Finite Group Databasebeta

← #25002790

Subgroups — #25002790

Order 11008.

1266 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582774C211yesmaximal, characteristic
2C2×C22⋊C4×Dic43C211yesmaximal, characteristic
3C2×#14582666C211yesmaximal, characteristic
4C2×#14582665C211yesmaximal, characteristic
5C2×#14582665C211yesmaximal, characteristic
6#19132817C211yesmaximal, characteristic
7C2×C43×#342C211yesmaximal, characteristic
8C24×Dic43C2211yescharacteristic
9C22×C4⋊Dic43C412yescomplemented
10C22×C22⋊Dic43C2211yescharacteristic
11C22×C22⋊Dic43C2211yescharacteristic
12C22×C22⋊Dic43C2211yescharacteristic
13C22×C4×Dic43—21no—
14#14582774—21no—
15#14582774—22no—
16#14582774—21no—
17C22⋊C4×Dic43—22no—
18C22⋊C4×Dic43—22no—
19C2×C43⋊#95—21no—
20C2×C43⋊#95—22no—
21C2×C43⋊#95C412yescomplemented
22#14582666C414yescomplemented
23#14582665—22no—
24#14582665—22no—
25C22×C22⋊C4×C43C2211yescharacteristic
26C22×C22⋊C4×C43C2211yescharacteristic
27C22×C22⋊C4×C43C2211yescharacteristic
28C43×#342C414yescomplemented
29C23×Dic43—21no—
30C23×Dic43—21no—
31C23×Dic43—21no—
32C23×Dic43—21no—
33C23×Dic43—21no—
34C23×Dic43—21no—
35C23×Dic43—44no—
36C23×Dic43C2×C412yes—
37C23×Dic43C2×C411yescharacteristic
38C23×Dic43C2×C411yescharacteristic
39C23×Dic43D411yescharacteristic
40C23×Dic43D412yes—
41C23×Dic43D411yescharacteristic
42C2×C4⋊Dic43—22no—
43C2×C4⋊Dic43—22no—
44C2×C4⋊Dic43—44no—
45C2×C22⋊Dic43—21no—
46C2×C22⋊Dic43—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—21no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43—21no—
51C2×C22⋊Dic43—21no—
52C2×C22⋊Dic43—21no—
53C2×C22⋊Dic43—21no—
54C2×C22⋊Dic43—21no—
55C2×C22⋊Dic43—21no—
56C2×C22⋊Dic43—21no—
57C2×C22⋊Dic43—21no—
58C2×C22⋊Dic43—21no—
59C2×C22⋊Dic43C2×C412yes—
60C2×C22⋊Dic43C2×C412yes—
61C2×C22⋊Dic43D412yes—
62C2×C22⋊Dic43Q812yes—
63C2×C4×Dic43—24no—
64C2×C4×Dic43—44no—
65C43⋊#95—24no—
66C43⋊#95—22no—
67C43⋊#95—22no—
68C43⋊#95—44no—
69C25×C43C2311yescharacteristic
70C23×C4×C43—21no—
71C23×C4×C43—21no—
72C23×C4×C43C2×C412yes—
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—21no—
77C2×C22⋊C4×C43—21no—
78C2×C22⋊C4×C43—21no—
79C2×C22⋊C4×C43—21no—
80C2×C22⋊C4×C43—21no—
81C2×C22⋊C4×C43—21no—
82C2×C22⋊C4×C43—21no—
83C2×C22⋊C4×C43—21no—
84C2×C22⋊C4×C43—21no—
85C2×C22⋊C4×C43C2×C412yes—
86C2×C22⋊C4×C43C2×C412yes—
87C2×C22⋊C4×C43C2×C412yes—
88C2×C22⋊C4×C43C2×C412yes—
89C2×C22⋊C4×C43D412yes—
90C2×C22⋊C4×C43Q812yes—
91C24×C43—42no—
92C24×C43—42no—
93C24×C43C22×C411yescharacteristic
94C24×C43C22×C411yescharacteristic
95C24×C43C22×C411yescharacteristic
96C24×C43C2×D411yescharacteristic
97C24×C43C2×D411yescharacteristic
98C24×C43C2×D411yescharacteristic
99C24×C43C2×D411yescharacteristic
100C24×C43C2×Q811yescharacteristic
101C24×C43C2×Q811yescharacteristic
102C24×C43#4111yescharacteristic
103C24×C43#4111yescharacteristic
104C24×C43#4111yescharacteristic
105C24×C43#4111yescharacteristic
106C24×C43#4111yescharacteristic
107C24×C43#4111yescharacteristic
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—42no—
115C22×C4×C43—42no—
116C22×C4×C43—42no—
117C22×C4×C43—42no—
