Finite Group Databasebeta

← #25004412

Subgroups — #25004412

Order 11008.

1210 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063247C211yesmaximal, characteristic
2C22×#13063245C211yesmaximal, characteristic
3C2×#14582800C211yesmaximal, characteristic
4C2×#14582661C211yesmaximal, characteristic, complemented
5C2×#14582653C211yesmaximal, characteristic, complemented
6#19132824C211yesmaximal, characteristic, complemented
7C2×C43×#340C211yesmaximal, characteristic, complemented
8C23×D172C2211yescharacteristic
9C23×C43⋊C8C2211yescharacteristic
10C22×C4⋊Dic43C2211yescharacteristic
11C22×(C2×D43)⋊C4—21no—
12C22×(C2×D43)⋊C4—21no—
13C22×C4×Dic43C2211yescharacteristic
14C2×#13063247—22no—
15C2×#13063247—22no—
16C2×#13063247—22no—
17C2×#13063245—22no—
18C2×#13063245—22no—
19C2×#13063245C414yescomplemented
20#14582800—22no—
21#14582800—22no—
22C2×C43⋊#95—21no—
23C2×C43⋊#95—21no—
24#14582661—22no—
25#14582653—22no—
26C23×C8×C43C2211yescharacteristic
27C22×C4⋊C4×C43C2211yescharacteristic
28C22×C4⋊C4×C43C2211yescharacteristic
29C43×#340—22no—
30C24×D43—21no—
31C22×D172—21no—
32C22×D172—21no—
33C22×D172—21no—
34C22×D172—21no—
35C22×D172—21no—
36C22×D172—21no—
37C22×D172—21no—
38C22×D172—21no—
39C22×D172—21no—
40C22×D172—21no—
41C22×D172—21no—
42C22×D172C2×C412yes—
43C22×D172D412yes—
44C22×D172D412yes—
45C23×Dic43—21no—
46C23×Dic43D411yescharacteristic
47C23×Dic43D411yescharacteristic
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⋊C8C2×C412yes—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43—21no—
57C2×C4⋊Dic43—21no—
58C2×C4⋊Dic43—21no—
59C2×C4⋊Dic43—21no—
60C2×C4⋊Dic43D412yes—
61C2×(C2×D43)⋊C4—24no—
62C2×(C2×D43)⋊C4—24no—
63C2×(C2×D43)⋊C4—42no—
64C2×(C2×D43)⋊C4—42no—
65C2×(C2×D43)⋊C4—42no—
66C2×(C2×D43)⋊C4—42no—
67C2×C4×Dic43—21no—
68C2×C4×Dic43—21no—
69C2×C4×Dic43—21no—
70C2×C4×Dic43—21no—
71C2×C4×Dic43—21no—
72C2×C4×Dic43—21no—
73#13063247—28no—
74#13063245—28no—
75C43⋊#95—42no—
76C43⋊#95—42no—
77C23×C4×C43—21no—
78C23×C4×C43—21no—
79C23×C4×C43C2311yescharacteristic
80C22×C8×C43—21no—
81C22×C8×C43—21no—
82C22×C8×C43—21no—
83C22×C8×C43—21no—
84C22×C8×C43—21no—
85C22×C8×C43—21no—
86C22×C8×C43D412yes—
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×C43—21no—
97C2×C4⋊C4×C43C2×C412yes—
98C2×C4⋊C4×C43D412yes—
99C24×C43C2×D411yescharacteristic
100C23×D43—22no—
101C23×D43—22no—
102C23×D43—22no—
103C23×D43—41no—
104C23×D43—41no—
105C23×D43—41no—
106C23×D43—41no—
107C23×D43—41no—
108C23×D43—41no—
109C23×D43—41no—
110C23×D43—41no—
111C23×D43—41no—
112C23×D43—41no—
113C23×D43—41no—
114C23×D43—41no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
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×C43—41no—
129C22×C4×C43C22×C411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
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×C4×C43#4111yescharacteristic
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—22no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—41no—
157C22×Dic43—41no—
