Finite Group Databasebeta

← C2×#13123828 #16727390

Subgroups — C2×#13123828 #16727390

Order 3328.

2026 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719233C211yesmaximal, characteristic
2#13123828C2116yesmaximal, direct product factor
3C2×#11718489C211yesmaximal, characteristic, complemented
4C2×#11718492C211yesmaximal, characteristic, complemented
5C2×#11718389C211yesmaximal, characteristic, complemented
6C2×#11718389C211yesmaximal, characteristic, complemented
7C2×#11718497C211yesmaximal, characteristic, complemented
8C2×#11718391C211yesmaximal, characteristic, complemented
9C2×#11718495C211yesmaximal, characteristic, complemented
10C2×#11718386C211yesmaximal, characteristic, complemented
11C2×#11718370C211yesmaximal, characteristic, complemented
12C2×#11718346C211yesmaximal, characteristic, complemented
13C2×#11718658C211yesmaximal, characteristic, complemented
14C2×#11718350C211yesmaximal, characteristic, complemented
15C2×D13×#97C211yesmaximal, characteristic, complemented
16C2×C13×#433C211yesmaximal, characteristic, complemented
17C2×C13×#117C2211yescharacteristic
18C2×C4×C22⋊D13C2211yescharacteristic
19C2×C4×C22⋊D13C2211yescharacteristic
20C22×#6099C2211yescharacteristic
21C23×#1055C2211yescharacteristic
22C22×#6094C2211yescharacteristic
23C22×C8×D13C2211yescharacteristic
24C22×C8×D13C2211yescharacteristic
25C22×C8×D13C2211yescharacteristic
26#11719233C418yes—
27#11719233C2218yes—
28C2×#88152C411yescharacteristic
29C2×#88150C411yescharacteristic
30C2×#88148C411yescharacteristic
31C2×#88143C411yescharacteristic
32C2×#88139C411yescharacteristic
33C2×#88138C411yescharacteristic
34C2×#88137C411yescharacteristic
35C2×#88133C411yescharacteristic
36C2×C4×D52C2211yescharacteristic
37C2×#88126C2211yescharacteristic
38C2×C42×D13C2211yescharacteristic
39C2×C4×Dic26C2211yescharacteristic
40C13×#433C2218yescomplemented
41C2×C13×C4⋊C8C2211yescharacteristic
42C2×C13×C4⋊C8C2211yescharacteristic
43C2×C13×C22⋊C8C2211yescharacteristic
44C2×C13×C22⋊C8C2211yescharacteristic
45C2×C13×#97C2211yescharacteristic
46C2×C4×C8×C13C2211yescharacteristic
47C2×#88060C2211yescharacteristic
48C2×#88060C2211yescharacteristic
49C2×#88060C2211yescharacteristic
50C2×#88060C2211yescharacteristic
51C2×#88055C2211yescharacteristic
52C2×#88055C2211yescharacteristic
53C2×#88055C2211yescharacteristic
54C2×#88054C2211yescharacteristic
55C2×#88054C2211yescharacteristic
56C2×#88054C2211yescharacteristic
57C2×#88054C2211yescharacteristic
58C2×C8×Dic13C2211yescharacteristic
59#11718658C2218yescomplemented
60C2×#88043C2211yescharacteristic
61C2×#88043C2211yescharacteristic