118C22×C4×C43—42no—
119C22×C4×C43—42no—
120C22×C4×C43—41no—
121C22×C4×C43—41no—
122C22×C4×C43C4214yescomplemented
123C22×Dic43—24no—
124C22×Dic43—24no—
125C22×Dic43—24no—
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—22no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—42no—
145C22×Dic43—42no—
146C22×Dic43—42no—
147C22×Dic43—42no—
148C22×Dic43—42no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43—42no—
153C22×Dic43—44no—
154C22×Dic43—44no—
155C22×Dic43—44no—
156C22×Dic43—44no—
157C22×Dic43—41no—
158C22×Dic43—41no—
159C22×Dic43C22⋊C412yes—
160C22×Dic43C22⋊C412yes—
161C22⋊C4×C43—22no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—22no—
164C22⋊C4×C43—22no—
165C22⋊C4×C43—22no—
166C22⋊C4×C43—22no—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—22no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—41no—
171C22⋊C4×C43—41no—
172C22⋊C4×C43C4⋊C414yescomplemented
173C22⋊Dic43—22no—
174C22⋊Dic43—22no—
175C22⋊Dic43—22no—
176C22⋊Dic43—22no—
177C22⋊Dic43—22no—
178C22⋊Dic43—41no—
179C22⋊Dic43—41no—
180C22⋊Dic43—41no—
181C22⋊Dic43—41no—
182C22⋊Dic43—41no—
183C22⋊Dic43—41no—
184C22⋊Dic43C4⋊C414yescomplemented
185C4⋊Dic43—44no—
186C4⋊Dic43—44no—
187C4×Dic43—48no—
188C23×C43—22no—
189C23×C43—22no—
190C23×C43—22no—
191C23×C43—22no—
192C23×C43—22no—
193C23×C43—22no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—42no—
199C23×C43—42no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—42no—
203C23×C43—42no—
204C23×C43—41no—
205C23×C43—42no—
206C23×C43—42no—
207C23×C43—42no—
208C23×C43—42no—
209C23×C43—41no—
210C23×C43C2×C4211yescharacteristic
211C23×C43C2×C22⋊C411yescharacteristic
212C23×C43C2×C4⋊C411yescharacteristic
213C23×C43C2×C4⋊C411yescharacteristic
214C23×C43#11711yescharacteristic
215C23×C43#11711yescharacteristic
216C23×C43#11711yescharacteristic
217C23×C43C4×D411yescharacteristic
218C23×C43C4×D411yescharacteristic
219C23×C43C4×D411yescharacteristic
220C23×C43C4×D411yescharacteristic
221C23×C43C4×D411yescharacteristic
222C23×C43C4×D411yescharacteristic
223C23×C43C4×D411yescharacteristic
224C23×C43C4×D411yescharacteristic
225C23×C43C4×Q811yescharacteristic
226C23×C43C4×Q811yescharacteristic
227C23×C43C4×Q811yescharacteristic
228C23×C43C4×Q811yescharacteristic
229C23×C43#12011yescharacteristic
230C23×C43#12111yescharacteristic
231C23×C43#12111yescharacteristic
232C23×C43C22⋊Q811yescharacteristic
233C23×C43C22⋊Q811yescharacteristic
234C23×C43C22⋊Q811yescharacteristic
235C23×C43C22⋊Q811yescharacteristic
236C23×C43#12311yescharacteristic
237C23×C43#12311yescharacteristic
238C23×C43#12311yescharacteristic
239C23×C43#12411yescharacteristic
240C23×C43#12511yescharacteristic
241C23×C43#12511yescharacteristic
242C23×C43#12611yescharacteristic
243C23×C43#12611yescharacteristic
244C23×C43C4⋊Q811yescharacteristic
245C2×C4×C43—24no—
246C2×C4×C43—24no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—44no—
250C2×C4×C43—44no—
251C2×C4×C43—44no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—44no—
255C2×C4×C43—44no—
256C2×C4×C43—42no—
257C2×C4×C43—81no—
258C2×C4×C43—81no—
