Finite Group Databasebeta

← #11866268

Subgroups — #11866268

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
1C3×#5545C211yesmaximal, characteristic, complemented
2C2×#63934C211yesmaximal, characteristic
3C2×D3×#214C211yesmaximal, characteristic, complemented
4#10593893C211yesmaximal, characteristic, complemented
5#10592715C211yesmaximal, characteristic, complemented
6C3×#5019C211yesmaximal, characteristic, complemented
7#10591489C211yesmaximal, characteristic, complemented
8#10591471C211yesmaximal, characteristic, complemented
9#10590610C211yesmaximal, characteristic, complemented
10#10590600C211yesmaximal, characteristic, complemented
11#10590559C211yesmaximal, characteristic, complemented
12#10590534C211yesmaximal, characteristic, complemented
13#10590366C211yesmaximal, characteristic, complemented
14#10590363C211yesmaximal, characteristic, complemented
15#10590324C211yesmaximal, characteristic, complemented
16#82544—31nomaximal
17#80430—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23C2×#3753C2211yescharacteristic
24#64084C2211yescharacteristic, complemented
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic
28C3×C4×#67—21no—
29C2×C3×(C2×D3)⋊C4—21no—
30C3×#893C2211yescharacteristic
31C3×#892C2211yescharacteristic
32C3×#67⋊C4—21no—
33C3×D3×C22⋊C4—21no—
34C3×C4×D12C2211yescharacteristic
35C3×#872C2211yescharacteristic
36C3×#869C2211yescharacteristic, complemented
37#63934—24no—
38D3×#214—24no—
39#63895—21no—
40#63895—21no—
41#63890—21no—
42#63890—21no—
43#63866C2211yescharacteristic, complemented
44#63864C2211yescharacteristic, complemented
45C2×#3716C2211yescharacteristic
46C2×#3715C2211yescharacteristic
47C2×#3715C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×#3711C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63637C2211yescharacteristic, complemented
52#63636C2211yescharacteristic, complemented
53C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
54C3×#810C2211yescharacteristic, complemented
55C3×#810C2211yescharacteristic, complemented
56C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
57Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63C3×#518—31no—
64C22×#214—31no—
65C2×#932—31no—
66C2×#914—31no—
67C2×D3×SD16—31no—
68#5724—31no—
69#5545D311yescharacteristic, complemented
70#5526—31no—
71C3×#461—31no—
72#5165—31no—
73#5162—31no—
74#5083—31no—
75#5019—31no—
76#5019—31no—
77#5019—31no—
78#5019D311yescharacteristic, complemented
79#5016—31no—
80#5016—31no—
81#5016—31no—
82#5016—31no—
83#5016—31no—
84#5016—61no—
85#5004—31no—
86#5002—31no—
87#4999—31no—
88#4844—31no—
89#4839—31no—
90#4819—31no—
91#4818—31no—
92#4804—31no—
93#4802—31no—
94C23×C3×D3—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C3×D3×D4—22no—
102C3×D3×D4D414yes—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110C2×#626—21no—
111C2×#624—21no—
112C2×D3×Dic3—21no—
113#3799—22no—
114#3799—22no—
115D3×Dic6—22no—
116D3×Dic6—22no—
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C32×C42C2311yescharacteristic
120#3754—22no—
121#3753—22no—
122#3752—21no—
123#3752—21no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#217—21no—
127C3×#214—22no—
128C3×#214—22no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4D411yescharacteristic
133C3×(C2×D3)⋊C4D411yescharacteristic
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4D411yescharacteristic
