Finite Group Databasebeta

← #15885453

Subgroups — #15885453

Order 3328.

864 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718858C211yesmaximal, characteristic, complemented
2C2×#11718857C211yesmaximal, characteristic, complemented
3#13123580C211yesmaximal, characteristic, complemented
4#13123404C211yesmaximal, characteristic, complemented
5#13115669C211yesmaximal, characteristic, complemented
6#13115612C211yesmaximal, characteristic, complemented
7#13115549C211yesmaximal, characteristic, complemented
8#13115542C211yesmaximal, characteristic, complemented
9#13115165C211yesmaximal, characteristic, complemented
10#13115165C211yesmaximal, characteristic, complemented
11#13115113C211yesmaximal, characteristic, complemented
12#13115113C211yesmaximal, characteristic, complemented
13#13114695C211yesmaximal, characteristic, complemented
14#13114646C211yesmaximal, characteristic, complemented
15C13×#3035C211yesmaximal, characteristic
16C2×C13×#135C2211yescharacteristic
17C2×C13×#135C2211yescharacteristic
18C13×#532C2211yescharacteristic
19C4×C13×#41C2211yescharacteristic
20C2×#88202C2211yescharacteristic
21C2×#88202C2211yescharacteristic
22C2×#88202C2211yescharacteristic
23C2×#88202C2211yescharacteristic
24C13×#464C411yescharacteristic, complemented
25C13×#464C411yescharacteristic, complemented
26C13×#463C411yescharacteristic, complemented
27C13×#463C411yescharacteristic, complemented
28C13×#462C411yescharacteristic, complemented
29C13×#461C411yescharacteristic, complemented
30C13×#460C411yescharacteristic, complemented
31C13×#459C411yescharacteristic, complemented
32C2×C13×C4⋊C8C2211yescharacteristic
33C13×#416C2211yescharacteristic
34C13×#416C2211yescharacteristic
35C2×#88077C2211yescharacteristic
36C2×#88077C2211yescharacteristic
37C2×#88077C2211yescharacteristic
38C2×#88077C2211yescharacteristic
39C2×#88077C2211yescharacteristic
40C2×#88077C2211yescharacteristic
41#11718895C2211yescharacteristic
42#11718895C2211yescharacteristic
43#11718858—24no—
44#11718857—24no—
45C2×#88059C2211yescharacteristic
46C2×#88059C2211yescharacteristic
47C2×#88055C2211yescharacteristic
48C2×C8×Dic13C2211yescharacteristic
49#11718673—21no—
50#11718672—21no—
51#11718672—21no—
52D4×#1055—21no—
53#11718660—21no—
54#11718660—21no—
55#11718660C2211yescharacteristic
56#11718660C2211yescharacteristic
57#11718593C2211yescharacteristic
58#11718585—21no—
59#11718585C2211yescharacteristic
60C2×C4⋊#1055—21no—
61C2×C4⋊#1055C2211yescharacteristic
62C4×#6099C2211yescharacteristic
63#11718144C2211yescharacteristic
64#11718144C2211yescharacteristic
65#11718142C2211yescharacteristic
66#11718142C2211yescharacteristic
67#11718124C2211yescharacteristic
68#11718124C2211yescharacteristic
69C2×C13×#41C2311yescharacteristic
70C2×C13×#41C2311yescharacteristic
71C2×C13×#41C2311yescharacteristic
72C13×#135—22no—
73C13×#135—22no—
74C13×#135—22no—
75C13×#135—22no—
76C2×C13×Q16C2×C411yescharacteristic
77C2×C13×Q16C2×C411yescharacteristic
78C2×C13×SD16C2×C411yescharacteristic
