Finite Group Databasebeta

← #11866299

Subgroups — #11866299

Order 1152.

1050 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595147C211yesmaximal, characteristic, complemented
2C2×#63925C211yesmaximal, characteristic
3C2×D3×#204C211yesmaximal, characteristic, complemented
4#10594604C211yesmaximal, characteristic, complemented
5#10592486C211yesmaximal, characteristic, complemented
6C3×#4787C211yesmaximal, characteristic, complemented
7C3×#4772C211yesmaximal, characteristic, complemented
8#10591434C211yesmaximal, characteristic, complemented
9#10591432C211yesmaximal, characteristic, complemented
10#10590760C211yesmaximal, characteristic, complemented
11#10590748C211yesmaximal, characteristic, complemented
12#10590694C211yesmaximal, characteristic, complemented
13#10590600C211yesmaximal, characteristic, complemented
14#10590565C211yesmaximal, characteristic, complemented
15#10590559C211yesmaximal, characteristic, complemented
16#80537—31nomaximal
17#78863—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21#64145C2211yescharacteristic, complemented
22C2×#3753C2211yescharacteristic
23C2×#3744C2211yescharacteristic
24#64102C2211yescharacteristic
25C3×#936C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×#893C2211yescharacteristic
30C3×#892C2211yescharacteristic
31#63969—21no—
32#63969—21no—
33#63964—21no—
34#63964—21no—
35#63925—24no—
36#63921—21no—
37D3×(C2×D3)⋊C4—21no—
38C4×#626—21no—
39#63898C2211yescharacteristic
40#63894C2211yescharacteristic
41#63880—21no—
42#63873C2211yescharacteristic, complemented
43#63866C2211yescharacteristic, complemented
44#63855C2211yescharacteristic
45C2×#3717C2211yescharacteristic
46C2×#3717C2211yescharacteristic
47C2×#3716C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×#3711C2211yescharacteristic
50D3×#204—24no—
51C32×#102C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#810C2211yescharacteristic, complemented
59#63572C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63565C2211yescharacteristic, complemented
63#5825—31no—
64C2×#949—31no—
65C2×D3×SD16—31no—
66C2×#911—31no—
67C22×#204—31no—
68#5675—31no—
69#5545—31no—
70#5521—31no—
71C3×#463—31no—
72C3×#416—31no—
73#5162—31no—
74#5153—31no—
75#5102—31no—
76#5057—31no—
77#5019—31no—
78#5004—31no—
79#4841—31no—
80#4839—31no—
81#4818—31no—
82#4818—31no—
83#4818—31no—
84#4818—31no—
85#4818—31no—
86#4802—31no—
87#4787—31no—
88#4787—31no—
89#4787—31no—
90#4787—31no—
91#4787—61no—
92#4787D311yescharacteristic, complemented
93#4772D311yescharacteristic, complemented
94C22×D32—21no—
95C2×C32×D4C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C3×#237—22no—
102C3×#237—22no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#627—21no—
109C2×#626—21no—
110C2×#624—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113D3×D12—22no—
114D3×D12D414yes—
115D3×Dic6—22no—
116D3×Dic6—22no—
117C2×C32×C8C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119#3757—21no—
120#3757—21no—
121#3753—22no—
122#3752—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125#3744—22no—
126C3×#217—21no—
127C3×#217—21no—
128C3×#213—22no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×#204—22no—
137C3×D3×C8—22no—
138#3724—21no—
139#3724—21no—
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3D411yescharacteristic
143Dic3⋊Dic3D411yescharacteristic
144#3722—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3D411yescharacteristic
147(C2×D3)⋊Dic3D411yescharacteristic
148#3717—22no—
149#3717—22no—
150#3716—22no—