158C22×Dic43—41no—
159C22×Dic43—41no—
160C22×Dic43—41no—
161C22×Dic43—41no—
162C22×Dic43D812yes—
163C22×Dic43SD1612yes—
164C2×D172—22no—
165C2×D172—22no—
166C2×D172—22no—
167C2×D172—22no—
168C2×D172—22no—
169C2×D172—22no—
170C2×D172—22no—
171C2×D172—22no—
172C2×D172—22no—
173C2×D172—22no—
174C2×D172—22no—
175C2×D172—22no—
176C2×D172—22no—
177C2×D172—22no—
178C2×D172—22no—
179C2×D172—41no—
180C2×D172—41no—
181C2×D172—41no—
182C2×D172—41no—
183C2×D172—41no—
184C2×D172—41no—
185C2×D172—41no—
186C2×D172—41no—
187C2×D172—41no—
188C2×D172—41no—
189C2×D172—41no—
190C2×D172—41no—
191C2×D172C22⋊C414yes—
192C2×C8×C43—22no—
193C2×C8×C43—22no—
194C2×C8×C43—22no—
195C2×C8×C43—41no—
196C2×C8×C43—41no—
197C2×C8×C43—41no—
198C2×C8×C43—41no—
199C4⋊C4×C43—22no—
200C4⋊C4×C43—22no—
201C4⋊C4×C43—22no—
202C4⋊C4×C43—22no—
203C4⋊C4×C43—41no—
204C4⋊C4×C43—41no—
205C4⋊C4×C43—41no—
206C4⋊C4×C43—41no—
207(C2×D43)⋊C4—48no—
208(C2×D43)⋊C4—48no—
209C4⋊Dic43—22no—
210C4⋊Dic43—22no—
211C4⋊Dic43—41no—
212C4⋊Dic43—41no—
213C4×Dic43—41no—
214C4×Dic43—41no—
215C4×Dic43—41no—
216C4×Dic43—41no—
217C2×C43⋊C8—22no—
218C2×C43⋊C8—22no—
219C2×C43⋊C8—22no—
220C2×C43⋊C8—41no—
221C2×C43⋊C8—41no—
222C2×C43⋊C8—41no—
223C2×C43⋊C8—41no—
224C23×C43C4×D411yescharacteristic
225C23×C43#12011yescharacteristic
226C23×C43#12111yescharacteristic
227C23×C43#12111yescharacteristic
228C23×C43#12111yescharacteristic
229C23×C43#12311yescharacteristic
230C23×C43#12411yescharacteristic
231C23×C43C2×D811yescharacteristic
232C23×C43C2×SD1611yescharacteristic
233C23×C43#13511yescharacteristic
234C23×C43#13511yescharacteristic
235C23×C43AGL(1,ℤ/8)11yescharacteristic
236C23×C43AGL(1,ℤ/8)11yescharacteristic
237C23×C43AGL(1,ℤ/8)11yescharacteristic
238C23×C43#13711yescharacteristic
239C22×D43—24no—
240C22×D43—42no—
241C22×D43—42no—
242C22×D43—42no—
243C22×D43—42no—
244C22×D43—42no—
245C22×D43—42no—
246C22×D43—42no—
247C22×D43—42no—
248C22×D43—42no—
249C22×D43—42no—
250C22×D43—42no—
251C22×D43—42no—
252C22×D43—42no—
253C22×D43—42no—
254C22×D43—42no—
255C22×D43—42no—
256C22×D43—42no—
257C22×D43—42no—
258C22×D43—81no—
259C22×D43—81no—
260C22×D43—81no—
261C22×D43—81no—
262C22×D43—81no—
263C22×D43—81no—
264C22×D43—81no—
265C22×D43—81no—
266C22×D43—81no—
267C22×D43—81no—
268C22×D43—81no—
269C22×D43—81no—
270C22×D43—81no—
271C22×D43—81no—
272C22×D43—81no—
273C22×D43—81no—
274C2×C4×C43—42no—
275C2×C4×C43—42no—
276C2×C4×C43—42no—
277C2×C4×C43—42no—
278C2×C4×C43—42no—
279C2×C4×C43—42no—
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—81no—
288C2×C4×C43C2×C22⋊C411yescharacteristic
289C2×C4×C43#11711yescharacteristic
290C2×C4×C43#11711yescharacteristic
291C2×C4×C43C4×D411yescharacteristic
292C2×C4×C43C4×D411yescharacteristic
293C2×C4×C43C4×D411yescharacteristic
294C2×C4×C43#12011yescharacteristic
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#12311yescharacteristic
308C2×C4×C43#12311yescharacteristic
309C2×C4×C43#12411yescharacteristic
310C2×C4×C43#12411yescharacteristic
