Finite Group Databasebeta

← #11787400

Subgroups — #11787400

Order 1152.

781 conjugacy classes of subgroups.

The subgroup lattice has 613 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64159C211yesmaximal, characteristic
2C2×#63817C211yesmaximal, characteristic, complemented
3C2×C3×#837C211yesmaximal, characteristic, complemented
4C3×#5234C211yesmaximal, characteristic, complemented
5C2×#63570C211yesmaximal, characteristic, complemented
6#10589165C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#70390—31nomaximal
9#70011—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12#64159—22no—
13#64159—22no—
14C2×#3756C411yescharacteristic, complemented
15C2×#3755C411yescharacteristic, complemented
16C2×#3754C411yescharacteristic, complemented
17C2×#3753C411yescharacteristic, complemented
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×#3712—21no—
24#63817—22no—
25#63817—22no—
26C2×#3710—21no—
27C3×#837—22no—
28C3×#830—21no—
29C3×#830—21no—
30#63570—22no—
31C2×#950—31no—
32C2×#950—31no—
33C2×#950—61no—
34C2×#907—31no—
35C2×#901—31no—
36C2×C3×#104—31no—
37C3×#408—31no—
38C2×#837D311yescharacteristic, complemented
39#5234D311yescharacteristic, complemented
40C2×#825—31no—
41C2×#805—31no—
42#4558—31no—
43#4558—31no—
44#4550—31no—
45#4524—31no—
46C32×#41—21no—
47C32×#41—21no—
48C32×#41—21no—
49C32×#41—21no—
50C2×C32×Q8C2×C411yescharacteristic
51C2×C32×D4—21no—
52C2×C32×D4C2×C411yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C2×#638—21no—
56#3828—21no—
57#3828—21no—
58#3828D412yes—
59#3828D412yes—
60C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
61C2×C4×C3⋊D3—21no—
62C2×#634C2×C411yescharacteristic
63C22×C3×Dic3—21no—
64#3756—22no—
65#3755—22no—
66#3754—22no—
67#3753—22no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
71C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
72C3×C4×Dic3—21no—
73C3×C4×Dic3—21no—
74C3×#208—21no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208D412yes—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8D411yescharacteristic
83C2×C3×C3⋊C8D411yescharacteristic
84#3712—24no—
85#3710—24no—
86#1876—91noSylow
87C2×C3×#41—21no—
88C2×C3×#41C2×D311yescharacteristic
89C2×C3×#41C2×D311yescharacteristic
90C2×#235—31no—
91C2×#235—31no—
92C2×#235—61no—
93C2×C3×M16—31no—
94C2×C3×M16—31no—
95C22×C3×C8—31no—
96C2×C3×C42—31no—
97#950—62no—
98#950—62no—
99#950—62no—
100#950—62no—
101#950—64no—
102#950—64no—
103C2×#216—31no—
104C2×#216—31no—
105C2×#216—61no—
106C2×#215—31no—
107C2×#215—31no—
108C2×#215—61no—
109C2×#214—31no—
110C2×#214—31no—
111C2×#214—61no—
112C2×#213—31no—
113C2×#213—31no—
114C2×#213—61no—
115C2×C4×Dic3C2×D311yescharacteristic
116C2×#208C2×D311yescharacteristic
117C2×#208C2×D311yescharacteristic
118C22×C3⋊C8—31no—
119C22×C3⋊C8—31no—
120C22×C3⋊C8—61no—
121C22×C3⋊C8C2×D311yescharacteristic
122#907—62no—
123#907—62no—
124#901—62no—
125#901—62no—
126C2×ΓL(1,𝔽25)—61no—
127C2×ΓL(1,𝔽25)—61no—
128C2×D3×C8—61no—
129C2×D3×C8—61no—
130C3×#104—62no—
131C3×C22⋊C8—61no—
132C3×C22⋊C8—61no—
133#837—22no—
134#830—21no—
135#830—21no—
136#825—62no—
137#805—62no—
138C23×C32—21no—
139C23×C32#4111yescharacteristic
140C22×C3⋊D3—21no—
141C32×Q8—21no—
142C32×Q8—21no—
143C32×D4—21no—
144C32×D4—21no—
145C32×D4—41no—
146C32×D4—41no—
147C2×C32×C4—21no—
148C2×C32×C4—41no—
149C2×C32×C4—41no—
150C2×C32×C4C22×C411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4#4111yescharacteristic
156#638—22no—
157#638—22no—
158C2×C3⋊Dic3—21no—
159C4⋊(C3⋊D3)—21no—
160C4⋊(C3⋊D3)C22⋊C412yes—
161C4×C3⋊D3—22no—
162C4×C3⋊D3—22no—
163#634—21no—
164#634C22⋊C412yes—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—41no—
