Finite Group Databasebeta

← C2×#13123982 #16728006

Subgroups — C2×#13123982 #16728006

Order 3328.

1926 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×#11719243C211yesmaximal, characteristic
2#13123982C2116yesmaximal, direct product factor
3C2×#11718489C211yesmaximal, characteristic, complemented
4C2×C8×Dic26C211yesmaximal, characteristic, complemented
5C2×#11718789C211yesmaximal, characteristic, complemented
6C2×#11718390C211yesmaximal, characteristic, complemented
7C2×#11718672C211yesmaximal, characteristic, complemented
8C2×#11718788C211yesmaximal, characteristic, complemented
9C2×#11718386C211yesmaximal, characteristic, complemented
10C2×#11718351C211yesmaximal, characteristic, complemented
11C2×#11718381C211yesmaximal, characteristic, complemented
12C2×#11718379C211yesmaximal, characteristic, complemented
13C2×#11718780C211yesmaximal, characteristic, complemented
14C2×#11718500C211yesmaximal, characteristic, complemented
15C2×#11718779C211yesmaximal, characteristic, complemented
16C2×C13×#436C211yesmaximal, characteristic, complemented
17C22×C13×M16C2211yescharacteristic
18C22×C13×M16C2211yescharacteristic
19C2×C4×D4×C13C2211yescharacteristic
20C2×#88193C411yescharacteristic
21C2×#88189C411yescharacteristic
22C2×C4×C22⋊D13C2211yescharacteristic
23C2×C4×C22⋊D13C2211yescharacteristic
24C2×#88180C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C22×#6099C2211yescharacteristic
27C23×#1055C2211yescharacteristic
28C22×#6094C2211yescharacteristic
29C22×C8×D13C2211yescharacteristic
30#11719243C418yes—
31#11719243C2218yes—
32C2×#88152C411yescharacteristic
33C2×#88143C411yescharacteristic
34C2×#88140C411yescharacteristic
35C2×#88139C411yescharacteristic
36C2×#88133C411yescharacteristic
37C2×#88132C411yescharacteristic
38C2×#88126C2211yescharacteristic
39C2×C4×Dic26C2211yescharacteristic
40C13×#436C2218yescomplemented
41C2×C13×C4⋊C8C2211yescharacteristic
42C2×C13×C22⋊C8C2211yescharacteristic
43C2×C13×C22⋊C8C2211yescharacteristic
44C2×C4×C8×C13C2211yescharacteristic
45C2×C22⋊#1055C2211yescharacteristic
46C2×C22⋊#1055C2211yescharacteristic
47#11718789C2218yescomplemented
48#11718788C2218yescomplemented
49#11718780C2218yescomplemented
50#11718779C2218yescomplemented
51C2×#88060C2211yescharacteristic
52C2×#88060C2211yescharacteristic
53C2×#88055C2211yescharacteristic
54C2×#88054C2211yescharacteristic
55C2×#88054C2211yescharacteristic
56C2×#88054C2211yescharacteristic
57C2×#88054C2211yescharacteristic
58C2×#88054C2211yescharacteristic
59C2×#88054C2211yescharacteristic
60C2×#88054C2211yescharacteristic
61C2×#88054C2211yescharacteristic
62C2×C8×Dic13C2211yescharacteristic
63C2×C8×Dic13C2211yescharacteristic
64C2×C8×Dic13C2211yescharacteristic
65#11718672C2218yescomplemented
