Finite Group Databasebeta

← #11861229

Subgroups — #11861229

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 659 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64159C211yesmaximal, characteristic
2C3×#5819C211yesmaximal, characteristic, complemented
3#10594780C211yesmaximal, characteristic, complemented
4C3×#5236C211yesmaximal, characteristic, complemented
5#10591663C214yesmaximal, complemented
6#10591662C214yesmaximal, complemented
7C2×#63578C211yesmaximal, characteristic, complemented
8#10591113C211yesmaximal, characteristic, complemented
9#10591057C211yesmaximal, characteristic, complemented
10#83812—31nomaximal
11#78990—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C2×#3828C2211yescharacteristic
14#64159C412yescomplemented
15#64159C412yescomplemented
16#64159C2212yes—
17#64159C2212yes—
18C2×#3756C411yescharacteristic, complemented
19C2×#3755C411yescharacteristic, complemented
20C2×#3754C411yescharacteristic, complemented
21C2×#3753C411yescharacteristic, complemented
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×#948—22no—
24C3×#948C2214yescomplemented
25C3×#926C2211yescharacteristic
26C2×C3×#208—22no—
27C2×C3×#208C2211yescharacteristic
28C2×C3×#208C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30#63818—22no—
31#63817—22no—
32#63817C2214yescomplemented
33C3×#837C2214yescomplemented
34#63578C2212yescomplemented
35#63578C2212yescomplemented
36#63570C2214yescomplemented
37#63554C2212yescomplemented
38Dic3×C3⋊C8C2212yescomplemented
39C3×#568—31no—
40C2×#950—31no—
41C2×#950—31no—
42C2×#950—61no—
43#5819D311yescharacteristic, complemented
44#5745—31no—
45#5745—31no—
46C3×#421—31no—
47#5236D311yescharacteristic, complemented
48#5145—34no—
49#5144—34no—
50#5139—31no—
51C2×#822—31no—
52C2×#822—31no—
53#5122—31no—
54#5005—31no—
55#4997—31no—
56#4824—34no—
57#4823—34no—
58C32×#41—21no—
59C32×#41—21no—
60C32×#41C2×C412yes—
61C32×#41C2312yes—
62C2×C32×Q8C2×C411yescharacteristic
63C2×C32×D4—21no—
64C2×C32×D4C2×C411yescharacteristic
65C22×C32×C4—21no—
66C22×C32×C4C2311yescharacteristic
67C2×#638—21no—
68#3828—21no—
69#3828—21no—
70#3828C2×C412yes—
71#3828C2312yes—
72C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×#634C2×C411yescharacteristic
75#3756C2×C412yes—
76#3756C2×C412yes—
77#3755C2×C412yes—
78#3755C2×C412yes—
79#3754C2×C412yes—
80#3754C2×C412yes—
81#3753C2×C412yes—
82#3753C2×C412yes—
83C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
84C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
85C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
86C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C2×C3⋊(C3⋊C8)C2311yescharacteristic
89C3×#217—21no—
90C3×C4⋊Dic3—21no—
91C3×C4×Dic3C2312yes—
92C3×#208—21no—
93C3×#208—21no—
94C3×#208—24no—
95C3×#208D412yes—
96C3×#208D412yes—
97C3×#208C2312yes—
98C3×#208C2312yes—
99C2×C3×C3⋊C8—21no—
