Finite Group Databasebeta

← #15875256

Subgroups — #15875256

Order 3328.

1010 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718386C211yesmaximal, characteristic, complemented
2C2×#11718379C211yesmaximal, characteristic, complemented
3C4×#88193C211yesmaximal, characteristic
4#13115628C211yesmaximal, characteristic, complemented
5#13115628C211yesmaximal, characteristic, complemented
6#13115551C211yesmaximal, characteristic, complemented
7#13115445C211yesmaximal, characteristic, complemented
8#13115442C211yesmaximal, characteristic, complemented
9#13115129C211yesmaximal, characteristic, complemented
10#13115125C211yesmaximal, characteristic, complemented
11#13115013C211yesmaximal, characteristic, complemented
12#13115012C211yesmaximal, characteristic, complemented
13#13114814C211yesmaximal, characteristic, complemented
14C8×#6101C211yesmaximal, characteristic, complemented
15C13×#1954C211yesmaximal, characteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17C2×#88193C411yescharacteristic
18C2×C4×C22⋊D13C2211yescharacteristic
19C2×C4×C22⋊D13C2211yescharacteristic
20C22×C4×Dic13C2211yescharacteristic
21C23×#1055C2211yescharacteristic
22C22×C8×D13C2211yescharacteristic
23C2×C13×C4⋊C8C2211yescharacteristic
24C2×C13×C22⋊C8C2211yescharacteristic
25C2×C13×C22⋊C8C2211yescharacteristic
26C2×C13×C22⋊C8C2211yescharacteristic
27C2×C13×C22⋊C8C2211yescharacteristic
28C2×C4×C8×C13C2211yescharacteristic
29#11718881C411yescharacteristic
30C4×C22⋊Dic13C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34C2×#88060C2211yescharacteristic
35C2×#88060C2211yescharacteristic
36C2×#88060C2211yescharacteristic
37C2×#88054C2211yescharacteristic
38C2×#88054C2211yescharacteristic
39C2×#88054C2211yescharacteristic
40C2×#88054C2211yescharacteristic
41C2×#88054C2211yescharacteristic
42C2×C8×Dic13C2211yescharacteristic
43C2×C8×Dic13C2211yescharacteristic
44C2×C8×Dic13C2211yescharacteristic
45#11718651C411yescharacteristic
46#11718633C411yescharacteristic
47#11718619C411yescharacteristic
48#11718618C411yescharacteristic
49#11718606C411yescharacteristic
50#11718603C411yescharacteristic
51C4×#6103C2211yescharacteristic
52C4×#6101C2211yescharacteristic
53#11718386—24no—
54#11718379—24no—
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×D4×C13C2×C411yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C22×C22⋊D13C2×C411yescharacteristic
65C22×C22⋊D13C2×C411yescharacteristic
66C23×Dic13C2×C411yescharacteristic
67C23×Dic13C2×C411yescharacteristic
68C22×C4×D13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C4×D4×C13—41no—
74C4×D4×C13—41no—
75C2×C13×C4⋊C4C2×C411yescharacteristic
76C2×C13×C22⋊C4C2×C411yescharacteristic
77C2×C13×C22⋊C4C2×C411yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×C22⋊Dic13C2×C411yescharacteristic
80C2×C22⋊Dic13C2×C411yescharacteristic
81C2×C22⋊Dic13C2×C411yescharacteristic
82C2×C22⋊Dic13C2×C411yescharacteristic
83#88193C818yescomplemented
84C4×C22⋊D13—22no—
85C4×C22⋊D13—22no—
86C4×C22⋊D13—41no—
87C4×C22⋊D13—41no—
88C2×#6103C2×C411yescharacteristic
89C2×#6103C2×C411yescharacteristic
90C2×#6103C2×C411yescharacteristic
91C2×#6103C2×C411yescharacteristic
92C2×#6101C2×C411yescharacteristic
93C2×#6101C2×C411yescharacteristic
94C2×#6101C2×C411yescharacteristic
95C2×#6101C2×C411yescharacteristic
