Finite Group Databasebeta

← #25004470

Subgroups — #25004470

Order 11008.

1186 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C2×D43)⋊C8C211yesmaximal, characteristic
2C2×#14582756C211yesmaximal, characteristic
3C2×#14582756C211yesmaximal, characteristic
4C2×#14582662C211yesmaximal, characteristic, complemented
5C2×#14582661C211yesmaximal, characteristic, complemented
6C2×#14582661C211yesmaximal, characteristic, complemented
7C2×C43×#340C211yesmaximal, characteristic, complemented
8C23×C4×D43C2211yescharacteristic
9C23×C43⋊C8C2211yescharacteristic
10C22×C4⋊Dic43C2211yescharacteristic
11C22×C4⋊Dic43C2211yescharacteristic
12C22×(C2×D43)⋊C4—21no—
13C22×(C2×D43)⋊C4—21no—
14C2×(C2×D43)⋊C8—22no—
15C2×(C2×D43)⋊C8—22no—
16C2×(C2×D43)⋊C8—22no—
17#14582756—22no—
18#14582756—22no—
19#14582756—22no—
20#14582756C414yescomplemented
21C2×C43⋊#95—21no—
22C2×C43⋊#95—21no—
23#14582662—22no—
24#14582661—22no—
25#14582661—22no—
26C23×C8×C43C2211yescharacteristic
27C22×C4⋊C4×C43C2211yescharacteristic
28C22×C4⋊C4×C43C2211yescharacteristic
29C43×#340—22no—
30C24×D43D411yescharacteristic
31C23×Dic43—21no—
32C23×Dic43—21no—
33C23×Dic43D411yescharacteristic
34C22×C4×D43—21no—
35C22×C4×D43—21no—
36C22×C4×D43—21no—
37C22×C4×D43—21no—
38C22×C4×D43—21no—
39C22×C4×D43—21no—
40C22×C4×D43—21no—
41C22×C4×D43—21no—
42C22×C4×D43—21no—
43C22×C4×D43—21no—
44C22×C4×D43—21no—
45C22×C4×D43—21no—
46C22×C4×D43C2×C412yes—
47C22×C4×D43D412yes—
48C22×C43⋊C8—21no—
49C22×C43⋊C8—21no—
50C22×C43⋊C8—21no—
51C22×C43⋊C8—21no—
52C22×C43⋊C8—21no—
53C22×C43⋊C8—21no—
54C22×C43⋊C8D412yes—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43—21no—
57C2×C4⋊Dic43—21no—
58C2×C4⋊Dic43—21no—
59C2×C4⋊Dic43—21no—
60C2×C4⋊Dic43—21no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43C2×C412yes—
66C2×C4⋊Dic43D412yes—
67C2×(C2×D43)⋊C4—24no—
68C2×(C2×D43)⋊C4—24no—
69C2×(C2×D43)⋊C4—42no—
70C2×(C2×D43)⋊C4—42no—
71C2×(C2×D43)⋊C4—42no—
72C2×(C2×D43)⋊C4—42no—
73(C2×D43)⋊C8—28no—
74C43⋊#95—24no—
75C43⋊#95—24no—
76C23×C4×C43—21no—
77C23×C4×C43—21no—
78C23×C4×C43C2311yescharacteristic
79C22×C8×C43—21no—
80C22×C8×C43—21no—
81C22×C8×C43—21no—
82C22×C8×C43—21no—
83C22×C8×C43—21no—
84C22×C8×C43—21no—
85C22×C8×C43D412yes—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43C2×C412yes—
97C2×C4⋊C4×C43D412yes—
98C24×C43C2×D411yescharacteristic
99C23×D43—21no—
100C23×D43—21no—
101C23×D43—21no—
102C23×D43—21no—
103C23×D43—21no—
104C23×D43—21no—
105C23×D43—21no—
106C23×D43—21no—
107C23×D43—21no—
108C23×D43—21no—
109C23×D43—21no—
110C23×D43—21no—
111C23×D43C22⋊C412yes—
112C23×D43SD1612yes—
113C23×D43Q1612yes—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—41no—
117C22×C4×C43—41no—
118C22×C4×C43—41no—
119C22×C4×C43—41no—
120C22×C4×C43—41no—
121C22×C4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43—41no—
124C22×C4×C43—41no—
125C22×C4×C43—41no—
126C22×C4×C43—41no—
127C22×C4×C43—41no—
128C22×C4×C43C22×C411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43#4111yescharacteristic
135C22×C4×C43#4111yescharacteristic
136C22×C4×C43#4111yescharacteristic
137C22×C4×C43#4111yescharacteristic
