Finite Group Databasebeta

← #15879452

Subgroups — #15879452

Order 3328.

1292 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D13C211yesmaximal, characteristic
2C2×#11718489C211yesmaximal, characteristic, complemented
3C2×#11718362C211yesmaximal, characteristic, complemented
4#13115777C211yesmaximal, characteristic, complemented
5#13115774C211yesmaximal, characteristic, complemented
6#13115774C211yesmaximal, characteristic, complemented
7#13115770C211yesmaximal, characteristic, complemented
8#13115770C211yesmaximal, characteristic, complemented
9#13114815C211yesmaximal, characteristic
10#13114815C211yesmaximal, characteristic
11#13114813C211yesmaximal, characteristic
12#13114599C211yesmaximal, characteristic
13#13114597C211yesmaximal, characteristic
14#13114593C211yesmaximal, characteristic
15C13×#1985C211yesmaximal, characteristic, complemented
16C22×Q8×D13C411yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×Q8×Dic13C411yescharacteristic
19C4×Q8×D13—24no—
20C4×Q8×D13—24no—
21C2×C4⋊C4×D13C411yescharacteristic
22C2×C4⋊C4×D13C411yescharacteristic
23C2×C4⋊C4×D13C411yescharacteristic
24C2×#88141C411yescharacteristic
25C2×#88141C411yescharacteristic
26C2×#88141C411yescharacteristic
27C2×C42×D13C2211yescharacteristic
28C2×C42×D13C2211yescharacteristic
29C2×C42×D13C2211yescharacteristic
30C2×C4×Dic26C2211yescharacteristic
31C2×C4×Dic26C2211yescharacteristic
32C2×C4×Dic26C2211yescharacteristic
33C2×C13×C4⋊C8C2211yescharacteristic
34C2×C13×#97C2211yescharacteristic
35C2×#88060C2211yescharacteristic
36C2×#88060C2211yescharacteristic
37C2×#88060C2211yescharacteristic
38C2×#88060C2211yescharacteristic
39C2×#88055C2211yescharacteristic
40C2×#88055C2211yescharacteristic
41C2×#88054C2211yescharacteristic
42C2×#88054C2211yescharacteristic
43C2×#88054C2211yescharacteristic
44C2×#88054C2211yescharacteristic
45C2×C8×Dic13C2211yescharacteristic
46C2×C8×Dic13C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49#11718489—24no—
50#11718362—24no—
51C13×#336C2211yescharacteristic
52C13×#336C2211yescharacteristic
53C13×#336C2211yescharacteristic
54C13×#336C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61#11718116C2211yescharacteristic
62#11718116C2211yescharacteristic
63C22×Q8×C13C2×C411yescharacteristic
64C2×Q8×D13—24no—
65C2×Q8×D13—24no—
66C2×Q8×D13—24no—
67C22×C4×D13C2×C411yescharacteristic
68C22×C4×D13C2×C411yescharacteristic
69C22×C4×D13C2×C411yescharacteristic
70C22×C4×D13C2×C411yescharacteristic
71C22×C4×D13C2×C411yescharacteristic
72C22×C4×D13C2×C411yescharacteristic
73C22×C4×D13C2311yescharacteristic
74C22×Dic26C2×C411yescharacteristic
75C22×Dic26C2×C411yescharacteristic
76C22×Dic26C2×C411yescharacteristic
77C22×C8×C13C2311yescharacteristic