100C2×C3×C3⋊C8—21no—
101C2×C3×C3⋊C8—24no—
102C2×C3×C3⋊C8C2312yes—
103#3712—24no—
104#3710—24no—
105#2957—91noSylow
106C2×C3×#41—21no—
107C2×C3×#41C2×D311yescharacteristic
108C2×C3×#41C2×D311yescharacteristic
109C2×#235—31no—
110C2×#235—31no—
111C2×#235—61no—
112C3×#131—34no—
113C3×#131—62no—
114C2×C3×M16—31no—
115C2×C3×M16—31no—
116C2×C3×M16—31no—
117C2×C3×M16—62no—
118C3×#117—31no—
119#950—32no—
120#950—32no—
121#950—32no—
122#950—32no—
123#950—32no—
124#950—32no—
125#950—32no—
126#950—32no—
127#950—62no—
128#950—62no—
129#950—62no—
130#950—62no—
131#948—22no—
132#948C2×D314yescomplemented
133C2×#216—31no—
134C2×#216—31no—
135C2×#216—61no—
136C2×#215—31no—
137C2×#215—31no—
138C2×#215—61no—
139C2×#214—31no—
140C2×#214—31no—
141C2×#214—61no—
142C2×#213—31no—
143C2×#213—31no—
144C2×#213—61no—
145#926C2×D311yescharacteristic
146C2×#208—22no—
147C2×#208C2×D311yescharacteristic
148C2×#208C2×D311yescharacteristic
149C2×#208C2×D311yescharacteristic
150C22×C3⋊C8—31no—
151C22×C3⋊C8—31no—
152C22×C3⋊C8—61no—
153#907—34no—
154#907—62no—
155D3×M16—62no—
156D3×M16—62no—
157#901—34no—
158#901—62no—
159C3×#104—34no—
160#837C2×D314yescomplemented
161#825—34no—
162#822—32no—
163#822—32no—
164#822—32no—
165#822—32no—
166#815—32no—
167C8×Dic3—32no—
168#805—34no—
169#803—32no—
170C4×C3⋊C8—32no—
171C23×C32—21no—
172C23×C32#4111yescharacteristic
173C22×C3⋊D3—21no—
174C32×Q8—21no—
175C32×Q8C22×C412yes—
176C32×D4—22no—
177C32×D4—22no—
178C32×D4—21no—
179C32×D4C22×C412yes—
180C2×C32×C4—21no—
181C2×C32×C4—22no—
182C2×C32×C4—22no—
183C2×C32×C4C22×C411yescharacteristic
184C2×C32×C4C22×C411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4#4111yescharacteristic
188C2×C32×C4C2411yescharacteristic
189#638—22no—
190#638—22no—
191C2×C3⋊Dic3—21no—
192C4⋊(C3⋊D3)—21no—
193C4⋊(C3⋊D3)C22×C412yes—
194C4×C3⋊D3—22no—
195C4×C3⋊D3—22no—
196#634—21no—
197#634C22×C412yes—
198C2×C3×Dic3—22no—
199C3⋊(C3⋊C8)C22×C411yescharacteristic
200C3⋊(C3⋊C8)C22×C411yescharacteristic
201C3⋊(C3⋊C8)C22×C411yescharacteristic
202C3⋊(C3⋊C8)C22×C411yescharacteristic
203C3×C3⋊C8—22no—
204C3×C3⋊C8—22no—
205C3×C3⋊C8C2×D414yes—
206C2×#135—91no—
207#568—31no—
208#568—91no—
209#444—94no—
210#443—94no—
211C2×#108—91no—
212#421—31no—
213#421—91no—
214#405—91no—
215C3×#41—21no—
216C3×#41—21no—
217C3×#41—21no—
218C3×#41—21no—
219C3×#41—22no—
220C3×#41—22no—
221C3×#41—41no—
222C3×#41—41no—
223C3×#41C4×D312yes—
224C3×#41C4×D312yes—
225C3×#41C22×D312yes—
226C3×#41C22×D312yes—
227C2×C3×Q8—21no—
228C2×C3×Q8C4×D311yescharacteristic
229C2×C3×Q8C4×D311yescharacteristic
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—41no—
234C2×C3×D4C4×D311yescharacteristic
235C2×C3×D4C4×D311yescharacteristic
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—41no—
240C22×C3×C4C22×D311yescharacteristic
241C22×C3×C4C22×D311yescharacteristic
242C2×#67—61no—
243C2×#67—61no—