79C2×C13×SD16C2×C411yescharacteristic
80C2×C13×SD16C2×C411yescharacteristic
81C2×C13×SD16C2×C411yescharacteristic
82C2×C13×D8C2×C411yescharacteristic
83C2×C13×D8C2×C411yescharacteristic
84C22×C8×C13C2311yescharacteristic
85C22×C8×C13C2311yescharacteristic
86C13×C4⋊Q8C2×C411yescharacteristic
87C13×#127C2×C411yescharacteristic
88C13×#124C2×C411yescharacteristic
89C13×#124C2×C411yescharacteristic
90C13×#121—21no—
91C13×#121—21no—
92C4×Q8×C13C2×C411yescharacteristic
93C4×Q8×C13C2×C411yescharacteristic
94C4×D4×C13—21no—
95C4×D4×C13—21no—
96C4×D4×C13—21no—
97C4×D4×C13—21no—
98C4×D4×C13C2×C411yescharacteristic
99C4×D4×C13C2×C411yescharacteristic
100C13×#117—21no—
101C13×#117C2311yescharacteristic
102C2×C42×C13—21no—
103C2×C42×C13C2311yescharacteristic
104#88202—22no—
105#88202—22no—
106#88202—22no—
107#88202—22no—
108#88202—41no—
109#88202—41no—
110#88202—41no—
111#88202—41no—
112C2×C4×Dic13C2311yescharacteristic
113C2×C4×Dic13C2311yescharacteristic
114C2×#6099—21no—
115C2×#6099—21no—
116C2×#6099—21no—
117C2×#6099—21no—
118C2×#6099C2311yescharacteristic
119C2×#6099C2311yescharacteristic
120C2×#6099C2311yescharacteristic
121C2×#6099C2311yescharacteristic
122C22×#1055—21no—
123C22×#1055—21no—
124C22×#1055—21no—
125C22×#1055—21no—
126C22×#1055C2311yescharacteristic
127C22×#1055C2311yescharacteristic
128C13×C4⋊C8C2×C411yescharacteristic
129C13×C4⋊C8C2×C411yescharacteristic
130C13×C4⋊C8C2×C411yescharacteristic
131C13×C4⋊C8C2×C411yescharacteristic
132C13×#103C2×C411yescharacteristic
133C13×#103C2×C411yescharacteristic
134C13×#103C2×C411yescharacteristic
135C13×#103C2×C411yescharacteristic
136C13×#102C2×C411yescharacteristic
137C13×#102C2×C411yescharacteristic
138C13×#102C2×C411yescharacteristic
139C13×#102C2×C411yescharacteristic
140#88077—22no—
141#88077—22no—
142#88077—22no—
143#88077—41no—
144#88077—41no—
145#88077D414yescomplemented
146#88071—21no—
147#88071—21no—
148C22⋊#1055—21no—
149C22⋊#1055—21no—
150C22⋊#1055—21no—
151C22⋊#1055—21no—
152#88059—22no—
153#88059—22no—
154#88055—22no—
155C8×Dic13—22no—
156C4⋊#1055—21no—
157C4⋊#1055—21no—
158C4⋊#1055—21no—
159C4⋊#1055—21no—
160C4⋊#1055—21no—
161C4⋊#1055—21no—
162C4⋊#1055D411yescharacteristic
163C4⋊#1055D411yescharacteristic
164C4⋊#1055D411yescharacteristic
165C4⋊#1055D411yescharacteristic
166#88043—21no—
167C4×#1055—21no—
168#23017—131nomaximal, Sylow
169C13×#41—21no—
170C13×#41—21no—
171C13×#41—21no—
172C13×#41—21no—
173C13×#41—21no—
174C13×#41—21no—
175C13×#41—21no—
176C13×#41—21no—
177C13×#41—21no—
178C13×#41—21no—
179C13×#41C2×D412yes—
180C13×#41#4112yes—
181C2×Q8×C13C22×C411yescharacteristic
182C2×Q8×C13C22×C411yescharacteristic
183C2×Q8×C13C22×C411yescharacteristic
184C2×D4×C13—21no—
185C2×D4×C13—21no—
186C2×D4×C13—21no—
187C2×D4×C13—21no—
188C2×D4×C13—21no—
189C2×D4×C13C22×C411yescharacteristic
190C2×D4×C13C22×C411yescharacteristic
191C2×D4×C13C22×C411yescharacteristic
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13#4111yescharacteristic
198C22×C4×C13#4111yescharacteristic
199C22×C4×C13C2411yescharacteristic