66C2×C4⋊#1055C2211yescharacteristic
67C2×#88043C2211yescharacteristic
68#11718500C2218yescomplemented
69#11718489C2218yescomplemented
70#11718390C2218yescomplemented
71#11718386C2218yescomplemented
72#11718381C2218yescomplemented
73#11718379C2218yescomplemented
74#11718351C2218yescomplemented
75C8×Dic26C2218yescomplemented
76C22×D4×C13C2×C411yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C22×C22⋊D13C2×C411yescharacteristic
80C22×C22⋊D13C2×C411yescharacteristic
81C23×Dic13C2×C411yescharacteristic
82C23×Dic13C2×C411yescharacteristic
83C22×C4×D13C2311yescharacteristic
84C22×Dic26C2×C411yescharacteristic
85C2×C13×M16—42no—
86C2×C13×M16—42no—
87C2×C13×M16C2314yes—
88C2×C13×M16C2314yes—
89C22×C8×C13C2311yescharacteristic
90C22×C8×C13C2311yescharacteristic
91C22×C8×C13C2311yescharacteristic
92C22×C8×C13C2311yescharacteristic
93C4×D4×C13C2×C414yes—
94C4×D4×C13C2314yes—
95C2×C13×C4⋊C4C2×C411yescharacteristic
96C2×C13×C22⋊C4C2×C411yescharacteristic
97C2×C13×C22⋊C4C2×C411yescharacteristic
98C2×C42×C13C2311yescharacteristic
99C2×C22⋊Dic13C2×C411yescharacteristic
100C2×C22⋊Dic13C2×C411yescharacteristic
101C2×C22⋊Dic13C2×C411yescharacteristic
102C2×C22⋊Dic13C2×C411yescharacteristic
103#88193C2×C418yes—
104#88189C2×C418yes—
105C4×C22⋊D13C2×C414yes—
106C4×C22⋊D13C2×C414yes—
107C4×C22⋊D13C2314yes—
108C4×C22⋊D13C2314yes—
109C2×#6103C2×C411yescharacteristic
110C2×#6103C2×C411yescharacteristic
111C2×#6103C2×C411yescharacteristic
112C2×#6103C2×C411yescharacteristic
113#88180C2×C414yes—
114#88180C2314yes—
115C2×C4⋊Dic13C2×C411yescharacteristic
116C2×C4⋊Dic13C2×C411yescharacteristic
117C2×C4⋊Dic13C2×C411yescharacteristic
118C2×#6101C2×C411yescharacteristic
119C2×#6101C2×C411yescharacteristic
120C2×#6101C2×C411yescharacteristic
121C2×#6101C2×C411yescharacteristic
122C2×#6101C2×C411yescharacteristic
123C2×#6101C2×C411yescharacteristic
124C2×C4×Dic13C2×C411yescharacteristic
125C2×C4×Dic13C2×C411yescharacteristic
126C2×C4×Dic13C2×C414yes—
127C2×C4×Dic13C2311yescharacteristic
128C2×C4×Dic13C2311yescharacteristic
129C2×C4×Dic13C2311yescharacteristic
130C2×C4×Dic13C2314yes—
131C2×#6099—42no—
132C2×#6099C2314yes—
133C22×#1055—42no—
134C22×#1055C2311yescharacteristic
135C22×#1055C2311yescharacteristic
136C22×#1055C2311yescharacteristic
137C22×#1055C2311yescharacteristic
138C22×#1055C2314yes—
139C2×#6094—42no—
140C2×#6094C2314yes—
141C2×C8×D13—42no—
142C2×C8×D13C2314yes—
143#88152C2×C418yes—
144#88143C2×C418yes—
145#88140C2×C418yes—
146#88139C2×C418yes—
147#88133C2×C418yes—
148#88132C2×C418yes—
149#88126C2×C414yes—
150#88126C2314yes—
151C4×Dic26C2×C414yes—
152C4×Dic26C2314yes—
153C13×C4⋊C8C2314yes—
154C13×C22⋊C8C2314yes—
155C13×C22⋊C8C2314yes—
156C4×C8×C13C2314yes—
157C22⋊#1055C2314yes—
158C22⋊#1055C2314yes—
