Finite Group Databasebeta

← #16791730

Subgroups — #16791730

Order 3328.

1486 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719082C212yesmaximal
2C2×#11719059C211yesmaximal, characteristic
3C2×C4×C4⋊#261C211yesmaximal, characteristic
4#13130022C212yesmaximal
5#13130021C212yesmaximal
6#13130016C212yesmaximal
7#13130014C211yesmaximal, characteristic
8#13130014C211yesmaximal, characteristic
9#13130014C211yesmaximal, characteristic
10#13130014C211yesmaximal, characteristic
11C4×C4⋊C4×D13C211yesmaximal, characteristic
12C22×C4⋊#261C2211yescharacteristic
13C22×C4⋊#261C2211yescharacteristic
14C22×C4⋊#261C2212yes—
15C22×C4⋊#261C2212yes—
16C22×C4⋊#261C2211yescharacteristic
17C22×C4⋊#261C2211yescharacteristic
18C22×C4×#261C2212yes—
19C2×C4⋊C4×D13C2211yescharacteristic
20C2×C4⋊C4×D13C2211yescharacteristic
21C2×C42×D13C2211yescharacteristic
22C2×C42×D13C2211yescharacteristic
23C2×C42×D13C2211yescharacteristic
24C2×(C2×#261)⋊C4C2212yes—
25C2×(C2×#261)⋊C4C2212yes—
26C2×(C2×#261)⋊C4C2212yes—
27C2×(C2×#261)⋊C4C2212yes—
28C2×(C2×#261)⋊C4C2212yes—
29C2×(C2×#261)⋊C4C2212yes—
30C2×(C2×#261)⋊C4C2212yes—
31C2×(C2×#261)⋊C4C2212yes—
32C2×(C2×#261)⋊C4C2212yes—
33#11719082—28no—
34#11719059—24no—
35C4×C4⋊#261—24no—
36C4×C13×C4⋊C4C411yescharacteristic, complemented
37C4⋊C4×Dic13C411yescharacteristic, complemented
38C4⋊C4×Dic13C411yescharacteristic, complemented
39C4×C4⋊Dic13C411yescharacteristic, complemented
40C4×#6101C411yescharacteristic, complemented
41C4×#6101C411yescharacteristic, complemented
42D13×#95C2211yescharacteristic
43D13×#95C2211yescharacteristic
44#11718310C411yescharacteristic, complemented
45#11718310C411yescharacteristic, complemented
46C23×#261C2312yes—
47C23×#261C2312yes—
48C23×#261C2312yes—
49C23×#261C2312yes—
50C22×C4×D13C2311yescharacteristic
51C22×C4×D13C2311yescharacteristic
52C22×C4×D13C2311yescharacteristic
53C22×C4×D13C2311yescharacteristic
54C22×C4×D13C2311yescharacteristic
55C22×C4×D13C2311yescharacteristic
56C22×C4×D13C2311yescharacteristic
57C2×C4⋊#261—22no—
58C2×C4⋊#261—22no—
59C2×C4⋊#261—22no—
60C2×C4⋊#261—22no—
61C2×C4⋊#261—24no—
62C2×C4⋊#261—24no—
63C2×C4⋊#261—22no—
64C2×C4⋊#261—24no—
65C2×C4⋊#261—24no—
66C2×C4⋊#261—22no—
67C2×C4⋊#261—22no—
68C2×C4⋊#261—22no—
69C2×C4⋊#261—22no—
70C2×C4⋊#261—22no—
71C2×C4⋊#261—42no—
72C2×C4⋊#261—42no—
73C2×C4⋊#261D414yes—
74C2×C4⋊#261Q814yes—
75C2×C4×#261—24no—
76C2×C4×#261—24no—
77C2×C4×#261—42no—
78C2×C13×C4⋊C4C2×C411yescharacteristic
79C2×C13×C4⋊C4C2×C411yescharacteristic
80C2×C42×C13C2×C411yescharacteristic
81C2×C42×C13C2×C411yescharacteristic
82C2×C42×C13C2×C411yescharacteristic
83C2×C4⋊Dic13C2×C411yescharacteristic
84C2×C4⋊Dic13C2×C411yescharacteristic