96C2×C4×Dic13—22no—
97C2×C4×Dic13—22no—
98C2×C4×Dic13C2×C411yescharacteristic
99C2×C4×Dic13C2×C411yescharacteristic
100C2×C4×Dic13C2311yescharacteristic
101C2×C4×Dic13C2311yescharacteristic
102C2×C4×Dic13C2311yescharacteristic
103C22×#1055—22no—
104C22×#1055—41no—
105C22×#1055—41no—
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110C2×C8×D13—22no—
111C2×C8×D13—41no—
112C2×C8×D13—41no—
113C13×C4⋊C8—41no—
114C13×C22⋊C8—22no—
115C13×C22⋊C8—22no—
116C13×C22⋊C8—41no—
117C13×C22⋊C8—41no—
118C4×C8×C13—41no—
119#88071C2×C411yescharacteristic
120#88071C2×C411yescharacteristic
121#88071C2×C411yescharacteristic
122#88071C2×C411yescharacteristic
123#88071C2×C411yescharacteristic
124#88071C2×C411yescharacteristic
125C22⋊#1055—22no—
126C22⋊#1055—41no—
127C22⋊#1055—41no—
128#88060—22no—
129#88060—41no—
130#88060—41no—
131#88054—22no—
132#88054—22no—
133#88054—22no—
134#88054—22no—
135#88054—41no—
136C8×Dic13—22no—
137C8×Dic13—41no—
138C8×Dic13D414yescomplemented
139#22133—131nomaximal, Sylow
140C24×C13C22×C411yescharacteristic
141C24×C13C22×C411yescharacteristic
142C23×D13C22×C411yescharacteristic
143C2×D4×C13—41no—
144C2×D4×C13—41no—
145C2×D4×C13C2×C814yescomplemented
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13C22×C411yescharacteristic
159C22×C4×C13C22×C411yescharacteristic
160C22×C4×C13C22×C411yescharacteristic
161C22×C4×C13C22×C411yescharacteristic
162C22×C4×C13C2411yescharacteristic
163C2×C22⋊D13—22no—
164C2×C22⋊D13—22no—
165C2×C22⋊D13—41no—
166C2×C22⋊D13—41no—
167C2×C22⋊D13C2×C814yes—
168C2×C22⋊D13C2×C814yescomplemented
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13—41no—
173C22×Dic13—41no—
174C22×Dic13C2×C814yescomplemented
175C22×Dic13C22×C411yescharacteristic
176C22×Dic13C22×C411yescharacteristic
177C22×Dic13C22×C411yescharacteristic
178C22×Dic13C22×C411yescharacteristic
179C22×Dic13C22×C411yescharacteristic
180C22×Dic13C22×C411yescharacteristic
181C22×Dic13C22×C411yescharacteristic
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×C8×C13—21no—
189C2×C8×C13—21no—
190C2×C8×C13—21no—
191C2×C8×C13—21no—
192C2×C8×C13—21no—
193C2×C8×C13—21no—
194C2×C8×C13—21no—
195C2×C8×C13—21no—
196C2×C8×C13—21no—
197C2×C8×C13—21no—
198C2×C8×C13—21no—
199C2×C8×C13C2×D412yes—
200C13×C4⋊C4—41no—
201C13×C22⋊C4—41no—
202C13×C22⋊C4—41no—
203C42×C13—21no—
204C42×C13—21no—
205C22⋊Dic13—22no—
206C22⋊Dic13—41no—
207C22⋊Dic13—41no—
208C22⋊Dic13C2×C814yescomplemented
209#6103—22no—
210#6103—41no—
211#6103—41no—
212#6103C2×C814yescomplemented
213#6101—22no—
214#6101—22no—
215#6101—41no—
216#6101C2×C814yescomplemented
217C4×Dic13—21no—
218C4×Dic13—21no—
219C4×Dic13—21no—
220C4×Dic13—21no—
221C4×Dic13—22no—
222C4×Dic13—22no—
223C4×Dic13C2×D412yes—
224C4×Dic13#4112yes—
225C2×#1055—21no—
226C2×#1055—21no—
227C2×#1055—21no—
228C2×#1055—21no—
229C2×#1055—21no—
230C2×#1055—21no—
231C2×#1055—21no—
232C2×#1055—21no—
233C2×#1055—21no—
234C2×#1055—21no—
235C2×#1055—21no—
236C2×#1055—44no—
237C2×#1055C2×D412yes—
238C8×D13—44no—
239C2×C8×D4—131no—
240C2×#431—131no—
241C4×#121—131no—
242#1954—131no—
243#1954—131no—
244#1954D1311yescharacteristic, complemented
245#1939—131no—
246#1923—131no—
247#1923—131no—
248#1869—131no—
249#1869—131no—
250#1850—131no—
251#1850—131no—
252#1797—131no—
253C8×C4⋊C4—131no—
254C23×C13—21no—
255C23×C13—21no—