159#88060C2314yes—
160#88060C2314yes—
161#88055C2314yes—
162#88054C2314yes—
163#88054C2314yes—
164#88054C2314yes—
165#88054C2314yes—
166#88054C2314yes—
167#88054C2314yes—
168#88054C2314yes—
169#88054C2314yes—
170C8×Dic13C2314yes—
171C8×Dic13C2314yes—
172C8×Dic13C2314yes—
173C4⋊#1055C2314yes—
174#88043C2314yes—
175C2×#2993—131nomaximal, Sylow
176C24×C13C22×C411yescharacteristic
177C24×C13C22×C411yescharacteristic
178C23×D13C22×C411yescharacteristic
179C2×D4×C13—42no—
180C2×D4×C13C22×C414yes—
181C22×C4×C13—22no—
182C22×C4×C13—22no—
183C22×C4×C13—22no—
184C22×C4×C13—22no—
185C22×C4×C13C22×C411yescharacteristic
186C22×C4×C13C22×C412yes—
187C22×C4×C13C22×C411yescharacteristic
188C22×C4×C13C22×C411yescharacteristic
189C22×C4×C13C22×C411yescharacteristic
190C22×C4×C13C22×C412yes—
191C22×C4×C13C2412yes—
192C22×C4×C13C2412yes—
193C22×C4×C13C2411yescharacteristic
194C2×C22⋊D13—24no—
195C2×C22⋊D13—42no—
196C2×C22⋊D13C22×C414yes—
197C2×C22⋊D13C22×C414yes—
198C22×Dic13—24no—
199C22×Dic13—42no—
200C22×Dic13C22×C414yes—
201C22×Dic13C22×C411yescharacteristic
202C22×Dic13C22×C411yescharacteristic
203C22×Dic13C22×C411yescharacteristic
204C22×Dic13C22×C411yescharacteristic
205C22×Dic13C22×C411yescharacteristic
206C22×Dic13C22×C411yescharacteristic
207C22×Dic13C22×C414yes—
208C22×Dic13C22×C411yescharacteristic
209C2×C4×D13—22no—
210C2×C4×D13—22no—
211C2×C4×D13C22×C412yes—
212C2×C4×D13C2412yes—
213C2×Dic26—24no—
214C2×Dic26C22×C414yes—
215C13×M16—44no—
216C13×M16—44no—
217C2×C8×C13—22no—
218C2×C8×C13—22no—
219C2×C8×C13—22no—
220C2×C8×C13—22no—
221C2×C8×C13C2412yes—
222C2×C8×C13C2412yes—
223C2×C8×C13C2412yes—
224C2×C8×C13C2412yes—
225C13×C4⋊C4C22×C414yes—
226C13×C22⋊C4C22×C414yes—
227C13×C22⋊C4C22×C414yes—
228C42×C13C22×C412yes—
229C42×C13C2412yes—
230C22⋊Dic13C22×C414yes—
231C22⋊Dic13C22×C414yes—
232C22⋊Dic13C22×C414yes—
233C22⋊Dic13C22×C414yes—
234#6103C22×C414yes—
235#6103C22×C414yes—
236#6103C22×C414yes—
237#6103C22×C414yes—
238C4⋊Dic13C22×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×C412yes—
250C4×Dic13C22×C414yes—
251C4×Dic13C22×C414yes—
252C4×Dic13C2412yes—
253C4×Dic13C2412yes—
254C4×Dic13C2412yes—
255#6099—44no—
256C2×#1055—22no—
257C2×#1055—22no—
258C2×#1055—22no—
259C2×#1055—22no—
260C2×#1055—44no—
261C2×#1055C2412yes—
262C2×#1055C2412yes—
263C2×#1055C2412yes—
264C2×#1055C2412yes—
265#6094—44no—
266C8×D13—44no—
267C2×#529—131no—
268#2993—1316no—
269C2×#446—131no—
270C2×C8×Q8—131no—
271C2×#436—131no—
272C2×#436—131no—
273C2×#436D1311yescharacteristic, complemented
274C2×#435—131no—
275C2×#435—131no—
276C2×C8×D4—131no—
277C2×#433—131no—
278C2×#433—131no—
279C2×#431—131no—
280C2×#424—131no—
281C2×#424—131no—
282C2×#423—131no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13C23×C412yes—
