Finite Group Databasebeta

← #16726372

Subgroups — #16726372

Order 3328.

4874 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719648C211yesmaximal, characteristic
2C2×#11719455C211yesmaximal, characteristic, complemented
3C2×D13×#131C211yesmaximal, characteristic, complemented
4#13123286C213yesmaximal, complemented
5#13123285C211yesmaximal, characteristic, complemented
6#13123284C213yesmaximal, complemented
7#13123284C213yesmaximal, complemented
8#13123283C211yesmaximal, characteristic, complemented
9#13123283C211yesmaximal, characteristic, complemented
10#13123282C213yesmaximal, complemented
11#13123279C213yesmaximal, complemented
12#13123278C213yesmaximal, complemented
13C2×#11718388C213yesmaximal, complemented
14D13×#408C213yesmaximal, complemented
15C13×#2880C211yesmaximal, characteristic, complemented
16C22×C13×#41C2211yescharacteristic
17#11719648—28no—
18#11719648—28no—
19C2×#88257C411yescharacteristic
20C2×#88257C413yes—
21C2×#88256C411yescharacteristic
22C2×#88256C413yes—
23C2×#41×D13C2213yes—
24C2×#41×D13C2211yescharacteristic
25C2×#41×D13C2213yes—
26C2×#41×D13C2211yescharacteristic
27C2×#88254C411yescharacteristic
28C2×#88254C411yescharacteristic
29C2×#88251C413yes—
30C2×#88251C413yes—
31C22×#6127C2213yes—
32C22×#6127C2213yes—
33C2×C13×#131C2211yescharacteristic, complemented
34C2×C13×#131C2211yescharacteristic, complemented
35C2×#88202C2211yescharacteristic, complemented
36C2×#88202C2211yescharacteristic, complemented
37#11719455—28no—
38D13×#131—28no—
39C2×#88161C2213yescomplemented
40C2×#88161C2213yescomplemented
41C2×M16×D13C2213yescomplemented
42C2×M16×D13C2213yescomplemented
43C2×#88155C2213yescomplemented
44C2×#88155C2213yescomplemented
45C22×#6094C2213yescomplemented
46C22×C8×D13C2213yescomplemented
47C13×#408C2213yescomplemented
48C13×#408C2213yescomplemented
49C13×#407C2213yescomplemented
50C2×C13×C22⋊C8C2213yescomplemented
51#11718895C2213yescomplemented
52#11718895C2213yescomplemented
53#11718868C2213yescomplemented
54C2×C22⋊#1055C2213yescomplemented
55#11718790C2213yescomplemented
56#11718790C2213yescomplemented
57#11718787C2213yescomplemented
58#11718787C2213yescomplemented
59#11718771C2213yescomplemented
60#11718771C2213yescomplemented
61C2×#88060C2213yescomplemented
62C2×#88060C2213yescomplemented
63#11718388C2213yescomplemented
64#11718388C2216yescomplemented
65#11718388C2211yescharacteristic, complemented
66#11718388C2213yescomplemented
67#11718388C2213yescomplemented
68#11718388C2213yescomplemented
69#11718388C2213yescomplemented
70#11718388C2213yescomplemented
71#11718388C2213yescomplemented
72#11718388C2216yescomplemented
73#11718388C2216yescomplemented
74#11718387C2216yescomplemented
75#11718387C2216yescomplemented