62C2×C4×#1055C2211yescharacteristic
63C2×C4×#1055C2211yescharacteristic
64#11718497C2218yescomplemented
65#11718495C2218yescomplemented
66#11718492C2218yescomplemented
67#11718489C2218yescomplemented
68#11718391C2218yescomplemented
69#11718389C2218yescomplemented
70#11718389C2218yescomplemented
71#11718386C2218yescomplemented
72#11718370C2218yescomplemented
73D13×#97C2218yescomplemented
74#11718350C2218yescomplemented
75#11718346C2218yescomplemented
76C23×C4×C13C2311yescharacteristic
77C22×C22⋊D13C2×C411yescharacteristic
78C22×C22⋊D13C2×C411yescharacteristic
79C22×D52C2×C411yescharacteristic
80C22×C4×D13C2×C411yescharacteristic
81C22×C4×D13C2×C411yescharacteristic
82C22×C4×D13C2311yescharacteristic
83C22×C4×D13C2311yescharacteristic
84C22×Dic26C2×C411yescharacteristic
85C22×C8×C13C2311yescharacteristic
86C22×C8×C13C2311yescharacteristic
87C22×C8×C13C2311yescharacteristic
88C22×C8×C13C2311yescharacteristic
89C13×#117C2×C414yes—
90C13×#117C2314yes—
91C2×C13×C4⋊C4C2×C411yescharacteristic
92C2×C13×C4⋊C4C2×C411yescharacteristic
93C2×C13×C22⋊C4C2×C411yescharacteristic
94C2×C13×C22⋊C4C2×C411yescharacteristic
95C2×C42×C13C2311yescharacteristic
96C2×C42×C13C2311yescharacteristic
97C2×C22⋊Dic13C2×C411yescharacteristic
98C2×C22⋊Dic13C2×C411yescharacteristic
99C4×C22⋊D13C2×C414yes—
100C4×C22⋊D13C2×C414yes—
101C4×C22⋊D13C2314yes—
102C4×C22⋊D13C2314yes—
103C2×#6103C2×C411yescharacteristic
104C2×#6103C2×C411yescharacteristic
105C2×#6103C2×C411yescharacteristic
106C2×#6103C2×C411yescharacteristic
107C2×#6103C2×C411yescharacteristic
108C2×#6103C2×C411yescharacteristic
109C2×C4⋊Dic13C2×C411yescharacteristic
110C2×C4⋊Dic13C2×C411yescharacteristic
111C2×#6101C2×C411yescharacteristic
112C2×#6101C2×C411yescharacteristic
113C2×#6101C2×C411yescharacteristic
114C2×#6101C2×C411yescharacteristic
115C2×#6101C2×C411yescharacteristic
116C2×#6101C2×C411yescharacteristic
117C2×C4×Dic13C2×C411yescharacteristic
118C2×C4×Dic13C2×C411yescharacteristic
119C2×C4×Dic13C2311yescharacteristic
120C2×C4×Dic13C2311yescharacteristic
121C2×#6099—24no—
122C2×#6099C2314yes—
123C22×#1055—24no—
124C22×#1055C2314yes—
125C22×#1055C2311yescharacteristic
126C22×#1055C2311yescharacteristic
127C22×#1055C2311yescharacteristic
128C22×#1055C2311yescharacteristic
129C2×#6094—24no—
130C2×#6094C2314yes—
131C2×C8×D13—24no—
132C2×C8×D13—24no—
133C2×C8×D13—24no—
134C2×C8×D13C2314yes—
135C2×C8×D13C2314yes—
136C2×C8×D13C2314yes—
137#88152C2×C418yes—
138#88150C2×C418yes—
139#88148C2×C418yes—
140#88143C2×C418yes—
141#88139C2×C418yes—
142#88138C2×C418yes—
143#88137C2×C418yes—
144#88133C2×C418yes—