138C3×Dic3⋊C4D411yescharacteristic
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145#3722—21no—
146#3722—21no—
147#3716—22no—
148#3715—22no—
149#3715—22no—
150#3714—22no—
151#3711—22no—
152D3×C3⋊C8—22no—
153#3042—91noSylow
154C22×C3×D4—31no—
155C2×#239—31no—
156C2×D3×Q8—31no—
157C2×D3×D4C2×D311yescharacteristic
158C2×#235—31no—
159C22×Dic6—31no—
160C2×C3×SD16—31no—
161C2×C3×SD16—31no—
162C3×C4⋊Q8—31no—
163C3×C4×D4—21no—
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4—61no—
168C3×C4×D4—61no—
169C3×C4×D4C2×D311yescharacteristic
170C3×C4×D4C2×D311yescharacteristic
171C3×#117—31no—
172C3×#117—31no—
173C2×C3×C22⋊C4—61no—
174C2×C3×C22⋊C4—61no—
175#947—31no—
176#944—31no—
177C2×#215—31no—
178C2×#215—31no—
179D4×Dic3C2×D311yescharacteristic
180C2×#214—31no—
181C2×#214—31no—
182C2×#214—31no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#214—61no—
186C2×#214—64no—
187C2×#214C2×D311yescharacteristic
188C2×#214C2×D311yescharacteristic
189#932—64no—
190C2×#213—31no—
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—61no—
194C4×#67—21no—
195C2×(C2×D3)⋊C4—21no—
196C2×#208—31no—
197C22×C3⋊C8—31no—
198#914—64no—
199D3×SD16—64no—
200C2×D24—31no—
201C2×#204—31no—
202C2×ΓL(1,𝔽25)—31no—
203C2×D3×C8—31no—
204#897—61no—
205#897—61no—
206#896—61no—
207#896—61no—
208#894—61no—
209#894—61no—
210#893C2×D311yescharacteristic
211#892C2×D311yescharacteristic
212#886—61no—
213#886—61no—
214#67⋊C4—21no—
215D3×C22⋊C4—21no—
216#875—31no—
217#875—31no—
218#875—31no—
219#875—61no—
220C4×D12C2×D311yescharacteristic
221#872C2×D311yescharacteristic
222#869—31no—
223#869C2×D311yescharacteristic, complemented
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#103—31no—
227#835—31no—
228#835—31no—
229#821—31no—
230#816—31no—
231Dic3⋊C8—31no—
232Dic3⋊C8—31no—
233#810—31no—
234#810—31no—
235#810—31no—
236#810—31no—
237#810—31no—
238#810—61no—
239#810C2×D311yescharacteristic, complemented
240#810C2×D311yescharacteristic, complemented
241#809—31no—
242#809—31no—
243#809—31no—
244#809—61no—
245C4⋊(C3⋊C8)—31no—
246C4⋊(C3⋊C8)—31no—
247C4⋊(C3⋊C8)—31no—
248C4⋊(C3⋊C8)—31no—
249C4⋊(C3⋊C8)—61no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251C23×C32—21no—
252C22×C3⋊D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—24no—
255C22×C3×D3—81no—
256C22×C3×D3—81no—
257C22×C3×D3C2×D411yescharacteristic
258C32×D4—21no—
259C32×D4C2×D412yes—
260C2×C32×C4—21no—
261C2×C32×C4—81no—
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3—21no—
266C4⋊(C3⋊D3)—21no—
267C4⋊(C3⋊D3)—21no—
268#634—21no—
269#634—21no—
270C3×#67—24no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—81no—
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—21no—
279C3×D12C2×D412yes—
280C3×C4×D3—81no—
281C3×C4×D3—81no—
282C3×C4×D3C2×D412yes—
283C3×C4×D3#4112yes—
284C3×Dic6—21no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288#627—42no—
289#626—42no—
290#624—42no—
291D3×Dic3—42no—
292C3⋊(C3⋊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—31no—
300#463—91no—
301#463—91no—
302#463—91no—
303#463—91no—
304#461—31no—
305#461—91no—
306#461—91no—
307#461—91no—
308#424—91no—
309#419—91no—
310#416—91no—
311C24×C3—61no—
312C23×D3—21no—
313C2×C3×Q8—31no—
314C2×C3×Q8—31no—
315C2×C3×D4—21no—
316C2×C3×D4—34no—
317C2×C3×D4—31no—
318C2×C3×D4—62no—
319C2×C3×D4—61no—
320C2×C3×D4C22×D311yescharacteristic
321C2×C3×D4C22×D311yescharacteristic