76D13×C22⋊C8C2216yescomplemented
77D13×C22⋊C8C2216yescomplemented
78C2×C13×#41—24no—
79C2×C13×#41—24no—
80C2×C13×#41C2×C411yescharacteristic
81C2×C13×#41C2×C413yes—
82C2×C13×#41C2313yes—
83C2×C13×#41C2311yescharacteristic
84C22×Q8×C13C2×C411yescharacteristic
85C22×D4×C13C2×C413yes—
86C23×C4×C13C2313yes—
87C22×C22⋊D13C2×C413yes—
88C22×C22⋊D13C2×C416yes—
89C22×C22⋊D13C2×C413yes—
90#88257—28no—
91#88257—224no—
92#88256—28no—
93#88256—224no—
94#41×D13—24no—
95#41×D13—24no—
96#41×D13—212no—
97#41×D13—212no—
98#41×D13—212no—
99#41×D13—212no—
100#41×D13D418yes—
101#41×D13D418yes—
102#88254—28no—
103#88254—28no—
104C2×#6131C2×C411yescharacteristic
105C2×#6131C2×C413yes—
106C2×#6131C2×C413yes—
107C2×#6131C2×C411yescharacteristic
108C2×Q8×D13C2×C411yescharacteristic
109C2×Q8×D13C2×C413yes—
110C2×Q8×D13C2×C413yes—
111C2×Q8×D13C2×C411yescharacteristic
112#88251—224no—
113#88251—224no—
114C2×#6129C2×C413yes—
115C2×#6129C2×C416yes—
116C2×#6129C2×C416yes—
117C2×#6129C2×C413yes—
118C2×#6129C2×C413yes—
119C2×#6129C2×C413yes—
120C2×D4×D13C2×C416yes—
121C2×D4×D13C2×C413yes—
122C2×D4×D13C2×C416yes—
123C2×D4×D13C2×C413yes—
124C2×D4×D13C2×C413yes—
125C2×D4×D13C2×C413yes—
126C2×#6127—212no—
127C2×#6127—212no—
128C2×#6127—212no—
129C2×#6127—212no—
130C2×#6127C2×C413yes—
131C2×#6127C2×C413yes—
132C2×#6127C2×C413yes—
133C2×#6127C2×C413yes—
134C2×#6127C2×C416yes—
135C2×#6127C2×C413yes—
136C2×#6127C2×C413yes—
137C2×#6127C2313yes—
138C2×#6127C2311yescharacteristic
139C2×#6127C2313yes—
140C2×#6127C2313yes—
141C2×#6127C2313yes—
142C2×#6127C2313yes—
143C22×D52C2×C413yes—
144C22×D52C2×C413yes—
145C22×C4×D13C2313yes—
146C22×C4×D13C2316yes—
147C22×C4×D13C2313yes—
148C22×Dic26C2×C413yes—
149C22×Dic26C2×C413yes—
150C13×#131—24no—
151C13×#131—24no—
152C2×C13×M16C2313yes—
153C2×C13×M16C2313yes—
154C22×C8×C13C2313yes—
155C22×C8×C13C2313yes—
156#88202—24no—
157#88202—24no—
158C2×#6099C2313yes—
159C2×#6099C2313yes—
160C22×#1055C2313yes—
161C22×#1055C2313yes—
162#88161—212no—
163#88161—212no—
164M16×D13—212no—
165M16×D13—212no—
166#88155—212no—
167#88155—212no—
168C2×#6094—212no—
169C2×#6094C2311yescharacteristic
170C2×#6094C2313yes—
171C2×#6094C2313yes—
172C2×#6094C2313yes—
173C2×#6094C2316yes—
174C2×C8×D13—212no—
175C2×C8×D13C2311yescharacteristic
176C2×C8×D13C2313yes—
177C2×C8×D13C2313yes—
178C2×C8×D13C2313yes—
179C2×C8×D13C2316yes—
180C13×C22⋊C8C2311yescharacteristic
181C13×C22⋊C8C2313yes—
182C13×C22⋊C8C2313yes—
183C13×C22⋊C8C2313yes—
184C13×C22⋊C8C2316yes—
185C22⋊#1055C2311yescharacteristic
186C22⋊#1055C2313yes—
187C22⋊#1055C2313yes—
188C22⋊#1055C2313yes—
189C22⋊#1055C2316yes—
190#88060C2311yescharacteristic
191#88060C2311yescharacteristic
192#88060C2313yes—
193#88060C2313yes—
194#88060C2313yes—
