Finite Group Databasebeta

← #25019272

Subgroups — #25019272

Order 11008.

1630 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582798C211yesmaximal, characteristic
2C2×#14582797C211yesmaximal, characteristic
3C2×#14582795C211yesmaximal, characteristic
4C2×#14582764C211yesmaximal, characteristic
5C2×C4⋊C4×Dic43C211yesmaximal, characteristic
6C2×C4×Dic43⋊C4C211yesmaximal, characteristic
7#19132859C212yesmaximal
8#19132858C212yesmaximal
9#19132824C212yesmaximal
10Dic43⋊#95C212yesmaximal
11C2×C43×#389C211yesmaximal, characteristic
12C22×C4⋊Dic43C2211yescharacteristic
13C22×C4⋊Dic43C2212yes—
14C22×C4⋊Dic43C2211yescharacteristic
15C22×Dic43⋊C4C2211yescharacteristic
16C22×Dic43⋊C4C2211yescharacteristic
17C22×Dic43⋊C4C2212yes—
18C22×Dic43⋊C4C2212yes—
19C22×C4×Dic43C2211yescharacteristic
20C22×C4×Dic43C2212yes—
21C22×C4×Dic43C2211yescharacteristic
22#14582798—24no—
23#14582797—24no—
24#14582795—24no—
25#14582764—24no—
26C4⋊C4×Dic43C418yescomplemented
27C4×Dic43⋊C4—24no—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2211yescharacteristic
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2212yes—
35C2×C43⋊#95C2212yes—
36C22×C4⋊C4×C43C2211yescharacteristic
37C22×C4⋊C4×C43C2212yes—
38C22×C4⋊C4×C43C2211yescharacteristic
39C22×C42×C43C2211yescharacteristic
40C43×#389—24no—
41C2×#95×C43C2212yes—
42C23×Dic43C2312yes—
43C23×Dic43C2311yescharacteristic
44C23×Dic43C2311yescharacteristic
45C23×Dic43C2311yescharacteristic
46C23×Dic43C2312yes—
47C23×Dic43C2311yescharacteristic
48C2×C4⋊Dic43—22no—
49C2×C4⋊Dic43—24no—
50C2×C4⋊Dic43—22no—
51C2×C4⋊Dic43—22no—
52C2×C4⋊Dic43—24no—
53C2×C4⋊Dic43—42no—
54C2×C4⋊Dic43C2×C414yes—
55C2×C4⋊Dic43D414yes—
56C2×C4⋊Dic43Q814yes—
57C2×Dic43⋊C4—22no—
58C2×Dic43⋊C4—22no—
59C2×Dic43⋊C4—22no—
60C2×Dic43⋊C4—22no—
61C2×Dic43⋊C4—22no—
62C2×Dic43⋊C4—22no—
63C2×Dic43⋊C4—24no—
64C2×Dic43⋊C4—24no—
65C2×Dic43⋊C4—24no—
66C2×Dic43⋊C4—24no—
67C2×Dic43⋊C4—42no—
68C2×Dic43⋊C4—42no—
69C2×C4×Dic43—22no—
70C2×C4×Dic43—22no—
71C2×C4×Dic43—22no—
72C2×C4×Dic43—42no—
73C2×C4×Dic43—42no—
74C2×C4×Dic43C2×C418yes—
75C2×C4×Dic43C2×C414yes—
76C2×C4×Dic43D414yes—
77C2×C4×Dic43Q814yes—
78C43⋊#95—24no—
79C43⋊#95—24no—
80C43⋊#95—24no—
81C43⋊#95—22no—
82C43⋊#95—22no—
83C43⋊#95—24no—
84C43⋊#95—24no—
85C43⋊#95C2×C418yes—
86C23×C4×C43C2312yes—
87C23×C4×C43C2311yescharacteristic
88C23×C4×C43C2311yescharacteristic
89C23×C4×C43C2312yes—
90C23×C4×C43C2311yescharacteristic
91C2×C4⋊C4×C43—22no—
92C2×C4⋊C4×C43—24no—
93C2×C4⋊C4×C43—22no—
94C2×C4⋊C4×C43—22no—
95C2×C4⋊C4×C43—24no—
96C2×C4⋊C4×C43—42no—
97C2×C4⋊C4×C43C2×C414yes—
98C2×C4⋊C4×C43D414yes—
99C2×C4⋊C4×C43Q814yes—
100C2×C42×C43—22no—
101C2×C42×C43—22no—
102C2×C42×C43—22no—
103#95×C43—24no—
104C24×C43C2411yescharacteristic
105C22×C4×C43—21no—
106C22×C4×C43—21no—
107C22×C4×C43—21no—
108C22×C4×C43—21no—
109C22×C4×C43—21no—