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—31no—
325C22×C3×C4—41no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C22×C3×C4—61no—
329C2×#67—21no—
330C2×#67—61no—
331C22×Dic3—21no—
332C22×Dic3—61no—
333#239—62no—
334#239—62no—
335D3×Q8—62no—
336D3×Q8—62no—
337D3×D4—22no—
338D3×D4D1214yes—
339#235—62no—
340#235—62no—
341C2×D12—31no—
342C2×D12—31no—
343C2×D12—61no—
344C2×D12—61no—
345C2×D12C22×D311yescharacteristic
346C2×C4×D3—21no—
347C2×C4×D3—21no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×C4×D3—61no—
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×SD16—62no—
363C2×C3×C8—31no—
364C2×C3×C8—31no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4C22×D311yescharacteristic
372C3×C4⋊C4C22×D311yescharacteristic
373C3×C22⋊C4—21no—
374C3×C22⋊C4—21no—
375C3×C22⋊C4—31no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—41no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C42—21no—
383C3×C42—31no—
384C3×C42—61no—
385C3×C42C22×D311yescharacteristic
386C3×C42C22×D311yescharacteristic
387#217—21no—
388#215—62no—
389#215—62no—
390#214—22no—
391#214—22no—
392#214—62no—
393#214—62no—
394#214—62no—
395#214—62no—
396#214—62no—
397#214—122no—
398#213—62no—
399#213—62no—
400#213—62no—
401#213—122no—
402(C2×D3)⋊C4—21no—
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
408(C2×D3)⋊C4—61no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—121no—
414(C2×D3)⋊C4—121no—
415(C2×D3)⋊C4#6711yescharacteristic
416(C2×D3)⋊C4#6711yescharacteristic
417C4⋊Dic3—21no—
418C4⋊Dic3—21no—
419C4⋊Dic3—61no—
420C4⋊Dic3—61no—
421C4⋊Dic3C22×D311yescharacteristic
422Dic3⋊C4—61no—
423Dic3⋊C4—61no—
424Dic3⋊C4#6711yescharacteristic
425Dic3⋊C4#6711yescharacteristic
426C4×Dic3—21no—
427C4×Dic3C22×D311yescharacteristic
428#208—62no—
429C2×C3⋊C8—31no—
430C2×C3⋊C8—31no—
431C2×C3⋊C8—31no—
432C2×C3⋊C8—31no—
433C2×C3⋊C8—61no—
434C2×C3⋊C8—61no—
435C2×C3⋊C8—62no—
436C2×C3⋊C8C22×D311yescharacteristic
437C2×C3⋊C8C22×D311yescharacteristic
438D24—62no—
439#204—62no—
440ΓL(1,𝔽25)—62no—
441D3×C8—62no—
442C22×C32—22no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32C22×D411yescharacteristic
446C2×C3⋊D3—41no—
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—84no—
455C2×C3×D3#12112yes—
456C32×C4—21no—
457C32×C4—21no—
458C32×C4—41no—
459C32×C4C22×D411yescharacteristic
460C32×C4C2×#4111yescharacteristic
461C3⋊Dic3—41no—
462C3×Dic3—21no—
463C3×Dic3—21no—
464C3×Dic3—41no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—91no—
469C22×Q8—91no—
470C22×D4—31no—
471AGL(1,ℤ/8)—184no—
472C2×SD16—31no—
473C2×SD16—31no—
474C2×SD16—91no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16—184no—
479C2×D8—91no—
480C2×D8—91no—
481C2×M16—91no—
482C22×C8—91no—
483C4⋊Q8—31no—
484C4⋊Q8—91no—
485#124—91no—
486#124—91no—
487#123—181no—
488#123—181no—
489C22⋊Q8—181no—
490C22⋊Q8—181no—
491C4×D4—31no—
492C4×D4—31no—
493C4×D4—31no—
494C4×D4—61no—
495C4×D4—61no—
496C4×D4D3211yescharacteristic
497#117—31no—
498#117—31no—
499C2×C22⋊C4—61no—
500C2×C22⋊C4—61no—
501C4⋊C8—31no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C4⋊C8—91no—
505#103—31no—
506#103—31no—
507#103—91no—
508#103—91no—
509#103—91no—
510#103—91no—
511#102—91no—
512#102—91no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—31no—
516C23×C3—41no—
517C23×C3—64no—
518C23×C3—61no—
519C23×C3—241no—
520C23×C3—241no—
521C22×D3—21no—
522C22×D3—24no—
523C22×D3—61no—
524C22×D3—61no—