85C2×#6101C2×C411yescharacteristic
86C2×#6101C2×C411yescharacteristic
87C2×#6101C2×C411yescharacteristic
88C2×#6101C2×C411yescharacteristic
89C2×C4×Dic13C2×C411yescharacteristic
90C2×C4×Dic13C2×C411yescharacteristic
91C2×C4×Dic13C2×C411yescharacteristic
92C2×C4×Dic13C2×C411yescharacteristic
93C2×C4×Dic13C2×C411yescharacteristic
94C2×C4×Dic13C2×C411yescharacteristic
95C2×C4×Dic13C2×C411yescharacteristic
96C2×C4×Dic13C2×C411yescharacteristic
97C2×C4×Dic13C2×C411yescharacteristic
98C4⋊C4×D13—22no—
99C4⋊C4×D13—22no—
100C4⋊C4×D13D414yes—
101C4⋊C4×D13Q814yes—
102C42×D13—22no—
103C42×D13—22no—
104C42×D13—22no—
105C42×D13—22no—
106C42×D13—22no—
107C42×D13—22no—
108(C2×#261)⋊C4—24no—
109(C2×#261)⋊C4—24no—
110(C2×#261)⋊C4—24no—
111(C2×#261)⋊C4—24no—
112(C2×#261)⋊C4—24no—
113(C2×#261)⋊C4—24no—
114(C2×#261)⋊C4—42no—
115(C2×#261)⋊C4—42no—
116(C2×#261)⋊C4—42no—
117C13×#95C2×C411yescharacteristic
118C13×#95C2×C411yescharacteristic
119#88071C2×C411yescharacteristic
120#88071C2×C411yescharacteristic
121#88071C2×C411yescharacteristic
122#88071C2×C411yescharacteristic
123#88071C2×C411yescharacteristic
124#88071C2×C411yescharacteristic
125#13884—131nomaximal, Sylow
126C23×D13C2411yescharacteristic
127C22×#261—22no—
128C22×#261—22no—
129C22×#261—22no—
130C22×#261—22no—
131C22×#261—22no—
132C22×#261—22no—
133C22×#261—22no—
134C22×#261—22no—
135C22×#261—22no—
136C22×#261—22no—
137C22×#261—22no—
138C22×#261—22no—
139C22×#261—22no—
140C22×#261—22no—
141C22×#261—22no—
142C22×#261—22no—
143C22×#261—22no—
144C22×#261—22no—
145C22×#261—22no—
146C22×#261—22no—
147C22×#261—22no—
148C22×#261—22no—
149C22×#261—22no—
150C22×#261—22no—
151C22×#261—22no—
152C22×#261—22no—
153C22×#261C2×D414yes—
154C22×#261C2×Q814yes—
155C22×C4×C13C22×C411yescharacteristic
156C22×C4×C13C22×C411yescharacteristic
157C22×C4×C13C22×C411yescharacteristic
158C22×C4×C13C22×C411yescharacteristic
159C22×C4×C13C22×C411yescharacteristic
160C22×C4×C13C22×C411yescharacteristic
161C22×C4×C13C22×C411yescharacteristic
162C22×Dic13C22×C411yescharacteristic
163C22×Dic13C22×C411yescharacteristic
164C22×Dic13C22×C411yescharacteristic
165C22×Dic13C22×C411yescharacteristic
166C22×Dic13C22×C411yescharacteristic
167C22×Dic13C22×C411yescharacteristic
168C22×Dic13C22×C411yescharacteristic
169C2×C4×D13—21no—
170C2×C4×D13—21no—
171C2×C4×D13—21no—
172C2×C4×D13—21no—
173C2×C4×D13—21no—
174C2×C4×D13—21no—
175C2×C4×D13—21no—
176C2×C4×D13—21no—
177C2×C4×D13—21no—
178C2×C4×D13—21no—
179C2×C4×D13—21no—
180C2×C4×D13—21no—
181C2×C4×D13—21no—
182C2×C4×D13—21no—
183C2×C4×D13—21no—
184C2×C4×D13—21no—
185C2×C4×D13—21no—
186C2×C4×D13—21no—
187C2×C4×D13—21no—
188C2×C4×D13—21no—
189C2×C4×D13—21no—
190C2×C4×D13—21no—