78C22×C8×C13C2311yescharacteristic
79C22×C8×C13C2311yescharacteristic
80C22×C8×C13C2311yescharacteristic
81C4×Q8×C13—22no—
82C4×Q8×C13—22no—
83C2×C13×C4⋊C4C2×C411yescharacteristic
84C2×C13×C4⋊C4C2×C411yescharacteristic
85C2×C13×C4⋊C4C2×C411yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×C42×C13C2311yescharacteristic
89Q8×Dic13—24no—
90C2×C4⋊Dic13C2×C411yescharacteristic
91C2×C4⋊Dic13C2×C411yescharacteristic
92C2×C4⋊Dic13C2×C411yescharacteristic
93C2×#6101C2×C411yescharacteristic
94C2×#6101C2×C411yescharacteristic
95C2×#6101C2×C411yescharacteristic
96C2×#6101C2×C411yescharacteristic
97C2×#6101C2×C411yescharacteristic
98C2×#6101C2×C411yescharacteristic
99C2×C4×Dic13C2×C411yescharacteristic
100C2×C4×Dic13C2×C411yescharacteristic
101C2×C4×Dic13C2×C411yescharacteristic
102C2×C4×Dic13C2×C411yescharacteristic
103C2×C4×Dic13C2×C411yescharacteristic
104C2×C4×Dic13C2×C411yescharacteristic
105C2×C4×Dic13C2311yescharacteristic
106C2×C4×Dic13C2311yescharacteristic
107C2×C4×Dic13C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110C22×#1055C2311yescharacteristic
111C22×#1055C2311yescharacteristic
112C4⋊C4×D13—24no—
113C4⋊C4×D13—24no—
114C4⋊C4×D13—24no—
115#88141—24no—
116#88141—24no—
117#88141—24no—
118C42×D13—22no—
119C42×D13—22no—
120C42×D13—22no—
121C42×D13—22no—
122C42×D13—22no—
123C42×D13—22no—
124C4×Dic26—22no—
125C4×Dic26—22no—
126C4×Dic26—22no—
127C4×Dic26—22no—
128C4×Dic26D414yes—
129C4×Dic26D414yes—
130C13×C4⋊C8—22no—
131C13×#97—22no—
132#88060—22no—
133#88060—22no—
134#88060—22no—
135#88060Q814yescomplemented
136#88055—22no—
137#88055—22no—
138#88054—22no—
139#88054—22no—
140#88054—22no—
141#88054—22no—
142C8×Dic13—22no—
143C8×Dic13—22no—
144C4⋊#1055—22no—
145#88043—22no—
146#22510—131nomaximal, Sylow
147C23×D13C22×C411yescharacteristic
148C2×Q8×C13—22no—
149C2×Q8×C13—22no—
150C2×Q8×C13—22no—
151C22×C4×C13C22×C411yescharacteristic
152C22×C4×C13C22×C411yescharacteristic
153C22×C4×C13C22×C411yescharacteristic
154C22×C4×C13C22×C411yescharacteristic
155C22×C4×C13C22×C411yescharacteristic
156C22×C4×C13C22×C411yescharacteristic
157C22×C4×C13C2411yescharacteristic
158C22×Dic13C22×C411yescharacteristic
159C22×Dic13C22×C411yescharacteristic
160C22×Dic13C22×C411yescharacteristic
161C22×Dic13C22×C411yescharacteristic
162C22×Dic13C22×C411yescharacteristic
163C22×Dic13C22×C411yescharacteristic
164C22×Dic13C22×C411yescharacteristic
165Q8×D13—232no—
166C2×C4×D13—22no—
167C2×C4×D13—22no—
168C2×C4×D13—22no—
169C2×C4×D13—22no—
170C2×C4×D13—21no—
171C2×C4×D13—21no—
172C2×C4×D13—21no—
173C2×C4×D13—21no—
174C2×C4×D13—22no—
175C2×C4×D13—22no—
176C2×C4×D13—22no—
177C2×C4×D13—22no—
178C2×C4×D13—22no—
179C2×C4×D13—22no—
180C2×C4×D13—22no—
181C2×C4×D13—22no—
182C2×C4×D13—22no—
183C2×C4×D13—22no—