167C2×C3×Dic3—41no—
168C3⋊(C3⋊C8)—21no—
169C3⋊(C3⋊C8)—21no—
170C3×C3⋊C8—21no—
171C3×C3⋊C8—22no—
172C3×C3⋊C8—21no—
173C3×C3⋊C8—41no—
174C2×#135—91no—
175C2×#131—91no—
176C2×#104—31no—
177C2×#104—91no—
178#408—31no—
179#341—91no—
180#336—91no—
181C3×#41—22no—
182C3×#41—22no—
183C3×#41—21no—
184C3×#41—21no—
185C3×#41—21no—
186C3×#41—21no—
187C3×#41—21no—
188C3×#41—21no—
189C3×#41—21no—
190C3×#41—21no—
191C3×#41—41no—
192C3×#41—41no—
193C2×C3×Q8—21no—
194C2×C3×Q8C4×D311yescharacteristic
195C2×C3×Q8C4×D311yescharacteristic
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—41no—
200C2×C3×D4C4×D311yescharacteristic
201C2×C3×D4C4×D311yescharacteristic
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—41no—
206C22×C3×C4—61no—
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C2×#67—61no—
210C2×#67—61no—
211C2×#67—121no—
212C22×Dic3—21no—
213#235—32no—
214#235—32no—
215#235—32no—
216#235—32no—
217#235—62no—
218#235—62no—
219#235—61no—
220#235—61no—
221#235—61no—
222#235—61no—
223#235—121no—
224#235—121no—
225C2×D12—31no—
226C2×D12—31no—
227C2×D12—61no—
228C2×C4×D3—61no—
229C2×C4×D3—61no—
230C2×C4×D3—121no—
231C2×Dic6—31no—
232C2×Dic6—31no—
233C2×Dic6—61no—
234C3×M16—32no—
235C3×M16—61no—
236C3×M16—61no—
237C3×M16—61no—
238C2×C3×C8—31no—
239C2×C3×C8—31no—
240C2×C3×C8—61no—
241C2×C3×C8—61no—
242C2×C3×C8—61no—
243C2×C3×C8—61no—
244C3×C42—61no—
245C3×C42—61no—
246#216—62no—
247#216—62no—
248#216—64no—
249#215—62no—
250#215—62no—
251#215—64no—
252#214—62no—
253#214—62no—
254#214—64no—
255#213—62no—
256#213—62no—
257#213—64no—
258C4×Dic3—21no—
259C4×Dic3—21no—
260#208—21no—
261#208—21no—
262#208—21no—
263#208#6712yes—
264C2×C3⋊C8—21no—
265C2×C3⋊C8—21no—
266C2×C3⋊C8—21no—
267C2×C3⋊C8—21no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—61no—
273C2×C3⋊C8—61no—
274C2×C3⋊C8—62no—
275C2×C3⋊C8—62no—
276C2×C3⋊C8—61no—
277C2×C3⋊C8—61no—
278C2×C3⋊C8—61no—
279C2×C3⋊C8—61no—
280C2×C3⋊C8#6711yescharacteristic
281C2×C3⋊C8#6711yescharacteristic
282ΓL(1,𝔽25)—64no—
283ΓL(1,𝔽25)—64no—
284D3×C8—64no—
285D3×C8—64no—
286C22×C32—21no—
287C22×C32—21no—
288C22×C32—41no—
289C22×C32—41no—
290C22×C32—41no—
291C22×C32C4×D411yescharacteristic
292C22×C32#12111yescharacteristic
293C22×C32#12311yescharacteristic
294C2×C3⋊D3—22no—
295C2×C3⋊D3—41no—
296C2×C3⋊D3—41no—
297C32×C4—41no—
298C32×C4C2×C22⋊C411yescharacteristic
299C32×C4C4×D411yescharacteristic
300C32×C4#12011yescharacteristic
301C32×C4#12111yescharacteristic
302C3⋊Dic3—22no—
303C3×Dic3—42no—
304C2×#41—91no—
305C2×#41D3211yescharacteristic
306#135—182no—
307#135—182no—
308C2×Q16—91no—
309C2×SD16—91no—
310C2×SD16—91no—
311C2×D8—91no—
312#131—182no—
313#131—182no—
314C2×M16—31no—
315C2×M16—31no—
316C2×M16—181no—
317C22×C8—31no—
318C22×C8—91no—
319C22×C8—181no—
320C2×C42—31no—
321#104—62no—
322#104—182no—
323C22⋊C8—61no—
324C22⋊C8—61no—
325C23×C3—21no—
326C23×C3—21no—
327C23×C3—21no—
328C23×C3—41no—
329C23×C3#23511yescharacteristic
330C23×C3#23711yescharacteristic
331C22×D3—61no—
332C22×D3—61no—
333C22×D3—121no—
334C3×Q8—22no—
335C3×Q8—21no—
336C3×Q8—21no—
337C3×Q8—21no—
338C3×Q8—21no—
339C3×Q8—41no—
340C3×D4—22no—
341C3×D4—21no—
342C3×D4—21no—
343C3×D4—21no—
344C3×D4—21no—
345C3×D4—41no—
346C3×D4—42no—
347C3×D4—42no—
348C3×D4—41no—
349C3×D4—41no—
350C3×D4—41no—
351C3×D4—41no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—41no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—41no—
364C2×C3×C4—41no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—62no—
368C2×C3×C4—121no—
369C2×C3×C4—121no—
370C2×C3×C4C2×C4×D311yescharacteristic
