Finite Group Databasebeta

← C2×#19137759 #25259202

Subgroups — C2×#19137759 #25259202

Order 11008.

2566 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
1C22×#13063305C211yesmaximal, characteristic
2#19137759C2116yesmaximal, direct product factor
3C2×#14582803C211yesmaximal, characteristic, complemented
4C2×#14582803C211yesmaximal, characteristic, complemented
5C2×#14582797C211yesmaximal, characteristic, complemented
6C2×#14582795C211yesmaximal, characteristic, complemented
7C2×#14582791C211yesmaximal, characteristic
8C2×#14582790C211yesmaximal, characteristic
9C2×#14582789C211yesmaximal, characteristic
10C2×#14582788C211yesmaximal, characteristic
11C2×#14582785C211yesmaximal, characteristic, complemented
12C2×#14582784C211yesmaximal, characteristic, complemented
13C2×#14582782C211yesmaximal, characteristic, complemented
14C2×#14582761C211yesmaximal, characteristic
15C2×#14582758C211yesmaximal, characteristic
16C2×C43×#387C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C2×#13063305C4116yescomplemented
20C2×#13063305C2218yes—
21C22×C4⋊Dic43C2211yescharacteristic
22C22×C4⋊Dic43C2211yescharacteristic
23C22×C4⋊Dic43C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37#14582803C2218yescomplemented
38#14582803C2218yescomplemented
39#14582797C2218yescomplemented
40#14582795C2218yescomplemented
41#14582791C2218yes—
42#14582790C2218yes—
43#14582789C2218yes—
44#14582788C2218yes—
45#14582785C2218yescomplemented
46#14582784C2218yescomplemented
47#14582782C2218yescomplemented
48#14582761C2218yes—
49#14582758C2218yes—
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C22×C4⋊C4×C43C2211yescharacteristic
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C42×C43C2211yescharacteristic
63C43×#387C2218yescomplemented
64C2×#95×C43C2211yescharacteristic
65C2×#95×C43C2211yescharacteristic
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C24×D43C2311yescharacteristic
69C22×Dic86—42no—
70C22×Dic86—42no—
71C22×Dic86C2×C418yes—
72C22×Dic86C2314yes—
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C22×C4×D43—42no—
81C22×C4×D43—42no—
82C22×C4×D43C2×C418yes—
83C22×C4×D43C2314yes—
84#13063305C2×C4164yescomplemented
85C2×C4⋊Dic43—42no—
86C2×C4⋊Dic43C2×C418yes—
87C2×C4⋊Dic43C2×C418yes—
88C2×C4⋊Dic43C2314yes—
89C2×C4⋊Dic43C2314yes—
90C2×C4⋊Dic43C2314yes—
91C2×Dic43⋊C4—42no—
92C2×Dic43⋊C4—42no—
93C2×Dic43⋊C4—42no—
94C2×Dic43⋊C4—42no—
95C2×Dic43⋊C4C2314yes—
96C2×Dic43⋊C4C2314yes—
97C2×Dic43⋊C4C2314yes—
98C2×Dic43⋊C4C2314yes—
99C2×(C2×D43)⋊C4—42no—
100C2×(C2×D43)⋊C4—42no—
101C2×(C2×D43)⋊C4—42no—
102C2×(C2×D43)⋊C4—42no—
103C2×(C2×D43)⋊C4C2×C418yes—
104C2×(C2×D43)⋊C4C2×C418yes—
105C2×(C2×D43)⋊C4C2314yes—
106C2×(C2×D43)⋊C4C2314yes—
107C2×(C2×D43)⋊C4C2314yes—
108C2×(C2×D43)⋊C4C2314yes—
109C2×(C2×D43)⋊C4C2314yes—
110C2×(C2×D43)⋊C4C2314yes—
111C2×C4×Dic43—42no—
112C2×C4×Dic43—42no—