259C2×C4×C43—82no—
260C2×Dic43—24no—
261C2×Dic43—24no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—24no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—44no—
269C2×Dic43—44no—
270C2×Dic43—44no—
271C2×Dic43—44no—
272C2×Dic43—42no—
273C2×Dic43—42no—
274C2×Dic43—44no—
275C2×Dic43—44no—
276C2×Dic43—42no—
277C2×Dic43—42no—
278C2×Dic43—44no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—42no—
282C2×Dic43—42no—
283C2×Dic43—42no—
284C2×Dic43—81no—
285C2×Dic43—81no—
286C2×Dic43—82no—
287C2×Dic43—81no—
288C2×Dic43—81no—
289C2×Dic43—81no—
290C2×Dic43—81no—
291C2×Dic43#9914yes—
292#10912—431nomaximal, Sylow
293C22×C43—21no—
294C22×C43—21no—
295C22×C43—21no—
296C22×C43—21no—
297C22×C43—21no—
298C22×C43—21no—
299C22×C43—21no—
300C22×C43—21no—
301C22×C43—21no—
302C22×C43—21no—
303C22×C43—21no—
304C22×C43—21no—
305C22×C43—22no—
306C22×C43—22no—
307C22×C43—22no—
308C22×C43—22no—
309C22×C43—22no—
310C22×C43—22no—
311C22×C43—22no—
312C22×C43—22no—
313C22×C43—22no—
314C22×C43—22no—
315C22×C43—22no—
316C22×C43—22no—
317C22×C43—41no—
318C22×C43—41no—
319C22×C43—41no—
320C22×C43—41no—
321C22×C43—41no—
322C22×C43—41no—
323C22×C43—41no—
324C22×C43—41no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43C4×C22⋊C411yescharacteristic
334C22×C43C4×C4⋊C411yescharacteristic
335C22×C43C4×C4⋊C411yescharacteristic
336C22×C43#38511yescharacteristic
337C22×C43#38511yescharacteristic
338C22×C43#38611yescharacteristic
339C22×C43#38711yescharacteristic
340C22×C43#38711yescharacteristic
341C22×C43#38711yescharacteristic
342C22×C43#38711yescharacteristic
343C22×C43#38811yescharacteristic
344C22×C43#38811yescharacteristic
345C22×C43#38911yescharacteristic
346C22×C43#38911yescharacteristic
347C22×C43#39111yescharacteristic
348C22×C43C2×#9912yes—
349C22×C43#41012yes—
350C4×C43—44no—
351C4×C43—44no—
352C4×C43—82no—
353Dic43—24no—
354Dic43—44no—
355Dic43—42no—
356Dic43—82no—
357Dic43—81no—
358Dic43—81no—
359C2×#385—431no—
360C2×C4×C22⋊C4—431no—
361C2×#342—431no—
362C2×#342—431no—
363C2×#342—431no—
364C2×#342D4311yescharacteristic
365C22⋊#95—431no—
366C2×C43—21no—
367C2×C43—21no—
368C2×C43—21no—
369C2×C43—21no—
370C2×C43—21no—
371C2×C43—21no—
372C2×C43—21no—
373C2×C43—21no—
374C2×C43—21no—
375C2×C43—21no—
376C2×C43—21no—
377C2×C43—21no—
378C2×C43#143611yescharacteristic
379C2×C43C4×#9912yes—
380C2×C43#189811yescharacteristic
381C2×C43#189911yescharacteristic
382C2×C43#199612yes—
383C24×C4—431no—
384C22×C4⋊C4—432no—
385C22×C22⋊C4—431no—
386C22×C22⋊C4—431no—
387C22×C22⋊C4—431no—
388C22×C22⋊C4C2×D4311yescharacteristic
389C22×C22⋊C4C2×D4311yescharacteristic
390C22×C22⋊C4C2×D4311yescharacteristic
391C22×C42—861no—
392#385—861no—
393#385—862no—
394#385—861no—
395C4×C22⋊C4—862no—
396C4×C22⋊C4—862no—
397C2×#95—432no—
398C2×#95—861no—
399C2×#95—862no—
400#342—434no—
401#342—862no—
402#342—862no—
403#342Dic4314yescomplemented
404C43#1091211yescharacteristic, complemented, Sylow
405C25C22×D4311yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—431no—
409C23×C4—432no—
410C23×C4—432no—
411C23×C4—431no—
412C23×C4—431no—
413C23×C4—431no—