138C22×C4×C43#4111yescharacteristic
139C22×C4×C43#4111yescharacteristic
140C22×C4×C43#4111yescharacteristic
141C22×C4×C43#4111yescharacteristic
142C22×Dic43—22no—
143C22×Dic43—21no—
144C22×Dic43—22no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—41no—
151C22×Dic43—41no—
152C22×Dic43—41no—
153C22×Dic43—41no—
154C22×Dic43—41no—
155C22×Dic43—41no—
156C22×Dic43—41no—
157C22×Dic43—41no—
158C22×Dic43—41no—
159C22×Dic43—41no—
160C22×Dic43—41no—
161C22×Dic43—41no—
162C22×Dic43C22⋊C412yes—
163C2×C4×D43—22no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—22no—
171C2×C4×D43—22no—
172C2×C4×D43—22no—
173C2×C4×D43—22no—
174C2×C4×D43—22no—
175C2×C4×D43—41no—
176C2×C4×D43—41no—
177C2×C4×D43—41no—
178C2×C4×D43—41no—
179C2×C4×D43—41no—
180C2×C4×D43—41no—
181C2×C4×D43—41no—
182C2×C4×D43—41no—
183C2×C4×D43—41no—
184C2×C4×D43—41no—
185C2×C4×D43—41no—
186C2×C4×D43—41no—
187C2×C4×D43—41no—
188C2×C4×D43—41no—
189C2×C4×D43—41no—
190C2×C4×D43—41no—
191C2×C8×C43—22no—
192C2×C8×C43—22no—
193C2×C8×C43—22no—
194C2×C8×C43—41no—
195C2×C8×C43—41no—
196C2×C8×C43—41no—
197C2×C8×C43—41no—
198C4⋊C4×C43—22no—
199C4⋊C4×C43—22no—
200C4⋊C4×C43—22no—
201C4⋊C4×C43—22no—
202C4⋊C4×C43—41no—
203C4⋊C4×C43—41no—
204C4⋊C4×C43—41no—
205C4⋊C4×C43—41no—
206(C2×D43)⋊C4—48no—
207(C2×D43)⋊C4—48no—
208C4⋊Dic43—22no—
209C4⋊Dic43—22no—
210C4⋊Dic43—22no—
211C4⋊Dic43—22no—
212C4⋊Dic43—41no—
213C4⋊Dic43—41no—
214C4⋊Dic43—41no—
215C4⋊Dic43—41no—
216C2×C43⋊C8—22no—
217C2×C43⋊C8—22no—
218C2×C43⋊C8—22no—
219C2×C43⋊C8—41no—
220C2×C43⋊C8—41no—
221C2×C43⋊C8—41no—
222C2×C43⋊C8—41no—
223C23×C43C2×C22⋊C411yescharacteristic
224C23×C43#12011yescharacteristic
225C23×C43#12111yescharacteristic
226C23×C43#12111yescharacteristic
227C23×C43#12311yescharacteristic
228C23×C43#12311yescharacteristic
229C23×C43#12311yescharacteristic
230C23×C43C2×SD1611yescharacteristic
231C23×C43C2×Q1611yescharacteristic
232C23×C43#13511yescharacteristic
233C23×C43#13511yescharacteristic
234C23×C43AGL(1,ℤ/8)11yescharacteristic
235C23×C43AGL(1,ℤ/8)11yescharacteristic
236C23×C43AGL(1,ℤ/8)11yescharacteristic
237C23×C43#13711yescharacteristic
238C22×D43—22no—
239C22×D43—22no—
240C22×D43—22no—
241C22×D43—22no—
242C22×D43—22no—
243C22×D43—22no—
244C22×D43—22no—
245C22×D43—22no—
246C22×D43—22no—
247C22×D43—22no—
248C22×D43—22no—
249C22×D43—22no—
250C22×D43—22no—
251C22×D43—22no—
252C22×D43—22no—
253C22×D43—22no—
254C22×D43—22no—
255C22×D43—22no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43#10314yes—
273C2×C4×C43—42no—
274C2×C4×C43—42no—
275C2×C4×C43—42no—
276C2×C4×C43—42no—
277C2×C4×C43—42no—
278C2×C4×C43—42no—
279C2×C4×C43—81no—
280C2×C4×C43—81no—
281C2×C4×C43—81no—
282C2×C4×C43—81no—
283C2×C4×C43—81no—
284C2×C4×C43—81no—
285C2×C4×C43—81no—
286C2×C4×C43—81no—
287C2×C4×C43#11711yescharacteristic
288C2×C4×C43#11711yescharacteristic
289C2×C4×C43C4×D411yescharacteristic
290C2×C4×C43C4×D411yescharacteristic
291C2×C4×C43C4×D411yescharacteristic
292C2×C4×C43C4×D411yescharacteristic
293C2×C4×C43#12011yescharacteristic
294C2×C4×C43#12111yescharacteristic
295C2×C4×C43#12111yescharacteristic