195#88060C2313yes—
196#88060C2313yes—
197#88060C2313yes—
198#88060C2316yes—
199#88060C2316yes—
200#60065—131nomaximal, Sylow
201C24×C13C22×C413yes—
202C23×D13C22×C413yes—
203C23×D13C22×C416yes—
204C23×D13C22×C413yes—
205C13×#41—24no—
206C13×#41—212no—
207C13×#41—26no—
208C13×#41—26no—
209C13×#41C2×D414yes—
210C13×#41C2×D414yes—
211C2×Q8×C13—24no—
212C2×Q8×C13C22×C413yes—
213C2×Q8×C13C22×C411yescharacteristic
214C2×D4×C13—212no—
215C2×D4×C13C22×C416yes—
216C2×D4×C13C22×C413yes—
217C2×D4×C13C22×C413yes—
218C22×C4×C13—26no—
219C22×C4×C13—26no—
220C22×C4×C13C22×C413yes—
221C22×C4×C13C22×C413yes—
222C22×C4×C13C22×C413yes—
223C22×C4×C13C2413yes—
224C22×C4×C13C2411yescharacteristic
225C22×C4×C13C2413yes—
226C2×C22⋊D13—212no—
227C2×C22⋊D13—224no—
228C2×C22⋊D13—212no—
229C2×C22⋊D13C22×C413yes—
230C2×C22⋊D13C22×C411yescharacteristic
231C2×C22⋊D13C22×C411yescharacteristic
232C2×C22⋊D13C22×C413yes—
233C2×C22⋊D13C22×C416yes—
234C2×C22⋊D13C22×C413yes—
235C2×C22⋊D13C22×C413yes—
236C2×C22⋊D13C22×C413yes—
237C2×C22⋊D13C22×C413yes—
238C2×C22⋊D13C22×C416yes—
239C22×Dic13C22×C413yes—
240C22×Dic13C22×C416yes—
241C22×Dic13C22×C413yes—
242#6131—24no—
243#6131—212no—
244#6131—212no—
245#6131C22⋊C418yes—
246Q8×D13—24no—
247Q8×D13—212no—
248Q8×D13—212no—
249Q8×D13C22⋊C418yes—
250#6129—212no—
251#6129—224no—
252#6129—224no—
253#6129—212no—
254#6129—212no—
255#6129C22⋊C4124yes—
256D4×D13—224no—
257D4×D13—212no—
258D4×D13—224no—
259D4×D13—212no—
260D4×D13—212no—
261D4×D13C22⋊C4124yes—
262#6127—26no—
263#6127—26no—
264#6127—224no—
265#6127—212no—
266#6127—212no—
267#6127—212no—
268#6127—212no—
269#6127—212no—
270#6127—22no—
271#6127—26no—
272#6127—26no—
273#6127—22no—
274#6127—26no—
275#6127—26no—
276#6127—26no—
277#6127—26no—
278#6127—212no—
279#6127C2×D4112yes—
280#6127C2×D4112yes—
281C2×D52—212no—
282C2×D52—212no—
283C2×D52C22×C413yes—
284C2×D52C22×C411yescharacteristic
285C2×D52C22×C413yes—
286C2×D52C22×C413yes—
287C2×D52C22×C413yes—
288C2×D52C22×C413yes—
289C2×C4×D13—26no—
290C2×C4×D13—26no—
291C2×C4×D13—212no—
292C2×C4×D13—212no—
293C2×C4×D13C22×C416yes—
294C2×C4×D13C22×C413yes—
295C2×C4×D13C22×C413yes—
296C2×C4×D13C22×C416yes—
297C2×C4×D13C22×C413yes—
298C2×C4×D13C22×C413yes—
299C2×C4×D13C2×D4112yes—
300C2×C4×D13C2×D4112yes—
301C2×C4×D13C2411yescharacteristic
302C2×C4×D13C2413yes—
303C2×C4×D13C2411yescharacteristic
304C2×C4×D13C2413yes—
305C2×Dic26—212no—
306C2×Dic26—212no—
307C2×Dic26C22×C411yescharacteristic
308C2×Dic26C22×C413yes—
309C2×Dic26C22×C413yes—
310C2×Dic26C22×C413yes—
311C2×Dic26C22×C413yes—
312C2×Dic26C22×C413yes—
313C13×M16—26no—
314C13×M16—26no—
315C2×C8×C13—26no—
316C2×C8×C13—26no—
317C2×C8×C13C2411yescharacteristic
318C2×C8×C13C2413yes—
319C2×C8×C13C2413yes—