110C22×C4×C43—21no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—22no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—22no—
128C22×C4×C43C22×C414yes—
129C22×C4×C43C22×C412yes—
130C22×C4×C43C2×D412yes—
131C22×C4×C43C2×D412yes—
132C22×C4×C43C2×D414yes—
133C22×C4×C43C2×D412yes—
134C22×C4×C43C2×Q814yes—
135C22×C4×C43C2×Q812yes—
136C22×C4×C43C2×Q812yes—
137C22×C4×C43C2×Q812yes—
138C22×C4×C43#4112yes—
139C22×C4×C43#4112yes—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—22no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—22no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—22no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—22no—
171C22×Dic43C22×C412yes—
172C22×Dic43C22×C414yes—
173C22×Dic43C22×C412yes—
174C22×Dic43C2×D412yes—
175C22×Dic43C2×D412yes—
176C22×Dic43C2×D414yes—
177C22×Dic43C2×Q812yes—
178C22×Dic43C2×Q812yes—
179C22×Dic43C2×Q814yes—
180C22×Dic43#4112yes—
181C22×Dic43#4112yes—
182C4⋊C4×C43—48no—
183C4⋊C4×C43—44no—
184C4⋊C4×C43C4⋊C4116yescomplemented
185C42×C43—44no—
186C4⋊Dic43—48no—
187C4⋊Dic43—44no—
188C4⋊Dic43C4⋊C4116yescomplemented
189Dic43⋊C4—28no—
190Dic43⋊C4—28no—
191Dic43⋊C4—48no—
192Dic43⋊C4—48no—
193C4×Dic43—48no—
194C4×Dic43—44no—
195C4×Dic43C4⋊C4116yescomplemented
196C23×C43C23×C411yescharacteristic
197C23×C43C22×D411yescharacteristic
198C23×C43C22×D411yescharacteristic
199C23×C43C22×D411yescharacteristic
200C23×C43C22×Q811yescharacteristic
201C23×C43C22×Q811yescharacteristic
202C23×C43C22×Q811yescharacteristic
203C23×C43C2×#4111yescharacteristic
204C23×C43C2×#4111yescharacteristic
205C23×C43C2×#4111yescharacteristic
206C23×C43C2×#4111yescharacteristic
207C23×C43H(5,𝔽2)11yescharacteristic
208C23×C43H(5,𝔽2)11yescharacteristic
209C23×C432−1+411yescharacteristic
210C23×C432−1+411yescharacteristic
211C2×C4×C43—24no—
212C2×C4×C43—24no—
213C2×C4×C43—24no—
214C2×C4×C43—24no—
215C2×C4×C43—24no—
216C2×C4×C43—24no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43C2×C4⋊C414yes—
239C2×C4×C43C2×C4⋊C414yes—
240C2×C4×C43C2×C4⋊C418yes—
241C2×C4×C43C2×C4⋊C414yes—
242C2×C4×C43#12714yes—
243C2×C4×C43C4⋊Q814yes—
244C2×C4×C43C4⋊Q814yes—
245C2×C4×C43C4⋊Q814yes—
246C2×Dic43—22no—
247C2×Dic43—24no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—24no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—24no—
261C2×Dic43—24no—
262C2×Dic43—24no—
263C2×Dic43—24no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—42no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43—42no—
282C2×Dic43—42no—
283C2×Dic43—42no—
284C2×Dic43—42no—
285C2×Dic43C2×C4⋊C414yes—
286C2×Dic43C2×C4⋊C414yes—
287C2×Dic43C2×C4⋊C418yes—
288#13954—431nomaximal, Sylow
289C22×C43C22×C4⋊C411yescharacteristic
290C22×C43C22×C4⋊C411yescharacteristic
291C22×C43C22×C4⋊C411yescharacteristic
292C22×C43C4×#4111yescharacteristic
293C22×C43C4×#4111yescharacteristic
294C22×C43#51811yescharacteristic