145C4×D52C2×C414yes—
146C4×D52C2314yes—
147#88126C2×C414yes—
148#88126C2314yes—
149C42×D13C2×C414yes—
150C42×D13C2314yes—
151C4×Dic26C2×C414yes—
152C4×Dic26C2314yes—
153C13×C4⋊C8C2314yes—
154C13×C4⋊C8C2314yes—
155C13×C22⋊C8C2314yes—
156C13×C22⋊C8C2314yes—
157C13×#97C2314yes—
158C4×C8×C13C2314yes—
159#88060C2314yes—
160#88060C2314yes—
161#88060C2314yes—
162#88060C2314yes—
163#88055C2314yes—
164#88055C2314yes—
165#88055C2314yes—
166#88054C2314yes—
167#88054C2314yes—
168#88054C2314yes—
169#88054C2314yes—
170C8×Dic13C2314yes—
171#88043C2314yes—
172#88043C2314yes—
173C4×#1055C2314yes—
174C4×#1055C2314yes—
175C2×#2968—131nomaximal, Sylow
176C24×C13C22×C411yescharacteristic
177C23×D13C22×C411yescharacteristic
178C23×D13C22×C411yescharacteristic
179C22×C4×C13—22no—
180C22×C4×C13—22no—
181C22×C4×C13C22×C411yescharacteristic
182C22×C4×C13C22×C411yescharacteristic
183C22×C4×C13C22×C411yescharacteristic
184C22×C4×C13C22×C411yescharacteristic
185C22×C4×C13C22×C411yescharacteristic
186C22×C4×C13C22×C412yes—
187C22×C4×C13C2412yes—
188C22×C4×C13C2411yescharacteristic
189C2×C22⋊D13—24no—
190C2×C22⋊D13—42no—
191C2×C22⋊D13C22×C414yes—
192C2×C22⋊D13C22×C414yes—
193C22×Dic13C22×C411yescharacteristic
194C22×Dic13C22×C411yescharacteristic
195C22×Dic13C22×C411yescharacteristic
196C22×Dic13C22×C411yescharacteristic
197C22×Dic13C22×C411yescharacteristic
198C22×Dic13C22×C411yescharacteristic
199C2×D52—24no—
200C2×D52C22×C414yes—
201C2×C4×D13—24no—
202C2×C4×D13—22no—
203C2×C4×D13—22no—
204C2×C4×D13—22no—
205C2×C4×D13—22no—
206C2×C4×D13—42no—
207C2×C4×D13C22×C412yes—
208C2×C4×D13C22×C414yes—
209C2×C4×D13C22×C412yes—
210C2×C4×D13C22×C414yes—
211C2×C4×D13C2412yes—
212C2×C4×D13C2412yes—
213C2×Dic26—42no—
214C2×Dic26C22×C414yes—
215C2×C8×C13—22no—
216C2×C8×C13—22no—
217C2×C8×C13—22no—
218C2×C8×C13—22no—
219C2×C8×C13C2412yes—
220C2×C8×C13C2412yes—
221C2×C8×C13C2412yes—
222C2×C8×C13C2412yes—
223C13×C4⋊C4C22×C414yes—
224C13×C4⋊C4C22×C414yes—
225C13×C22⋊C4C22×C414yes—
226C13×C22⋊C4C22×C414yes—
227C42×C13C22×C412yes—
228C42×C13C22×C412yes—
229C42×C13C2412yes—
230C42×C13C2412yes—
231C22⋊Dic13C22×C414yes—
232C22⋊Dic13C22×C414yes—
233#6103C22×C414yes—
234#6103C22×C414yes—
235#6103C22×C414yes—
236#6103C22×C414yes—
237#6103C22×C414yes—
238#6103C22×C414yes—
239C4⋊Dic13C22×C414yes—
240C4⋊Dic13C22×C414yes—
241#6101C22×C414yes—
242#6101C22×C414yes—
243#6101C22×C414yes—
244#6101C22×C414yes—
245#6101C22×C414yes—
246#6101C22×C414yes—
247C4×Dic13C22×C412yes—
248C4×Dic13C22×C412yes—
249C4×Dic13C22×C414yes—
250C4×Dic13C22×C414yes—
251C4×Dic13C2412yes—
252C4×Dic13C2412yes—
253#6099—28no—