244C2×#67—121no—
245#235—32no—
246#235—32no—
247#235—32no—
248#235—32no—
249#235—62no—
250#235—62no—
251#235—61no—
252#235—61no—
253#235—61no—
254#235—61no—
255#235—121no—
256#235—121no—
257C2×D12—31no—
258C2×D12—31no—
259C2×D12—61no—
260C2×C4×D3—61no—
261C2×C4×D3—61no—
262C2×C4×D3—121no—
263C2×Dic6—31no—
264C2×Dic6—31no—
265C2×Dic6—61no—
266C3×M16—32no—
267C3×M16—32no—
268C3×M16—32no—
269C3×M16—32no—
270C3×M16—64no—
271C3×M16—61no—
272C3×M16—61no—
273C2×C3×C8—32no—
274C2×C3×C8—64no—
275C2×C3×C8—61no—
276C2×C3×C8—61no—
277C3×C4⋊C4—61no—
278C3×C22⋊C4—61no—
279C3×C42—32no—
280#217—21no—
281#216—32no—
282#216—32no—
283#216—32no—
284#216—32no—
285#216—62no—
286#216—62no—
287#215—32no—
288#215—32no—
289#215—32no—
290#215—32no—
291#215—62no—
292#215—62no—
293#214—32no—
294#214—32no—
295#214—32no—
296#214—32no—
297#214—62no—
298#214—62no—
299#213—32no—
300#213—32no—
301#213—32no—
302#213—32no—
303#213—62no—
304#213—62no—
305C4⋊Dic3—21no—
306C4×Dic3C22×D312yes—
307#208—21no—
308#208—21no—
309#208—24no—
310#208#6712yes—
311#208#6712yes—
312#208C22×D312yes—
313#208C22×D312yes—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—24no—
317C2×C3⋊C8—31no—
318C2×C3⋊C8—31no—
319C2×C3⋊C8—31no—
320C2×C3⋊C8—31no—
321C2×C3⋊C8—31no—
322C2×C3⋊C8—31no—
323C2×C3⋊C8—31no—
324C2×C3⋊C8—31no—
325C2×C3⋊C8—31no—
326C2×C3⋊C8—31no—
327C2×C3⋊C8—31no—
328C2×C3⋊C8—31no—
329C2×C3⋊C8—61no—
330C2×C3⋊C8—61no—
331C2×C3⋊C8—61no—
332C2×C3⋊C8—61no—
333C2×C3⋊C8—61no—
334C2×C3⋊C8—61no—
335C2×C3⋊C8C22×D312yes—
336ΓL(1,𝔽25)—64no—
337ΓL(1,𝔽25)—64no—
338D3×C8—64no—
339D3×C8—64no—
340C22×C32—22no—
341C22×C32—41no—
342C22×C32—81no—
343C22×C32C4×D411yescharacteristic
344C22×C32C4×D411yescharacteristic
345C22×C32C2×#4111yescharacteristic
346C2×C3⋊D3—22no—
347C2×C3⋊D3—81no—
348C32×C4—22no—
349C32×C4C4×D411yescharacteristic
350C32×C4C4×D411yescharacteristic
351C32×C4C23×C411yescharacteristic
352C32×C4C22×D411yescharacteristic
353C3⋊Dic3—22no—
354C3×Dic3—42no—
355C2×#41—91no—
356C2×#41D3211yescharacteristic
357#135—92no—
358#135—92no—
359#135—92no—
360#135—92no—
361C2×Q16—91no—
362C2×SD16—91no—
363C2×SD16—91no—
364C2×D8—91no—
365#131—34no—
366#131—62no—
367#131—94no—
368#131—182no—
369C2×M16—31no—
370C2×M16—31no—
371C2×M16—31no—
372C2×M16—62no—
373C2×M16—182no—
374C22×C8—91no—
375#117—31no—
376#108—92no—
377#108—92no—
378#104—34no—
379#104—94no—
380#97—92no—
381C4×C8—92no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—41no—
386C23×C3#23511yescharacteristic
387C23×C3#23711yescharacteristic
388C22×D3—61no—
389C22×D3—61no—
390C22×D3—121no—
391C3×Q8—21no—
392C3×Q8—21no—
393C3×Q8—22no—
394C3×Q8—41no—
395C3×Q8C2×C4×D312yes—
396C3×Q8C2×C4×D312yes—
397C3×D4—22no—
398C3×D4—22no—
399C3×D4—22no—
400C3×D4—22no—
401C3×D4—21no—
402C3×D4—21no—
403C3×D4—22no—
404C3×D4—41no—
405C3×D4—42no—
406C3×D4—42no—
407C3×D4C2×C4×D312yes—