295C22×C43#51911yescharacteristic
296C22×C43#52511yescharacteristic
297C22×C43#52511yescharacteristic
298C22×C43C2×#12711yescharacteristic
299C22×C43C2×C4⋊Q811yescharacteristic
300C22×C43C2×C4⋊Q811yescharacteristic
301C22×C43C2×C4⋊Q811yescharacteristic
302C22×C43#53311yescharacteristic
303C22×C43#53311yescharacteristic
304C22×C43#53711yescharacteristic
305C22×C43#53711yescharacteristic
306C22×C43#54411yescharacteristic
307C22×C43#54411yescharacteristic
308C22×C43#54611yescharacteristic
309C22×C43#54611yescharacteristic
310C22×C43#54611yescharacteristic
311C22×C43#54611yescharacteristic
312C22×C43#54811yescharacteristic
313C22×C43#54811yescharacteristic
314C22×C43#54811yescharacteristic
315C22×C43#54811yescharacteristic
316C22×C43#55411yescharacteristic
317C22×C43#55411yescharacteristic
318C22×C43#55411yescharacteristic
319C22×C43#55411yescharacteristic
320C22×C43#55711yescharacteristic
321C22×C43#55711yescharacteristic
322C22×C43#55711yescharacteristic
323C22×C43#55711yescharacteristic
324C4×C43—28no—
325C4×C43—42no—
326C4×C43—42no—
327C4×C43—82no—
328C4×C43#38418yes—
329Dic43—24no—
330Dic43—28no—
331Dic43—24no—
332Dic43—42no—
333Dic43—42no—
334Dic43—82no—
335C2×#389—431no—
336C2×#389—431no—
337C2×#389—431no—
338C2×#389D4311yescharacteristic
339C2×#382—431no—
340C2×C4×C4⋊C4—431no—
341C2×C4×C4⋊C4—431no—
342#1444—432no—
343#1444—432no—
344C4⋊#95—432no—
345C4⋊#95—432no—
346C2×C43C2×#38411yescharacteristic
347C2×C43#229611yescharacteristic
348C2×C43#231611yescharacteristic
349C2×C43#234911yescharacteristic
350C2×C43#234911yescharacteristic
351C2×C43#235111yescharacteristic
352C2×C43#235111yescharacteristic
353C2×C43#254011yescharacteristic
354C2×C43#254011yescharacteristic
355C2×C43#255011yescharacteristic
356C2×C43#255011yescharacteristic
357C2×C43#255011yescharacteristic
358C2×C43#255011yescharacteristic
359C2×C43#258411yescharacteristic
360C2×C43#258411yescharacteristic
361C22×C4⋊C4—431no—
362C22×C4⋊C4—431no—
363C22×C4⋊C4—431no—
364C22×C4⋊C4—431no—
365C22×C4⋊C4—432no—
366C22×C4⋊C4—432no—
367C22×C4⋊C4—432no—
368C22×C4⋊C4C2×D4311yescharacteristic
369C22×C4⋊C4C2×D4312yes—
370C22×C4⋊C4C2×D4311yescharacteristic
371C22×C42—431no—
372C22×C42—432no—
373C22×C42—431no—
374C22×C42C2×D4311yescharacteristic
375#389—24no—
376#389—864no—
377#389—864no—
378#389—864no—
379#382—864no—
380C4×C4⋊C4—438no—
381C4×C4⋊C4—864no—
382C2×#95—432no—
383C2×#95—431no—
384C2×#95—431no—
385C2×#95—432no—
386C2×#95—432no—
387C2×#95—432no—
388C2×#95—432no—
389C2×#95—432no—
390C2×#95C2×D4312yes—
391C43#1395411yescharacteristic, complemented, Sylow
392C23×C4—432no—
393C23×C4—431no—
394C23×C4—431no—
395C23×C4—431no—
396C23×C4—431no—
397C23×C4—432no—
398C23×C4C22×D4312yes—
399C23×C4C22×D4311yescharacteristic
400C23×C4C22×D4311yescharacteristic
401C23×C4C22×D4312yes—
402C23×C4C22×D4311yescharacteristic