296C2×C4×C43#12111yescharacteristic
297C2×C4×C43#12111yescharacteristic
298C2×C4×C43#12111yescharacteristic
299C2×C4×C43#12111yescharacteristic
300C2×C4×C43#12311yescharacteristic
301C2×C4×C43#12311yescharacteristic
302C2×C4×C43#12311yescharacteristic
303C2×C4×C43#12311yescharacteristic
304C2×C4×C43#12311yescharacteristic
305C2×C4×C43#12311yescharacteristic
306C2×C4×C43#12311yescharacteristic
307C2×C4×C43#12411yescharacteristic
308C2×C4×C43#12411yescharacteristic
309C2×C4×C43#12411yescharacteristic
310C2×C4×C43#12411yescharacteristic
311C2×C4×C43#12611yescharacteristic
312C2×C4×C43#12611yescharacteristic
313C2×C4×C43#12611yescharacteristic
314C2×C4×C43#12611yescharacteristic
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—81no—
329C2×Dic43—81no—
330C2×Dic43—81no—
331C2×Dic43—81no—
332C2×Dic43—81no—
333C2×Dic43—81no—
334C2×Dic43—81no—
335C2×Dic43—81no—
336C4×D43—42no—
337C4×D43—42no—
338C4×D43—42no—
339C4×D43—42no—
340C4×D43—42no—
341C4×D43—42no—
342C4×D43—42no—
343C4×D43—42no—
344C8×C43—42no—
345C43⋊C8—42no—
346#11200—431nomaximal, Sylow
347C22×C43#38111yescharacteristic
348C22×C43#38611yescharacteristic
349C22×C43#38611yescharacteristic
350C22×C43#39411yescharacteristic
351C22×C43#39411yescharacteristic
352C22×C43#39711yescharacteristic
353C22×C43#39711yescharacteristic
354C22×C43C2×#10311yescharacteristic
355C22×C43#41611yescharacteristic
356C22×C43#41711yescharacteristic
357C22×C43#41811yescharacteristic
358C22×C43#44911yescharacteristic
359C22×C43#44911yescharacteristic
360C22×C43#45011yescharacteristic
361C22×C43#45111yescharacteristic
362C22×C43#46511yescharacteristic
363C22×C43#46511yescharacteristic
364C22×C43#46711yescharacteristic
365C22×C43#46711yescharacteristic
366C22×C43#46811yescharacteristic
367C22×C43#46811yescharacteristic
368C22×C43#46911yescharacteristic
369C22×C43#46911yescharacteristic
370C22×C43#48111yescharacteristic
371C22×C43#48111yescharacteristic
372C22×C43#48211yescharacteristic
373C22×C43#48211yescharacteristic
374C22×C43#48211yescharacteristic
375C22×C43#48211yescharacteristic
376C22×C43#48311yescharacteristic
377C22×C43#48411yescharacteristic
378C22×C43#48411yescharacteristic
379C22×C43#48411yescharacteristic
380C22×C43#48511yescharacteristic
381C22×C43#48511yescharacteristic
382C2×D43—24no—
383C2×D43—24no—
384C2×D43—24no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—42no—
396C2×D43—42no—
397C4×C43—82no—
398C4×C43—82no—
399C4×C43#38811yescharacteristic
400C4×C43#38811yescharacteristic
401C4×C43#38811yescharacteristic
402C4×C43#38811yescharacteristic
403C4×C43#39411yescharacteristic
404C4×C43#39411yescharacteristic
405C4×C43#39711yescharacteristic
406C4×C43#39711yescharacteristic
407Dic43—42no—
408Dic43—82no—
409Dic43—82no—
410C22×C22⋊C8—431no—
411C2×#380—431no—
412C2×#380—431no—
413C2×#340—431no—
414C2×#340—431no—
415C2×#340—431no—
416C2×#340D4311yescharacteristic, complemented
417C2×C43#144011yescharacteristic
418C2×C43#182411yescharacteristic
419C2×C43#182511yescharacteristic
420C2×C43#187211yescharacteristic
421C2×C43#187511yescharacteristic
422C2×C43#189211yescharacteristic