408C3×D4C2×C4×D312yes—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4—41no—
424C2×C3×C4—62no—
425C2×C3×C4C2×C4×D311yescharacteristic
426C2×C3×C4C2×C4×D311yescharacteristic
427C2×C3×C4C2×C4×D311yescharacteristic
428C2×C3×C4C2×C4×D311yescharacteristic
429C2×C3×C4#23511yescharacteristic
430C2×C3×C4D3×D411yescharacteristic
431C2×C3×C4D3×D411yescharacteristic
432C2×C3×C4#23711yescharacteristic
433C2×C3×C4C2×#6711yescharacteristic
434C2×C3×C4C2×#6711yescharacteristic
435C2×C3×C4C23×D311yescharacteristic
436C2×C3×C4C23×D311yescharacteristic
437#67—62no—
438#67—62no—
439#67—62no—
440#67—62no—
441#67—122no—
442#67—122no—
443C2×Dic3—22no—
444C2×Dic3—61no—
445C2×Dic3—61no—
446C2×Dic3—121no—
447D12—32no—
448D12—32no—
449D12—62no—
450D12—61no—
451D12—61no—
452D12—121no—
453C4×D3—62no—
454C4×D3—62no—
455C4×D3—62no—
456C4×D3—62no—
457C4×D3—122no—
458C4×D3—122no—
459Dic6—32no—
460Dic6—32no—
461Dic6—62no—
462Dic6—61no—
463Dic6—61no—
464Dic6—121no—
465C3×C8—34no—
466C3×C8—62no—
467C3×C8—62no—
468C3⋊C8—22no—
469C3⋊C8—22no—
470C3⋊C8—31no—
471C3⋊C8—31no—
472C3⋊C8—31no—
473C3⋊C8—31no—
474C3⋊C8—31no—
475C3⋊C8—31no—
476C3⋊C8—31no—
477C3⋊C8—31no—
478C3⋊C8—61no—
479C3⋊C8—61no—
480C3⋊C8—61no—
481C3⋊C8—61no—
482C3⋊C8C2×#6714yes—
483C2×C32—21no—
484C2×C32—21no—
485C2×C32—21no—
486C2×C32—42no—
487C2×C32C2×C4×D411yescharacteristic
488C3⋊D3—42no—
489#41—21no—
490#41—21no—
491#41—92no—
492#41—92no—
493#41—181no—
494#41—181no—
495#41#62412yes—
496#41C2×D3212yes—
497C2×Q8—91no—
498C2×Q8#62411yescharacteristic
499C2×D4—21no—
500C2×D4—91no—
501C2×D4—181no—
502C2×D4#62411yescharacteristic
503C22×C4—21no—
504C22×C4—181no—
505C22×C4C2×D3211yescharacteristic
506Q16—92no—
507Q16—92no—
508SD16—92no—
509SD16—92no—
510SD16—92no—
511SD16—92no—
512D8—92no—
513D8—92no—
514M16—32no—
515M16—32no—
516M16—32no—
517M16—32no—
518M16—64no—
519M16—61no—
520M16—61no—
521M16—184no—
522C2×C8—32no—
523C2×C8—64no—
524C2×C8—61no—
525C2×C8—61no—
526C2×C8—91no—
527C2×C8—91no—
528C2×C8—91no—
529C2×C8—91no—
530C2×C8—91no—
531C2×C8—91no—
532C2×C8—184no—
533C4⋊C4—61no—
534C22⋊C4—61no—
535C42—32no—
536C22×C3—22no—
537C22×C3—22no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—21no—
541C22×C3—42no—
542C22×C3—41no—
543C22×C3—41no—
544C22×C3—42no—
545C22×C3—81no—
546C22×C3—81no—
547C22×C3—82no—
548C22×C3#67⋊C411yescharacteristic
549C22×C3#67⋊C411yescharacteristic
550C22×C3C4×#6711yescharacteristic
551C22×C3C4×#6711yescharacteristic
552C22×C3C2×#23511yescharacteristic
553C22×C3C2×#23711yescharacteristic
554C2×D3—62no—
555C2×D3—62no—
556C2×D3—122no—
557C2×D3—241no—
558C2×D3—241no—
559C2×D3—242no—
560C3×C4—22no—
561C3×C4—22no—
562C3×C4—21no—
563C3×C4—21no—
564C3×C4—21no—
565C3×C4—21no—
566C3×C4—42no—
567C3×C4—122no—
568C3×C4#67⋊C411yescharacteristic
569C3×C4#67⋊C411yescharacteristic
570C3×C4C4×#6711yescharacteristic
571C3×C4C4×#6711yescharacteristic