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—434no—
410C2×C4⋊C4—434no—
411C2×C4⋊C4—434no—
412C2×C4⋊C4—862no—
413C2×C4⋊C4—862no—
414C2×C4⋊C4—862no—
415C2×C4⋊C4—862no—
416C2×C4⋊C4—862no—
417C2×C4⋊C4—862no—
418C2×C4⋊C4—864no—
419C2×C4⋊C4—864no—
420C2×C4⋊C4—864no—
421C2×C4⋊C4—864no—
422C2×C4⋊C4—862no—
423C2×C4⋊C4—862no—
424C2×C4⋊C4—864no—
425C2×C4⋊C4—864no—
426C2×C4⋊C4—862no—
427C2×C4⋊C4—1722no—
428C2×C4⋊C4—1722no—
429C2×C4⋊C4—1722no—
430C2×C4⋊C4Dic8614yes—
431C2×C4⋊C4C4×D4314yes—
432C2×C4⋊C4C22⋊D4314yes—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—434no—
437C2×C42—434no—
438C2×C42—434no—
439C2×C42—438no—
440C2×C42—862no—
441C2×C42—862no—
442C2×C42—862no—
443C2×C42—1722no—
444C2×C42—1722no—
445#95—24no—
446#95—438no—
447#95—862no—
448#95—862no—
449#95—864no—
450#95—864no—
451#95—864no—
452#95—864no—
453#95—864no—
454C24C23×D4311yescharacteristic
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—432no—
479C22×C4—434no—
480C22×C4—432no—
481C22×C4—432no—
482C22×C4—432no—
483C22×C4—434no—
484C22×C4—432no—
485C22×C4—432no—
486C22×C4—434no—
487C22×C4—432no—
488C22×C4—432no—
489C22×C4—862no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—862no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—862no—
497C22×C4—861no—
498C22×C4—862no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—862no—
514C22×C4—862no—
515C22×C4—862no—
516C22×C4—862no—
517C22×C4—862no—
518C22×C4—862no—
519C22×C4—862no—
520C22×C4C2×Dic8614yes—
521C22×C4C2×Dic8612yes—
522C22×C4C2×C4×D4314yes—
523C22×C4C2×C4×D4312yes—
524C22×C4D4×D4312yes—
525C22×C4D4×D4312yes—
526C22×C4#1062190012yes—
527C22×C4Q8×D4312yes—
528C22×C4Q8×D4312yes—
529C22×C4#1062190212yes—
530C22×C4C2×C22⋊D4314yes—
531C22×C4C2×C22⋊D4312yes—
532C4⋊C4—48no—
533C4⋊C4—44no—
534C4⋊C4—4316no—
535C4⋊C4—868no—
536C4⋊C4—868no—
537C4⋊C4—1728no—
538C4⋊C4—1728no—
539C4⋊C4—1728no—
540C4⋊C4—1724no—
541C4⋊C4Dic43⋊C4116yescomplemented
542C42—44no—
543C42—4316no—
544C42—1728no—
545C42—1724no—
546C23C22×C4×D4311yescharacteristic
547C23C2×D4×D4311yescharacteristic
548C23C2×D4×D4311yescharacteristic
549C23C22×C22⋊D4311yescharacteristic
550C23C2×Q8×D4311yescharacteristic
551C23C2×Q8×D4311yescharacteristic
552C23C22×Dic8611yescharacteristic
553C23#41×D4311yescharacteristic
554C23#41×D4311yescharacteristic
555C23C2×#1062190011yescharacteristic
556C23C2×#1062190211yescharacteristic
557C23#1306337011yescharacteristic
558C23#1306337111yescharacteristic
559C23#1306337211yescharacteristic
560C23#1306337311yescharacteristic
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—434no—
589C2×C4—434no—
590C2×C4—438no—
591C2×C4—864no—
592C2×C4—864no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—864no—
596C2×C4—862no—
597C2×C4—864no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—864no—
608C2×C4—864no—
609C2×C4—862no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—862no—
