Finite Group Databasebeta

← #25112887

Subgroups — #25112887

Order 11008.

1194 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583589C211yesmaximal, characteristic
2D4×C4⋊Dic43C211yesmaximal, characteristic
3#19135564C211yesmaximal, characteristic, complemented
4#19135550C211yesmaximal, characteristic, complemented
5#19135028C211yesmaximal, characteristic, complemented
6#19135018C211yesmaximal, characteristic, complemented
7#19134900C211yesmaximal, characteristic, complemented
8#19134900C211yesmaximal, characteristic, complemented
9#19134691C211yesmaximal, characteristic, complemented
10#19134682C211yesmaximal, characteristic, complemented
11#19134601C211yesmaximal, characteristic, complemented
12#19134426C211yesmaximal, characteristic, complemented
13#19134315C211yesmaximal, characteristic, complemented
14C2×#14582662C211yesmaximal, characteristic, complemented
15C2×C43×#435C211yesmaximal, characteristic
16#14583589—24no—
17#14583589C418yescomplemented
18C2×#13063318—21no—
19C2×#13063317C2211yescharacteristic
20C2×#13063315—21no—
21C2×#13063306—21no—
22C2×#13063304C2211yescharacteristic
23C2×#13063304C2211yescharacteristic
24C2×C4×Dic86C2211yescharacteristic
25C2×D4×Dic43—21no—
26C2×#13063284C2211yescharacteristic
27C2×#13063281—21no—
28C22×C4⋊Dic43C2211yescharacteristic
29C22×C4⋊Dic43C2211yescharacteristic
30C22×C4⋊Dic43C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35#14582798—21no—
36#14582774—21no—
37#14582774—21no—
38#14582769C2211yescharacteristic
39#14582759C2211yescharacteristic
40#14582759C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C22×M16×C43C2211yescharacteristic
55C23×C8×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C43×#435—24no—
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C2×#97×C43C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C23×Dic43—21no—
64C23×Dic43—21no—
65C23×Dic43—21no—
66#13063318—28no—
67#13063317—22no—
68#13063317C2×C414yescomplemented
69#13063315—28no—
70#13063306—28no—
71#13063304—22no—
72#13063304—22no—
73#13063304C2×C414yescomplemented
74#13063304C2×C414yescomplemented
75C4×Dic86—22no—
76C4×Dic86C2×C414yescomplemented
77D4×Dic43—44no—
78#13063284—22no—
79#13063284C2×C414yescomplemented
80#13063281—28no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—22no—
84C2×C4⋊Dic43—22no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—41no—
90C2×C4⋊Dic43—41no—
91C2×C4⋊Dic43C2×C414yescomplemented
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43—21no—
112#13063250—22no—
113#13063250—22no—
114#13063250—41no—
115#13063250—41no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×D4×C43D411yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C2×M16×C43—22no—
123C2×M16×C43—22no—
124C2×M16×C43—41no—
125C22×C8×C43—22no—
126C22×C8×C43—22no—
127C22×C8×C43—41no—
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C4×D4×C43C2×C414yes—
133C4×D4×C43D414yes—
134C2×C4⋊C4×C43D411yescharacteristic
135C2×C22⋊C4×C43D411yescharacteristic
136C2×C22⋊C4×C43D411yescharacteristic
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—22no—
139C22⋊C8×C43—22no—
140C22⋊C8×C43—22no—
141#97×C43—22no—
142C24×C43C2×D411yescharacteristic
143C24×C43C2×D411yescharacteristic
144C2×D4×C43—22no—
145C2×D4×C43—22no—
146C2×D4×C43C22⋊C414yes—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C22×C412yes—
156C22×C4×C43C22×C412yes—
157C22×C4×C43C2×D412yes—