572C3×C4C22×C4×D311yescharacteristic
573C3×C4C22×C4×D311yescharacteristic
574C3×C4C2×D3×D411yescharacteristic
575C3×C4C22×#6711yescharacteristic
576Dic3—42no—
577Dic3—62no—
578Dic3—62no—
579Dic3—122no—
580C32#295711yescharacteristic, complemented, Sylow
581C23—21no—
582C23—181no—
583C23#380411yescharacteristic
584Q8—21no—
585Q8—92no—
586Q8—181no—
587Q8C2×#62412yes—
588D4—22no—
589D4—22no—
590D4—21no—
591D4—92no—
592D4—182no—
593D4—182no—
594D4—181no—
595D4C2×#62412yes—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—62no—
600C2×C4—181no—
601C2×C4—182no—
602C2×C4—182no—
603C2×C4#380411yescharacteristic
604C2×C4C2×#62411yescharacteristic
605C2×C4C2×#62411yescharacteristic
606C2×C4D3×#6711yescharacteristic
607C2×C4D3×#6711yescharacteristic
608C2×C4C22×D3211yescharacteristic
609C8—34no—
610C8—62no—
611C8—62no—
612C8—91no—
613C8—91no—
614C8—91no—
615C8—91no—
616C2×C3—22no—
617C2×C3—21no—
618C2×C3—21no—
619C2×C3—21no—
620C2×C3—21no—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—21no—
624C2×C3—41no—
625C2×C3—41no—
626C2×C3—42no—
627C2×C3—42no—
628C2×C3—82no—
629C2×C3C2×#67⋊C411yescharacteristic
630C2×C3C2×C4×#6711yescharacteristic
631D3—122no—
632D3—122no—
633D3—242no—
634C22—22no—
635C22—41no—
636C22—81no—
637C22—182no—
638C22—721no—
639C22#6395211yescharacteristic
640C22#6395211yescharacteristic
641C22C2×#380411yescharacteristic
642C4—22no—
643C4—122no—
644C4—182no—
645C4#6395211yescharacteristic
646C4#6395211yescharacteristic
647C4C22×#62411yescharacteristic
648C4C2×D3×#6711yescharacteristic
649C3—21no—
650C3#7899011yescharacteristic, complemented
651C3#8381211yescharacteristic, complemented
652C2—21no—
653C2—21no—
654C2—21no—
655C2—42no—
656C2—362no—
657C2C2×#6395211yescharacteristic
subgroupG/H
centerC4C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×C4×D4
prime radicalC2×#64159C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2957
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5819C2semidirect
3. #10594780C2semidirect
4. C3×#5236C2semidirect
5. #10591663C2semidirect
6. #10591662C2semidirect
7. C2×#63578C2semidirect
8. #10591113C2semidirect
9. #10591057C2semidirect
14. #64159C4semidirect
15. #64159C4semidirect
18. C2×#3756C4semidirect
19. C2×#3755C4semidirect
20. C2×#3754C4semidirect
21. C2×#3753C4semidirect
24. C3×#948C22semidirect
32. #63817C22semidirect
33. C3×#837C22semidirect
34. #63578C22semidirect
35. #63578C22semidirect
36. #63570C22semidirect
37. #63554C22semidirect
38. Dic3×C3⋊C8C22semidirect
43. #5819D3semidirect
47. #5236D3semidirect
132. #948C2×D3semidirect
160. #837C2×D3semidirect
580. C32#2957semidirect
650. C3#78990semidirect
651. C3#83812semidirect

Maximal subgroups

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

subgroupindex
C2×#641592
C3×#58192
#105947802
C3×#52362
#105916632
#105916622
C2×#635782
#105911132
#105910572
#838123
#789903