200C22×Dic13—21no—
201C22×Dic13—21no—
202C13×Q16—22no—
203C13×Q16—22no—
204C13×SD16—22no—
205C13×SD16—22no—
206C13×SD16—22no—
207C13×SD16—22no—
208C13×D8—22no—
209C13×D8—22no—
210C2×C8×C13—21no—
211C2×C8×C13—21no—
212C2×C8×C13—21no—
213C2×C8×C13—21no—
214C2×C8×C13C22×C411yescharacteristic
215C2×C8×C13C22×C411yescharacteristic
216C2×C8×C13C22×C411yescharacteristic
217C2×C8×C13C22×C411yescharacteristic
218C13×C4⋊C4—21no—
219C13×C4⋊C4—21no—
220C13×C4⋊C4—21no—
221C13×C4⋊C4—21no—
222C13×C4⋊C4C22×C411yescharacteristic
223C13×C4⋊C4C22×C411yescharacteristic
224C13×C22⋊C4—21no—
225C13×C22⋊C4—21no—
226C13×C22⋊C4—21no—
227C13×C22⋊C4—21no—
228C13×C22⋊C4—21no—
229C13×C22⋊C4—21no—
230C13×C22⋊C4—21no—
231C42×C13—21no—
232C42×C13—21no—
233C42×C13—21no—
234C42×C13C22×C411yescharacteristic
235C42×C13C22×C411yescharacteristic
236C42×C13C2×D411yescharacteristic
237C42×C13C2×D411yescharacteristic
238C4×Dic13—21no—
239C4×Dic13—21no—
240C4×Dic13—21no—
241C4×Dic13C2×D412yes—
242#6099—21no—
243#6099—21no—
244#6099—21no—
245#6099—21no—
246#6099—21no—
247#6099—21no—
248#6099—21no—
249#6099—42no—
250#6099—42no—
251#6099—42no—
252#6099—42no—
253#6099C2×D412yes—
254C2×#1055—21no—
255C2×#1055—21no—
256C2×#1055—21no—
257C2×#1055—21no—
258C2×#1055—21no—
259C2×#1055—21no—
260C2×#1055—21no—
261C2×#1055—21no—
262C2×#1055—42no—
263C2×#1055—42no—
264C2×#1055—42no—
265C2×#1055—42no—
266C2×#1055C2×D411yescharacteristic
267C2×#1055C2×D411yescharacteristic
268C2×#1055C2×D411yescharacteristic
269C2×#1055C2×D411yescharacteristic
270#3035D1311yescharacteristic
271C2×#444—131no—
272C2×#443—131no—
273#2935—131no—
274#2906—131no—
275#1963—131no—
276#1950—131no—
277#1938—131no—
278#1937—131no—
279#1876—131no—
280#1876—131no—
281#1866—131no—
282#1866—131no—
283#1768—131no—
284#1759—131no—
285C23×C13—21no—
286C23×C13—21no—
287C23×C13—21no—
288C23×C13C2×#4111yescharacteristic
289Q8×C13—21no—
290Q8×C13—21no—
291Q8×C13—21no—
292Q8×C13—21no—
293Q8×C13—21no—
294Q8×C13C4×D412yes—
295D4×C13—22no—
296D4×C13—22no—
297D4×C13—21no—
298D4×C13—21no—
299D4×C13—21no—
300D4×C13—21no—
301D4×C13—21no—
302D4×C13—42no—
303D4×C13—41no—
304D4×C13—41no—
305D4×C13—41no—
306D4×C13—41no—
307D4×C13—81no—
308D4×C13C4×D412yes—
309C2×C4×C13—21no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—21no—
313C2×C4×C13—21no—
314C2×C4×C13—21no—
315C2×C4×C13—21no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13—42no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13—81no—
324C2×C4×C13C4×D411yescharacteristic
325C2×C4×C13C4×D411yescharacteristic
326C2×C4×C13C4×D411yescharacteristic
327C2×C4×C13C4×D411yescharacteristic
328C2×C4×C13C23×C411yescharacteristic
329C2×C4×C13C22×D411yescharacteristic
330C2×C4×C13C22×D411yescharacteristic
331C2×C4×C13C2×#4111yescharacteristic
332C2×C4×C13H(5,𝔽2)11yescharacteristic
333C2×C4×C132−1+411yescharacteristic
334C2×Dic13—22no—
335C2×Dic13—41no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338C2×Dic13—41no—
339C2×Dic13—41no—
340C8×C13—21no—
341C8×C13—21no—