113C2×C4×Dic43—42no—
114C2×C4×Dic43C2314yes—
115C2×C4×Dic43C2314yes—
116C2×C4×Dic43C2314yes—
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43—42no—
135C2×C4⋊C4×C43C2×C418yes—
136C2×C4⋊C4×C43C2314yes—
137C2×C4⋊C4×C43C2314yes—
138C2×C42×C43—42no—
139C2×C42×C43C2314yes—
140#95×C43C2314yes—
141#95×C43C2314yes—
142#95×C43C2314yes—
143#95×C43C2314yes—
144C24×C43C2411yescharacteristic
145C23×D43—22no—
146C23×D43—22no—
147C23×D43—22no—
148C23×D43—22no—
149C23×D43—22no—
150C23×D43—22no—
151C23×D43C22×C414yes—
152C23×D43C2412yes—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
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—22no—
171C22×C4×C43C22×C414yes—
172C22×C4×C43C22×C414yes—
173C22×C4×C43C22×C414yes—
174C22×C4×C43C2412yes—
175C22×C4×C43C2412yes—
176C22×C4×C43C2412yes—
177C22×C4×C43C2412yes—
178C22×C4×C43C2412yes—
179C22×C4×C43C2412yes—
180C22×C4×C43C2412yes—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43C22×C414yes—
200C22×Dic43C22×C414yes—
201C22×Dic43C22×C414yes—
202C22×Dic43C2412yes—
203C22×Dic43C2412yes—
204C22×Dic43C2412yes—
205C22×Dic43C2412yes—
206C22×Dic43C2412yes—
207C22×Dic43C2412yes—
208C22×Dic43C2412yes—
209C2×C4×D43—416no—
210C2×C4×D43—44no—
211C2×C4×D43—44no—
212C2×C4×D43C22×C4116yes—
213C2×Dic86—416no—
214C2×Dic86—44no—
215C2×Dic86—44no—
216C2×Dic86C22×C4116yes—
217C4⋊C4×C43—44no—
218C4⋊C4×C43C22×C4116yes—
219C42×C43—44no—
220(C2×D43)⋊C4—44no—
221(C2×D43)⋊C4—44no—
222(C2×D43)⋊C4—44no—
223(C2×D43)⋊C4—44no—
224(C2×D43)⋊C4C22×C4116yes—
225(C2×D43)⋊C4C22×C4116yes—
226C4⋊Dic43—44no—
227C4⋊Dic43C22×C4116yes—
228C4⋊Dic43C22×C4116yes—
229Dic43⋊C4—44no—
230Dic43⋊C4—44no—
231Dic43⋊C4—44no—
232Dic43⋊C4—44no—
233C4×Dic43—44no—
234C4×Dic43—44no—
235C4×Dic43—44no—
236C23×C43C23×C412yes—
237C23×C43H(5,𝔽2)12yes—
238C23×C43H(5,𝔽2)12yes—
239C23×C43H(5,𝔽2)12yes—
240C23×C432−1+412yes—
241C23×C432−1+412yes—
242C23×C432−1+412yes—
243C23×C43C2511yescharacteristic
244C22×D43—28no—
245C22×D43—28no—
246C22×D43—28no—
247C22×D43—22no—
248C22×D43—22no—
249C22×D43—22no—
250C22×D43—22no—
251C22×D43—22no—
252C22×D43—22no—
253C22×D43—44no—
254C22×D43—44no—
255C22×D43—44no—
256C22×D43—44no—
257C22×D43C23×C414yes—
258C2×C4×C43—28no—
259C2×C4×C43—28no—
260C2×C4×C43—28no—
261C2×C4×C43—22no—
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×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—44no—
280C2×C4×C43—44no—
281C2×C4×C43—44no—
282C2×C4×C43—44no—
283C2×C4×C43C23×C414yes—
284C2×C4×C43C23×C414yes—
285C2×C4×C43C23×C414yes—
286C2×Dic43—28no—
287C2×Dic43—28no—
288C2×Dic43—28no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—44no—
308C2×Dic43—44no—
309C2×Dic43—44no—
310C2×Dic43—44no—
311C2×Dic43C23×C414yes—
312C2×Dic43C23×C414yes—
313C2×Dic43C23×C414yes—
314C4×D43—416no—
315Dic86—416no—
316C2×#2378—431nomaximal, Sylow
317C22×C43#51814yes—
