—861no—
524C2×C42—861no—
525C2×C42—861no—
526C2×C42—861no—
527C2×C42C22×D4311yescharacteristic
528#107—434no—
529#107—434no—
530#107—434no—
531#107—434no—
532#106—434no—
533#106—434no—
534#106—434no—
535#106—434no—
536#106—434no—
537C4⋊C8C22×D4314yes—
538#103—434no—
539#103—434no—
540#103—434no—
541#102—434no—
542#102—434no—
543#102—434no—
544C22⋊C8C22×D4314yes—
545C22⋊C8C22×D4314yes—
546#97C22×D4314yes—
547C24—861no—
548C24C2×D17211yescharacteristic
549C24C2×D17211yescharacteristic
550C2×Q8—432no—
551C2×Q8—864no—
552C2×Q8—861no—
553C2×Q8—862no—
554C2×Q8—862no—
555C2×Q8—3442no—
556C2×D4—42no—
557C2×D4—432no—
558C2×D4—864no—
559C2×D4—864no—
560C2×D4—861no—
561C2×D4—862no—
562C2×D4—862no—
563C2×D4—3442no—
564C2×D4—3442no—
565C2×D4C2×D17214yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—864no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—864no—
579C22×C4—1724no—
580C22×C4—1724no—
581C22×C4C2×D17212yes—
582C22×C4C2×D17212yes—
583C22×C4C2×D17211yescharacteristic
584C22×C4C2×D17211yescharacteristic
585C22×C4C2×D17211yescharacteristic
586C22×C4C2×D17211yescharacteristic
587C22×C4C23×D4312yes—
588C22×C4C23×D4312yes—
589C22×C4C23×D4311yescharacteristic
590SD16—868no—
591M16—28no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—28no—
596C2×C8#1062190014yes—
597C2×C8C23×D4312yes—
598C2×C8C23×D4312yes—
599C2×C8C23×D4312yes—
600C2×C8C23×D4312yes—
601C4⋊C4—432no—
602C4⋊C4—432no—
603C4⋊C4—432no—
604C4⋊C4—432no—
605C4⋊C4—432no—
606C4⋊C4—432no—
607C4⋊C4—861no—
608C4⋊C4—861no—
609C4⋊C4—864no—
610C4⋊C4—861no—
611C4⋊C4—861no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—864no—
615C4⋊C4—864no—
616C4⋊C4—864no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4C2×D17214yes—
621C22⋊C4—864no—
622C22⋊C4—864no—
623C22⋊C4—864no—
624C22⋊C4—864no—
625C22⋊C4—864no—
626C22⋊C4—864no—
627C22⋊C4—864no—
628C22⋊C4—864no—
629C22⋊C4C2×D17214yes—
630C22⋊C4C2×D17214yes—
631C42—864no—
632C42—864no—
633C42—864no—
634C42—864no—
635C42C2×D17212yes—
636C42C23×D4312yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—862no—
644C23—1722no—
645C23—1722no—
646C23—1722no—
647C23C22×D17212yes—
648C23C22×D17212yes—
649C23C22×D17211yescharacteristic
650Q8—862no—
651Q8—862no—
652Q8—3444no—
653Q8—1722no—
654D4—44no—
655D4—862no—
656D4—862no—
657D4—3444no—
658D4—3444no—
659D4—1722no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—862no—
677C2×C4—1728no—
678C2×C4—1728no—
679C2×C4—1722no—
680C2×C4—1722no—
681C2×C4—1722no—
682C2×C4—1722no—
683C2×C4—1722no—
684C2×C4—1722no—
685C2×C4—1722no—
686C2×C4C22×D17212yes—
687C2×C4C22×D17212yes—
688C2×C4C22×D17212yes—
689C2×C4C22×D17212yes—
690C2×C4C22×D17211yescharacteristic
691C2×C4C2×#1062190012yes—
692C2×C4#1306337212yes—
693C2×C4C24×D4311yescharacteristic
694C8—22no—
695C8—22no—
696C8—22no—
697C8C2×#1062190014yes—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—3444no—
707C22—1722no—
708C22—1722no—
709C22—1722no—
710C22#1458355312yes—
711C22#1458369912yes—
712C22#1458371112yes—
713C22C23×D17211yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—1722no—
719C4—1722no—
720C4—1722no—
721C4—1722no—
722C4—1722no—
723C4—1722no—
724C4—1722no—
725C4#1458355312yes—
726C4C22×#1062190011yescharacteristic
727C4C2×#1306337211yescharacteristic
728C2—42no—
729C2—42no—
730C2—3442no—
731C2#1914711214yesdirect product factor
732C2C2×#1458355311yescharacteristic
733C2C2×#1458369911yescharacteristic
734C2C2×#1458371111yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#435C2
socleC23×C43C22×D4
prime radicalC2×#14583614C2
hypercenterC2×#435D43
hypocenterC43C2×#3348
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#14583589C2semidirect
3. #19147112C2direct (N × H)
4. C2×#14583308C2semidirect
5. C2×#14583218C2semidirect
6. C2×#14583241C2semidirect
7. C2×#14583241C2semidirect
8. C2×#14583224C2semidirect
9. C2×#14583185C2semidirect
10. C2×#14583200C2semidirect
11. C2×#14583145C2semidirect
12. C2×#14583128C2semidirect
13. C2×#14583001C2semidirect
14. C2×#14582941C2semidirect
15. C2×#14582937C2semidirect
16. C2×C43×#435C2semidirect
21. #14583589C22semidirect
42. #14583308C22semidirect
43. #14583241C22semidirect
44. #14583241C22semidirect
45. #14583224C22semidirect
46. #14583218C22semidirect
47. #14583200C22semidirect
48. #14583185C22semidirect
49. #14583145C22semidirect
50. #14583128C22semidirect
51. #14583001C22semidirect
52. #14582941C22semidirect
53. #14582937C22semidirect
72. C43×#435C22semidirect
374. C2×#435D43semidirect
379. C2×C43#3348semidirect
422. #435C2×D43semidirect
444. C43C2×#3348semidirect
731. C2#19147112direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836142
C2×#145835892
#191471122
C2×#145833082
C2×#145832182
C2×#145832412
C2×#145832242
C2×#145831852
C2×#145832002
C2×#145831452
C2×#145831282
C2×#145830012
C2×#145829412
C2×#145829372
C2×C43×#4352
C2×#334843