184C2×C4×D13—41no—
185C2×C4×D13—41no—
186C2×C4×D13—41no—
187C2×C4×D13M1614yes—
188C2×C4×D13C2×Q812yes—
189C2×C4×D13#4112yes—
190C2×Dic26—22no—
191C2×Dic26—22no—
192C2×Dic26—22no—
193C2×Dic26—22no—
194C2×Dic26—22no—
195C2×Dic26—22no—
196C2×Dic26—22no—
197C2×Dic26C22⋊C414yes—
198C2×Dic26M1614yes—
199C2×C8×C13—21no—
200C2×C8×C13—21no—
201C2×C8×C13—21no—
202C2×C8×C13—21no—
203C2×C8×C13—21no—
204C2×C8×C13—21no—
205C2×C8×C13—21no—
206C2×C8×C13—21no—
207C2×C8×C13—21no—
208C2×C8×C13—21no—
209C2×C8×C13—21no—
210C2×C8×C13C2×Q812yescomplemented
211C13×C4⋊C4—22no—
212C13×C4⋊C4—22no—
213C13×C4⋊C4—22no—
214C42×C13—21no—
215C42×C13—21no—
216C42×C13—21no—
217C42×C13—21no—
218C42×C13C2×D412yes—
219C42×C13C2×D412yes—
220C4⋊Dic13—22no—
221C4⋊Dic13—22no—
222C4⋊Dic13C22⋊C414yes—
223#6101—22no—
224#6101—22no—
225#6101—22no—
226#6101—22no—
227#6101C22⋊C414yes—
228#6101C22⋊C414yes—
229C4×Dic13—22no—
230C4×Dic13—22no—
231C4×Dic13—21no—
232C4×Dic13—21no—
233C4×Dic13—22no—
234C4×Dic13—22no—
235C4×Dic13—22no—
236C4×Dic13—22no—
237C4×Dic13C2×D412yes—
238C4×Dic13C2×D412yes—
239C4×Dic13C2×D412yes—
240C4×Dic13C2×D412yes—
241C2×#1055—21no—
242C2×#1055—21no—
243C2×#1055—21no—
244C2×#1055—21no—
245C2×#1055—21no—
246C2×#1055—21no—
247C2×#1055—21no—
248C2×#1055—21no—
249C2×#1055—21no—
250C2×#1055—21no—
251C2×#1055—21no—
252C2×#1055C2×Q812yescomplemented
253C22×C4×Q8—131no—
254C2×#446—131no—
255C2×#446—131no—
256#1985—131no—
257#1985—131no—
258#1985—131no—
259#1985D1311yescharacteristic, complemented
260#1984—131no—
261#1984—131no—
262#1797—131no—
263#1797—131no—
264#1797—131no—
265#1749—131no—
266#1749—131no—
267C4×C22⋊C8—131no—
268C23×C13C23×C411yescharacteristic
269C22×D13—21no—
270C22×D13—21no—
271C22×D13—21no—
272C22×D13—21no—
273C22×D13C4×Q812yes—
274C22×D13C2×M1612yes—
275C22×D13#13112yes—
276Q8×C13—28no—
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—21no—
289C2×C4×C13—21no—
290C2×C4×C13—21no—
291C2×C4×C13C2×C22⋊C412yes—
292C2×C4×C13C2×C22⋊C412yes—
293C2×C4×C13C2×M1612yes—
294C2×C4×C13C2×M1612yes—
295C2×C4×C13C22×D411yescharacteristic
296C2×C4×C13C22×D411yescharacteristic
297C2×C4×C13C22×Q811yescharacteristic
298C2×C4×C13C2×#4111yescharacteristic
299C2×C4×C132−1+411yescharacteristic
300C2×C4×C132−1+411yescharacteristic
301C2×Dic13—21no—
302C2×Dic13—21no—
303C2×Dic13—21no—
304C2×Dic13—21no—
305C2×Dic13—21no—
306C2×Dic13—21no—
307C2×Dic13—21no—
308C2×Dic13—21no—
309C2×Dic13—21no—
310C2×Dic13—21no—
311C2×Dic13—21no—
312C2×Dic13—21no—
313C2×Dic13—21no—
314C2×Dic13C2×C22⋊C412yes—
315C2×Dic13C2×C22⋊C412yes—
316C2×Dic13C2×C22⋊C412yes—
317C2×Dic13C2×C22⋊C412yes—
318C2×Dic13C4×Q812yes—
319C2×Dic13C2×M1612yes—
320C2×Dic13C2×M1612yes—
321C2×Dic13C2×M1612yes—
322C4×D13—28no—
323C4×D13—28no—