311C2×C4×C43#12411yescharacteristic
312C2×C4×C43#12611yescharacteristic
313C2×C4×C43#12611yescharacteristic
314C2×C4×C43#12611yescharacteristic
315C2×C4×C43#12611yescharacteristic
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—42no—
331C2×Dic43—42no—
332C2×Dic43—42no—
333C2×Dic43—81no—
334C2×Dic43—81no—
335C2×Dic43—81no—
336C2×Dic43—81no—
337D172—24no—
338D172—24no—
339D172—42no—
340D172—42no—
341D172—42no—
342D172—42no—
343D172—42no—
344D172—42no—
345C8×C43—42no—
346C43⋊C8—42no—
347#11189—431nomaximal, Sylow
348C22×C43#38611yescharacteristic
349C22×C43#38811yescharacteristic
350C22×C43#38811yescharacteristic
351C22×C43#39411yescharacteristic
352C22×C43#39411yescharacteristic
353C22×C43#39411yescharacteristic
354C22×C43#39711yescharacteristic
355C22×C43C4×D811yescharacteristic
356C22×C43C4×SD1611yescharacteristic
357C22×C43#44011yescharacteristic
358C22×C43#44211yescharacteristic
359C22×C43#44711yescharacteristic
360C22×C43#44911yescharacteristic
361C22×C43#45011yescharacteristic
362C22×C43#45211yescharacteristic
363C22×C43#45911yescharacteristic
364C22×C43#45911yescharacteristic
365C22×C43#46011yescharacteristic
366C22×C43#46111yescharacteristic
367C22×C43#46311yescharacteristic
368C22×C43#46311yescharacteristic
369C22×C43#46311yescharacteristic
370C22×C43#46411yescharacteristic
371C22×C43#46511yescharacteristic
372C22×C43#46611yescharacteristic
373C22×C43#46811yescharacteristic
374C22×C43#46911yescharacteristic
375C22×C43#48011yescharacteristic
376C22×C43#48111yescharacteristic
377C22×C43#48211yescharacteristic
378C22×C43#48211yescharacteristic
379C22×C43#48611yescharacteristic
380C22×C43#48811yescharacteristic
381C22×C43#48911yescharacteristic
382C22×C43#49011yescharacteristic
383C2×D43—44no—
384C2×D43—44no—
385C2×D43—44no—
386C2×D43—82no—
387C2×D43—82no—
388C2×D43—82no—
389C2×D43—82no—
390C2×D43—82no—
391C2×D43—82no—
392C2×D43—82no—
393C2×D43—82no—
394C2×D43—82no—
395C2×D43—82no—
396C2×D43—82no—
397C2×D43—82no—
398C4×C43—82no—
399C4×C43—82no—
400C4×C43#38111yescharacteristic
401C4×C43#38611yescharacteristic
402C4×C43#38811yescharacteristic
403C4×C43#38811yescharacteristic
404C4×C43#39411yescharacteristic
405C4×C43#39711yescharacteristic
406C4×C43#39711yescharacteristic
407C4×C43#39711yescharacteristic
408Dic43—42no—
409Dic43—42no—
410Dic43—82no—
411C22×#102—431no—
412C22×#102—431no—
413C2×#390—431no—
414C2×#340—431no—
415C2×#340D4311yescharacteristic, complemented
416C2×#336—431no—
417C4⋊#95—431no—
418C2×C43#144011yescharacteristic
419C2×C43#187711yescharacteristic
420C2×C43#187911yescharacteristic
421C2×C43#192511yescharacteristic
422C2×C43#192611yescharacteristic
423C2×C43#193411yescharacteristic
424C2×C43#193611yescharacteristic
425C2×C43#203311yescharacteristic
426C2×C43#203411yescharacteristic
427C2×C43#204111yescharacteristic
428C2×C43#204211yescharacteristic
429C2×C43#205411yescharacteristic
430C2×C43#205511yescharacteristic
431C2×C43#207111yescharacteristic
432C2×C43#207311yescharacteristic