254C2×#1055—22no—
255C2×#1055—22no—
256C2×#1055—28no—
257C2×#1055#4114yes—
258C2×#1055#4114yes—
259C2×#1055C2412yes—
260C2×#1055C2412yes—
261C2×#1055C2412yes—
262C2×#1055C2412yes—
263#6094—28no—
264C8×D13—28no—
265C8×D13—28no—
266C8×D13—28no—
267C2×#529—131no—
268#2968—1316no—
269C2×#446—131no—
270C2×#446—131no—
271C2×#435—131no—
272C2×#435—131no—
273C2×#435—131no—
274C2×#435—131no—
275C2×C8×D4—131no—
276C2×C8×D4—131no—
277C2×#433—131no—
278C2×#433D1311yescharacteristic, complemented
279C2×#431—131no—
280C2×#405—131no—
281C2×#405—131no—
282C22×#97—131no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13C23×C412yes—
287C23×C13C23×C411yescharacteristic
288C22×D13—22no—
289C22×D13—22no—
290C22×D13—22no—
291C22×D13—22no—
292C22×D13—22no—
293C22×D13#13114yes—
294C22×D13C23×C412yes—
295C22×D13C23×C412yes—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—24no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13C23×C412yes—
305C2×C4×C13C23×C412yes—
306C2×C4×C13C23×C412yes—
307C2×C4×C13C23×C412yes—
308C2×C4×C13C23×C412yes—
309C2×C4×C13C23×C411yescharacteristic
310C2×C4×C13C2×#4112yes—
311C2×C4×C13C2×#4112yes—
312C2×C4×C13C2511yescharacteristic
313C22⋊D13—28no—
314C22⋊D13—44no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13C23×C412yes—
322C2×Dic13C23×C412yes—
323C2×Dic13C23×C412yes—
324C2×Dic13C23×C412yes—
325C2×Dic13C23×C412yes—
326C2×Dic13C23×C412yes—
327D52—28no—
328C4×D13—28no—
329C4×D13—24no—
330C4×D13—24no—
331C4×D13—22no—
332C4×D13—22no—
333C4×D13—22no—
334C4×D13—22no—
335C4×D13—44no—
336Dic26—44no—
337C8×C13—22no—
338C8×C13—22no—
339C8×C13—22no—
340C8×C13—22no—
341#1055—22no—
342#1055—22no—
343#1055C2×#4114yes—
344#1055C2×#4114yes—
345C22×M16—131no—
346C22×M16—131no—
347C23×C8—131no—
348C23×C8—131no—
349C23×C8—131no—
350C23×C8—131no—
351#529—138no—
352#529—138no—
353C2×#126—131no—
354C2×#126—131no—
355C2×#125—131no—
356C2×#124—131no—
357C2×#123—131no—
358C2×#123—131no—
359C2×C22⋊Q8—131no—
360C2×#121—131no—
361C2×C4×Q8—131no—
362C2×C4×D4—131no—
363C2×C4×D4—131no—
364C2×C4×D4—131no—
365C2×#117—131no—
366C2×#117C2×D1311yescharacteristic
367C22×C42—131no—
368#446—138no—
369#446—138no—
370#435—138no—
371#435—138no—
372#435—138no—
373#435—138no—
374C8×D4—138no—
375C8×D4—138no—
376#433—138no—
377#433C2×D1318yescomplemented
378#431—138no—
379C2×C4⋊C8—131no—
380C2×C4⋊C8—131no—
381C2×C4⋊C8—131no—
382C2×C4⋊C8—131no—
383C2×C4⋊C8C2×D1311yescharacteristic
384C2×C4⋊C8C2×D1311yescharacteristic
385C2×C22⋊C8—131no—
386C2×C22⋊C8—131no—
387C2×C22⋊C8—131no—
388C2×C22⋊C8—131no—
389C2×C22⋊C8C2×D1311yescharacteristic
390C2×C22⋊C8C2×D1311yescharacteristic