191C2×C4×D13—21no—
192C2×C4×D13—21no—
193C2×C4×D13—21no—
194C2×C4×D13—21no—
195C2×C4×D13—21no—
196C2×C4×D13—21no—
197C2×C4×D13C2×D412yes—
198C2×C4×D13C2×D412yes—
199C2×C4×D13C2×D412yes—
200C2×C4×D13C2×D412yes—
201C2×C4×D13C2×Q812yes—
202C2×C4×D13C2×Q812yes—
203C2×C4×D13C2×Q812yes—
204C2×C4×D13C2×Q812yes—
205C2×C4×D13#4112yes—
206C2×C4×D13#4112yes—
207C2×C4×D13#4112yes—
208C2×C4×D13#4112yes—
209C2×C4×D13#4112yes—
210C2×C4×D13#4112yes—
211C4⋊#261—28no—
212C4⋊#261—28no—
213C4⋊#261—48no—
214C4⋊#261—48no—
215C4⋊#261—44no—
216C4⋊#261—44no—
217C4×#261—48no—
218C13×C4⋊C4—22no—
219C13×C4⋊C4C4⋊C414yescomplemented
220C42×C13—22no—
221C42×C13—22no—
222C42×C13—22no—
223C4⋊Dic13—22no—
224C4⋊Dic13C4⋊C414yescomplemented
225#6101—22no—
226#6101—22no—
227#6101C4⋊C414yescomplemented
228#6101C4⋊C414yescomplemented
229C4×Dic13—22no—
230C4×Dic13—22no—
231C4×Dic13—22no—
232C4×Dic13—22no—
233C4×Dic13—22no—
234C4×Dic13—22no—
235C4×Dic13—22no—
236C4×Dic13—22no—
237C4×Dic13—22no—
238C2×#387—132no—
239C2×#384—131no—
240C2×C4×C4⋊C4—131no—
241C2×C4×C4⋊C4—131no—
242#1442—132no—
243#1441—132no—
244#1436—132no—
245C4⋊#95—131no—
246C4⋊#95—131no—
247C4⋊#95—131no—
248C4⋊#95—131no—
249C23×C13C23×C411yescharacteristic
250C22×D13C22×D411yescharacteristic
251C22×D13C22×D411yescharacteristic
252C22×D13C22×Q811yescharacteristic
253C22×D13C22×Q811yescharacteristic
254C22×D13C2×#4111yescharacteristic
255C22×D13C2×#4111yescharacteristic
256C22×D13C2×#4111yescharacteristic
257C22×D13C2×#4111yescharacteristic
258C22×D13C2×#4111yescharacteristic
259C22×D13C2×#4111yescharacteristic
260C22×D13H(5,𝔽2)11yescharacteristic
261C22×D13H(5,𝔽2)11yescharacteristic
262C22×D132−1+411yescharacteristic
263C22×D132−1+411yescharacteristic
264C2×#261—24no—
265C2×#261—24no—
266C2×#261—24no—
267C2×#261—24no—
268C2×#261—24no—
269C2×#261—24no—
270C2×#261—42no—
271C2×#261—42no—
272C2×#261—42no—
273C2×#261—42no—
274C2×#261—42no—
275C2×#261—42no—
276C2×#261—42no—
277C2×#261—42no—
278C2×#261—42no—
279C2×#261—42no—
280C2×#261—42no—
281C2×#261—42no—
282C2×#261—42no—
283C2×#261—42no—
284C2×#261—42no—
285C2×#261—42no—
286C2×#261—42no—
287C2×#261—42no—
288C2×#261—42no—
289C2×#261—42no—
290C2×#261—42no—
291C2×#261—42no—
292C2×C4×C13—21no—
293C2×C4×C13—21no—
294C2×C4×C13—21no—
295C2×C4×C13—21no—
296C2×C4×C13—21no—
297C2×C4×C13—21no—
298C2×C4×C13—21no—
299C2×C4×C13—21no—
300C2×C4×C13—21no—
301C2×C4×C13—21no—
302C2×C4×C13—21no—
303C2×C4×C13—21no—
304C2×C4×C13—21no—
305C2×C4×C13—21no—
306C2×C4×C13C2×C4⋊C412yes—
307C2×C4×C13C2×C4⋊C412yes—
308C2×C4×C13C2×C4⋊C412yes—
309C2×C4×C13#11712yes—
310C2×C4×C13#11712yes—
311C2×C4×C13C4×D412yes—
312C2×C4×C13C4×Q812yes—
313C2×Dic13—21no—
314C2×Dic13—21no—