318C22×C43#51914yes—
319C22×C43#52014yes—
320C22×C43#56214yes—
321C22×C43#56214yes—
322C22×C43#56314yes—
323C22×C43#56314yes—
324C22×C43C24×C411yescharacteristic
325C22×C43C2×H(5,𝔽2)11yescharacteristic
326C22×C43C2×H(5,𝔽2)11yescharacteristic
327C22×C43C2×H(5,𝔽2)11yescharacteristic
328C22×C43C2×2−1+411yescharacteristic
329C22×C43C2×2−1+411yescharacteristic
330C22×C43C2×2−1+411yescharacteristic
331C2×D43—24no—
332C2×D43—24no—
333C2×D43—24no—
334C2×D43—416no—
335C2×D43—42no—
336C2×D43—42no—
337C2×D43—42no—
338C2×D43—42no—
339C4×C43—24no—
340C4×C43—24no—
341C4×C43—24no—
342C4×C43—42no—
343C4×C43—42no—
344C4×C43—42no—
345C4×C43—42no—
346Dic43—24no—
347Dic43—24no—
348Dic43—24no—
349Dic43—42no—
350Dic43—42no—
351Dic43—42no—
352Dic43—42no—
353C22×C22⋊Q8—431no—
354#2378—4316no—
355C2×#391—431no—
356C2×#391—431no—
357C2×#389—431no—
358C2×#389—431no—
359C2×#388—431no—
360C2×#388—431no—
361C2×#388—431no—
362C2×#388—431no—
363C2×#387—431no—
364C2×#387—431no—
365C2×#387—431no—
366C2×#387D4311yescharacteristic, complemented
367C2×#381—431no—
368C2×#380—431no—
369C2×C43#237818yescomplemented
370C2×C43C2×#51811yescharacteristic
371C2×C43C2×#51911yescharacteristic
372C2×C43C2×#52011yescharacteristic
373C2×C43C2×#56211yescharacteristic
374C2×C43C2×#56211yescharacteristic
375C2×C43C2×#56311yescharacteristic
376C2×C43C2×#56311yescharacteristic
377D43—44no—
378C23×Q8—431no—
379C24×C4—431no—
380C2×C22⋊Q8—438no—
381C2×C22⋊Q8—4316no—
382C22×C4⋊C4—431no—
383C22×C4⋊C4—431no—
384C22×C4⋊C4—431no—
385C22×C4⋊C4—431no—
386C22×C4⋊C4—431no—
387C22×C4⋊C4—431no—
388C22×C4⋊C4—431no—
389C22×C4⋊C4C2×D4311yescharacteristic
390C22×C4⋊C4C2×D4311yescharacteristic
391C22×C22⋊C4—431no—
392C22×C22⋊C4—431no—
393C22×C22⋊C4—431no—
394C22×C22⋊C4—431no—
395C22×C22⋊C4—431no—
396C22×C22⋊C4—431no—
397C22×C42—431no—
398C22×C42—431no—
399C22×C42—431no—
400C22×C42C2×D4311yescharacteristic
401#391—438no—
402#391—438no—
403#389—438no—
404#389—438no—
405#388—438no—
406#388—438no—
407#388—438no—
408#388—438no—
409#387—438no—
410#387—438no—
411#387—438no—
412#387C2×D4318yescomplemented
413#381—438no—
414#380—438no—
415C2×#95—431no—
416C2×#95—431no—
417C2×#95—431no—
418C2×#95—431no—
419C2×#95—431no—
420C2×#95—431no—
421C2×#95—431no—
422C2×#95—431no—
423C2×#95—431no—
424C2×#95—431no—
425C2×#95C2×D4311yescharacteristic
426C2×#95C2×D4311yescharacteristic
427C2×#95C2×D4311yescharacteristic
428C2×#95C2×D4311yescharacteristic
429C43C2×#237811yescharacteristic, complemented, Sylow
430C25—431no—
431C22×Q8—438no—
432C22×Q8—434no—
433C22×Q8—1722no—
434C22×Q8—1722no—
435C23×C4—431no—
436C23×C4—431no—
437C23×C4—431no—
438C23×C4—438no—
439C23×C4—434no—
440C23×C4—431no—
441C23×C4—431no—
442C23×C4—431no—
443C23×C4—431no—
444C23×C4—1722no—
445C23×C4—1722no—
446C23×C4C22×D4311yescharacteristic
447C23×C4C22×D4311yescharacteristic
448C23×C4C22×D4311yescharacteristic