391#405—138no—
392#405—138no—
393C2×#97—131no—
394C2×#97—131no—
395C2×#97—131no—
396C2×#97—131no—
397C2×#97—131no—
398C2×#97—138no—
399C2×#97C2×D1311yescharacteristic
400C2×C4×C8—131no—
401C2×C4×C8—131no—
402C2×C4×C8—131no—
403C2×C4×C8C2×D1311yescharacteristic
404C22×C13—22no—
405C22×C13—22no—
406C22×C13—22no—
407C22×C13—44no—
408C22×C13C4×#4112yes—
409C22×C13C2×#13112yes—
410C22×C13#56812yes—
411C22×C13C24×C411yescharacteristic
412C2×D13—22no—
413C2×D13—28no—
414C2×D13—22no—
415C2×D13—22no—
416C2×D13—22no—
417C2×D13—22no—
418C2×D13—44no—
419C2×D13C2×#13114yes—
420C4×C13—22no—
421C4×C13—22no—
422C4×C13—22no—
423C4×C13—22no—
424C4×C13—22no—
425C4×C13C4×#4112yes—
426C4×C13C22×#4111yescharacteristic
427C4×C13C22×#4111yescharacteristic
428Dic13—22no—
429Dic13—22no—
430Dic13—22no—
431Dic13—22no—
432Dic13—22no—
433Dic13—22no—
434C22×Q8—131no—
435C22×D4—131no—
436C22×D4—131no—
437C22×D4—131no—
438C23×C4—131no—
439C23×C4—131no—
440C23×C4—131no—
441C23×C4—131no—
442C23×C4C22×D1311yescharacteristic
443C2×M16—134no—
444C2×M16—134no—
445C2×M16—264no—
446C2×M16—264no—
447C22×C8—131no—
448C22×C8—131no—
449C22×C8—134no—
450C22×C8—131no—
451C22×C8—131no—
452C22×C8—134no—
453C22×C8—134no—
454C22×C8—134no—
455C22×C8—264no—
456C22×C8—264no—
457C22×C8—264no—
458C22×C8—264no—
459C22×C8C22×D1311yescharacteristic
460C22×C8C22×D1311yescharacteristic
461C22×C8C22×D1311yescharacteristic
462C22×C8C22×D1311yescharacteristic
463#126—138no—
464#126—138no—
465#125—138no—
466#124—138no—
467#123—138no—
468#123—138no—
469C22⋊Q8—138no—
470#121—138no—
471C4×Q8—134no—
472C4×Q8—134no—
473C4×D4—134no—
474C4×D4—134no—
475C4×D4—134no—
476C4×D4—134no—
477C4×D4—134no—
478C4×D4—134no—
479#117—134no—
480#117—134no—
481#117C4×D1314yes—
482#117C22×D1314yes—
483C2×C4⋊C4—131no—
484C2×C4⋊C4—131no—
485C2×C4⋊C4—131no—
486C2×C4⋊C4—131no—
487C2×C4⋊C4—131no—
488C2×C4⋊C4—131no—
489C2×C4⋊C4—131no—
490C2×C4⋊C4—131no—
491C2×C4⋊C4C4×D1311yescharacteristic
492C2×C4⋊C4C4×D1311yescharacteristic
493C2×C22⋊C4—131no—
494C2×C22⋊C4—131no—
495C2×C22⋊C4—131no—
496C2×C22⋊C4—131no—
497C2×C22⋊C4—131no—
498C2×C22⋊C4—131no—
499C2×C22⋊C4—131no—
500C2×C22⋊C4—131no—
501C2×C22⋊C4C4×D1311yescharacteristic
502C2×C22⋊C4C4×D1311yescharacteristic
503C2×C42—131no—
504C2×C42—131no—
505C2×C42—131no—
506C2×C42—131no—
507C2×C42—134no—
508C2×C42—134no—
509C2×C42C22×D1311yescharacteristic
510C2×C42C22×D1311yescharacteristic
511C4⋊C8—134no—
512C4⋊C8—134no—
513C4⋊C8—134no—
514C4⋊C8—134no—
515C4⋊C8C22×D1314yes—
516C4⋊C8C22×D1314yes—
517C22⋊C8—134no—
518C22⋊C8—134no—
519C22⋊C8—134no—
520C22⋊C8—134no—
521C22⋊C8C22×D1314yes—