256C23×C13—21no—
257C23×C13—21no—
258C23×C13—21no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—21no—
266C23×C13C22×C812yes—
267C23×C13C22×C812yes—
268C23×C13C23×C411yescharacteristic
269C22×D13—21no—
270C22×D13—21no—
271C22×D13—21no—
272C22×D13—21no—
273C22×D13—21no—
274C22×D13—21no—
275C22×D13C22×C812yes—
276D4×C13—44no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—21no—
284C2×C4×C13—21no—
285C2×C4×C13—21no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13—41no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13C22×C812yes—
297C2×C4×C13C22×D411yescharacteristic
298C2×C4×C13C2×#4111yescharacteristic
299C2×C4×C13H(5,𝔽2)11yescharacteristic
300C2×C4×C13H(5,𝔽2)11yescharacteristic
301C2×C4×C13H(5,𝔽2)11yescharacteristic
302C2×C4×C132−1+411yescharacteristic
303C22⋊D13—28no—
304C22⋊D13—44no—
305C2×Dic13—21no—
306C2×Dic13—21no—
307C2×Dic13—21no—
308C2×Dic13—21no—
309C2×Dic13—21no—
310C2×Dic13—21no—
311C2×Dic13—28no—
312C2×Dic13—21no—
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—44no—
322C2×Dic13C4×D412yes—
323C2×Dic13C4×D412yes—
324C2×Dic13C22×C812yes—
325C2×Dic13C22×C812yes—
326C2×Dic13C22×C812yes—
327C2×Dic13#13112yes—
328C4×D13—41no—
329C4×D13—41no—
330C4×D13—41no—
331C4×D13—41no—
332C8×C13—22no—
333C8×C13—41no—
334C8×C13—41no—
335C8×C13—41no—
336#1055—22no—
337#1055—41no—
338#1055—41no—
339#1055—41no—
340C23×C8—131no—
341C23×C8—131no—
342C2×#121—131no—
343C2×C4×D4—131no—
344C2×C4×D4—131no—
345C2×C4×D4C2×D1311yescharacteristic
346C22×C42—131no—
347C8×D4—264no—
348#431—264no—
349C2×C4⋊C8—131no—
350C2×C4⋊C8—131no—
351C2×C4⋊C8—131no—
352C2×C4⋊C8—131no—
353C2×C4⋊C8—131no—
354C2×C4⋊C8C2×D1311yescharacteristic
355C2×C22⋊C8—131no—
356C2×C22⋊C8—131no—
357C2×C22⋊C8—131no—
358C2×C22⋊C8—131no—
359C2×C22⋊C8—131no—
360C2×C22⋊C8—131no—
361C2×C22⋊C8C2×D1311yescharacteristic
362C2×C22⋊C8C2×D1311yescharacteristic
363C2×C22⋊C8C2×D1311yescharacteristic
364C2×C22⋊C8C2×D1311yescharacteristic
365C2×C4×C8—131no—
366C2×C4×C8—131no—
367C2×C4×C8—131no—
368C2×C4×C8C2×D1311yescharacteristic
369#390—131no—
370#389—131no—
371#388—131no—
372#388—131no—
373#386—131no—
374#386—131no—
375#380—131no—
376C4×C4⋊C4—131no—
377C4×C22⋊C4—131no—
378C4×C22⋊C4—131no—
379#336—131no—
380#336—131no—
381#336—131no—
382#336—131no—
383#336—131no—
384#336—131no—
385C22×C13—22no—
386C22×C13—22no—
387C22×C13—22no—
388C22×C13—22no—
389C22×C13—22no—
390C22×C13—22no—
391C22×C13—41no—
392C22×C13—41no—
393C22×C13—41no—
394C22×C13—41no—
395C22×C13—41no—
396C22×C13—41no—
397C22×C13—41no—
398C22×C13—41no—
399C22×C13C2×C4×D411yescharacteristic
400C22×C13#51811yescharacteristic
401C22×C13#52011yescharacteristic
402C22×C13C23×C811yescharacteristic
403C22×C13C2×#13111yescharacteristic
404C22×C13#56811yescharacteristic
405C22×C13#56811yescharacteristic
406C2×D13—22no—
407C2×D13—22no—
408C2×D13—22no—
409C2×D13—41no—
410C2×D13—41no—
411C2×D13—41no—
412C2×D13—41no—
413C4×C13—22no—
414C4×C13—41no—
415C4×C13—41no—
416C4×C13—41no—
417C4×C13#53511yescharacteristic
418C4×C13#53711yescharacteristic
419C4×C13#54011yescharacteristic
420C4×C13#54211yescharacteristic
421Dic13—22no—
422Dic13—22no—
423Dic13—22no—
424Dic13—41no—
425Dic13—41no—
426Dic13—41no—
427Dic13C8×D414yes—
428C22×D4—131no—
429C22×D4—131no—
430C22×D4C4×D1311yescharacteristic