315C2×Dic13—21no—
316C2×Dic13—21no—
317C2×Dic13—21no—
318C2×Dic13—21no—
319C2×Dic13—21no—
320C2×Dic13—21no—
321C2×Dic13—21no—
322C2×Dic13—21no—
323C2×Dic13—21no—
324C2×Dic13—21no—
325C2×Dic13—21no—
326C2×Dic13—21no—
327C2×Dic13C2×C4⋊C412yes—
328C2×Dic13C2×C4⋊C412yes—
329C2×Dic13C2×C4⋊C412yes—
330C2×Dic13#11712yes—
331C2×Dic13#11712yes—
332C2×Dic13C4×D412yes—
333C2×Dic13C4×Q812yes—
334C4×D13—22no—
335C4×D13—22no—
336C4×D13—22no—
337C4×D13—22no—
338C4×D13—22no—
339C4×D13—22no—
340C4×D13—22no—
341C4×D13—22no—
342C4×D13—22no—
343C4×D13—22no—
344C4×D13—22no—
345C4×D13—22no—
346C4×D13—22no—
347C4×D13—22no—
348C4×D13—22no—
349C4×D13—22no—
350C4×D13—41no—
351C4×D13—41no—
352C4×D13—41no—
353C4×D13—41no—
354C4×D13—41no—
355C4×D13—41no—
356C4×D13—41no—
357C4×D13—41no—
358C4×D13C22⋊Q814yes—
359C4×D13#12314yes—
360C4×D13#12514yes—
361C4×D13#12614yes—
362C22×C4⋊C4—131no—
363C22×C4⋊C4—131no—
364C22×C4⋊C4—131no—
365C22×C4⋊C4—131no—
366C22×C4⋊C4—131no—
367C22×C4⋊C4—131no—
368C22×C4⋊C4—132no—
369C22×C4⋊C4—132no—
370C22×C42—131no—
371C22×C42—131no—
372C22×C42—131no—
373C22×C42—132no—
374#387—268no—
375#384—264no—
376C4×C4⋊C4—131no—
377C4×C4⋊C4—131no—
378C4×C4⋊C4—131no—
379C4×C4⋊C4—131no—
380C4×C4⋊C4—131no—
381C4×C4⋊C4—131no—
382C4×C4⋊C4—131no—
383C4×C4⋊C4—264no—
384C4×C4⋊C4#26111yescharacteristic, complemented
385C2×#95—131no—
386C2×#95—131no—
387C2×#95—132no—
388C2×#95—132no—
389C2×#95—132no—
390C2×#95—132no—
391C2×#95—132no—
392C2×#95—132no—
393C2×#95—132no—
394C2×#95—132no—
395C2×#95—132no—
396C22×C13C22×C4⋊C411yescharacteristic
397C22×C13C2×#11711yescharacteristic
398C22×C13C2×#11711yescharacteristic
399C22×C13C2×C4×D411yescharacteristic
400C22×C13C2×C4×Q811yescharacteristic
401C22×C13#52011yescharacteristic
402C22×C13#52011yescharacteristic
403C2×D13C2×C22⋊Q811yescharacteristic
404C2×D13C2×#12311yescharacteristic
405C2×D13C2×#12511yescharacteristic
406C2×D13C2×#12611yescharacteristic
407C2×D13#53211yescharacteristic
408C2×D13#53211yescharacteristic
409C2×D13#53311yescharacteristic
410C2×D13#53311yescharacteristic
411C2×D13#54011yescharacteristic
412C2×D13#54111yescharacteristic
413C2×D13#54211yescharacteristic
414C2×D13#54211yescharacteristic
415C2×D13D4211yescharacteristic
416C2×D13#54611yescharacteristic
417C2×D13#54711yescharacteristic
418C2×D13#54811yescharacteristic
419C2×D13D4×Q811yescharacteristic
420C2×D13D4×Q811yescharacteristic
421C2×D13#55011yescharacteristic
422C2×D13#55211yescharacteristic
423C2×D13#55311yescharacteristic
424C2×D13#55411yescharacteristic
425C2×D13#55411yescharacteristic
426C2×D13#55611yescharacteristic
427C2×D13#55711yescharacteristic
428C2×D13#55711yescharacteristic
429C2×D13Q8211yescharacteristic