522C22⋊C8C22×D1314yes—
523#97—134no—
524#97—134no—
525#97—134no—
526#97—134no—
527#97—134no—
528#97C22×D1314yes—
529C4×C8—134no—
530C4×C8—134no—
531C4×C8—134no—
532C4×C8C22×D1314yes—
533C2×C13—42no—
534C2×C13#296814yescomplemented
535C2×C13C2×C4×#4111yescharacteristic
536C2×C13C22×#13111yescharacteristic
537C2×C13C2×#56811yescharacteristic
538D13—24no—
539D13—42no—
540C24—131no—
541C24—131no—
542C24C2×C4×D1311yescharacteristic
543C2×Q8—134no—
544C2×Q8—522no—
545C2×D4—134no—
546C2×D4—134no—
547C2×D4—134no—
548C2×D4—264no—
549C2×D4—264no—
550C2×D4—522no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—131no—
554C22×C4—131no—
555C22×C4—131no—
556C22×C4—131no—
557C22×C4—131no—
558C22×C4—131no—
559C22×C4—132no—
560C22×C4—134no—
561C22×C4—132no—
562C22×C4—132no—
563C22×C4—132no—
564C22×C4—134no—
565C22×C4—264no—
566C22×C4—262no—
567C22×C4—262no—
568C22×C4—262no—
569C22×C4—262no—
570C22×C4—522no—
571C22×C4C2×C4×D1311yescharacteristic
572C22×C4C2×C4×D1311yescharacteristic
573C22×C4C2×C4×D1311yescharacteristic
574C22×C4C2×C4×D1311yescharacteristic
575C22×C4C2×C4×D1311yescharacteristic
576C22×C4C2×C4×D1312yes—
577C22×C4C23×D1312yes—
578C22×C4C23×D1311yescharacteristic
579M16—268no—
580M16—268no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—134no—
586C2×C8—134no—
587C2×C8—132no—
588C2×C8—132no—
589C2×C8—132no—
590C2×C8—132no—
591C2×C8—268no—
592C2×C8—268no—
593C2×C8—268no—
594C2×C8—268no—
595C2×C8—262no—
596C2×C8—262no—
597C2×C8C23×D1312yes—
598C2×C8C23×D1312yes—
599C2×C8C23×D1312yes—
600C2×C8C23×D1312yes—
601C4⋊C4—134no—
602C4⋊C4—134no—
603C4⋊C4—134no—
604C4⋊C4—134no—
605C4⋊C4—134no—
606C4⋊C4—134no—
607C4⋊C4—134no—
608C4⋊C4—134no—
609C4⋊C4C2×C4×D1314yes—
610C4⋊C4C2×C4×D1314yes—
611C22⋊C4—134no—
612C22⋊C4—134no—
613C22⋊C4—134no—
614C22⋊C4—134no—
615C22⋊C4—134no—
616C22⋊C4—134no—
617C22⋊C4—134no—
618C22⋊C4—134no—
619C22⋊C4C2×C4×D1314yes—
620C22⋊C4C2×C4×D1314yes—
621C42—132no—
622C42—134no—
623C42—134no—
624C42—132no—
625C42—132no—
626C42—132no—
627C42C2×C4×D1312yes—
628C42C2×C4×D1312yes—
629C42C23×D1312yes—
630C42C23×D1312yes—
631C13C2×#296811yescharacteristic, complemented, Sylow
632C23—22no—
633C23—22no—
634C23—22no—
635C23—134no—
636C23—132no—
637C23—132no—
638C23—262no—
639C23—262no—
640C23—262no—
641C23—262no—
642C23—262no—
643C23C22×C4×D1312yes—
644C23C22×C4×D1311yescharacteristic
645Q8—524no—
646D4—268no—
647D4—268no—
648D4—524no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—132no—
658C2×C4—132no—
659C2×C4—132no—
660C2×C4—132no—
661C2×C4—132no—
662C2×C4—132no—
663C2×C4—268no—
664C2×C4—262no—
665C2×C4—262no—