433D43—84no—
434C23×D4—431no—
435C23×C8—431no—
436C23×C8C2×D4311yescharacteristic
437C22×C4⋊C4—431no—
438C22×C4⋊C4C2×D4311yescharacteristic
439C22×C4⋊C4C2×D4311yescharacteristic
440C22×C22⋊C4—861no—
441C22×C22⋊C4—861no—
442C22×C42—431no—
443C2×#102—434no—
444C2×#102—862no—
445C2×#102—862no—
446C2×#102—862no—
447C2×#102—862no—
448C2×#102—862no—
449#390—862no—
450#390—862no—
451C2×#95—861no—
452C2×#95—861no—
453#340—22no—
454#340—862no—
455#336—862no—
456C43#1118911yescharacteristic, complemented, Sylow
457C25—861no—
458C22×D4—432no—
459C22×D4—432no—
460C22×D4—432no—
461C22×D4—861no—
462C22×D4—861no—
463C22×D4—861no—
464C22×D4—861no—
465C22×D4—861no—
466C22×D4—861no—
467C22×D4—861no—
468C22×D4—861no—
469C22×D4—861no—
470C22×D4—861no—
471C22×D4—861no—
472C23×C4—21no—
473C23×C4—21no—
474C23×C4—431no—
475C23×C4—431no—
476C23×C4—861no—
477C23×C4C22×D4311yescharacteristic
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483C22×C8—21no—
484C22×C8—432no—
485C22×C8—861no—
486C22×C8—861no—
487C22×C8—861no—
488C22×C8—861no—
489C22×C8—861no—
490C22×C8—861no—
491C22×C8D17212yes—
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—21no—
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⋊C4C4×D4312yes—
509C2×C4⋊C4C22⋊D4312yes—
510C2×C22⋊C4—864no—
511C2×C22⋊C4—864no—
512C2×C22⋊C4—1722no—
513C2×C22⋊C4—1722no—
514C2×C22⋊C4—1722no—
515C2×C22⋊C4—1722no—
516C2×C42—861no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42—861no—
520C2×C42—861no—
521C2×C42—861no—
522#102—868no—
523#102—868no—
524#95—1722no—
525#95—1722no—
526C24—862no—
527C24—862no—
528C24—862no—
529C24—1721no—
530C24—1721no—
531C24—1721no—
532C24—1721no—
533C24—1721no—
534C24—1721no—
535C24—1721no—
536C24—1721no—
537C24—1721no—
538C24—1721no—
539C24—1721no—
540C24—1721no—
541C24D4×D4311yescharacteristic
542C2×D4—434no—
543C2×D4—862no—
544C2×D4—862no—
545C2×D4—862no—
546C2×D4—862no—
547C2×D4—862no—
548C2×D4—862no—
549C2×D4—862no—
550C2×D4—862no—
551C2×D4—862no—
552C2×D4—862no—
553C2×D4—862no—
554C2×D4—862no—
555C2×D4—862no—
556C2×D4—862no—
557C2×D4—862no—
558C2×D4—1721no—
559C2×D4—1721no—
560C2×D4—1721no—
561C2×D4—1721no—
562C2×D4—1721no—
563C2×D4—1721no—
564C2×D4—1721no—
565C2×D4—1721no—
566C2×D4—1721no—
567C2×D4—1721no—
568C2×D4—1721no—
569C2×D4—1721no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—432no—
585C22×C4—432no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—861no—
598C22×C4—862no—
599C22×C4—1721no—
600C22×C4—1721no—
601C22×C4—1721no—
602C22×C4—1721no—
603C22×C4—1721no—
604C22×C4—1721no—
605C22×C4C2×C4×D4311yescharacteristic
606C22×C4C2×D17211yescharacteristic
607C22×C4#1062189811yescharacteristic
608C22×C4#1062189811yescharacteristic
609C22×C4#1062189811yescharacteristic
610C22×C4#1062189811yescharacteristic
611C22×C4D4×D4311yescharacteristic
612C22×C4D4×D4311yescharacteristic
613C22×C4D4×D4311yescharacteristic
614C22×C4#1062190011yescharacteristic
615C22×C4#1062190011yescharacteristic
616C22×C4#1062190211yescharacteristic