423C2×C43#189511yescharacteristic
424C2×C43#203411yescharacteristic
425C2×C43#203411yescharacteristic
426C2×C43#203611yescharacteristic
427C2×C43#203611yescharacteristic
428C2×C43#207611yescharacteristic
429C2×C43#207611yescharacteristic
430C2×C43#207711yescharacteristic
431C2×C43#207711yescharacteristic
432D43—44no—
433C24×C4—431no—
434C23×C8—431no—
435C23×C8C2×D4311yescharacteristic
436C22×C4⋊C4—431no—
437C22×C4⋊C4—431no—
438C22×C4⋊C4C2×D4311yescharacteristic
439C22×C4⋊C4C2×D4311yescharacteristic
440C22×C22⋊C4—861no—
441C22×C22⋊C4—861no—
442C2×C22⋊C8—862no—
443C2×C22⋊C8—862no—
444C2×C22⋊C8—862no—
445#380—434no—
446#380—862no—
447#380—862no—
448#380—862no—
449C2×#95—861no—
450C2×#95—861no—
451#340—22no—
452#340—862no—
453#340—862no—
454#340—862no—
455C43#1120011yescharacteristic, complemented, Sylow
456C25—431no—
457C23×C4—21no—
458C23×C4—21no—
459C23×C4—431no—
460C23×C4—432no—
461C23×C4—432no—
462C23×C4—861no—
463C23×C4—861no—
464C23×C4—861no—
465C23×C4—861no—
466C23×C4—861no—
467C23×C4—861no—
468C23×C4—861no—
469C23×C4—861no—
470C23×C4—861no—
471C23×C4—861no—
472C23×C4—861no—
473C23×C4—861no—
474C23×C4—861no—
475C23×C4—861no—
476C23×C4C22×D4311yescharacteristic
477C22×C8—21no—
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483C22×C8—432no—
484C22×C8—861no—
485C22×C8—861no—
486C22×C8—861no—
487C22×C8—861no—
488C22×C8—861no—
489C22×C8—861no—
490C22×C8D17212yes—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—432no—
502C2×C4⋊C4—432no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
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⋊C4C4×D4312yes—
514C2×C4⋊C4C22⋊D4312yes—
515C2×C22⋊C4—864no—
516C2×C22⋊C4—864no—
517C2×C22⋊C4—1722no—
518C2×C22⋊C4—1722no—
519C2×C22⋊C4—1722no—
520C2×C22⋊C4—1722no—
521C22⋊C8—868no—
522#95—864no—
523#95—864no—
524C24—432no—
525C24—432no—
526C24—432no—
527C24—861no—
528C24—861no—
529C24—861no—
530C24—861no—
531C24—861no—
532C24—861no—
533C24—861no—
534C24—861no—
535C24—861no—
536C24—861no—
537C24—861no—
538C24—861no—
539C24D4×D4311yescharacteristic
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—432no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—862no—
562C22×C4—862no—
563C22×C4—862no—
564C22×C4—862no—
565C22×C4—862no—
566C22×C4—862no—
567C22×C4—862no—
568C22×C4—862no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4—862no—
572C22×C4—862no—
573C22×C4—862no—
574C22×C4—862no—
575C22×C4—1721no—
576C22×C4—1721no—
577C22×C4—1721no—
578C22×C4—1721no—
579C22×C4—1721no—
580C22×C4—1721no—
581C22×C4—1721no—
582C22×C4—1721no—
583C22×C4—1721no—
584C22×C4—1721no—
585C22×C4—1721no—
586C22×C4—1721no—
587C22×C4—1721no—
588C22×C4—1721no—
589C22×C4—1721no—
590C22×C4—1721no—
591C22×C4—1721no—
592C22×C4—1721no—
593C22×C4—1721no—
594C22×C4—1721no—
595C22×C4—1721no—
596C22×C4—1721no—
597C22×C4—1721no—
598C22×C4—1721no—
599C22×C4—1721no—
600C22×C4—1721no—
601C22×C4—1721no—
602C22×C4—1721no—
603C22×C4C2×C4×D4311yescharacteristic
604C22×C4C2×D17211yescharacteristic
605C22×C4#1062189811yescharacteristic
606C22×C4#1062189811yescharacteristic
607C22×C4#1062189811yescharacteristic