430C2×D13#55911yescharacteristic
431#261—44no—
432#261—44no—
433#261—82no—
434#261—82no—
435C4×C13—22no—
436C4×C13—22no—
437C4×C13—22no—
438C4×C13—22no—
439C4×C13—41no—
440C4×C13—41no—
441C4×C13#38714yescomplemented
442Dic13—22no—
443Dic13—22no—
444Dic13—22no—
445Dic13—22no—
446Dic13—41no—
447Dic13—41no—
448Dic13#38714yescomplemented
449C23×C4—131no—
450C23×C4—131no—
451C23×C4—131no—
452C23×C4—131no—
453C23×C4—131no—
454C23×C4—132no—
455C23×C4—132no—
456C23×C4—131no—
457C23×C4—131no—
458C23×C4—132no—
459C23×C4—132no—
460C2×C4⋊C4—131no—
461C2×C4⋊C4—131no—
462C2×C4⋊C4—131no—
463C2×C4⋊C4—134no—
464C2×C4⋊C4—134no—
465C2×C4⋊C4—134no—
466C2×C4⋊C4—134no—
467C2×C4⋊C4—131no—
468C2×C4⋊C4—131no—
469C2×C4⋊C4—131no—
470C2×C4⋊C4—262no—
471C2×C4⋊C4—262no—
472C2×C4⋊C4—262no—
473C2×C4⋊C4—262no—
474C2×C4⋊C4—262no—
475C2×C4⋊C4—262no—
476C2×C4⋊C4—262no—
477C2×C4⋊C4—264no—
478C2×C4⋊C4—264no—
479C2×C4⋊C4—264no—
480C2×C4⋊C4—262no—
481C2×C4⋊C4—262no—
482C2×C4⋊C4—262no—
483C2×C4⋊C4—262no—
484C2×C4⋊C4—262no—
485C2×C4⋊C4—264no—
486C2×C4⋊C4—522no—
487C2×C4⋊C4—522no—
488C2×C4⋊C4C2×#26111yescharacteristic
489C2×C4⋊C4C2×#26111yescharacteristic
490C2×C42—131no—
491C2×C42—131no—
492C2×C42—131no—
493C2×C42—131no—
494C2×C42—131no—
495C2×C42—131no—
496C2×C42—131no—
497C2×C42—131no—
498C2×C42—131no—
499C2×C42—262no—
500C2×C42—262no—
501C2×C42—262no—
502C2×C42—262no—
503C2×C42—262no—
504C2×C42—262no—
505C2×C42—264no—
506C2×C42—264no—
507C2×C42—522no—
508C2×C42C2×#26111yescharacteristic
509C2×C42C2×#26111yescharacteristic
510C2×C42C2×#26111yescharacteristic
511#95—131no—
512#95—131no—
513#95—131no—
514#95—131no—
515#95—131no—
516#95—131no—
517#95—264no—
518#95—264no—
519#95—264no—
520#95—264no—
521#95—264no—
522#95—264no—
523#95—522no—
524#95—522no—
525#95—522no—
526#95C2×#26111yescharacteristic
527#95C2×#26111yescharacteristic
528C2×C13#228511yescharacteristic
529C2×C13C2×#38711yescharacteristic
530C2×C13#231411yescharacteristic
531C2×C13D4×C4⋊C411yescharacteristic
532C2×C13Q8×C4⋊C411yescharacteristic
533C2×C13#235211yescharacteristic
534C2×C13#235511yescharacteristic
535D13#244511yescharacteristic
536D13#244611yescharacteristic
537D13#245111yescharacteristic
538D13#245211yescharacteristic
539D13#250611yescharacteristic
540D13#250711yescharacteristic
541D13#251111yescharacteristic
542D13#251211yescharacteristic
543C24—131no—
544C22×C4—131no—
545C22×C4—132no—
546C22×C4—132no—
547C22×C4—132no—
548C22×C4—132no—
549C22×C4—132no—
550C22×C4—132no—
551C22×C4—131no—
552C22×C4—131no—
553C22×C4—131no—
554C22×C4—131no—
555C22×C4—132no—
556C22×C4—132no—
557C22×C4—132no—
558C22×C4—132no—
559C22×C4—132no—
560C22×C4—132no—
561C22×C4—132no—
562C22×C4—132no—
563C22×C4—134no—