320C2×C8×C13C2411yescharacteristic
321#6099—26no—
322#6099—26no—
323C2×#1055—26no—
324C2×#1055—26no—
325C2×#1055C2411yescharacteristic
326C2×#1055C2413yes—
327C2×#1055C2413yes—
328C2×#1055C2411yescharacteristic
329#6094—22no—
330#6094—26no—
331#6094—26no—
332#6094—26no—
333#6094—212no—
334C8×D13—22no—
335C8×D13—26no—
336C8×D13—26no—
337C8×D13—26no—
338C8×D13—212no—
339C2×#585—131no—
340C2×#568—131no—
341C22×#131—131no—
342#2880—133no—
343#2880—133no—
344#2880—133no—
345#2880—133no—
346#2880—131no—
347#2880—131no—
348#2880—131no—
349#2880D1311yescharacteristic, complemented
350#2879—133no—
351#2879—133no—
352C2×#408—133no—
353C2×#408—133no—
354C23×C13—26no—
355C23×C13—43no—
356C23×C13—43no—
357C23×C13C23×C413yes—
358C23×C13C23×C411yescharacteristic
359C23×C13C23×C413yes—
360C22×D13—26no—
361C22×D13—212no—
362C22×D13—43no—
363C22×D13—43no—
364C22×D13—46no—
365C22×D13—46no—
366C22×D13—43no—
367C22×D13—43no—
368C22×D13C2×C22⋊C4112yes—
369C22×D13C23×C411yescharacteristic
370C22×D13C23×C413yes—
371C22×D13C23×C413yes—
372C22×D13C23×C411yescharacteristic
373Q8×C13—26no—
374Q8×C13C2×C22⋊C414yes—
375D4×C13—212no—
376D4×C13—26no—
377D4×C13C2×C22⋊C4112yes—
378C2×C4×C13—26no—
379C2×C4×C13—26no—
380C2×C4×C13—26no—
381C2×C4×C13—23no—
382C2×C4×C13—23no—
383C2×C4×C13—21no—
384C2×C4×C13—21no—
385C2×C4×C13C23×C411yescharacteristic
386C2×C4×C13C23×C413yes—
387C2×C4×C13C23×C413yes—
388C2×C4×C13C22×D416yes—
389C2×C4×C13C22×D416yes—
390C2×C4×C13C2511yescharacteristic
391C22⋊D13—212no—
392C22⋊D13—26no—
393C22⋊D13—22no—
394C22⋊D13—26no—
395C22⋊D13—26no—
396C22⋊D13—22no—
397C22⋊D13—26no—
398C22⋊D13—26no—
399C22⋊D13—26no—
400C22⋊D13C2×C22⋊C4124yes—
401C2×Dic13—26no—
402C2×Dic13—212no—
403C2×Dic13C2×C22⋊C4112yes—
404C2×Dic13C23×C413yes—
405C2×Dic13C23×C411yescharacteristic
406C2×Dic13C23×C411yescharacteristic
407C2×Dic13C23×C413yes—
408D52—26no—
409D52—22no—
410D52—26no—
411D52—26no—
412D52—26no—
413D52C2×C22⋊C4112yes—
414C4×D13—212no—
415C4×D13—26no—
416C4×D13—26no—
417C4×D13—21no—
418C4×D13—21no—
419C4×D13—23no—
420C4×D13—23no—
421C4×D13—212no—
422C4×D13C2×C22⋊C4112yes—
423C4×D13C2×C22⋊C4112yes—
424C4×D13C22×D412yes—
425C4×D13C22×D416yes—
426C4×D13C22×D416yes—
427C4×D13C22×D412yes—
428Dic26—26no—
429Dic26—22no—
430Dic26—26no—
431Dic26—26no—
432Dic26—26no—
433Dic26C2×C22⋊C4112yes—
434C8×C13—21no—
435C8×C13—23no—
436C8×C13—23no—
437C8×C13—21no—
438#1055—21no—
439#1055—23no—
440#1055—23no—
441#1055—21no—
442#585—268no—
443#585—268no—
444C2×2−1+4—131no—
445C2×2−1+4—133no—
446C2×2−1+4—131no—
447C2×2−1+4—131no—
448C2×H(5,𝔽2)—133no—
449C2×H(5,𝔽2)—131no—
450C2×H(5,𝔽2)—133no—
451C2×H(5,𝔽2)—133no—
452C22×#41—131no—
453C22×#41—133no—
454C22×#41—133no—
455C22×#41—131no—
456C22×#41—133no—