615C2×C4—1722no—
616C2×C4—1722no—
617C2×C4—1722no—
618C2×C4—1722no—
619C2×C4—1722no—
620C2×C4—1722no—
621C2×C4—1722no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4C4⋊C4×D4314yes—
631C2×C4C4⋊C4×D4314yes—
632C2×C4C2×Dic43⋊C418yes—
633C2×C4C2×Dic43⋊C414yes—
634C2×C4#1306332114yes—
635C2×C4#1306332314yes—
636C2×C4#1306332414yes—
637C2×C4#1306332414yes—
638C22C2×C4⋊C4×D4311yescharacteristic
639C22C2×C4⋊C4×D4311yescharacteristic
640C22C22×Dic43⋊C411yescharacteristic
641C22C4×#1062190011yescharacteristic
642C22C4×#1062190211yescharacteristic
643C22#1458337111yescharacteristic
644C22#1458337511yescharacteristic
645C22#1458340911yescharacteristic
646C22#1458341211yescharacteristic
647C22C2×#1306332111yescharacteristic
648C22C2×#1306332311yescharacteristic
649C22C2×#1306332411yescharacteristic
650C22C2×#1306332411yescharacteristic
651C22#1458345411yescharacteristic
652C22#1458345511yescharacteristic
653C22#1458347811yescharacteristic
654C22#1458347911yescharacteristic
655C22#1458352611yescharacteristic
656C22#1458352911yescharacteristic
657C22#1458353711yescharacteristic
658C22#1458354011yescharacteristic
659C22#1458354311yescharacteristic
660C22#1458354611yescharacteristic
661C22#1458355511yescharacteristic
662C22#1458355611yescharacteristic
663C22#1458355911yescharacteristic
664C22#1458356011yescharacteristic
665C22#1458360511yescharacteristic
666C22#1458360611yescharacteristic
667C22#1458360811yescharacteristic
668C22#1458361011yescharacteristic
669C22#1458362411yescharacteristic
670C22#1458362511yescharacteristic
671C22#1458362611yescharacteristic
672C22#1458362811yescharacteristic
673C4—28no—
674C4—42no—
675C4—42no—
676C4—82no—
677C4—864no—
678C4—864no—
679C4—868no—
680C4—3442no—
681C4—1722no—
682C4—1722no—
683C4#1458276818yes—
684C2C2×#1458276811yescharacteristic
685C2#1913707611yescharacteristic
686C2#1913721011yescharacteristic
687C2#1913750011yescharacteristic
688C2#1913750411yescharacteristic
689C2#1913751311yescharacteristic
690C2#1913751411yescharacteristic
691C2#1913953111yescharacteristic
692C2#1913953311yescharacteristic
693C2#1913961211yescharacteristic
694C2#1913961411yescharacteristic
695C2#1913961811yescharacteristic
696C2#1913961911yescharacteristic
697C2#1913998011yescharacteristic
698C2#1913998211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#389C2
socle, prime radical, cosocleC24×C43C24
hypercenterC2×#389D43
hypocenterC43#13954
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
26. C4⋊C4×Dic43C4semidirect
184. C4⋊C4×C43C4⋊C4semidirect
188. C4⋊Dic43C4⋊C4semidirect
195. C4×Dic43C4⋊C4semidirect
391. C43#13954semidirect
541. C4⋊C4Dic43⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#145827982
C2×#145827972
C2×#145827952
C2×#145827642
C2×C4⋊C4×Dic432
C2×C4×Dic43⋊C42
#191328592
#191328582
#191328242
Dic43⋊#952
C2×C43×#3892
#1395443