290C23×C13C23×C412yes—
291C23×C13C23×C411yescharacteristic
292C22×D13—22no—
293C22×D13—22no—
294C22×D13—22no—
295C22×D13C23×C412yes—
296D4×C13—44no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—24no—
302C2×C4×C13—24no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13C23×C412yes—
308C2×C4×C13C23×C412yes—
309C2×C4×C13C23×C412yes—
310C2×C4×C13C23×C412yes—
311C2×C4×C13C23×C411yescharacteristic
312C2×C4×C13H(5,𝔽2)12yes—
313C2×C4×C132−1+412yes—
314C2×C4×C13C2511yescharacteristic
315C22⋊D13—28no—
316C22⋊D13—44no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—28no—
324C2×Dic13—44no—
325C2×Dic13#13114yes—
326C2×Dic13C23×C412yes—
327C2×Dic13C23×C412yes—
328C2×Dic13C23×C412yes—
329C2×Dic13C23×C412yes—
330C2×Dic13C23×C412yes—
331C2×Dic13C23×C412yes—
332C2×Dic13C23×C412yes—
333C4×D13—24no—
334C4×D13—22no—
335C4×D13—22no—
336Dic26—28no—
337C8×C13—22no—
338C8×C13—22no—
339C8×C13—22no—
340C8×C13—22no—
341#1055—22no—
342#1055—22no—
343#1055—22no—
344#1055—22no—
345C22×M16—131no—
346C22×M16—131no—
347C22×M16C2×D1311yescharacteristic
348C22×M16C2×D1311yescharacteristic
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×D4C2×D1311yescharacteristic
365C2×#117—131no—
366C2×#117—131no—
367C22×C42—131no—
368#446—138no—
369C8×Q8—138no—
370#436—138no—
371#436—138no—
372#436C2×D1318yescomplemented
373#435—138no—
374#435—138no—
375C8×D4—138no—
376#433—138no—
377#433—138no—
378#431—138no—
379#424—138no—
380#424—138no—
381#423—138no—
382C2×C4⋊C8—131no—
383C2×C4⋊C8—131no—
384C2×C4⋊C8—131no—
385C2×C4⋊C8—131no—
386C2×C4⋊C8—131no—
387C2×C4⋊C8—131no—
388C2×C4⋊C8—131no—
389C2×C4⋊C8—131no—
390C2×C4⋊C8—131no—
391C2×C4⋊C8C2×D1311yescharacteristic
392C2×C22⋊C8—131no—
393C2×C22⋊C8—131no—
394C2×C22⋊C8—131no—
395C2×C22⋊C8—131no—
396C2×C22⋊C8C2×D1311yescharacteristic
397C2×C22⋊C8C2×D1311yescharacteristic
398C2×#97—131no—
399C2×#97—131no—
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—22no—
408C22×C13—22no—
409C22×C13—22no—
410C22×C13—44no—
411C22×C13—44no—
412C22×C13#52012yes—
413C22×C13C2×#13112yes—
414C22×C13#56812yes—
415C22×C13C24×C411yescharacteristic
416C2×D13—22no—
417C2×D13—22no—
418C2×D13—22no—
419C2×D13—44no—
420C4×C13—22no—
421C4×C13—22no—
422C4×C13—22no—
423C4×C13—22no—
424C4×C13#52012yes—
425C4×C13C2×H(5,𝔽2)11yescharacteristic
426C4×C13C2×2−1+411yescharacteristic
427Dic13—22no—
428Dic13—22no—
429Dic13—22no—
430Dic13—22no—
431Dic13—22no—
432Dic13—22no—
433Dic13C2×#13114yes—
434C22×Q8—131no—
435C22×D4—131no—
436C22×D4—131no—
437C22×D4C4×D1311yescharacteristic
438C23×C4—131no—
439C23×C4—131no—
440C23×C4—131no—
441C23×C4C22×D1311yescharacteristic
442C23×C4C22×D1311yescharacteristic
443C2×M16—42no—
444C2×M16—42no—
445C2×M16—134no—
446C2×M16—134no—
447C2×M16—522no—
448C2×M16—522no—