525C22×D3—81no—
526C22×D3—81no—
527C22×D3—121no—
528C22×D3C2×#6711yescharacteristic
529C3×Q8—61no—
530C3×Q8—61no—
531C3×Q8—61no—
532C3×Q8—61no—
533C3×D4—21no—
534C3×D4—21no—
535C3×D4—22no—
536C3×D4—32no—
537C3×D4—41no—
538C3×D4—64no—
539C3×D4—61no—
540C3×D4C2×D1212yes—
541C3×D4D3×D412yes—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—31no—
548C2×C3×C4—32no—
549C2×C3×C4—32no—
550C2×C3×C4—31no—
551C2×C3×C4—31no—
552C2×C3×C4—41no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—81no—
557C2×C3×C4—81no—
558C2×C3×C4—82no—
559C2×C3×C4—241no—
560C2×C3×C4—241no—
561C2×C3×C4—241no—
562C2×C3×C4D3×D411yescharacteristic
563C2×C3×C4D3×D411yescharacteristic
564C2×C3×C4C2×#6711yescharacteristic
565C2×C3×C4C2×#6711yescharacteristic
566C2×C3×C4C23×D311yescharacteristic
567C2×C3×C4C23×D311yescharacteristic
568#67—24no—
569#67—122no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—81no—
576C2×Dic3—121no—
577C2×Dic3—122no—
578C2×Dic3C2×#6711yescharacteristic
579C2×Dic3C2×#6711yescharacteristic
580C2×Dic3C2×#6711yescharacteristic
581D12—21no—
582D12—61no—
583D12—61no—
584D12—61no—
585D12—61no—
586D12—121no—
587D12—121no—
588D12—122no—
589D12C2×D1212yes—
590C4×D3—81no—
591C4×D3—81no—
592C4×D3—122no—
593C4×D3—122no—
594C4×D3—122no—
595C4×D3C2×D1212yes—
596C4×D3#23512yes—
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—61no—
610C3×C8—61no—
611C3⋊C8—21no—
612C3⋊C8—21no—
613C3⋊C8—61no—
614C3⋊C8—61no—
615C3⋊C8—61no—
616C3⋊C8—61no—
617C3⋊C8—121no—
618C3⋊C8—121no—
619C2×C32—42no—
620C2×C32C2×#12111yescharacteristic
621C2×C32#57711yescharacteristic
622C2×C32#57711yescharacteristic
623C3⋊D3—81no—
624C3×D3—22no—
625C3×D3—42no—
626C24—61no—
627#41—182no—
628#41—182no—
629C2×Q8—31no—
630C2×Q8—31no—
631C2×Q8—91no—
632C2×Q8—181no—
633C2×Q8—182no—
634C2×Q8—182no—
635C2×D4—34no—
636C2×D4—31no—
637C2×D4—62no—
638C2×D4—61no—
639C2×D4—91no—
640C2×D4—181no—
641C2×D4C2×D3211yescharacteristic
642C22×C4—21no—
643C22×C4—31no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—181no—
648C22×C4—181no—
649SD16—62no—
650SD16—62no—
651SD16—182no—
652SD16—182no—
653SD16—182no—
654SD16—182no—
655D8—182no—
656D8—182no—
657M16—182no—
658C2×C8—31no—
659C2×C8—31no—
660C2×C8—91no—
661C2×C8—91no—
662C2×C8—182no—
663C4⋊C4—31no—
664C4⋊C4—31no—
665C4⋊C4—31no—
666C4⋊C4—61no—
667C4⋊C4—61no—
668C4⋊C4—181no—
669C4⋊C4—181no—
670C4⋊C4C2×D3211yescharacteristic
671C22⋊C4—21no—
672C22⋊C4—31no—
673C22⋊C4—31no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C22⋊C4—61no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C22⋊C4—181no—
682C42—31no—
683C42—61no—
684C42C2×D3211yescharacteristic
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—21no—
688C22×C3—32no—
689C22×C3—42no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—62no—
697C22×C3—81no—
698C22×C3—81no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—244no—
702C22×C3C2×D3×D411yescharacteristic
703C22×C3C22×#6711yescharacteristic
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—22no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—84no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3—121no—
716C2×D3—241no—
717C2×D3—241no—
718C2×D3—241no—
719C2×D3#93012yes—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—32no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—41no—
731C3×C4—61no—
732C3×C4—61no—
733C3×C4—81no—
734C3×C4—121no—
735C3×C4—121no—