151#3715—22no—
152#3711—22no—
153#3042—91noSylow
154C2×C3×#41—31no—
155C2×D3×Q8—31no—
156C2×#237C2×D311yescharacteristic
157C2×D3×D4—31no—
158C22×D12—31no—
159C22×Dic6—31no—
160C2×C3×SD16—31no—
161C2×C3×D8—31no—
162C22×C3×C8—31no—
163C3×#124—31no—
164C3×C4×D4—31no—
165C3×#117—31no—
166#949—64no—
167#944—31no—
168#944—31no—
169#944—31no—
170C2×#215—31no—
171C2×#215—31no—
172C2×#215—31no—
173#936—31no—
174#936—31no—
175#936—61no—
176#936C2×D311yescharacteristic, complemented
177#935—61no—
178#935—61no—
179D4×Dic3—31no—
180C2×#214—31no—
181C2×#214—31no—
182C2×#213—31no—
183C2×#213—31no—
184C2×#213—61no—
185C2×#213C2×D311yescharacteristic
186C4×#67—61no—
187C2×(C2×D3)⋊C4—61no—
188#926—31no—
189#924—61no—
190#924—61no—
191C2×#208—31no—
192D3×SD16—64no—
193#911—64no—
194C2×#204—31no—
195C2×#204—31no—
196C2×#204—31no—
197C2×#204—31no—
198C2×#204—31no—
199C2×#204—61no—
200C2×#204—64no—
201C2×#204C2×D311yescharacteristic
202C2×ΓL(1,𝔽25)—31no—
203C2×D3×C8C2×D311yescharacteristic
204#893—31no—
205#893—31no—
206#893—31no—
207#893—31no—
208#893—61no—
209#893C2×D311yescharacteristic
210#892C2×D311yescharacteristic
211#883—61no—
212#883—61no—
213#67⋊C4—61no—
214D3×C22⋊C4—61no—
215D3×C22⋊C4—61no—
216D3×C22⋊C4—61no—
217#878—61no—
218#878—61no—
219C4×D12—31no—
220C4×D12—61no—
221C4×D12—61no—
222#872—31no—
223#869—31no—
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#103—31no—
227C3×#103—31no—
228C3×#102—21no—
229C3×#102—31no—
230C3×#102C2×D311yescharacteristic, complemented
231C3×#102C2×D311yescharacteristic, complemented
232#835—31no—
233#832C2×D311yescharacteristic, complemented
234#816—31no—
235#816C2×D311yescharacteristic, complemented
236Dic3⋊C8—31no—
237Dic3⋊C8—31no—
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—61no—
242Dic3⋊C8C2×D311yescharacteristic, complemented
243#810—31no—
244#810—31no—
245#810—31no—
246#810—31no—
247#810—61no—
248#810C2×D311yescharacteristic, complemented
249#810C2×D311yescharacteristic, complemented
250C4⋊(C3⋊C8)—31no—
251C23×C32—21no—
252C22×C3⋊D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3C2×D411yescharacteristic
255C2×D32—24no—
256C2×D32—81no—
257C2×D32—81no—
258C32×D4—21no—
259C32×D4—21no—
260C2×C32×C4—21no—
261C2×C32×C4C2411yescharacteristic
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3C2×D411yescharacteristic
264C2×C3⋊Dic3C2×D411yescharacteristic
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)C2×D412yes—
267C4×C3⋊D3—81no—
268#634—21no—
269#634—21no—
270C3×#67—42no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—42no—
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—21no—
279C3×D12C2×D412yes—
280C3×C4×D3—81no—
281C3×C4×D3C2×D412yes—
282C3×C4×D3#4112yes—
283C3×Dic6—21no—
284C3×Dic6—21no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287#627—42no—
288#626—24no—
289#624—81no—
290D3×Dic3—42no—
291D3×Dic3—81no—
292C32×C8—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×AGL(1,ℤ/8)—91no—
297C22×SD16—91no—
298#536—91no—
299#518—91no—
300#463—31no—
301#463—91no—
302#463—91no—
303#463—91no—
304#461—91no—
305#461—91no—
306#461—91no—
307#461—91no—
308#424—91no—
309#419—91no—
310#416—31no—
311C23×D3—61no—
312C23×D3—61no—
313C3×#41—62no—
314C3×#41—62no—
315C2×C3×Q8—31no—
316C2×C3×Q8—31no—
317C2×C3×D4—21no—
318C2×C3×D4—31no—
319C2×C3×D4—61no—
320C2×C3×D4C22×D311yescharacteristic
321C2×C3×D4C22×D311yescharacteristic
322C22×C3×C4—31no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C2×#67—21no—
326C2×#67—61no—