608C22×C4#1062189811yescharacteristic
609C22×C4D4×D4311yescharacteristic
610C22×C4D4×D4311yescharacteristic
611C22×C4D4×D4311yescharacteristic
612C22×C4#1062190011yescharacteristic
613C22×C4#1062190011yescharacteristic
614C22×C4#1062190211yescharacteristic
615C22×C4#1062190211yescharacteristic
616C22×C4C2×C22⋊D4311yescharacteristic
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—862no—
625C2×C8—862no—
626C2×C8—862no—
627C2×C8—1721no—
628C2×C8—1721no—
629C2×C8—1721no—
630C2×C8—1721no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—862no—
640C4⋊C4—862no—
641C4⋊C4—862no—
642C4⋊C4—862no—
643C4⋊C4—1721no—
644C4⋊C4—1721no—
645C4⋊C4—1721no—
646C4⋊C4—1721no—
647C22⋊C4—1728no—
648C22⋊C4—1728no—
649C23—434no—
650C23—862no—
651C23—862no—
652C23—862no—
653C23—862no—
654C23—862no—
655C23—862no—
656C23—862no—
657C23—862no—
658C23—862no—
659C23—862no—
660C23—862no—
661C23—862no—
662C23—862no—
663C23—862no—
664C23—862no—
665C23—862no—
666C23—862no—
667C23—862no—
668C23—1721no—
669C23—1721no—
670C23—1721no—
671C23—1721no—
672C23—1721no—
673C23—1721no—
674C23—1721no—
675C23—1721no—
676C23—1721no—
677C23—1721no—
678C23—1721no—
679C23—1721no—
680C23—1721no—
681C23—1721no—
682C23—1721no—
683C23—1721no—
684C23C22⋊C4×D4311yescharacteristic
685C23#1306329311yescharacteristic
686C23#1306329811yescharacteristic
687C23#1306330011yescharacteristic
688C23#1306330711yescharacteristic
689C23#1306330711yescharacteristic
690C23#1306331011yescharacteristic
691C23SD16×D4311yescharacteristic
692C23Q16×D4311yescharacteristic
693C23#1306334411yescharacteristic
694C23#1306334611yescharacteristic
695C23#1306334911yescharacteristic
696C23#1306335211yescharacteristic
697C23#1306335211yescharacteristic
698C23#1306335711yescharacteristic
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—3441no—
717C2×C4—3441no—
718C2×C4—3441no—
719C2×C4—3441no—
720C2×C4—3441no—
721C2×C4—3441no—
722C2×C4—3441no—
723C2×C4—3441no—
724C2×C4—1722no—
725C2×C4—1722no—
726C2×C4—1722no—
727C2×C4—1722no—
728C2×C4—1722no—
729C2×C4—1722no—
730C2×C4—1721no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1722no—
735C2×C4—1722no—
736C2×C4—1722no—
737C2×C4—1722no—
738C2×C4—1722no—
739C2×C4—1722no—
740C2×C4—1722no—
741C2×C4—1722no—
742C2×C4#1306328211yescharacteristic
743C2×C4#1306328311yescharacteristic
744C2×C4(C22⋊D43)⋊C411yescharacteristic
745C2×C4C4×C22⋊D4311yescharacteristic
746C2×C4#1306328711yescharacteristic
747C2×C4C4×D17211yescharacteristic
748C2×C4#1306329511yescharacteristic
749C2×C4#1306329611yescharacteristic
750C2×C4#1306329711yescharacteristic
751C2×C4#1306329811yescharacteristic
752C2×C4#1306329811yescharacteristic
753C2×C4#1306329911yescharacteristic
754C2×C4#1306330011yescharacteristic
755C2×C4#1306330711yescharacteristic
756C2×C4#1306330811yescharacteristic
757C2×C4#1306330911yescharacteristic
758C2×C4#1306331011yescharacteristic
759C2×C4#1306331011yescharacteristic
760C2×C4#1306331011yescharacteristic
761C2×C4#1306331011yescharacteristic
762C2×C4#1306331111yescharacteristic
763C2×C4#1306331111yescharacteristic
764C2×C4#1306331311yescharacteristic