449C23×C4C22×D4311yescharacteristic
450C23×C4C22×D4311yescharacteristic
451C23×C4C22×D4311yescharacteristic
452C23×C4C22×D4311yescharacteristic
453C22⋊Q8—4364no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—438no—
456C2×C4⋊C4—438no—
457C2×C4⋊C4—434no—
458C2×C4⋊C4—434no—
459C2×C4⋊C4—434no—
460C2×C4⋊C4—434no—
461C2×C4⋊C4—434no—
462C2×C4⋊C4—434no—
463C2×C4⋊C4—434no—
464C2×C4⋊C4—1722no—
465C2×C4⋊C4—1722no—
466C2×C4⋊C4—1722no—
467C2×C4⋊C4—1722no—
468C2×C4⋊C4—1722no—
469C2×C4⋊C4C4×D4318yes—
470C2×C4⋊C4C22×D4314yes—
471C2×C4⋊C4C22×D4314yes—
472C2×C22⋊C4—438no—
473C2×C22⋊C4—438no—
474C2×C22⋊C4—434no—
475C2×C22⋊C4—434no—
476C2×C22⋊C4—434no—
477C2×C22⋊C4—434no—
478C2×C22⋊C4—434no—
479C2×C22⋊C4—434no—
480C2×C22⋊C4—1722no—
481C2×C22⋊C4—1722no—
482C2×C22⋊C4—1722no—
483C2×C22⋊C4—1722no—
484C2×C42—42no—
485C2×C42—434no—
486C2×C42—434no—
487C2×C42—434no—
488C2×C42—1722no—
489C2×C42—1722no—
490C2×C42—1722no—
491C2×C42C22×D4314yes—
492#95—434no—
493#95—434no—
494#95—434no—
495#95—434no—
496#95—434no—
497#95—434no—
498#95—434no—
499#95—434no—
500#95—434no—
501#95—434no—
502#95C22×D4314yes—
503#95C22×D4314yes—
504#95C22×D4314yes—
505#95C22×D4314yes—
506C24—434no—
507C24—432no—
508C24—862no—
509C24—862no—
510C24—862no—
511C24—862no—
512C24—862no—
513C24—862no—
514C24C23×D4311yescharacteristic
515C2×Q8—4316no—
516C2×Q8—17216no—
517C2×Q8—1724no—
518C2×Q8—1724no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—434no—
538C22×C4—434no—
539C22×C4—434no—
540C22×C4—432no—
541C22×C4—432no—
542C22×C4—432no—
543C22×C4—4316no—
544C22×C4—432no—
545C22×C4—432no—
546C22×C4—432no—
547C22×C4—432no—
548C22×C4—862no—
549C22×C4—862no—
550C22×C4—862no—
551C22×C4—862no—
552C22×C4—862no—
553C22×C4—862no—
554C22×C4—862no—
555C22×C4—862no—
556C22×C4—862no—
557C22×C4—862no—
558C22×C4—862no—
559C22×C4—862no—
560C22×C4—862no—
561C22×C4—862no—
562C22×C4—862no—
563C22×C4—862no—
564C22×C4—862no—
565C22×C4—862no—
566C22×C4—17216no—
567C22×C4—1724no—
568C22×C4—1724no—
569C22×C4C2×C4×D4314yes—
570C22×C4C2×C4×D4314yes—
571C22×C4C2×C4×D4314yes—
572C22×C4C23×D4312yes—
573C22×C4C23×D4312yes—
574C22×C4C23×D4312yes—
575C22×C4C23×D4312yes—
576C22×C4C23×D4312yes—
577C22×C4C23×D4312yes—
578C22×C4C23×D4312yes—
579C4⋊C4—44no—
580C4⋊C4—4316no—
581C4⋊C4—4316no—
582C4⋊C4—1724no—
583C4⋊C4—1724no—
584C4⋊C4—1724no—
585C4⋊C4—1724no—
586C4⋊C4—1724no—
587C4⋊C4C2×C4×D43116yes—
588C22⋊C4—4316no—
589C22⋊C4—4316no—
590C22⋊C4—1724no—
591C22⋊C4—1724no—
592C22⋊C4—1724no—
593C22⋊C4—1724no—
594C42—44no—
595C42—1724no—
596C42—1724no—
597C42—1724no—
598C23—434no—
599C23—868no—
600C23—868no—
601C23—868no—
602C23—862no—
603C23—862no—
604C23—862no—
605C23—862no—
606C23—862no—
607C23—862no—
608C23—1724no—
609C23—1724no—
610C23—1724no—
611C23—1724no—
612C23C22×C4×D4312yes—
613C23#1306337012yes—
614C23#1306337112yes—
615C23#1306337112yes—