342C8×C13—21no—
343C8×C13—21no—
344#1055—21no—
345#1055—21no—
346#1055—21no—
347#1055—21no—
348#1055—22no—
349#1055—41no—
350#1055—41no—
351#1055—41no—
352C2×#135C2×D1311yescharacteristic
353C2×#135C2×D1311yescharacteristic
354C2×#131—131no—
355C2×#131—131no—
356C2×#131—131no—
357C2×#131—131no—
358#532C2×D1311yescharacteristic
359C4×#41C2×D1311yescharacteristic
360#464Dic1311yescharacteristic, complemented
361#464Dic1311yescharacteristic, complemented
362#463Dic1311yescharacteristic, complemented
363#463Dic1311yescharacteristic, complemented
364#462Dic1311yescharacteristic, complemented
365#461Dic1311yescharacteristic, complemented
366#460Dic1311yescharacteristic, complemented
367#459Dic1311yescharacteristic, complemented
368#444—264no—
369#443—264no—
370#436—261no—
371#435—261no—
372#435—261no—
373C8×D4—261no—
374C2×#108—131no—
375C2×#108—131no—
376#424—131no—
377#424—131no—
378#424—261no—
379#424—261no—
380#423—131no—
381#423—261no—
382C2×C4⋊C8—131no—
383C2×C4⋊C8—261no—
384C2×C4⋊C8C2×D1311yescharacteristic
385C2×#104—131no—
386C2×#104—131no—
387C2×#104—131no—
388C2×#104—131no—
389C2×#104—131no—
390C2×#104—131no—
391#416C2×D1311yescharacteristic
392#416C2×D1311yescharacteristic
393#408—131no—
394#408—131no—
395C4×M16—131no—
396C2×#97—131no—
397C2×C4×C8—131no—
398#376—131no—
399#341—131no—
400#341—131no—
401#339—131no—
402#339—131no—
403#336—131no—
404#336—131no—
405C22×C13—21no—
406C22×C13—21no—
407C22×C13—22no—
408C22×C13—41no—
409C22×C13—41no—
410C22×C13—41no—
411C22×C13—41no—
412C22×C13—41no—
413C22×C13—41no—
414C22×C13—41no—
415C22×C13—41no—
416C22×C13C2×C4×D411yescharacteristic
417C22×C13#54711yescharacteristic
418C22×C13#55311yescharacteristic
419C4×C13—22no—
420C4×C13—21no—
421C4×C13—21no—
422C4×C13—21no—
423C4×C13—21no—
424C4×C13—41no—
425C4×C13—41no—
426C4×C13—41no—
427C4×C13—41no—
428C4×C13C2×C4×D411yescharacteristic
429C4×C13#52011yescharacteristic
430C4×C13D4211yescharacteristic
431C4×C13#54811yescharacteristic
432Dic13—42no—
433Dic13—81no—
434C2×#41C22×D1311yescharacteristic
435C2×#41C22×D1311yescharacteristic
436C2×#41C22×D1311yescharacteristic
437#135—22no—
438#135—22no—
439#135—22no—
440#135—22no—
441C2×Q16C2×Dic1311yescharacteristic
442C2×Q16C2×Dic1311yescharacteristic
443C2×SD16C2×Dic1311yescharacteristic
444C2×SD16C2×Dic1311yescharacteristic
445C2×SD16C2×Dic1311yescharacteristic
446C2×SD16C2×Dic1311yescharacteristic
447C2×D8C2×Dic1311yescharacteristic
448C2×D8C2×Dic1311yescharacteristic
449#131—262no—
450#131—262no—
451#131—262no—
452#131—262no—
453#131—521no—
454#131—521no—
455#131—521no—
456#131—521no—
457C2×M16—131no—
458C2×M16—131no—
459C2×M16—131no—
460C2×M16—131no—
461C2×M16—261no—
462C2×M16—261no—
463C2×M16—261no—
464C2×M16—261no—
465C22×C8—131no—
466C22×C8—131no—
467C22×C8—261no—
468C22×C8—261no—
469C22×C8—261no—
470C22×C8—261no—
471C22×C8C22×D1311yescharacteristic
472C22×C8C22×D1311yescharacteristic
473C4⋊Q8C2×Dic1311yescharacteristic
474#127C2×Dic1311yescharacteristic
475#124C2×Dic1311yescharacteristic