414C23×C4—861no—
415C23×C4—861no—
416C23×C4—861no—
417C23×C4—861no—
418C23×C4—861no—
419C23×C4—861no—
420C23×C4—1724no—
421C23×C4C4×D4312yes—
422C2×C4⋊C4—862no—
423C2×C4⋊C4—862no—
424C2×C4⋊C4—1724no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—432no—
438C2×C22⋊C4—432no—
439C2×C22⋊C4—432no—
440C2×C22⋊C4—432no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C22⋊C4Dic8612yes—
456C2×C22⋊C4C4×D4312yes—
457C2×C22⋊C4D17212yes—
458C2×C22⋊C4C2×Dic4312yes—
459C2×C22⋊C4C2×Dic4312yes—
460C2×C22⋊C4C2×Dic4312yes—
461C2×C42—864no—
462C2×C42—1724no—
463#95—862no—
464#95—862no—
465#95—864no—
466#95—1724no—
467C24—42no—
468C24—42no—
469C24C2×Dic8611yescharacteristic
470C24C2×C4×D4311yescharacteristic
471C24C2×C4×D4311yescharacteristic
472C24C2×D17211yescharacteristic
473C24#1062189811yescharacteristic
474C24#1062189811yescharacteristic
475C24D4×D4311yescharacteristic
476C24D4×D4311yescharacteristic
477C24D4×D4311yescharacteristic
478C24#1062190011yescharacteristic
479C24#1062190011yescharacteristic
480C24#1062190011yescharacteristic
481C24Q8×D4311yescharacteristic
482C24#1062190211yescharacteristic
483C24C22×Dic4311yescharacteristic
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—432no—
499C22×C4—432no—
500C22×C4—864no—
501C22×C4—864no—
502C22×C4—864no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—862no—
506C22×C4—862no—
507C22×C4—862no—
508C22×C4—861no—
509C22×C4—862no—
510C22×C4—862no—
511C22×C4—862no—
512C22×C4—862no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—862no—
521C22×C4—1722no—
522C22×C4—1722no—
523C22×C4—1722no—
524C22×C4—1724no—
525C22×C4—1724no—
526C22×C4—1724no—
527C22×C4—1724no—
528C22×C4—1722no—
529C22×C4—1722no—
530C22×C4—1721no—
531C22×C4—1721no—
532C22×C4—1722no—
533C22×C4—1722no—
534C22×C4—1722no—
535C22×C4—1722no—
536C22×C4C4×Dic4314yescomplemented
537C4⋊C4—1724no—
538C4⋊C4—1724no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C22⋊C4—434no—
551C22⋊C4—862no—
552C22⋊C4—862no—
553C22⋊C4—862no—
554C22⋊C4—862no—
555C22⋊C4—862no—
556C22⋊C4—1721no—
557C22⋊C4—1721no—
558C22⋊C4—1721no—
559C22⋊C4—1721no—
560C22⋊C4—1721no—
561C22⋊C4—1721no—
562C22⋊C4C4⋊Dic4314yescomplemented
563C42—1728no—
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—22no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—42no—
575C23—42no—
576C23—41no—
577C23—41no—
578C23—42no—
579C23—41no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—41no—
585C23—42no—
586C23C2×C4×Dic4311yescharacteristic
587C23C22⋊C4×D4311yescharacteristic
588C23C4⋊C4×D4311yescharacteristic
589C23C2×C4⋊Dic4311yescharacteristic
590C23#1306328111yescharacteristic
591C23#1306328311yescharacteristic
592C23#1306328411yescharacteristic
593C23(C22⋊D43)⋊C411yescharacteristic
594C23(C22⋊D43)⋊C411yescharacteristic
595C23#1306328711yescharacteristic
596C23D4×Dic4311yescharacteristic
597C23D4×Dic4311yescharacteristic
598C23D4×Dic4311yescharacteristic
599C23C4×D17211yescharacteristic
600C23C4×D17211yescharacteristic
601C23#1306329011yescharacteristic
602C23C4×Dic8611yescharacteristic
603C23C4×Dic8611yescharacteristic