617C22×C4#1062190211yescharacteristic
618C22×C4C2×C22⋊D4311yescharacteristic
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—862no—
627C2×C8—862no—
628C2×C8—862no—
629C2×C8—1721no—
630C2×C8—1721no—
631C2×C8—1721no—
632C2×C8—1721no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C4⋊C4—41no—
641C4⋊C4—862no—
642C4⋊C4—862no—
643C4⋊C4—1721no—
644C4⋊C4—1721no—
645C22⋊C4—1728no—
646C22⋊C4—1728no—
647C42—1721no—
648C42—1721no—
649C42—1721no—
650C42—1721no—
651C23—864no—
652C23—3441no—
653C23—3441no—
654C23—3441no—
655C23—3441no—
656C23—3441no—
657C23—3441no—
658C23—3441no—
659C23—3441no—
660C23—3441no—
661C23—3441no—
662C23—3441no—
663C23—3441no—
664C23—3441no—
665C23—3441no—
666C23—3441no—
667C23—3441no—
668C23—1722no—
669C23—1722no—
670C23—1722no—
671C23—1722no—
672C23—1722no—
673C23—1722no—
674C23—1722no—
675C23—1722no—
676C23—1722no—
677C23—1722no—
678C23—1722no—
679C23—1722no—
680C23—1722no—
681C23—1722no—
682C23—1722no—
683C23—1722no—
684C23—1722no—
685C23—1722no—
686C23(C22⋊D43)⋊C411yescharacteristic
687C23#1306329311yescharacteristic
688C23#1306329811yescharacteristic
689C23#1306329811yescharacteristic
690C23#1306330011yescharacteristic
691C23#1306331011yescharacteristic
692C23#1306331111yescharacteristic
693C23D8×D4311yescharacteristic
694C23SD16×D4311yescharacteristic
695C23#1306334611yescharacteristic
696C23#1306334811yescharacteristic
697C23#1306334911yescharacteristic
698C23#1306335211yescharacteristic
699C23#1306335211yescharacteristic
700C23#1306335711yescharacteristic
701D4—864no—
702D4—864no—
703D4—1722no—
704D4—1722no—
705D4—1722no—
706D4—1722no—
707D4—1722no—
708D4—1722no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—3441no—
730C2×C4—3441no—
731C2×C4—3441no—
732C2×C4—3441no—
733C2×C4—1722no—
734C2×C4—1722no—
735C2×C4—1722no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4—1721no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1721no—
743C2×C4—1721no—
744C2×C4C22⋊C4×D4311yescharacteristic
745C2×C4#1306328211yescharacteristic
746C2×C4#1306328311yescharacteristic
747C2×C4C4×C22⋊D4311yescharacteristic
748C2×C4#1306328711yescharacteristic
749C2×C4C4×D17211yescharacteristic
750C2×C4#1306329511yescharacteristic
751C2×C4#1306329611yescharacteristic
752C2×C4#1306329711yescharacteristic
753C2×C4#1306329811yescharacteristic
754C2×C4#1306329911yescharacteristic
755C2×C4#1306330011yescharacteristic
756C2×C4#1306330711yescharacteristic
757C2×C4#1306330711yescharacteristic
758C2×C4#1306330711yescharacteristic
759C2×C4#1306330811yescharacteristic
760C2×C4#1306330911yescharacteristic
761C2×C4#1306331011yescharacteristic
762C2×C4#1306331011yescharacteristic
763C2×C4#1306331011yescharacteristic
764C2×C4#1306331011yescharacteristic
765C2×C4#1306331111yescharacteristic
766C2×C4#1306331311yescharacteristic
767C2×C4#1306331411yescharacteristic
768C2×C4#1306331911yescharacteristic
769C2×C4#1306332011yescharacteristic
770C2×C4#1306332011yescharacteristic
771C2×C4#1306332011yescharacteristic