158C22×C4×C43C2×D412yes—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2411yescharacteristic
164C22×Dic43—24no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—42no—
174C22×Dic43—42no—
175C22×Dic43—42no—
176C22×Dic43—42no—
177C22×Dic43—42no—
178C22×Dic43—42no—
179C22×Dic43—81no—
180C22×Dic43—81no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86C22×C412yes—
187M16×C43—44no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—44no—
200C2×C8×C43#4112yes—
201C4⋊C4×C43C22⋊C414yes—
202C22⋊C4×C43C22⋊C414yes—
203C22⋊C4×C43C22⋊C414yes—
204C42×C43C22×C412yes—
205C42×C43C2×D412yes—
206C22⋊Dic43—24no—
207C22⋊Dic43—24no—
208C22⋊Dic43—24no—
209C22⋊Dic43—42no—
210C22⋊Dic43—42no—
211C4⋊Dic43—24no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—42no—
223C4⋊Dic43—42no—
224C4⋊Dic43—42no—
225C4⋊Dic43—81no—
226C4⋊Dic43C22×C412yes—
227C4⋊Dic43C22×C412yes—
228C4⋊Dic43C22×C412yes—
229C4⋊Dic43#4112yes—
230Dic43⋊C4—24no—
231Dic43⋊C4—24no—
232Dic43⋊C4—24no—
233Dic43⋊C4—24no—
234Dic43⋊C4—24no—
235C4×Dic43—24no—
236C4×Dic43—24no—
237C4×Dic43—42no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43C2×C22⋊C412yes—
249C23×C43C2×C22⋊C412yes—
250C23×C43AGL(1,ℤ/8)12yes—
251C23×C43#13712yes—
252C23×C43C22×D411yescharacteristic
253D4×C43—28no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43C2×C22⋊C412yes—
271C2×C4×C43C2×C22⋊C412yes—
272C2×C4×C43C2×C22⋊C412yes—
273C2×C4×C43C2×C22⋊C412yes—
274C2×C4×C43C23×C411yescharacteristic
275C2×C4×C43C22×D411yescharacteristic
276C2×C4×C43C2×#4111yescharacteristic
277C2×C4×C43C2×#4111yescharacteristic
278C2×C4×C43H(5,𝔽2)11yescharacteristic
279C2×C4×C432−1+411yescharacteristic
280C2×Dic43—22no—
281C2×Dic43—22no—
282C2×Dic43—22no—
283C2×Dic43—22no—
284C2×Dic43—22no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—48no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—84no—
306C2×Dic43—84no—
307Dic86—22no—
308Dic86—22no—
309Dic86—41no—
310Dic86—41no—
311C8×C43—22no—
312C8×C43—41no—
313C8×C43—41no—
314C8×C43—41no—
315#22491—431nomaximal, Sylow
316C22×C43—22no—
317C22×C43—22no—
318C22×C43—22no—
319C22×C43—22no—
320C22×C43—22no—
321C22×C43—22no—
322C22×C43—22no—
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43#41714yes—
330C22×C43C22×C22⋊C411yescharacteristic
331C22×C43#54611yescharacteristic
332C22×C43#54711yescharacteristic
333C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
334C22×C43C2×#13711yescharacteristic
335C22×C43#57711yescharacteristic
336C22×C43#57811yescharacteristic
337C4×C43—22no—
338C4×C43—22no—
339C4×C43—22no—
340C4×C43—22no—
341C4×C43C4×#4111yescharacteristic
342C4×C43#52011yescharacteristic
343C4×C43#54611yescharacteristic
344C4×C43#54711yescharacteristic
345Dic43—42no—
346Dic43—42no—
347Dic43—42no—
348Dic43—42no—
349Dic43—42no—
350Dic43—81no—
351Dic43—81no—
352Dic43—81no—
353C2×#552—431no—
354C2×#435D4311yescharacteristic
355D4×C4⋊C4—431no—
356#1992—431no—
357#1989—431no—
358#1894—431no—
359#1892—431no—
360#1872—431no—
361#1872—431no—
362#1825—431no—
363#1823—431no—
364#1803—431no—
365#1763—431no—
366#1736—431no—
367C2×#340—431no—
368C2×C43—24no—
369C2×C43—42no—
370C2×C43#233911yescharacteristic
371C2×C43C2×#41711yescharacteristic
372C2×C43#289811yescharacteristic
373C2×C43#331011yescharacteristic
374C2×C43#331211yescharacteristic
375C2×C43#334311yescharacteristic
376C2×C43#334411yescharacteristic
377C22×M16C2×D4311yescharacteristic
378C23×C8C2×D4311yescharacteristic
379#552—438no—
380#552—864no—
381C2×#126—861no—