327C22×Dic3—21no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330D3×Q8—62no—
331D3×Q8—62no—
332#237—22no—
333#237—22no—
334D3×D4—34no—
335D3×D4—62no—
336C2×D12—31no—
337C2×D12—31no—
338C2×D12—34no—
339C2×D12—61no—
340C2×D12—62no—
341C2×D12—61no—
342C2×D12C22×D311yescharacteristic
343C2×C4×D3—21no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×C4×D3—121no—
351C2×C4×D3C22×D311yescharacteristic
352C2×Dic6—31no—
353C2×Dic6—31no—
354C2×Dic6—61no—
355C2×Dic6—62no—
356C2×Dic6—62no—
357C2×Dic6—61no—
358C2×Dic6—61no—
359C2×Dic6C22×D311yescharacteristic
360C2×Dic6C22×D311yescharacteristic
361C3×SD16—62no—
362C3×D8—62no—
363C2×C3×C8—21no—
364C2×C3×C8—31no—
365C2×C3×C8—31no—
366C2×C3×C8—62no—
367C2×C3×C8C22×D311yescharacteristic
368C2×C3×C8C22×D311yescharacteristic
369C3×C4⋊C4—21no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4C22×D311yescharacteristic
372C3×C4⋊C4C22×D311yescharacteristic
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C42—31no—
378C3×C42—61no—
379#217—21no—
380#217—21no—
381#217—31no—
382#217—31no—
383#217—61no—
384#217—61no—
385#217—61no—
386#217—61no—
387#217—61no—
388#217—121no—
389#217—121no—
390#215—62no—
391#215—62no—
392#215—62no—
393#214—62no—
394#214—62no—
395#213—22no—
396#213—62no—
397#213—62no—
398#213—122no—
399(C2×D3)⋊C4—21no—
400(C2×D3)⋊C4—21no—
401(C2×D3)⋊C4—31no—
402(C2×D3)⋊C4—31no—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
408(C2×D3)⋊C4—121no—
409C4⋊Dic3—31no—
410C4⋊Dic3—31no—
411C4⋊Dic3—61no—
412C4⋊Dic3—61no—
413C4⋊Dic3C22×D311yescharacteristic
414Dic3⋊C4—31no—
415Dic3⋊C4—31no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418Dic3⋊C4—61no—
419Dic3⋊C4—61no—
420Dic3⋊C4—61no—
421Dic3⋊C4—61no—
422C4×Dic3—21no—
423C4×Dic3—31no—
424C4×Dic3—31no—
425C4×Dic3—61no—
426C4×Dic3C22×D311yescharacteristic
427#208—62no—
428C2×C3⋊C8—31no—
429C2×C3⋊C8—31no—
430C2×C3⋊C8—61no—
431C2×C3⋊C8C22×D311yescharacteristic
432C2×C3⋊C8C22×D311yescharacteristic
433#204—22no—
434#204—62no—
435#204—62no—
436#204—62no—
437#204—62no—
438#204—62no—
439#204—122no—
440ΓL(1,𝔽25)—62no—
441D3×C8—22no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32C22×D411yescharacteristic
446C2×C3⋊D3—22no—
447C2×C3⋊D3—41no—
448C2×C3⋊D3—41no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—22no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3#12112yes—
455D32—84no—
456C32×C4—41no—
457C32×C4C22×D411yescharacteristic
458C32×C4C2×#4111yescharacteristic
459C3⋊Dic3—21no—
460C3⋊Dic3—21no—
461C3⋊Dic3—41no—
462C3×Dic3—21no—
463C3×Dic3—21no—
464C3×Dic3—41no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—31no—
469C22×Q8—91no—
470C22×D4—91no—
471AGL(1,ℤ/8)—184no—
472C2×SD16—31no—
473C2×SD16—91no—
474C2×SD16—91no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16—184no—
479C2×D8—31no—
480C2×D8—91no—
481C2×M16—91no—
482C22×C8—31no—
483C4⋊Q8—91no—
484C4⋊Q8—91no—
485#124—31no—
486#124—91no—
487#123—181no—
488#123—181no—
489C22⋊Q8—181no—
490C22⋊Q8—181no—
491C4×D4—31no—
492C4×D4—91no—
493C4×D4—91no—
494C4×D4—91no—
495C4×D4—181no—
496C4×D4—181no—
497#117—31no—
498#117—91no—
499C2×C22⋊C4—181no—
500C2×C22⋊C4—181no—
501C4⋊C8—31no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C4⋊C8—91no—
505#103—31no—
506#103—31no—
507#103—31no—
508#103—91no—
509#103—91no—
510#103—91no—
511#102—31no—
512#102D3211yescharacteristic, complemented
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—31no—
516C23×C3—41no—
517C23×C3—61no—
518C22×D3—21no—
519C22×D3—64no—
520C22×D3—61no—
521C22×D3—61no—
522C22×D3—64no—
523C22×D3—121no—