324C4×D13—22no—
325C4×D13—22no—
326C4×D13—22no—
327C4×D13—22no—
328C4×D13—28no—
329C4×D13—44no—
330C4×D13—44no—
331C4×D13—44no—
332Dic26—28no—
333Dic26—28no—
334Dic26—28no—
335C8×C13—22no—
336C8×C13—41no—
337C8×C13—41no—
338C8×C13—41no—
339#1055—22no—
340#1055—41no—
341#1055—41no—
342#1055—41no—
343C23×Q8—131no—
344C2×C4×Q8—131no—
345C2×C4×Q8—131no—
346C2×C4×Q8—131no—
347C2×C4×Q8—131no—
348C2×C4×Q8—131no—
349C2×C4×Q8—131no—
350C2×C4×Q8—131no—
351C2×C4×Q8—264no—
352C2×C4×Q8—264no—
353C2×C4×Q8C2×D1311yescharacteristic
354C22×C4⋊C4—131no—
355C22×C4⋊C4—131no—
356C22×C4⋊C4—131no—
357C22×C42—131no—
358C22×C42—131no—
359C22×C42—131no—
360#446—264no—
361#446—264no—
362C2×C4⋊C8—131no—
363C2×C4⋊C8—131no—
364C2×C4⋊C8—131no—
365C2×C4⋊C8—131no—
366C2×C4⋊C8—131no—
367C2×C4⋊C8C2×D1311yescharacteristic
368C2×C22⋊C8—131no—
369C2×C22⋊C8—131no—
370C2×C22⋊C8—131no—
371C2×C22⋊C8—131no—
372C2×#97—131no—
373C2×#97—131no—
374C2×#97—131no—
375C2×#97C2×D1311yescharacteristic
376C2×C4×C8—131no—
377C2×C4×C8—131no—
378#336—131no—
379#336—131no—
380#336—131no—
381#336—131no—
382#336—131no—
383#336—131no—
384#336—131no—
385#336—131no—
386#336C2×D1311yescharacteristic
387#336C2×D1311yescharacteristic
388#336C2×D1311yescharacteristic
389#336C2×D1311yescharacteristic
390C22×C13C22×C22⋊C411yescharacteristic
391C22×C13C2×C4×Q811yescharacteristic
392C22×C13#51911yescharacteristic
393C22×C13C22×M1611yescharacteristic
394C22×C13C22×M1611yescharacteristic
395C22×C13C2×#13111yescharacteristic
396C22×C13#56811yescharacteristic
397C2×D13—22no—
398C2×D13—22no—
399C2×D13—22no—
400C2×D13—22no—
401C2×D13—22no—
402C2×D13—22no—
403C2×D13#44614yescomplemented
404C4×C13—22no—
405C4×C13—22no—
406C4×C13—22no—
407C4×C13—22no—
408C4×C13—41no—
409C4×C13—41no—
410C4×C13#54811yescharacteristic
411C4×C13#54811yescharacteristic
412C4×C13D4×Q811yescharacteristic
413C4×C13D4×Q811yescharacteristic
414Dic13—22no—
415Dic13—22no—
416Dic13—22no—
417Dic13—22no—
418Dic13—22no—
419Dic13—41no—
420Dic13#40714yes—
421C22×Q8—131no—
422C22×Q8—131no—
423C22×Q8—131no—
424C22×Q8—264no—
425C22×Q8—264no—
426C22×Q8—264no—
427C22×Q8C4×D1311yescharacteristic
428C23×C4—131no—
429C23×C4—131no—
430C23×C4—131no—
431C23×C4—131no—
432C23×C4—131no—
433C23×C4—131no—
434C23×C4—131no—
435C22×C8—131no—
436C22×C8—131no—
437C22×C8—131no—
438C22×C8—131no—
439C22×C8C22×D1311yescharacteristic
440C22×C8C22×D1311yescharacteristic
441C22×C8C22×D1311yescharacteristic
442C22×C8C22×D1311yescharacteristic
443C4×Q8—22no—
444C4×Q8—22no—
445C4×Q8—134no—
446C4×Q8—134no—
447C4×Q8—262no—
448C4×Q8—262no—
449C4×Q8—262no—
450C4×Q8—262no—
451C4×Q8—264no—
452C4×Q8—264no—
453C4×Q8—264no—
454C4×Q8—264no—
455C2×C4⋊C4—131no—
456C2×C4⋊C4—131no—
457C2×C4⋊C4—131no—
458C2×C4⋊C4—131no—