431C23×C4—131no—
432C23×C4—131no—
433C23×C4—131no—
434C23×C4C22×D1311yescharacteristic
435C23×C4C22×D1311yescharacteristic
436C22×C8—131no—
437C22×C8—131no—
438C22×C8—131no—
439C22×C8—131no—
440C22×C8—262no—
441C22×C8—262no—
442C22×C8—521no—
443C22×C8—521no—
444C22×C8—521no—
445C22×C8—521no—
446C22×C8C22×D1311yescharacteristic
447C22×C8C22×D1311yescharacteristic
448C22×C8C22×D1311yescharacteristic
449C22×C8C22×D1311yescharacteristic
450#121—138no—
451C4×D4—41no—
452C4×D4—41no—
453C4×D4—262no—
454C4×D4—262no—
455C4×D4—521no—
456C4×D4—521no—
457C2×C4⋊C4—131no—
458C2×C4⋊C4—131no—
459C2×C4⋊C4—131no—
460C2×C4⋊C4—131no—
461C2×C4⋊C4C4×D1311yescharacteristic
462C2×C22⋊C4—131no—
463C2×C22⋊C4—131no—
464C2×C22⋊C4—131no—
465C2×C22⋊C4—131no—
466C2×C22⋊C4—131no—
467C2×C22⋊C4—131no—
468C2×C22⋊C4—131no—
469C2×C22⋊C4—131no—
470C2×C22⋊C4C4×D1311yescharacteristic
471C2×C22⋊C4C4×D1311yescharacteristic
472C2×C42—131no—
473C2×C42—131no—
474C2×C42—131no—
475C2×C42—131no—
476C2×C42—131no—
477C2×C42—262no—
478C2×C42—262no—
479C2×C42C22×D1311yescharacteristic
480C4⋊C8—41no—
481C4⋊C8—262no—
482C4⋊C8—262no—
483C4⋊C8—262no—
484C4⋊C8—262no—
485C4⋊C8—521no—
486C22⋊C8—22no—
487C22⋊C8—22no—
488C22⋊C8—41no—
489C22⋊C8—41no—
490C22⋊C8—262no—
491C22⋊C8—262no—
492C22⋊C8—521no—
493C22⋊C8—521no—
494C22⋊C8—521no—
495C22⋊C8—521no—
496C4×C8—41no—
497C4×C8—134no—
498C4×C8—262no—
499C4×C8—521no—
500#95—131no—
501#95—131no—
502#95—131no—
503#95—131no—
504#95—131no—
505#95—131no—
506C2×C13—42no—
507C2×C13—42no—
508C2×C13#232411yescharacteristic
509C2×C13C2×C8×D411yescharacteristic
510C2×C13#293011yescharacteristic
511C2×C13#297211yescharacteristic
512C2×C13#298111yescharacteristic
513C2×C13#298811yescharacteristic
514C2×C13#299311yescharacteristic
515D13—42no—
516C24—131no—
517C24C2×C4×D1311yescharacteristic
518C24C2×C4×D1311yescharacteristic
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—134no—
522C2×D4—134no—
523C2×D4—262no—
524C2×D4—262no—
525C2×D4—521no—
526C2×D4—521no—
527C2×D4C8×D1314yescomplemented
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—131no—
541C22×C4—134no—
542C22×C4—131no—
543C22×C4—131no—
544C22×C4—131no—
545C22×C4—131no—
546C22×C4—131no—
547C22×C4—131no—
548C22×C4—262no—
549C22×C4—262no—
550C22×C4—262no—
551C22×C4—261no—
552C22×C4—261no—
553C22×C4—261no—
554C22×C4—261no—
555C22×C4—261no—
556C22×C4—261no—
557C22×C4—521no—
558C22×C4—521no—
559C22×C4C2×C4×D1311yescharacteristic
560C22×C4C2×C4×D1311yescharacteristic
561C22×C4C2×C4×D1311yescharacteristic
562C22×C4C2×C4×D1311yescharacteristic
563C22×C4C23×D1311yescharacteristic
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—132no—
576C2×C8—261no—
577C2×C8—261no—
578C2×C8—261no—
579C2×C8—261no—
580C2×C8—261no—
581C2×C8—261no—
582C2×C8—261no—
583C2×C8—261no—
584C2×C8—261no—
585C2×C8—261no—
586C2×C8—261no—
587C2×C8—524no—
588C2×C8—524no—
589C2×C8D4×D1312yes—
590C4⋊C4—41no—
591C4⋊C4—134no—
592C4⋊C4—262no—
593C4⋊C4—262no—
594C4⋊C4—521no—
595C22⋊C4—41no—
596C22⋊C4—41no—
597C22⋊C4—134no—
598C22⋊C4—134no—
599C22⋊C4—262no—
600C22⋊C4—262no—
601C22⋊C4—521no—
602C22⋊C4—521no—
603C22⋊C4—521no—
604C22⋊C4—521no—
605C42—21no—
606C42—21no—
607C42—132no—
608C42—132no—
609C42—262no—
610C42—262no—
611C42—261no—
612C42—261no—
613C42—261no—
614C42—261no—
615C13#2213311yescharacteristic, complemented, Sylow