457C22×#41—133no—
458C22×#41C2×D1311yescharacteristic
459#568—268no—
460C2×#131—131no—
461C2×#131—131no—
462C2×#131—133no—
463C2×#131—133no—
464C2×#131—133no—
465C2×#131—133no—
466C2×#131—268no—
467C2×#131C2×D1311yescharacteristic, complemented
468C2×#131C2×D1311yescharacteristic, complemented
469C22×M16—133no—
470C22×M16—133no—
471C22×M16—133no—
472C23×C8—133no—
473#408—133no—
474#408—133no—
475#408—133no—
476#408—133no—
477#408—133no—
478#408—133no—
479#408—133no—
480#408—131no—
481#408—136no—
482#408—133no—
483#408—133no—
484#408—133no—
485#408—133no—
486#408—133no—
487#408—133no—
488#408—136no—
489#408—136no—
490#408C2×D1313yescomplemented
491#408C2×D1313yescomplemented
492#407—133no—
493#407—133no—
494#407—133no—
495#407—136no—
496#407—136no—
497#407C2×D1313yescomplemented
498C2×C22⋊C8—133no—
499C2×C22⋊C8—133no—
500C2×C22⋊C8—133no—
501C2×C22⋊C8—136no—
502C2×C22⋊C8—136no—
503C2×C22⋊C8C2×D1313yescomplemented
504C22×C13—23no—
505C22×C13—23no—
506C22×C13—23no—
507C22×C13—21no—
508C22×C13—23no—
509C22×C13—23no—
510C22×C13—21no—
511C22×C13—21no—
512C22×C13—86no—
513C22×C13C22×C22⋊C416yes—
514C22×C13C24×C411yescharacteristic
515C2×D13—21no—
516C2×D13—23no—
517C2×D13—21no—
518C2×D13—23no—
519C2×D13—21no—
520C2×D13—23no—
521C2×D13—23no—
522C2×D13—21no—
523C2×D13—23no—
524C2×D13—21no—
525C2×D13—412no—
526C2×D13—812no—
527C2×D13—86no—
528C2×D13C22×C22⋊C416yes—
529C2×D13C22×C22⋊C412yes—
530C4×C13—21no—
531C4×C13—23no—
532C4×C13C22×C22⋊C416yes—
533C4×C13C23×D411yescharacteristic
534C4×C13C23×D411yescharacteristic
535Dic13—23no—
536Dic13—21no—
537Dic13C22×C22⋊C412yes—
538Dic13C22×C22⋊C416yes—
5392−1+4—268no—
5402−1+4—268no—
5412−1+4—268no—
5422−1+4—2624no—
543H(5,𝔽2)—2624no—
544H(5,𝔽2)—2624no—
545H(5,𝔽2)—2624no—
546H(5,𝔽2)—268no—
547C2×#41—24no—
548C2×#41—24no—
549C2×#41—138no—
550C2×#41—138no—
551C2×#41—131no—
552C2×#41—133no—
553C2×#41—133no—
554C2×#41—131no—
555C2×#41—133no—
556C2×#41—136no—
557C2×#41—133no—
558C2×#41—136no—
559C2×#41—133no—
560C2×#41—133no—
561C2×#41—133no—
562C2×#41—133no—
563C2×#41—133no—
564C2×#41—133no—
565C2×#41—136no—
566C2×#41—133no—
567C2×#41—133no—
568C2×#41—133no—
569C2×#41—133no—
570C2×#41—133no—
571C2×#41—131no—
572C2×#41—133no—
573C2×#41—133no—
574C2×#41—2612no—
575C2×#41—2612no—
576C2×#41—2612no—
577C2×#41—2612no—
578C2×#41—2612no—
579C2×#41—2612no—
580C2×#41—2612no—
581C2×#41—2612no—
582C2×#41—264no—
583C2×#41—264no—
584C2×#41C4×D1311yescharacteristic
585C2×#41C4×D1313yes—
586C2×#41C22×D1313yes—
587C2×#41C22×D1311yescharacteristic
588C22×Q8—131no—
589C22×Q8—133no—
590C22×Q8—133no—
591C22×Q8—131no—
592C22×Q8—133no—
593C22×Q8—133no—
594C22×Q8C4×D1311yescharacteristic
595C22×D4—133no—
596C22×D4—133no—
597C22×D4—136no—
598C22×D4—133no—