772C8—42no—
773C8—1722no—
774C22—3442no—
775C22—3442no—
776C22—3442no—
777C22—3442no—
778C22—3442no—
779C22—3442no—
780C22—3442no—
781C22—3442no—
782C22—3442no—
783C22—3442no—
784C22—3442no—
785C22—3442no—
786C22—1724no—
787C22—1724no—
788C22—1724no—
789C22#1458277511yescharacteristic
790C22#1458278811yescharacteristic
791C22#1458279111yescharacteristic
792C22#1458281411yescharacteristic
793C22#1458281611yescharacteristic
794C22#1458281711yescharacteristic
795C22#1458282811yescharacteristic
796C22#1458297911yescharacteristic
797C22#1458298411yescharacteristic
798C22#1458300211yescharacteristic
799C22#1458300811yescharacteristic
800C22#1458303111yescharacteristic
801C22#1458304311yescharacteristic
802C22#1458304811yescharacteristic
803C22#1458306011yescharacteristic
804C22#1458309311yescharacteristic
805C22#1458309311yescharacteristic
806C22#1458309811yescharacteristic
807C22#1458310311yescharacteristic
808C22#1458311311yescharacteristic
809C22#1458311711yescharacteristic
810C22#1458311711yescharacteristic
811C22#1458312411yescharacteristic
812C22#1458312911yescharacteristic
813C22#1458313611yescharacteristic
814C22#1458314611yescharacteristic
815C22#1458315311yescharacteristic
816C22#1458321411yescharacteristic
817C22#1458321911yescharacteristic
818C22#1458322511yescharacteristic
819C22#1458322611yescharacteristic
820C22#1458324411yescharacteristic
821C22#1458325511yescharacteristic
822C22#1458326011yescharacteristic
823C22#1458326211yescharacteristic
824C4—82no—
825C4—82no—
826C4—3442no—
827C4—1722no—
828C4—1722no—
829C4#1458276111yescharacteristic
830C4#1458277711yescharacteristic
831C4#1458278911yescharacteristic
832C4#1458279011yescharacteristic
833C4#1458281511yescharacteristic
834C4#1458282511yescharacteristic
835C4#1458282611yescharacteristic
836C4#1458282811yescharacteristic
837C2—3444no—
838C2#1913284311yescharacteristic
839C2#1913492611yescharacteristic
840C2#1913494011yescharacteristic
841C2#1913521311yescharacteristic
842C2#1913522011yescharacteristic
843C2#1913527911yescharacteristic
844C2#1913529311yescharacteristic
845C2#1913577911yescharacteristic
846C2#1913578611yescharacteristic
847C2#1913582711yescharacteristic
848C2#1913583211yescharacteristic
849C2#1913590711yescharacteristic
850C2#1913591411yescharacteristic
851C2#1913600211yescharacteristic
852C2#1913601211yescharacteristic
subgroupG/H
centerC24D4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#340C2
socleC24×C43C2×D4
prime radicalC23×D172C22
cosocleC23×C4×C43C23
hypercenterC2×#340D43
hypocenterC43#11189
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×#14582661C2semidirect
5. C2×#14582653C2semidirect
6. #19132824C2semidirect
7. C2×C43×#340C2semidirect
19. C2×#13063245C4semidirect
415. C2×#340D43semidirect
456. C43#11189semidirect

Maximal subgroups

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

subgroupindex
C22×#130632472
C22×#130632452
C2×#145828002
C2×#145826612
C2×#145826532
#191328242
C2×C43×#3402
#1118943