459C2×C4⋊C4—131no—
460C2×C4⋊C4—131no—
461C2×C4⋊C4—131no—
462C2×C4⋊C4—131no—
463C2×C4⋊C4—131no—
464C2×C4⋊C4—264no—
465C2×C4⋊C4—264no—
466C2×C4⋊C4—264no—
467C2×C4⋊C4C4×D1311yescharacteristic
468C2×C4⋊C4C4×D1311yescharacteristic
469C2×C4⋊C4C4×D1311yescharacteristic
470C2×C42—131no—
471C2×C42—131no—
472C2×C42—131no—
473C2×C42—131no—
474C2×C42—131no—
475C2×C42—131no—
476C2×C42—131no—
477C2×C42—131no—
478C2×C42—131no—
479C2×C42—262no—
480C2×C42—262no—
481C2×C42—262no—
482C2×C42—262no—
483C2×C42—262no—
484C2×C42—262no—
485C2×C42C22×D1311yescharacteristic
486C2×C42C22×D1311yescharacteristic
487C2×C42C22×D1311yescharacteristic
488C4⋊C8—22no—
489C4⋊C8—262no—
490C4⋊C8—262no—
491C4⋊C8—262no—
492C4⋊C8—262no—
493C4⋊C8—262no—
494C22⋊C8—134no—
495C22⋊C8—262no—
496C22⋊C8—262no—
497C22⋊C8—262no—
498#97—22no—
499#97—262no—
500#97—262no—
501#97—262no—
502C4×C8—262no—
503C4×C8—262no—
504C2×C13Q8×C22⋊C411yescharacteristic
505C2×C13C2×#40711yescharacteristic
506C2×C13#288011yescharacteristic
507C2×C13C2×#44611yescharacteristic
508C2×C13Q8×M1611yescharacteristic
509C2×C13#298311yescharacteristic
510C2×C13#298411yescharacteristic
511D13—24no—
512C24—131no—
513C2×Q8—22no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—134no—
517C2×Q8—134no—
518C2×Q8—262no—
519C2×Q8—262no—
520C2×Q8—262no—
521C2×Q8—262no—
522C2×Q8—262no—
523C2×Q8—262no—
524C2×Q8—2632no—
525C2×Q8—262no—
526C22×C4—131no—
527C22×C4—131no—
528C22×C4—131no—
529C22×C4—131no—
530C22×C4—131no—
531C22×C4—131no—
532C22×C4—134no—
533C22×C4—132no—
534C22×C4—132no—
535C22×C4—131no—
536C22×C4—262no—
537C22×C4—262no—
538C22×C4—262no—
539C22×C4—262no—
540C22×C4—262no—
541C22×C4—262no—
542C22×C4—262no—
543C22×C4—262no—
544C22×C4—262no—
545C22×C4—262no—
546C22×C4—262no—
547C22×C4—262no—
548C22×C4—262no—
549C22×C4—261no—
550C22×C4—261no—
551C22×C4—261no—
552C22×C4—261no—
553C22×C4—262no—
554C22×C4—521no—
555C22×C4—521no—
556C22×C4—521no—
557C22×C4C2×C4×D1311yescharacteristic
558C22×C4C2×C4×D1311yescharacteristic
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×C8Q8×D1312yescomplemented
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—134no—
592C4⋊C4—134no—
593C4⋊C4—134no—
594C4⋊C4—262no—
595C4⋊C4—262no—
596C4⋊C4—262no—
597C4⋊C4—262no—
598C4⋊C4—262no—
599C4⋊C4—262no—
600C42—21no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—132no—
605C42—132no—
606C42—132no—
607C42—132no—
608C42—262no—
609C42—262no—
610C42—262no—
611C42—262no—
612C42—262no—
613C42—262no—
614C42—261no—
615C42—261no—
616C42D4×D1312yes—
617C42D4×D1312yes—
618C13#2251011yescharacteristic, complemented, Sylow
619C23—132no—
620C23—132no—
621C23—132no—
622C23—261no—
623C23—261no—
624C23—261no—
625C23—261no—
626C23C22×C4×D1311yescharacteristic
627Q8—28no—
628Q8—268no—