564C22×C4—134no—
565C22×C4—131no—
566C22×C4—131no—
567C22×C4—261no—
568C22×C4—261no—
569C22×C4—261no—
570C22×C4—261no—
571C22×C4—261no—
572C22×C4—261no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—261no—
581C22×C4—261no—
582C22×C4—261no—
583C22×C4—261no—
584C22×C4—261no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—261no—
592C22×C4—261no—
593C22×C4—261no—
594C22×C4—261no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—262no—
600C22×C4—262no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—262no—
606C22×C4—262no—
607C22×C4—262no—
608C22×C4—262no—
609C22×C4—262no—
610C22×C4—262no—
611C22×C4—262no—
612C22×C4—262no—
613C22×C4—262no—
614C22×C4—262no—
615C22×C4—262no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4—262no—
620C22×C4—262no—
621C22×C4C22×#26111yescharacteristic
622C22×C4C22×#26111yescharacteristic
623C22×C4C22×#26111yescharacteristic
624C22×C4C22×#26111yescharacteristic
625C22×C4C22×#26111yescharacteristic
626C22×C4C22×#26111yescharacteristic
627C22×C4C22×#26111yescharacteristic
628C4⋊C4—22no—
629C4⋊C4—134no—
630C4⋊C4—134no—
631C4⋊C4—134no—
632C4⋊C4—262no—
633C4⋊C4—262no—
634C4⋊C4—268no—
635C4⋊C4—268no—
636C4⋊C4—262no—
637C4⋊C4—524no—
638C4⋊C4—524no—
639C4⋊C4—528no—
640C4⋊C4—528no—
641C4⋊C4C4⋊#26114yescomplemented
642C42—22no—
643C42—22no—
644C42—22no—
645C42—262no—
646C42—262no—
647C42—262no—
648C42—262no—
649C42—262no—
650C42—262no—
651C42—262no—
652C42—262no—
653C42—262no—
654C42—528no—
655C13#1388411yescharacteristic, complemented, Sylow
656C23—131no—
657C23—131no—
658C23—131no—
659C23—131no—
660C23—131no—
661C23—131no—
662C23—131no—
663C23—131no—
664C23—131no—
665C23—131no—
666C23—131no—
667C23—131no—
668C23—131no—
669C23—131no—
670C23C23×#26111yescharacteristic
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—132no—
686C2×C4—132no—
687C2×C4—132no—
688C2×C4—134no—
689C2×C4—134no—
690C2×C4—134no—
691C2×C4—134no—
692C2×C4—132no—
693C2×C4—132no—
694C2×C4—132no—
695C2×C4—132no—
696C2×C4—262no—
697C2×C4—262no—
698C2×C4—262no—
699C2×C4—262no—
700C2×C4—262no—
701C2×C4—262no—
702C2×C4—262no—
703C2×C4—262no—
704C2×C4—262no—
705C2×C4—262no—
706C2×C4—262no—
707C2×C4—262no—
708C2×C4—262no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—262no—
712C2×C4—261no—
713C2×C4—261no—
714C2×C4—261no—
715C2×C4—261no—
716C2×C4—261no—
717C2×C4—261no—
718C2×C4—261no—
719C2×C4—261no—
720C2×C4—264no—
721C2×C4—264no—
722C2×C4—264no—
723C2×C4—264no—
724C2×C4—264no—
725C2×C4—264no—
726C2×C4—261no—
727C2×C4—261no—
728C2×C4—261no—
729C2×C4—261no—
730C2×C4—261no—
731C2×C4—261no—
732C2×C4—521no—
733C2×C4—521no—
734C2×C4—521no—
735C2×C4—521no—
736C2×C4—521no—
737C2×C4—521no—
738C2×C4—521no—