666C2×C4—262no—
667C2×C4—262no—
668C2×C4—262no—
669C2×C4—262no—
670C2×C4—264no—
671C2×C4—264no—
672C2×C4—262no—
673C2×C4—262no—
674C2×C4—262no—
675C2×C4—262no—
676C2×C4—524no—
677C2×C4C22×C4×D1312yes—
678C2×C4C22×C4×D1312yes—
679C2×C4C22×C4×D1312yes—
680C2×C4C22×C4×D1312yes—
681C2×C4C22×C4×D1312yes—
682C2×C4C22×C4×D1311yescharacteristic
683C2×C4#41×D1312yes—
684C2×C4#41×D1312yes—
685C2×C4C24×D1311yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—22no—
690C8—134no—
691C8—134no—
692C8—262no—
693C8—262no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—44no—
698C22—134no—
699C22—262no—
700C22—262no—
701C22—268no—
702C22—262no—
703C22—262no—
704C22—262no—
705C22—524no—
706C22#1171922712yes—
707C22D13×#13112yes—
708C22#1171945512yes—
709C22C23×C4×D1311yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—262no—
716C4—262no—
717C4—262no—
718C4—262no—
719C4—262no—
720C4—262no—
721C4#1171922712yes—
722C4C2×#41×D1311yescharacteristic
723C4C2×#41×D1311yescharacteristic
724C2—42no—
725C2—264no—
726C2—522no—
727C2#1312382814yesdirect product factor
728C2C2×#1171922711yescharacteristic
729C2C2×D13×#13111yescharacteristic
730C2C2×#1171945511yescharacteristic
subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC2×C13×#433C2
socleC23×C13C23×C4
prime radicalC2×#88138C4
cosocleC2×C4×C13C25
hypercenterC2×#433D13
hypocenterC13C2×#2968
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #13123828C2direct (N × H)
3. C2×#11718489C2semidirect
4. C2×#11718492C2semidirect
5. C2×#11718389C2semidirect
6. C2×#11718389C2semidirect
7. C2×#11718497C2semidirect
8. C2×#11718391C2semidirect
9. C2×#11718495C2semidirect
10. C2×#11718386C2semidirect
11. C2×#11718370C2semidirect
12. C2×#11718346C2semidirect
13. C2×#11718658C2semidirect
14. C2×#11718350C2semidirect
15. C2×D13×#97C2semidirect
16. C2×C13×#433C2semidirect
40. C13×#433C22semidirect
59. #11718658C22semidirect
64. #11718497C22semidirect
65. #11718495C22semidirect
66. #11718492C22semidirect
67. #11718489C22semidirect
68. #11718391C22semidirect
69. #11718389C22semidirect
70. #11718389C22semidirect
71. #11718386C22semidirect
72. #11718370C22semidirect
73. D13×#97C22semidirect
74. #11718350C22semidirect
75. #11718346C22semidirect
278. C2×#433D13semidirect
377. #433C2×D13semidirect
534. C2×C13#2968semidirect
631. C13C2×#2968semidirect
727. C2#13123828direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192332
#131238282
C2×#117184892
C2×#117184922
C2×#117183892
C2×#117184972
C2×#117183912
C2×#117184952
C2×#117183862
C2×#117183702
C2×#117183462
C2×#117186582
C2×#117183502
C2×D13×#972
C2×C13×#4332
C2×#296813