524C22×D3—241no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3—241no—
528C22×D3D3×D411yescharacteristic
529C3×Q8—61no—
530C3×Q8—61no—
531C3×Q8—61no—
532C3×Q8—61no—
533C3×D4—21no—
534C3×D4—21no—
535C3×D4—21no—
536C3×D4—21no—
537C3×D4—32no—
538C3×D4—41no—
539C3×D4—41no—
540C3×D4—61no—
541C3×D4—122no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—31no—
546C2×C3×C4—32no—
547C2×C3×C4—32no—
548C2×C3×C4—31no—
549C2×C3×C4—31no—
550C2×C3×C4—41no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—122no—
555C2×C3×C4—241no—
556C2×C3×C4C23×D311yescharacteristic
557C2×C3×C4C23×D311yescharacteristic
558#67—42no—
559#67—64no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—31no—
566C2×Dic3—31no—
567C2×Dic3—42no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—121no—
573C2×Dic3—122no—
574C2×Dic3—241no—
575C2×Dic3D3×D411yescharacteristic
576C2×Dic3D3×D411yescharacteristic
577C2×Dic3D3×D411yescharacteristic
578D12—21no—
579D12—32no—
580D12—32no—
581D12—62no—
582D12—64no—
583D12—61no—
584D12—61no—
585D12—121no—
586D12D3×D412yes—
587C4×D3—81no—
588C4×D3—122no—
589C4×D3—241no—
590C4×D3—241no—
591C4×D3—241no—
592C4×D3—241no—
593C4×D3—241no—
594C4×D3—242no—
595C4×D3#23512yes—
596C4×D3D3×D412yes—
597Dic6—21no—
598Dic6—21no—
599Dic6—21no—
600Dic6—21no—
601Dic6—61no—
602Dic6—61no—
603Dic6—61no—
604Dic6—61no—
605Dic6—121no—
606Dic6—121no—
607Dic6—122no—
608Dic6—122no—
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—41no—
612C3×C8—61no—
613C3×C8—61no—
614C3⋊C8—21no—
615C3⋊C8—21no—
616C3⋊C8—61no—
617C3⋊C8—61no—
618C3⋊C8—121no—
619C2×C32—81no—
620C2×C32C2×#12111yescharacteristic
621C2×C32#57711yescharacteristic
622C2×C32#57711yescharacteristic
623C3⋊D3—42no—
624C3×D3—22no—
625C3×D3—42no—
626C24—181no—
627#41—62no—
628#41—62no—
629C2×Q8—31no—
630C2×Q8—31no—
631C2×Q8—91no—
632C2×Q8—181no—
633C2×Q8—182no—
634C2×Q8—182no—
635C2×D4—31no—
636C2×D4—61no—
637C2×D4—94no—
638C2×D4—91no—
639C2×D4—182no—
640C2×D4—181no—
641C2×D4C2×D3211yescharacteristic
642C22×C4—31no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—181no—
646C22×C4—181no—
647C22×C4—181no—
648C22×C4—181no—
649SD16—62no—
650SD16—182no—
651SD16—182no—
652SD16—182no—
653SD16—182no—
654SD16—182no—
655D8—62no—
656D8—182no—
657M16—182no—
658C2×C8—31no—
659C2×C8—31no—
660C2×C8—62no—
661C2×C8—91no—
662C2×C8C2×D3211yescharacteristic
663C4⋊C4—31no—
664C4⋊C4—91no—
665C4⋊C4—91no—
666C4⋊C4—181no—
667C4⋊C4—181no—
668C4⋊C4—181no—
669C4⋊C4—181no—
670C4⋊C4C2×D3211yescharacteristic
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—91no—
676C22⋊C4—91no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C22⋊C4—181no—
682C42—31no—
683C42—61no—
684C42—91no—
685C22×C3—21no—
686C22×C3—32no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—62no—
696C22×C3—81no—
697C22×C3—81no—
698C22×C3—81no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3C2×D3×D411yescharacteristic
702C22×C3C2×D3×D411yescharacteristic
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—22no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—62no—
709C2×D3—62no—
710C2×D3—122no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3—241no—
716C2×D3—241no—
717C2×D3—244no—
718C2×D3—244no—
719C2×D3#88412yes—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—32no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—61no—
726C3×C4—61no—
727C3×C4—81no—
728C3×C4—121no—
729C3×C4—121no—
730C3×C4—121no—
731C3×C4C2×#23511yescharacteristic
732C3×C4C2×D3×D411yescharacteristic
733C3×C4C2×D3×D411yescharacteristic