599C22×D4—133no—
600C22×D4—136no—
601C22×D4—133no—
602C22×D4—136no—
603C22×D4—133no—
604C22×D4—133no—
605C22×D4—133no—
606C22×D4C4×D1313yes—
607C23×C4—133no—
608C23×C4—136no—
609C23×C4—133no—
610C23×C4C22×D1313yes—
611#131—24no—
612#131—24no—
613#131—2612no—
614#131—2612no—
615#131—2612no—
616#131—2612no—
617#131—264no—
618#131—264no—
619C2×M16—133no—
620C2×M16—133no—
621C2×M16—133no—
622C2×M16—131no—
623C2×M16—136no—
624C2×M16—133no—
625C2×M16—133no—
626C2×M16—2612no—
627C2×M16—2612no—
628C2×M16—2612no—
629C2×M16C22×D1313yes—
630C2×M16C22×D1313yes—
631C22×C8—133no—
632C22×C8—133no—
633C22×C8—131no—
634C22×C8—133no—
635C22×C8—133no—
636C22×C8—133no—
637C22×C8—136no—
638C22×C8—2612no—
639C22×C8C22×D1313yes—
640C22×C8C22×D1313yes—
641C22⋊C8—133no—
642C22⋊C8—131no—
643C22⋊C8—133no—
644C22⋊C8—136no—
645C22⋊C8—133no—
646C22⋊C8—133no—
647C22⋊C8—131no—
648C22⋊C8—131no—
649C22⋊C8—133no—
650C22⋊C8—133no—
651C22⋊C8—133no—
652C22⋊C8—133no—
653C22⋊C8—136no—
654C22⋊C8—136no—
655C22⋊C8—133no—
656C22⋊C8C22×D1313yes—
657C22⋊C8C22×D1316yes—
658C22⋊C8C22×D1311yescharacteristic
659C22⋊C8C22×D1313yes—
660C22⋊C8C22×D1313yes—
661C2×C13—26no—
662C2×C13—43no—
663C2×C13—41no—
664C2×C13C23×C22⋊C411yescharacteristic
665C2×C13#357311yescharacteristic
666C2×C13#357311yescharacteristic
667D13—22no—
668D13—26no—
669D13—43no—
670D13—41no—
671C24—133no—
672C24—136no—
673C24—133no—
674C24C2×C4×D1313yes—
675#41—24no—
676#41—212no—
677#41—26no—
678#41—26no—
679#41—138no—
680#41—1324no—
681#41—1312no—
682#41—1312no—
683#41—262no—
684#41—266no—
685#41—266no—
686#41—262no—
687#41—266no—
688#41—266no—
689#41—266no—
690#41—266no—
691#41—2612no—
692#41—2612no—
693#41—2612no—
694#41—2612no—
695#41—2624no—
696#41—2612no—
697#41—2612no—
698#41—2624no—
699#41—2612no—
700#41—2612no—
701#41—2624no—
702#41—2612no—
703#41—2612no—
704#41—264no—
705#41—2612no—
706#41—266no—
707#41—266no—
708#41D4×D1314yes—
709#41D4×D1314yes—
710C2×Q8—24no—
711C2×Q8—138no—
712C2×Q8—133no—
713C2×Q8—133no—
714C2×Q8—133no—
715C2×Q8—131no—
716C2×Q8—133no—
717C2×Q8—133no—
718C2×Q8—2612no—
719C2×Q8—2612no—
720C2×Q8—2612no—
721C2×Q8—2612no—
722C2×Q8—264no—
723C2×Q8C2×C4×D1313yes—
724C2×Q8C2×C4×D1311yescharacteristic
725C2×D4—212no—
726C2×D4—136no—
727C2×D4—1324no—
728C2×D4—133no—
729C2×D4—133no—
730C2×D4—131no—
731C2×D4—133no—
732C2×D4—133no—
733C2×D4—133no—
734C2×D4—131no—
735C2×D4—133no—
736C2×D4—136no—
737C2×D4—133no—
738C2×D4—133no—
739C2×D4—133no—
740C2×D4—131no—
741C2×D4—133no—
742C2×D4—133no—
743C2×D4—2612no—
744C2×D4—2612no—
745C2×D4—2612no—
746C2×D4—2612no—
747C2×D4—2624no—
748C2×D4—2612no—
749C2×D4—2624no—
750C2×D4—2624no—
751C2×D4—2612no—
752C2×D4—2612no—
753C2×D4C2×C4×D1316yes—
754C2×D4C2×C4×D1313yes—
755C2×D4C2×C4×D1313yes—