476#124C2×Dic1311yescharacteristic
477#121—21no—
478#121—21no—
479C4×Q8C2×Dic1311yescharacteristic
480C4×Q8C2×Dic1311yescharacteristic
481C4×D4—21no—
482C4×D4—21no—
483C4×D4—21no—
484C4×D4—21no—
485C4×D4C2×Dic1311yescharacteristic
486C4×D4C2×Dic1311yescharacteristic
487#117—21no—
488#117C22×D1311yescharacteristic
489C2×C42—21no—
490C2×C42—131no—
491C2×C42—131no—
492C2×C42C22×D1311yescharacteristic
493#108—262no—
494#108—262no—
495C4⋊C8—131no—
496C4⋊C8—131no—
497C4⋊C8—131no—
498C4⋊C8—131no—
499C4⋊C8—261no—
500C4⋊C8—261no—
501C4⋊C8—261no—
502C4⋊C8—261no—
503C4⋊C8—261no—
504C4⋊C8—261no—
505C4⋊C8C2×Dic1311yescharacteristic
506C4⋊C8C2×Dic1311yescharacteristic
507C4⋊C8C2×Dic1311yescharacteristic
508C4⋊C8C2×Dic1311yescharacteristic
509#104—134no—
510#104—262no—
511#104—262no—
512#104—262no—
513#104—521no—
514#104—521no—
515#103C2×Dic1311yescharacteristic
516#103C2×Dic1311yescharacteristic
517#103C2×Dic1311yescharacteristic
518#103C2×Dic1311yescharacteristic
519#102C2×Dic1311yescharacteristic
520#102C2×Dic1311yescharacteristic
521#102C2×Dic1311yescharacteristic
522#102C2×Dic1311yescharacteristic
523C22⋊C8—261no—
524C22⋊C8—261no—
525C22⋊C8—261no—
526C22⋊C8—261no—
527#97—262no—
528#97—261no—
529C4×C8—262no—
530C4×C8—261no—
531#95—261no—
532#95—261no—
533C2×C13—21no—
534C2×C13—21no—
535C2×C13—42no—
536C2×C13—81no—
537C2×C13—81no—
538C2×C13#236111yescharacteristic
539C2×C13#295511yescharacteristic
540C2×C13#295711yescharacteristic
541#41—21no—
542#41—21no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41D4×D1312yes—
552#41#612912yes—
553C2×Q8C22×Dic1311yescharacteristic
554C2×Q8C22×Dic1311yescharacteristic
555C2×Q8C22×Dic1311yescharacteristic
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4C22×Dic1311yescharacteristic
562C2×D4C22×Dic1311yescharacteristic
563C2×D4C22×Dic1311yescharacteristic
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—261no—
570C22×C4—261no—
571C22×C4#612911yescharacteristic
572C22×C4#612911yescharacteristic
573C22×C4C23×D1311yescharacteristic
574Q16—22no—
575Q16—22no—
576SD16—22no—
577SD16—22no—
578SD16—22no—
579SD16—22no—
580D8—22no—
581D8—22no—
582M16—132no—
583M16—261no—
584M16—261no—
585M16—261no—
586M16—261no—
587M16—261no—
588M16—261no—
589M16—261no—
590M16—522no—
591M16—522no—
592M16—522no—
593M16—522no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—131no—
599C2×C8—131no—
600C2×C8—131no—
601C2×C8—131no—
602C2×C8—261no—
603C2×C8—261no—
604C2×C8—261no—
605C2×C8—261no—
606C2×C8—261no—
607C2×C8—261no—
608C2×C8—261no—
609C2×C8—261no—
610C2×C8—522no—
611C2×C8—522no—
612C2×C8—522no—
613C2×C8—522no—
614C2×C8C22×Dic1311yescharacteristic
615C2×C8C22×Dic1311yescharacteristic
616C2×C8C22×Dic1311yescharacteristic
617C2×C8C22×Dic1311yescharacteristic
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4C22×Dic1311yescharacteristic
623C4⋊C4C22×Dic1311yescharacteristic
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—132no—
635C42—261no—
636C42—261no—
637C42—261no—
638C42D4×D1311yescharacteristic
639C42D4×D1311yescharacteristic