616C23#1306337212yes—
617C23#1306337212yes—
618C23#1306337312yes—
619C23C24×D4311yescharacteristic
620Q8—17216no—
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—28no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
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—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—434no—
647C2×C4—434no—
648C2×C4—434no—
649C2×C4—868no—
650C2×C4—868no—
651C2×C4—868no—
652C2×C4—862no—
653C2×C4—862no—
654C2×C4—862no—
655C2×C4—862no—
656C2×C4—862no—
657C2×C4—862no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—17216no—
671C2×C4—1724no—
672C2×C4—1724no—
673C2×C4—1724no—
674C2×C4—1724no—
675C2×C4C22×C4×D4314yes—
676C2×C4C22×C4×D4314yes—
677C2×C4C22×C4×D4314yes—
678C22—864no—
679C22—864no—
680C22—864no—
681C22—1722no—
682C22—1722no—
683C22—1722no—
684C22—1722no—
685C22—17216no—
686C22#1458337314yes—
687C22#1458337514yes—
688C22#1458337814yes—
689C22#1458364514yes—
690C22#1458364614yes—
691C22#1458365114yes—
692C22#1458365314yes—
693C22C23×C4×D4311yescharacteristic
694C22C2×#1306337011yescharacteristic
695C22C2×#1306337111yescharacteristic
696C22C2×#1306337111yescharacteristic
697C22C2×#1306337211yescharacteristic
698C22C2×#1306337211yescharacteristic
699C22C2×#1306337311yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—864no—
708C4—864no—
709C4—864no—
710C4—1722no—
711C4—1722no—
712C4—1722no—
713C4—1722no—
714C2—1724no—
715C2#1913775918yesdirect product factor
716C2C2×#1458337311yescharacteristic
717C2C2×#1458337511yescharacteristic
718C2C2×#1458337811yescharacteristic
719C2C2×#1458364511yescharacteristic
720C2C2×#1458364611yescharacteristic
721C2C2×#1458365111yescharacteristic
722C2C2×#1458365311yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#387C2
socleC24×C43C24
prime radicalC24×D43C23
cosocleC23×C43C25
hypercenterC2×#387D43
hypocenterC43C2×#2378
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #19137759C2direct (N × H)
3. C2×#14582803C2semidirect
4. C2×#14582803C2semidirect
5. C2×#14582797C2semidirect
6. C2×#14582795C2semidirect
11. C2×#14582785C2semidirect
12. C2×#14582784C2semidirect
13. C2×#14582782C2semidirect
16. C2×C43×#387C2semidirect
19. C2×#13063305C4semidirect
37. #14582803C22semidirect
38. #14582803C22semidirect
39. #14582797C22semidirect
40. #14582795C22semidirect
45. #14582785C22semidirect
46. #14582784C22semidirect
47. #14582782C22semidirect
63. C43×#387C22semidirect
84. #13063305C2×C4semidirect
366. C2×#387D43semidirect
369. C2×C43#2378semidirect
412. #387C2×D43semidirect
429. C43C2×#2378semidirect
715. C2#19137759direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633052
#191377592
C2×#145828032
C2×#145827972
C2×#145827952
C2×#145827912
C2×#145827902
C2×#145827892
C2×#145827882
C2×#145827852
C2×#145827842
C2×#145827822
C2×#145827612
C2×#145827582
C2×C43×#3872
C2×#237843