756C22×C4—26no—
757C22×C4—26no—
758C22×C4—133no—
759C22×C4—133no—
760C22×C4—133no—
761C22×C4—1312no—
762C22×C4—1312no—
763C22×C4—131no—
764C22×C4—133no—
765C22×C4—136no—
766C22×C4—133no—
767C22×C4—136no—
768C22×C4—136no—
769C22×C4—133no—
770C22×C4—133no—
771C22×C4—133no—
772C22×C4—131no—
773C22×C4—2612no—
774C22×C4—2612no—
775C22×C4—266no—
776C22×C4—266no—
777C22×C4C2×C4×D1313yes—
778C22×C4C2×C4×D1313yes—
779C22×C4C2×C4×D1313yes—
780C22×C4C23×D1313yes—
781C22×C4C23×D1311yescharacteristic
782C22×C4C23×D1313yes—
783M16—26no—
784M16—26no—
785M16—262no—
786M16—266no—
787M16—266no—
788M16—266no—
789M16—2612no—
790M16—266no—
791M16—266no—
792C2×C8—26no—
793C2×C8—26no—
794C2×C8—131no—
795C2×C8—131no—
796C2×C8—133no—
797C2×C8—133no—
798C2×C8—262no—
799C2×C8—266no—
800C2×C8—266no—
801C2×C8—266no—
802C2×C8—2612no—
803C2×C8—266no—
804C2×C8—266no—
805C2×C8C23×D1311yescharacteristic
806C2×C8C23×D1313yes—
807C2×C8C23×D1313yes—
808C2×C8C23×D1311yescharacteristic
809C13#6006511yescharacteristic, complemented, Sylow
810C23—26no—
811C23—43no—
812C23—43no—
813C23—131no—
814C23—133no—
815C23—1312no—
816C23—133no—
817C23—131no—
818C23—2612no—
819C23—266no—
820C23—523no—
821C23—523no—
822C23—523no—
823C23—523no—
824C23—526no—
825C23—526no—
826C23C22×C4×D1313yes—
827C23C22×C4×D1311yescharacteristic
828C23C22×C4×D1313yes—
829Q8—26no—
830Q8—1312no—
831Q8—262no—
832Q8—266no—
833Q8—266no—
834Q8—266no—
835Q8—266no—
836Q8C22⋊C4×D1314yes—
837D4—212no—
838D4—26no—
839D4—1324no—
840D4—1312no—
841D4—262no—
842D4—266no—
843D4—266no—
844D4—266no—
845D4—262no—
846D4—266no—
847D4—266no—
848D4—266no—
849D4—262no—
850D4—266no—
851D4—266no—
852D4—266no—
853D4—2612no—
854D4—266no—
855D4C22⋊C4×D13112yes—
856C2×C4—26no—
857C2×C4—26no—
858C2×C4—26no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—23no—
862C2×C4—23no—
863C2×C4—1312no—
864C2×C4—131no—
865C2×C4—133no—
866C2×C4—1312no—
867C2×C4—1312no—
868C2×C4—132no—
869C2×C4—136no—
870C2×C4—136no—
871C2×C4—132no—
872C2×C4—133no—
873C2×C4—131no—
874C2×C4—2612no—
875C2×C4—2612no—
876C2×C4—2612no—
877C2×C4—266no—
878C2×C4—266no—
879C2×C4—266no—
880C2×C4—263no—
881C2×C4—263no—
882C2×C4—261no—
883C2×C4—261no—
884C2×C4C22×C4×D1313yes—
885C2×C4C22×C4×D1311yescharacteristic
886C2×C4C22×C4×D1313yes—
887C2×C4C2×D4×D1316yes—
888C2×C4C2×D4×D1316yes—
889C2×C4C24×D1311yescharacteristic
890C8—21no—
891C8—21no—
892C8—23no—
893C8—23no—
894C8—261no—
895C8—263no—
896C8—263no—
897C8—261no—
898C22—23no—
899C22—23no—
900C22—21no—
901C22—23no—
902C22—21no—
903C22—23no—
904C22—21no—
905C22—23no—
906C22—86no—
907C22—132no—
908C22—136no—
909C22—261no—
910C22—263no—
911C22—261no—
912C22—263no—
913C22—263no—
914C22—261no—
915C22—261no—
916C22—263no—
917C22—261no—
918C22—263no—