449C2×M16C22×D1314yes—
450C2×M16C22×D1314yes—
451C22×C8—131no—
452C22×C8—131no—
453C22×C8—131no—
454C22×C8—131no—
455C22×C8—134no—
456C22×C8—134no—
457C22×C8—522no—
458C22×C8—522no—
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×D4C4×D1314yes—
478C4×D4C22×D1314yes—
479#117—134no—
480#117—134no—
481#117—134no—
482#117—134no—
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⋊C4—131no—
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—134no—
506C2×C42—134no—
507C2×C42—131no—
508C2×C42—131no—
509C2×C42—131no—
510C2×C42C22×D1311yescharacteristic
511C4⋊C8—134no—
512C4⋊C8—134no—
513C4⋊C8—134no—
514C4⋊C8—134no—
515C4⋊C8—134no—
516C4⋊C8—134no—
517C4⋊C8—134no—
518C4⋊C8—134no—
519C4⋊C8—134no—
520C4⋊C8C22×D1314yes—
521C22⋊C8—134no—
522C22⋊C8—134no—
523C22⋊C8—134no—
524C22⋊C8—134no—
525C22⋊C8C22×D1314yes—
526C22⋊C8C22×D1314yes—
527#97—134no—
528#97—134no—
529C4×C8—134no—
530C4×C8—134no—
531C4×C8—134no—
532C4×C8C22×D1314yes—
533C2×C13—42no—
534C2×C13—42no—
535C2×C13#299314yescomplemented
536C2×C13C2×#52011yescharacteristic
537C2×C13C22×#13111yescharacteristic
538C2×C13C2×#56811yescharacteristic
539D13—42no—
540C24—131no—
541C24C2×C4×D1311yescharacteristic
542C24C2×C4×D1311yescharacteristic
543C2×Q8—134no—
544C2×Q8—264no—
545C2×D4—42no—
546C2×D4—134no—
547C2×D4—134no—
548C2×D4—264no—
549C2×D4—522no—
550C2×D4C2×C4×D1314yes—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—131no—
556C22×C4—131no—
557C22×C4—131no—
558C22×C4—131no—
559C22×C4—134no—
560C22×C4—131no—
561C22×C4—131no—
562C22×C4—131no—
563C22×C4—134no—
564C22×C4—132no—
565C22×C4—132no—
566C22×C4—264no—
567C22×C4—262no—
568C22×C4—262no—
569C22×C4—522no—
570C22×C4C2×C4×D1311yescharacteristic
571C22×C4C2×C4×D1312yes—
572C22×C4C2×C4×D1311yescharacteristic
573C22×C4C2×C4×D1311yescharacteristic
574C22×C4C2×C4×D1311yescharacteristic
575C22×C4C2×C4×D1312yes—
576C22×C4C23×D1312yes—
577C22×C4C23×D1312yes—
578C22×C4C23×D1311yescharacteristic
579M16—44no—
580M16—44no—
581M16—524no—
582M16—524no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—132no—
588C2×C8—132no—
589C2×C8—132no—
590C2×C8—132no—
591C2×C8—262no—
592C2×C8—262no—
593C2×C8—262no—
594C2×C8—262no—
595C2×C8—524no—
596C2×C8—524no—
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⋊C4—134no—
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—132no—
623C42—134no—
624C42—134no—
625C42—132no—
626C42—132no—
627C42—132no—
628C42—132no—
629C42C2×C4×D1312yes—
630C42C23×D1312yes—
631C13C2×#299311yescharacteristic, complemented, Sylow
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—132no—
639C23—262no—
640C23—262no—
641C23—262no—
642C23C22×C4×D1312yes—
643C23C22×C4×D1312yes—
644C23C22×C4×D1311yescharacteristic
645Q8—268no—
646D4—44no—
647D4—268no—