734C3×C4D3×#4111yescharacteristic
735Dic3—21no—
736Dic3—21no—
737Dic3—41no—
738Dic3—41no—
739Dic3—41no—
740Dic3—61no—
741Dic3—61no—
742Dic3—61no—
743Dic3—61no—
744Dic3—121no—
745Dic3—121no—
746Dic3—121no—
747Dic3—121no—
748Dic3—241no—
749Dic3#88412yes—
750C32#304211yescharacteristic, complemented, Sylow
751C23—21no—
752C23—31no—
753C23—61no—
754C23—184no—
755C23—181no—
756C23—721no—
757C23—721no—
758Q8—61no—
759Q8—61no—
760Q8—61no—
761Q8—61no—
762Q8—181no—
763Q8—181no—
764Q8—362no—
765D4—21no—
766D4—21no—
767D4—32no—
768D4—61no—
769D4—92no—
770D4—122no—
771D4—184no—
772D4—181no—
773C2×C4—21no—
774C2×C4—31no—
775C2×C4—32no—
776C2×C4—32no—
777C2×C4—31no—
778C2×C4—31no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—91no—
783C2×C4—91no—
784C2×C4—122no—
785C2×C4—181no—
786C2×C4—241no—
787C2×C4—362no—
788C2×C4—721no—
789C2×C4—721no—
790C2×C4—721no—
791C2×C4C22×D3211yescharacteristic
792C8—21no—
793C8—61no—
794C8—61no—
795C8—181no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—62no—
800C2×C3—81no—
801C2×C3—81no—
802C2×C3—122no—
803C2×C3—161no—
804C2×C3C2×#88411yescharacteristic
805C2×C3D3×#12111yescharacteristic
806C2×C3#577011yescharacteristic
807C2×C3#577011yescharacteristic
808C2×C3#577011yescharacteristic
809C2×C3#577511yescharacteristic
810D3—22no—
811D3—42no—
812D3—122no—
813D3—122no—
814D3—242no—
815C22—32no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—61no—
820C22—61no—
821C22—62no—
822C22—121no—
823C22—121no—
824C22—182no—
825C22—361no—
826C22—361no—
827C22—724no—
828C22D32×D411yescharacteristic
829C4—32no—
830C4—41no—
831C4—61no—
832C4—61no—
833C4—121no—
834C4—121no—
835C4—121no—
836C4—181no—
837C4—181no—
838C4—361no—
839C4D3×#23511yescharacteristic
840C4D32×D411yescharacteristic
841C3—21no—
842C3#7886311yescharacteristic, complemented
843C3#8053711yescharacteristic, complemented
844C2—62no—
845C2—81no—
846C2—122no—
847C2—362no—
848C2D3×#88411yescharacteristic
849C2#1059473611yescharacteristic
850C2#1059475711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#63925C2
hypercenter#102D32
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595147C2semidirect
3. C2×D3×#204C2semidirect
4. #10594604C2semidirect
5. #10592486C2semidirect
6. C3×#4787C2semidirect
7. C3×#4772C2semidirect
8. #10591434C2semidirect
9. #10591432C2semidirect
10. #10590760C2semidirect
11. #10590748C2semidirect
12. #10590694C2semidirect
13. #10590600C2semidirect
14. #10590565C2semidirect
15. #10590559C2semidirect
21. #64145C22semidirect
25. C3×#936C22semidirect
42. #63873C22semidirect
43. #63866C22semidirect
51. C32×#102C22semidirect
52. #63641C22semidirect
53. #63637C22semidirect
54. C3×#832C22semidirect
55. C3×#816C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#810C22semidirect
59. #63572C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63567C22semidirect
62. #63565C22semidirect
92. #4787D3semidirect
93. #4772D3semidirect
176. #936C2×D3semidirect
230. C3×#102C2×D3semidirect
231. C3×#102C2×D3semidirect
233. #832C2×D3semidirect
235. #816C2×D3semidirect
242. Dic3⋊C8C2×D3semidirect
248. #810C2×D3semidirect
249. #810C2×D3semidirect
512. #102D32semidirect
750. C32#3042semidirect
842. C3#78863semidirect
843. C3#80537semidirect

Maximal subgroups

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

subgroupindex
#105951472
C2×#639252
C2×D3×#2042
#105946042
#105924862
C3×#47872
C3×#47722
#105914342
#105914322
#105907602
#105907482
#105906942
#105906002
#105905652
#105905592
#805373
#788633