604C23Q8×Dic4311yescharacteristic
605C23#1306329511yescharacteristic
606C23#1306329811yescharacteristic
607C23#1306330011yescharacteristic
608C23#1306330211yescharacteristic
609C23#1306330211yescharacteristic
610C23#1306330311yescharacteristic
611C23#1306330511yescharacteristic
612C23#1306330711yescharacteristic
613C23#1306330911yescharacteristic
614C23#1306331011yescharacteristic
615C23#1306331111yescharacteristic
616C23#1306331511yescharacteristic
617C23#1306331611yescharacteristic
618C23#1306331811yescharacteristic
619C23#1306332011yescharacteristic
620C23#1306332411yescharacteristic
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—44no—
626C2×C4—44no—
627C2×C4—44no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—44no—
631C2×C4—44no—
632C2×C4—42no—
633C2×C4—81no—
634C2×C4—81no—
635C2×C4—82no—
636C2×C4—434no—
637C2×C4—864no—
638C2×C4—864no—
639C2×C4—862no—
640C2×C4—862no—
641C2×C4—862no—
642C2×C4—862no—
643C2×C4—864no—
644C2×C4—862no—
645C2×C4—3441no—
646C2×C4—3441no—
647C2×C4—3442no—
648C2×C4—3441no—
649C2×C4—3441no—
650C2×C4—3441no—
651C2×C4—3441no—
652C2×C4—1724no—
653C2×C4—1724no—
654C2×C4—1724no—
655C2×C4—1724no—
656C2×C4—1724no—
657C2×C4—1722no—
658C2×C4—1722no—
659C2×C4—1722no—
660C2×C4—1721no—
661C2×C4—1721no—
662C2×C4—1722no—
663C2×C4—1722no—
664C2×C4—1722no—
665C2×C4—1722no—
666C2×C4—1724no—
667C2×C4—1724no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22C22⋊C4×Dic4311yescharacteristic
709C22C4×C4⋊Dic4311yescharacteristic
710C22C4⋊C4×Dic4311yescharacteristic
711C22#1458277311yescharacteristic
712C22#1458277411yescharacteristic
713C22#1458277711yescharacteristic
714C22#1458278211yescharacteristic
715C22#1458278411yescharacteristic
716C22#1458278511yescharacteristic
717C22#1458278611yescharacteristic
718C22#1458279111yescharacteristic
719C22#1458279211yescharacteristic
720C22#1458279611yescharacteristic
721C22#1458279811yescharacteristic
722C22#1458280311yescharacteristic
723C22#99×D4312yes—
724C22#1458287112yes—
725C4—44no—
726C4—44no—
727C4—82no—
728C4—864no—
729C4—3442no—
730C4—3441no—
731C4—3441no—
732C4—1724no—
733C4—1722no—
734C2—21no—
735C2—21no—
736C2—21no—
737C2—21no—
738C2—21no—
739C2—21no—
740C2—21no—
741C2—21no—
742C2—21no—
743C2—21no—
744C2—21no—
745C2—21no—
746C2#1913282911yescharacteristic
747C2#99×Dic4312yes—
748C2#1913504711yescharacteristic
749C2#1913505211yescharacteristic
750C2#1913557812yes—
subgroupG/H
centerC23C22⋊C4×D43
commutatorC23×C43C2×C42
FrattiniC25C22×D43
FittingC2×C43×#342C2
socleC23×C43C2×C22⋊C4
prime radical, cosocleC25×C43C23
hypercenterC2×#342D43
hypocenterC43#10912
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
9. C22×C4⋊Dic43C4semidirect
21. C2×C43⋊#95C4semidirect
22. #14582666C4semidirect
28. C43×#342C4semidirect
122. C22×C4×C43C42semidirect
172. C22⋊C4×C43C4⋊C4semidirect
184. C22⋊Dic43C4⋊C4semidirect
403. #342Dic43semidirect
404. C43#10912semidirect
536. C22×C4C4×Dic43semidirect
562. C22⋊C4C4⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827742
C2×C22⋊C4×Dic432
C2×#145826662
C2×#145826652
#191328172
C2×C43×#3422
#1091243