382C2×#125—431no—
383C2×#125—861no—
384C2×#123—861no—
385C2×C22⋊Q8—431no—
386C2×C22⋊Q8—431no—
387C2×C4×Q8—431no—
388C2×C4×D4—861no—
389C2×C4×D4C2×D4311yescharacteristic
390C2×#117—431no—
391C2×#117—861no—
392C22×C4⋊C4—431no—
393C22×C4⋊C4—431no—
394C22×C4⋊C4—431no—
395#435—24no—
396C2×C4⋊C8C2×D4311yescharacteristic
397C2×#103—431no—
398C2×#103—431no—
399C2×#103—431no—
400C2×#103—431no—
401C2×C22⋊C8C2×D4311yescharacteristic
402C2×C22⋊C8C2×D4311yescharacteristic
403C2×#97C2×D4311yescharacteristic
404#389—861no—
405#385—861no—
406#385—861no—
407#384—431no—
408#380—431no—
409#380—431no—
410C4×C4⋊C4—431no—
411#340—431no—
412#340—431no—
413#340—431no—
414#340—431no—
415#340—431no—
416#340—431no—
417#340—431no—
418#340—431no—
419#340—431no—
420#340—431no—
421#340—431no—
422#340—431no—
423C43#2249111yescharacteristic, complemented, Sylow
424C22×Q8—431no—
425C22×D4D17211yescharacteristic
426C23×C4—861no—
427C23×C4—861no—
428C23×C4—861no—
429C23×C4C22×D4311yescharacteristic
430C23×C4C22×D4311yescharacteristic
431C2×M16—22no—
432C2×M16—22no—
433C2×M16—41no—
434C22×C8—22no—
435C22×C8—22no—
436C22×C8—41no—
437C22×C8C22×D4311yescharacteristic
438C22×C8C22×D4311yescharacteristic
439C22×C8C22×D4311yescharacteristic
440C22×C8C22×D4311yescharacteristic
441#126—868no—
442#125—434no—
443#125—868no—
444#125—862no—
445#123—868no—
446C22⋊Q8—434no—
447C22⋊Q8—434no—
448C22⋊Q8—862no—
449C22⋊Q8—862no—
450C4×Q8—434no—
451C4×Q8—862no—
452C4×D4—1724no—
453C4×D4C4×D4314yes—
454C4×D4C22⋊D4314yes—
455#117—434no—
456#117—862no—
457#117—868no—
458C2×C4⋊C4—434no—
459C2×C4⋊C4—431no—
460C2×C4⋊C4—431no—
461C2×C4⋊C4—431no—
462C2×C4⋊C4—431no—
463C2×C4⋊C4—431no—
464C2×C4⋊C4—431no—
465C2×C4⋊C4—431no—
466C2×C4⋊C4—862no—
467C2×C4⋊C4—862no—
468C2×C4⋊C4—861no—
469C2×C4⋊C4—861no—
470C2×C4⋊C4—861no—
471C2×C4⋊C4—861no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—862no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4—1721no—
480C2×C4⋊C4—1721no—
481C2×C4⋊C4D17211yescharacteristic
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4D17211yescharacteristic
488C2×C22⋊C4D17211yescharacteristic
489C2×C42—861no—
490C2×C42—861no—
491C2×C42—861no—
492C2×C42C22×D4311yescharacteristic
493C4⋊C8—22no—
494#103—862no—
495#103—862no—
496#103—1721no—
497#103—1721no—
498C22⋊C8—22no—
499C22⋊C8—22no—
500#97—22no—
501#95—861no—
502#95—861no—
503#95—861no—
504C24C2×D17211yescharacteristic
505C24C2×D17211yescharacteristic
506C2×Q8—432no—
507C2×Q8—861no—
508C2×Q8—861no—
509C2×Q8—861no—
510C2×Q8—861no—
511C2×Q8—861no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4(C2×D43)⋊C414yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—864no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4—861no—
531C22×C4—861no—
532C22×C4—3441no—
533C22×C4—3441no—
534C22×C4—1722no—
535C22×C4—1722no—
536C22×C4—1722no—
537C22×C4—1722no—
538C22×C4—1722no—
539C22×C4—1722no—
540C22×C4C2×C4×D4312yes—
541C22×C4C2×C4×D4312yes—
542C22×C4C2×D17211yescharacteristic
543C22×C4C2×D17211yescharacteristic
544C22×C4C2×D17211yescharacteristic
545C22×C4C2×D17211yescharacteristic
546C22×C4C2×C22⋊D4312yes—
547C22×C4C2×C22⋊D4312yes—
548C22×C4C23×D4311yescharacteristic
549M16—44no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—44no—
562C2×C8#1062190012yes—
563C4⋊C4—432no—
564C4⋊C4—432no—
565C4⋊C4—432no—
566C4⋊C4—432no—
567C4⋊C4—864no—
568C4⋊C4—864no—
569C4⋊C4—864no—
570C4⋊C4—864no—
571C4⋊C4—864no—
572C4⋊C4—864no—
573C4⋊C4—861no—