629Q8—268no—
630Q8—268no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—132no—
646C2×C4—132no—
647C2×C4—132no—
648C2×C4—132no—
649C2×C4—132no—
650C2×C4—132no—
651C2×C4—132no—
652C2×C4—132no—
653C2×C4—268no—
654C2×C4—268no—
655C2×C4—268no—
656C2×C4—261no—
657C2×C4—261no—
658C2×C4—261no—
659C2×C4—261no—
660C2×C4—261no—
661C2×C4—261no—
662C2×C4—261no—
663C2×C4—261no—
664C2×C4—261no—
665C2×C4—261no—
666C2×C4—262no—
667C2×C4—262no—
668C2×C4—262no—
669C2×C4—262no—
670C2×C4—261no—
671C2×C4—261no—
672C2×C4—261no—
673C2×C4—524no—
674C2×C4—524no—
675C2×C4—524no—
676C2×C4C22⋊C4×D1312yes—
677C2×C4C22⋊C4×D1312yes—
678C2×C4M16×D1312yes—
679C2×C4M16×D1312yes—
680C2×C4C2×D4×D1311yescharacteristic
681C2×C4C2×D4×D1311yescharacteristic
682C2×C4C2×Q8×D1311yescharacteristic
683C2×C4#8825411yescharacteristic
684C2×C4#41×D1311yescharacteristic
685C2×C4#8825711yescharacteristic
686C8—22no—
687C8—41no—
688C8—41no—
689C8—41no—
690C8—262no—
691C8—521no—
692C8—521no—
693C8—521no—
694C22—134no—
695C22—262no—
696C22—262no—
697C22—262no—
698C22—262no—
699C22—262no—
700C22—262no—
701C22C2×C22⋊C4×D1311yescharacteristic
702C22C4×Q8×D1311yescharacteristic
703C22#1171927711yescharacteristic
704C22C2×M16×D1311yescharacteristic
705C22C2×M16×D1311yescharacteristic
706C22D13×#13111yescharacteristic
707C22#1171945511yescharacteristic
708C4—22no—
709C4—22no—
710C4—22no—
711C4—22no—
712C4—41no—
713C4—41no—
714C4—134no—
715C4—262no—
716C4—262no—
717C4—262no—
718C4—262no—
719C4—262no—
720C4—521no—
721C4#1171933711yescharacteristic
722C4#1171933811yescharacteristic
723C4#1171938211yescharacteristic
724C4#1171943211yescharacteristic
725C2—264no—
726C2#1311767011yescharacteristic
727C2D13×#40711yescharacteristic
728C2#1312328411yescharacteristic
729C2D13×#44611yescharacteristic
730C2#1312378811yescharacteristic
731C2#1312391811yescharacteristic
732C2#1312392211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1985C2
prime radicalC23×D13C22×C4
cosocleC22×C4×C13C24
hypercenter#1985D13
hypocenterC13#22510
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1985

Complements

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

NH ≅ G/Ntype
2. C2×#11718489C2semidirect
3. C2×#11718362C2semidirect
4. #13115777C2semidirect
5. #13115774C2semidirect
6. #13115774C2semidirect
7. #13115770C2semidirect
8. #13115770C2semidirect
15. C13×#1985C2semidirect
135. #88060Q8semidirect
210. C2×C8×C13C2×Q8semidirect
252. C2×#1055C2×Q8semidirect
259. #1985D13semidirect
403. C2×D13#446semidirect
587. C2×C8Q8×D13semidirect
618. C13#22510semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D132
C2×#117184892
C2×#117183622
#131157772
#131157742
#131157702
#131148152
#131148132
#131145992
#131145972
#131145932
C13×#19852
#2251013