765C2×C4#1306331411yescharacteristic
766C2×C4#1306331911yescharacteristic
767C2×C4#1306332011yescharacteristic
768C2×C4#1306332011yescharacteristic
769C2×C4#1306332011yescharacteristic
770C8—42no—
771C8—1722no—
772C22—864no—
773C22—864no—
774C22—864no—
775C22—1722no—
776C22—1722no—
777C22—1722no—
778C22—1722no—
779C22—1722no—
780C22—1722no—
781C22—1722no—
782C22—1722no—
783C22—1722no—
784C22—1722no—
785C22—1722no—
786C22—1722no—
787C22#1458276111yescharacteristic
788C22#1458277511yescharacteristic
789C22#1458277711yescharacteristic
790C22#1458281411yescharacteristic
791C22#1458281611yescharacteristic
792C22#1458282611yescharacteristic
793C22#1458282811yescharacteristic
794C22#103×D4311yescharacteristic
795C22#1458289211yescharacteristic
796C22#1458289911yescharacteristic
797C22#1458290211yescharacteristic
798C22#1458304111yescharacteristic
799C22#1458304311yescharacteristic
800C22#1458304811yescharacteristic
801C22#1458305311yescharacteristic
802C22#1458312711yescharacteristic
803C22#1458312911yescharacteristic
804C22#1458313911yescharacteristic
805C22#1458314111yescharacteristic
806C22#1458314611yescharacteristic
807C22#1458314811yescharacteristic
808C22#1458315111yescharacteristic
809C22#1458315311yescharacteristic
810C22#1458321611yescharacteristic
811C22#1458321911yescharacteristic
812C22#1458322111yescharacteristic
813C22#1458322111yescharacteristic
814C22#1458322211yescharacteristic
815C22#1458322511yescharacteristic
816C22#1458322811yescharacteristic
817C22#1458323311yescharacteristic
818C22#1458323311yescharacteristic
819C22#1458323611yescharacteristic
820C22#1458323811yescharacteristic
821C22#1458324211yescharacteristic
822C4—82no—
823C4—82no—
824C4—3442no—
825C4—3442no—
826C4—1722no—
827C4#1458278811yescharacteristic
828C4#1458278911yescharacteristic
829C4#1458279011yescharacteristic
830C4#1458279111yescharacteristic
831C4#1458281511yescharacteristic
832C4#1458281711yescharacteristic
833C4#1458282511yescharacteristic
834C4#1458282811yescharacteristic
835C2—1724no—
836C2#1913284311yescharacteristic
837C2#1913468411yescharacteristic
838C2#1913468811yescharacteristic
839C2#1913489911yescharacteristic
840C2#1913491411yescharacteristic
841C2#1913501711yescharacteristic
842C2#1913503211yescharacteristic
843C2#1913578211yescharacteristic
844C2#1913578611yescharacteristic
845C2#1913579611yescharacteristic
846C2#1913580011yescharacteristic
847C2#1913602511yescharacteristic
848C2#1913602711yescharacteristic
849C2#1913603011yescharacteristic
850C2#1913603311yescharacteristic
subgroupG/H
centerC24D4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#340C2
socleC24×C43C2×D4
prime radicalC24×D43D4
cosocleC23×C4×C43C23
hypercenterC2×#340D43
hypocenterC43#11200
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×#14582662C2semidirect
5. C2×#14582661C2semidirect
6. C2×#14582661C2semidirect
7. C2×C43×#340C2semidirect
20. #14582756C4semidirect
416. C2×#340D43semidirect
455. C43#11200semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D43)⋊C82
C2×#145827562
C2×#145826622
C2×#145826612
C2×C43×#3402
#1120043