919C22—5212no—
920C22—1046no—
921C22—10412no—
922C22C2×C22⋊C4×D1316yes—
923C22C23×C4×D1311yescharacteristic
924C4—21no—
925C4—23no—
926C4—132no—
927C4—136no—
928C4—263no—
929C4—261no—
930C4C2×C22⋊C4×D1316yes—
931C4C22×D4×D1311yescharacteristic
932C4C22×D4×D1311yescharacteristic
933C2—26no—
934C2—41no—
935C2—43no—
936C2—262no—
937C2—266no—
938C2—521no—
939C2—523no—
940C2C22×C22⋊C4×D1311yescharacteristic
941C2#1312954711yescharacteristic
942C2#1312954911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D13
commutator, socleC22×C13C24×C4
FittingC13×#2880C2
prime radicalC2×#11719648C2
cosocleC2×C4×C13C25
hypercenter#2880D13
hypocenterC13#60065
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#11719455C2semidirect
3. C2×D13×#131C2semidirect
4. #13123286C2semidirect
5. #13123285C2semidirect
6. #13123284C2semidirect
7. #13123284C2semidirect
8. #13123283C2semidirect
9. #13123283C2semidirect
10. #13123282C2semidirect
11. #13123279C2semidirect
12. #13123278C2semidirect
13. C2×#11718388C2semidirect
14. D13×#408C2semidirect
15. C13×#2880C2semidirect
33. C2×C13×#131C22semidirect
34. C2×C13×#131C22semidirect
35. C2×#88202C22semidirect
36. C2×#88202C22semidirect
39. C2×#88161C22semidirect
40. C2×#88161C22semidirect
41. C2×M16×D13C22semidirect
42. C2×M16×D13C22semidirect
43. C2×#88155C22semidirect
44. C2×#88155C22semidirect
45. C22×#6094C22semidirect
46. C22×C8×D13C22semidirect
47. C13×#408C22semidirect
48. C13×#408C22semidirect
49. C13×#407C22semidirect
50. C2×C13×C22⋊C8C22semidirect
51. #11718895C22semidirect
52. #11718895C22semidirect
53. #11718868C22semidirect
54. C2×C22⋊#1055C22semidirect
55. #11718790C22semidirect
56. #11718790C22semidirect
57. #11718787C22semidirect
58. #11718787C22semidirect
59. #11718771C22semidirect
60. #11718771C22semidirect
61. C2×#88060C22semidirect
62. C2×#88060C22semidirect
63. #11718388C22semidirect
64. #11718388C22semidirect
65. #11718388C22semidirect
66. #11718388C22semidirect
67. #11718388C22semidirect
68. #11718388C22semidirect
69. #11718388C22semidirect
70. #11718388C22semidirect
71. #11718388C22semidirect
72. #11718388C22semidirect
73. #11718388C22semidirect
74. #11718387C22semidirect
75. #11718387C22semidirect
76. D13×C22⋊C8C22semidirect
77. D13×C22⋊C8C22semidirect
349. #2880D13semidirect
467. C2×#131C2×D13semidirect
468. C2×#131C2×D13semidirect
490. #408C2×D13semidirect
491. #408C2×D13semidirect
497. #407C2×D13semidirect
503. C2×C22⋊C8C2×D13semidirect
809. C13#60065semidirect

Maximal subgroups

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

subgroupindex
C2×#117196482
C2×#117194552
C2×D13×#1312
#131232862
#131232852
#131232842
#131232832
#131232822
#131232792
#131232782
C2×#117183882
D13×#4082
C13×#28802
#6006513