640C42C22×Dic1311yescharacteristic
641C42C22×Dic1311yescharacteristic
642C13#2301711yescharacteristic, complemented, Sylow
643C23—21no—
644C23—21no—
645C23—21no—
646C23C2×#612911yescharacteristic
647Q8—21no—
648Q8—21no—
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8D4×Dic1312yes—
653D4—22no—
654D4—22no—
655D4—21no—
656D4—21no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—42no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4D4×Dic1312yes—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—81no—
682C2×C4—262no—
683C2×C4—521no—
684C2×C4—521no—
685C2×C4—521no—
686C2×C4—521no—
687C2×C4—521no—
688C2×C4D4×Dic1311yescharacteristic
689C2×C4D4×Dic1311yescharacteristic
690C2×C4D4×Dic1311yescharacteristic
691C2×C4D4×Dic1311yescharacteristic
692C2×C4C2×D4×D1311yescharacteristic
693C2×C4C2×D4×D1311yescharacteristic
694C2×C4C2×#612911yescharacteristic
695C2×C4#8825611yescharacteristic
696C2×C4#8825711yescharacteristic
697C2×C4C23×Dic1311yescharacteristic
698C8—21no—
699C8—21no—
700C8—21no—
701C8—21no—
702C8—261no—
703C8—261no—
704C8—261no—
705C8—261no—
706C8—262no—
707C8—521no—
708C8—521no—
709C8—521no—
710C22—21no—
711C22—21no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22#1171931611yescharacteristic
722C22#1171932311yescharacteristic
723C22C2×D4×Dic1311yescharacteristic
724C4—21no—
725C4—21no—
726C4—22no—
727C4—21no—
728C4—21no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—522no—
734C4—1041no—
735C4#1171930311yescharacteristic
736C4#1171931411yescharacteristic
737C4C2×D4×Dic1311yescharacteristic
738C4#1171953211yescharacteristic
739C2—21no—
740C2—21no—
741C2—42no—
742C2—81no—
743C2—81no—
744C2#1311785611yescharacteristic
745C2#1312373911yescharacteristic
746C2#1312375311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalC13×#3035C2
socleC22×C13C2×C4×D4
cosocleC22×C4×C13C24
hypercenter#3035D13
hypocenterC13#23017
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. C2×#11718858C2semidirect
2. C2×#11718857C2semidirect
3. #13123580C2semidirect
4. #13123404C2semidirect
5. #13115669C2semidirect
6. #13115612C2semidirect
7. #13115549C2semidirect
8. #13115542C2semidirect
9. #13115165C2semidirect
10. #13115165C2semidirect
11. #13115113C2semidirect
12. #13115113C2semidirect
13. #13114695C2semidirect
14. #13114646C2semidirect
24. C13×#464C4semidirect
25. C13×#464C4semidirect
26. C13×#463C4semidirect
27. C13×#463C4semidirect
28. C13×#462C4semidirect
29. C13×#461C4semidirect
30. C13×#460C4semidirect
31. C13×#459C4semidirect
145. #88077D4semidirect
360. #464Dic13semidirect
361. #464Dic13semidirect
362. #463Dic13semidirect
363. #463Dic13semidirect
364. #462Dic13semidirect
365. #461Dic13semidirect
366. #460Dic13semidirect
367. #459Dic13semidirect
642. C13#23017semidirect

Maximal subgroups

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

subgroupindex
C2×#117188582
C2×#117188572
#131235802
#131234042
#131156692
#131156122
#131155492
#131155422
#131151652
#131151132
#131146952
#131146462
C13×#30352
#2301713