648D4—524no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—134no—
660C2×C4—132no—
661C2×C4—132no—
662C2×C4—132no—
663C2×C4—132no—
664C2×C4—132no—
665C2×C4—132no—
666C2×C4—132no—
667C2×C4—268no—
668C2×C4—262no—
669C2×C4—262no—
670C2×C4—262no—
671C2×C4—262no—
672C2×C4—262no—
673C2×C4—262no—
674C2×C4—264no—
675C2×C4—262no—
676C2×C4—262no—
677C2×C4—524no—
678C2×C4C22×C4×D1312yes—
679C2×C4C22×C4×D1312yes—
680C2×C4C22×C4×D1312yes—
681C2×C4C22×C4×D1312yes—
682C2×C4C22×C4×D1311yescharacteristic
683C2×C4#8825112yes—
684C2×C4#8825712yes—
685C2×C4C24×D1311yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—22no—
690C8—262no—
691C8—262no—
692C8—262no—
693C8—262no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—44no—
701C22—44no—
702C22—262no—
703C22—262no—
704C22—262no—
705C22—524no—
706C22#1171925112yes—
707C22#1171945012yes—
708C22D13×#13112yes—
709C22C23×C4×D1311yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—134no—
715C4—262no—
716C4—262no—
717C4—262no—
718C4—262no—
719C4—262no—
720C4—262no—
721C4#1171925112yes—
722C4C2×#8825111yescharacteristic
723C4C2×#8825711yescharacteristic
724C2—42no—
725C2—42no—
726C2—522no—
727C2#1312398214yesdirect product factor
728C2C2×#1171925111yescharacteristic
729C2C2×D13×#13111yescharacteristic
730C2C2×#1171945011yescharacteristic
subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC2×C13×#436C2
socleC23×C13C23×C4
prime radicalC2×#88193C4
cosocleC2×C4×C13C25
hypercenterC2×#436D13
hypocenterC13C2×#2993
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
2. #13123982C2direct (N × H)
3. C2×#11718489C2semidirect
4. C2×C8×Dic26C2semidirect
5. C2×#11718789C2semidirect
6. C2×#11718390C2semidirect
7. C2×#11718672C2semidirect
8. C2×#11718788C2semidirect
9. C2×#11718386C2semidirect
10. C2×#11718351C2semidirect
11. C2×#11718381C2semidirect
12. C2×#11718379C2semidirect
13. C2×#11718780C2semidirect
14. C2×#11718500C2semidirect
15. C2×#11718779C2semidirect
16. C2×C13×#436C2semidirect
40. C13×#436C22semidirect
47. #11718789C22semidirect
48. #11718788C22semidirect
49. #11718780C22semidirect
50. #11718779C22semidirect
65. #11718672C22semidirect
68. #11718500C22semidirect
69. #11718489C22semidirect
70. #11718390C22semidirect
71. #11718386C22semidirect
72. #11718381C22semidirect
73. #11718379C22semidirect
74. #11718351C22semidirect
75. C8×Dic26C22semidirect
273. C2×#436D13semidirect
372. #436C2×D13semidirect
535. C2×C13#2993semidirect
631. C13C2×#2993semidirect
727. C2#13123982direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192432
#131239822
C2×#117184892
C2×C8×Dic262
C2×#117187892
C2×#117183902
C2×#117186722
C2×#117187882
C2×#117183862
C2×#117183512
C2×#117183812
C2×#117183792
C2×#117187802
C2×#117185002
C2×#117187792
C2×C13×#4362
C2×#299313