739C2×C4—521no—
740C2×C4—522no—
741C2×C4—522no—
742C2×C4—522no—
743C2×C4—522no—
744C2×C4—522no—
745C2×C4—522no—
746C2×C4—522no—
747C2×C4—522no—
748C2×C4—522no—
749C2×C4—522no—
750C2×C4—522no—
751C2×C4—522no—
752C2×C4—522no—
753C2×C4—522no—
754C2×C4—522no—
755C2×C4—522no—
756C2×C4—522no—
757C2×C4—522no—
758C2×C4—522no—
759C2×C4—522no—
760C2×C4—522no—
761C2×C4—522no—
762C2×C4C2×C4⋊#26112yes—
763C2×C4C2×C4⋊#26112yes—
764C2×C4C2×C4⋊#26112yes—
765C2×C4#8823712yes—
766C2×C4#8823712yes—
767C2×C4D4×#26112yes—
768C2×C4Q8×#26112yes—
769C22—131no—
770C22—131no—
771C22—131no—
772C22—131no—
773C22—131no—
774C22—131no—
775C22—131no—
776C22—131no—
777C22—131no—
778C22—131no—
779C22—131no—
780C22—131no—
781C22—131no—
782C22—131no—
783C22—131no—
784C22—131no—
785C22—131no—
786C22—131no—
787C22—131no—
788C22—131no—
789C22—131no—
790C22—131no—
791C22—131no—
792C22—131no—
793C22—131no—
794C22—131no—
795C22—131no—
796C22—131no—
797C22C22×C4⋊#26111yescharacteristic
798C22C2×#8823711yescharacteristic
799C22C2×#8823711yescharacteristic
800C22C2×D4×#26111yescharacteristic
801C22C2×Q8×#26111yescharacteristic
802C22#1171963111yescharacteristic
803C22#1171963111yescharacteristic
804C4—22no—
805C4—22no—
806C4—22no—
807C4—22no—
808C4—41no—
809C4—41no—
810C4—134no—
811C4—262no—
812C4—262no—
813C4—262no—
814C4—262no—
815C4—524no—
816C4—524no—
817C4—521no—
818C4—521no—
819C4—1042no—
820C4—1042no—
821C4#1171908214yescomplemented
822C2—131no—
823C2—131no—
824C2—131no—
825C2—131no—
826C2—131no—
827C2—131no—
828C2—131no—
829C2—131no—
830C2#1313128511yescharacteristic
831C2C2×#1171908211yescharacteristic
832C2#1313131411yescharacteristic
833C2D4×C4⋊#26111yescharacteristic
834C2Q8×C4⋊#26111yescharacteristic
835C2#1313135211yescharacteristic
836C2#1313135511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutator, socleC23×C13C23×C4
FittingC4×C13×C4⋊C4C4
prime radical, cosocleC23×D13C24
hypercenterC4×C4⋊C4#261
hypocenterC13#13884
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
36. C4×C13×C4⋊C4C4semidirect
37. C4⋊C4×Dic13C4semidirect
38. C4⋊C4×Dic13C4semidirect
39. C4×C4⋊Dic13C4semidirect
40. C4×#6101C4semidirect
41. C4×#6101C4semidirect
44. #11718310C4semidirect
45. #11718310C4semidirect
219. C13×C4⋊C4C4⋊C4semidirect
224. C4⋊Dic13C4⋊C4semidirect
227. #6101C4⋊C4semidirect
228. #6101C4⋊C4semidirect
384. C4×C4⋊C4#261semidirect
441. C4×C13#387semidirect
448. Dic13#387semidirect
641. C4⋊C4C4⋊#261semidirect
655. C13#13884semidirect
821. C4#11719082semidirect

Maximal subgroups

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

subgroupindex
C2×#117190822
C2×#117190592
C2×C4×C4⋊#2612
#131300222
#131300212
#131300162
#131300142
C4×C4⋊C4×D132
#1388413