736C3×C4—121no—
737C3×C4C22×D1211yescharacteristic
738C3×C4C2×#23511yescharacteristic
739C3×C4C2×D3×D411yescharacteristic
740C3×C4D3×#4111yescharacteristic
741Dic3—21no—
742Dic3—21no—
743Dic3—41no—
744Dic3—41no—
745Dic3—41no—
746Dic3—121no—
747Dic3—121no—
748Dic3—241no—
749Dic3#93012yes—
750C32#304211yescharacteristic, complemented, Sylow
751C23—21no—
752C23—31no—
753C23—64no—
754C23—61no—
755C23—181no—
756C23—241no—
757C23—241no—
758Q8—61no—
759Q8—61no—
760Q8—61no—
761Q8—61no—
762Q8—181no—
763Q8—181no—
764Q8—362no—
765D4—21no—
766D4—32no—
767D4—64no—
768D4—61no—
769D4—181no—
770D4—181no—
771D4—362no—
772D4D3×D1212yes—
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—81no—
783C2×C4—181no—
784C2×C4—241no—
785C2×C4—241no—
786C2×C4—241no—
787C2×C4—362no—
788C2×C4—362no—
789C2×C4D3×#6711yescharacteristic
790C2×C4D3×#6711yescharacteristic
791C2×C4C22×D3211yescharacteristic
792C8—61no—
793C8—61no—
794C8—181no—
795C8—181no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—42no—
800C2×C3—42no—
801C2×C3—62no—
802C2×C3—82no—
803C2×C3—122no—
804C2×C3D3×#12111yescharacteristic
805C2×C3#576211yescharacteristic
806C2×C3#577811yescharacteristic
807C2×C3C2×#93011yescharacteristic
808C2×C3#583611yescharacteristic
809C2×C3#583611yescharacteristic
810D3—22no—
811D3—42no—
812D3—241no—
813D3—241no—
814D3—481no—
815C22—22no—
816C22—32no—
817C22—41no—
818C22—41no—
819C22—61no—
820C22—61no—
821C22—62no—
822C22—121no—
823C22—121no—
824C22—244no—
825C22—361no—
826C22—361no—
827C22—361no—
828C22C2×D3×#6711yescharacteristic
829C4—21no—
830C4—21no—
831C4—32no—
832C4—41no—
833C4—61no—
834C4—61no—
835C4—121no—
836C4—121no—
837C4—121no—
838C4—361no—
839C4C2×D3×D1211yescharacteristic
840C4D3×#23511yescharacteristic
841C3—21no—
842C3#8043011yescharacteristic, complemented
843C3#8254411yescharacteristic, complemented
844C2—42no—
845C2—62no—
846C2—122no—
847C2—721no—
848C2D3×#93011yescharacteristic
849C2#1059510511yescharacteristic
850C2#1059546411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×#63934C2
hypercenterC4×D4D32
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5545C2semidirect
3. C2×D3×#214C2semidirect
4. #10593893C2semidirect
5. #10592715C2semidirect
6. C3×#5019C2semidirect
7. #10591489C2semidirect
8. #10591471C2semidirect
9. #10590610C2semidirect
10. #10590600C2semidirect
11. #10590559C2semidirect
12. #10590534C2semidirect
13. #10590366C2semidirect
14. #10590363C2semidirect
15. #10590324C2semidirect
24. #64084C22semidirect
36. C3×#869C22semidirect
43. #63866C22semidirect
44. #63864C22semidirect
51. #63637C22semidirect
52. #63636C22semidirect
53. C4⋊(C3⋊(C3⋊C8))C22semidirect
54. C3×#810C22semidirect
55. C3×#810C22semidirect
56. C3×C4⋊(C3⋊C8)C22semidirect
57. Dic3⋊(C3⋊C8)C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63567C22semidirect
60. #63565C22semidirect
61. #63565C22semidirect
62. #63564C22semidirect
69. #5545D3semidirect
78. #5019D3semidirect
223. #869C2×D3semidirect
239. #810C2×D3semidirect
240. #810C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
750. C32#3042semidirect
842. C3#80430semidirect
843. C3#82544semidirect

Maximal subgroups

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

subgroupindex
C3×#55452
C2×#639342
C2×D3×#2142
#105938932
#105927152
C3×#50192
#105914892
#105914712
#105906102
#105906002
#105905592
#105905342
#105903662
#105903632
#105903242
#825443
#804303