574C4⋊C4—861no—
575C4⋊C4—861no—
576C4⋊C4—861no—
577C4⋊C4—861no—
578C4⋊C4—861no—
579C4⋊C4—861no—
580C4⋊C4—861no—
581C4⋊C4—861no—
582C4⋊C4—861no—
583C4⋊C4—3441no—
584C4⋊C4—1722no—
585C4⋊C4—1722no—
586C4⋊C4—1722no—
587C4⋊C4(C2×D43)⋊C414yes—
588C22⋊C4—864no—
589C22⋊C4—864no—
590C22⋊C4—864no—
591C22⋊C4—1722no—
592C22⋊C4—1722no—
593C22⋊C4(C2×D43)⋊C414yes—
594C22⋊C4(C2×D43)⋊C414yes—
595C42—864no—
596C42—864no—
597C42—1722no—
598C42C2×C4×D4312yes—
599C42C2×C22⋊D4312yes—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23C2×(C2×D43)⋊C412yes—
611C23C2×(C2×D43)⋊C412yes—
612C23#1306335312yes—
613C23#1306335812yes—
614C23C22×D17211yescharacteristic
615Q8—862no—
616Q8—862no—
617Q8—1721no—
618Q8—1721no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—862no—
637C2×C4—862no—
638C2×C4—862no—
639C2×C4—862no—
640C2×C4—862no—
641C2×C4—3444no—
642C2×C4—3444no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4—1721no—
647C2×C4—1721no—
648C2×C4—1721no—
649C2×C4—1721no—
650C2×C4—1721no—
651C2×C4—1721no—
652C2×C4—1721no—
653C2×C4—1728no—
654C2×C4—1721no—
655C2×C4—1721no—
656C2×C4—1721no—
657C2×C4—1721no—
658C2×C4—1721no—
659C2×C4—1721no—
660C2×C4—1721no—
661C2×C4—1721no—
662C2×C4—1721no—
663C2×C4C2×(C2×D43)⋊C412yes—
664C2×C4C2×(C2×D43)⋊C412yes—
665C2×C4C2×(C2×D43)⋊C412yes—
666C2×C4C2×(C2×D43)⋊C412yes—
667C2×C4C22×C4×D4311yescharacteristic
668C2×C4C22×C22⋊D4311yescharacteristic
669C2×C4#41×D4311yescharacteristic
670C2×C4C2×#1062190011yescharacteristic
671C2×C4#1306337011yescharacteristic
672C2×C4#1306337211yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1458290114yes—
691C22C22×(C2×D43)⋊C411yescharacteristic
692C22#1458354411yescharacteristic
693C22#1458355311yescharacteristic
694C22C2×#1306335311yescharacteristic
695C22C2×#1306335811yescharacteristic
696C22#1458371111yescharacteristic
697C22#1458371611yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—3441no—
703C4—3441no—
704C4—3441no—
705C4—1722no—
706C4—1722no—
707C4—1722no—
708C4—1722no—
709C4—1722no—
710C4C4×#1062190011yescharacteristic
711C4#1458337811yescharacteristic
712C4#1458354311yescharacteristic
713C4#1458354811yescharacteristic
714C2—24no—
715C2—42no—
716C2#1913742011yescharacteristic
717C2C2×#1458290111yescharacteristic
718C2#1914312911yescharacteristic
719C2#1914661811yescharacteristic
720C2#1914664811yescharacteristic
721C2#1914703711yescharacteristic
722C2#1914705211yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#435C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
cosocleC22×C4×C43C24
hypercenterC2×#435D43
hypocenterC43#22491
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
3. #19135564C2semidirect
4. #19135550C2semidirect
5. #19135028C2semidirect
6. #19135018C2semidirect
7. #19134900C2semidirect
8. #19134900C2semidirect
9. #19134691C2semidirect
10. #19134682C2semidirect
11. #19134601C2semidirect
12. #19134426C2semidirect
13. #19134315C2semidirect
14. C2×#14582662C2semidirect
17. #14583589C4semidirect
68. #13063317C2×C4semidirect
73. #13063304C2×C4semidirect
74. #13063304C2×C4semidirect
76. C4×Dic86C2×C4semidirect
79. #13063284C2×C4semidirect
91. C2×C4⋊Dic43C2×C4semidirect
423. C43#22491semidirect

Maximal subgroups

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

subgroupindex
C2×#145835892
D4×C4⋊Dic432
#191355642
#191355502
#191350282
#191350182
#191349002
#191346912
#191346822
#191346012
#191344262
#191343152
C2×#145826622
C2×C43×#4352
#2249143