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—132no—
629C23—261no—
630C23—261no—
631C23—261no—
632C23—261no—
633C23—261no—
634C23—261no—
635C23C2×C8×D1312yes—
636C23C2×C8×D1312yes—
637C23C22×C4×D1311yescharacteristic
638D4—44no—
639D4—268no—
640D4—524no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—132no—
661C2×C4—132no—
662C2×C4—132no—
663C2×C4—132no—
664C2×C4—132no—
665C2×C4—132no—
666C2×C4—268no—
667C2×C4—261no—
668C2×C4—261no—
669C2×C4—261no—
670C2×C4—261no—
671C2×C4—261no—
672C2×C4—261no—
673C2×C4—261no—
674C2×C4—261no—
675C2×C4—261no—
676C2×C4—261no—
677C2×C4—261no—
678C2×C4—261no—
679C2×C4—261no—
680C2×C4—261no—
681C2×C4—261no—
682C2×C4—524no—
683C2×C4—521no—
684C2×C4—521no—
685C2×C4—521no—
686C2×C4—521no—
687C2×C4C2×C8×D1312yes—
688C2×C4C2×D4×D1311yescharacteristic
689C2×C4#8825111yescharacteristic
690C2×C4#8825111yescharacteristic
691C2×C4#8825111yescharacteristic
692C2×C4#41×D1311yescharacteristic
693C2×C4#8825711yescharacteristic
694C8—22no—
695C8—41no—
696C8—41no—
697C8—41no—
698C8—262no—
699C8—521no—
700C8—521no—
701C8—521no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—262no—
717C22—262no—
718C22—262no—
719C22—521no—
720C22—521no—
721C22—521no—
722C22—521no—
723C22#1171919111yescharacteristic
724C22C4×D4×D1311yescharacteristic
725C22#1171925111yescharacteristic
726C22C22×C8×D1311yescharacteristic
727C22#1171945011yescharacteristic
728C22D13×#13111yescharacteristic
729C22#1171945511yescharacteristic
730C4—22no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—134no—
735C4—262no—
736C4—262no—
737C4—262no—
738C4—521no—
739C4—521no—
740C4—521no—
741C4#1171930211yescharacteristic
742C4#1171932011yescharacteristic
743C4#1171937411yescharacteristic
744C4#1171942011yescharacteristic
745C2—42no—
746C2—42no—
747C2—522no—
748C2#1311752211yescharacteristic
749C2C8×D4×D1311yescharacteristic
750C2#1312353611yescharacteristic
751C2#1312385811yescharacteristic
752C2#1312390911yescharacteristic
753C2#1312394311yescharacteristic
754C2#1312398211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutatorC22×C13C23×C8
FittingC13×#1954C2
socleC23×C13C23×C4
prime radicalC2×#88193C4
cosocleC22×C4×C13C24
hypercenter#1954D13
hypocenterC13#22133
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1954

Complements

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

NH ≅ G/Ntype
1. C2×#11718386C2semidirect
2. C2×#11718379C2semidirect
4. #13115628C2semidirect
5. #13115628C2semidirect
6. #13115551C2semidirect
7. #13115445C2semidirect
8. #13115442C2semidirect
9. #13115129C2semidirect
10. #13115125C2semidirect
11. #13115013C2semidirect
12. #13115012C2semidirect
13. #13114814C2semidirect
14. C8×#6101C2semidirect
15. C13×#1954C2semidirect
83. #88193C8semidirect
138. C8×Dic13D4semidirect
145. C2×D4×C13C2×C8semidirect
168. C2×C22⋊D13C2×C8semidirect
174. C22×Dic13C2×C8semidirect
208. C22⋊Dic13C2×C8semidirect
212. #6103C2×C8semidirect
216. #6101C2×C8semidirect
244. #1954D13semidirect
527. C2×D4C8×D13semidirect
615. C13#22133semidirect

Maximal subgroups

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

subgroupindex
C2×#117183862
C2×#117183792
C4×#881932
#131156282
#131155512
#131154452
#131154422
#131151292
#131151252
#131150132
#131150122
#131148142
C8×#61012
C13×#19542
#2213313