371C2×C3×C4C2×C4×D311yescharacteristic
372C2×C3×C4#23511yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4D3×D411yescharacteristic
378C2×C3×C4D3×D411yescharacteristic
379C2×C3×C4#23711yescharacteristic
380C2×C3×C4C2×#6711yescharacteristic
381C2×C3×C4C2×#6711yescharacteristic
382#67—62no—
383#67—62no—
384#67—62no—
385#67—62no—
386#67—122no—
387#67—122no—
388C2×Dic3—22no—
389C2×Dic3—41no—
390C2×Dic3—41no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—121no—
394D12—32no—
395D12—32no—
396D12—62no—
397D12—61no—
398D12—61no—
399D12—121no—
400C4×D3—62no—
401C4×D3—62no—
402C4×D3—62no—
403C4×D3—62no—
404C4×D3—122no—
405C4×D3—122no—
406Dic6—32no—
407Dic6—32no—
408Dic6—62no—
409Dic6—61no—
410Dic6—61no—
411Dic6—121no—
412C3×C8—61no—
413C3×C8—62no—
414C3×C8—61no—
415C3×C8—121no—
416C3⋊C8—21no—
417C3⋊C8—22no—
418C3⋊C8—21no—
419C3⋊C8—41no—
420C3⋊C8—62no—
421C3⋊C8—62no—
422C3⋊C8—61no—
423C3⋊C8—61no—
424C3⋊C8—61no—
425C3⋊C8—61no—
426C2×C32—21no—
427C2×C32—21no—
428C2×C32—81no—
429C2×C32#38611yescharacteristic
430C2×C32#44311yescharacteristic
431C2×C32#44411yescharacteristic
432C3⋊D3—42no—
433#41—21no—
434#41—21no—
435#41—21no—
436#41—21no—
437#41—92no—
438#41—92no—
439#41—181no—
440#41—181no—
441C2×Q8—91no—
442C2×Q8#62411yescharacteristic
443C2×D4—21no—
444C2×D4—91no—
445C2×D4—181no—
446C2×D4#62411yescharacteristic
447C22×C4—21no—
448C22×C4—61no—
449C22×C4—181no—
450C22×C4C2×D3211yescharacteristic
451Q16—182no—
452SD16—182no—
453SD16—182no—
454D8—182no—
455M16—32no—
456M16—61no—
457M16—61no—
458M16—61no—
459M16—184no—
460C2×C8—31no—
461C2×C8—31no—
462C2×C8—61no—
463C2×C8—61no—
464C2×C8—61no—
465C2×C8—61no—
466C2×C8—91no—
467C2×C8—91no—
468C2×C8—184no—
469C2×C8—181no—
470C2×C8—181no—
471C42—61no—
472C42—61no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—42no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—81no—
490C22×C3—81no—
491C22×C3#67⋊C411yescharacteristic
492C22×C3#88311yescharacteristic
493C22×C3#88311yescharacteristic
494C22×C3#88411yescharacteristic
495C22×C3C4×#6711yescharacteristic
496C22×C3#93811yescharacteristic
497C2×D3—62no—
498C2×D3—62no—
499C2×D3—122no—
500C2×D3—121no—
501C2×D3—121no—
502C2×D3—121no—
503C2×D3—121no—
504C2×D3—241no—
505C2×D3—241no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—42no—
511C3×C4—41no—
512C3×C4—41no—
513C3×C4—122no—
514C3×C4D3×C22⋊C411yescharacteristic
515C3×C4D3×C22⋊C411yescharacteristic
516C3×C4#67⋊C411yescharacteristic
517C3×C4#88411yescharacteristic
518C3×C4C4×#6711yescharacteristic
519C3×C4#93711yescharacteristic
520C3×C4#93711yescharacteristic
521C3×C4#93811yescharacteristic
522Dic3—42no—
523Dic3—62no—
524Dic3—62no—
525Dic3—122no—
526C32#187611yescharacteristic, complemented, Sylow
527C23—21no—
528C23—181no—
529C23#380411yescharacteristic
530Q8—21no—
531Q8—21no—
532Q8—92no—
533Q8—181no—
534D4—21no—
535D4—21no—
536D4—41no—
537D4—41no—
538D4—92no—
539D4—182no—
540D4—182no—
541D4—181no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—62no—
546C2×C4—121no—
547C2×C4—121no—
548C2×C4—181no—
549C2×C4—182no—
550C2×C4—182no—
551C2×C4#380411yescharacteristic
552C2×C4C2×#62411yescharacteristic
553C2×C4D3×#6711yescharacteristic
554C2×C4D3×#6711yescharacteristic
555C2×C4#381111yescharacteristic
556C2×C4#381111yescharacteristic
557C8—61no—
558C8—61no—
559C8—62no—
560C8—121no—
561C8—181no—
562C8—181no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—41no—
571C2×C3—41no—
572C2×C3—82no—
573C2×C3—81no—
574C2×C3—81no—
575C2×C3#482311yescharacteristic
576C2×C3#482411yescharacteristic
577C2×C3#495611yescharacteristic
578C2×C3#495611yescharacteristic
579C2×C3#514411yescharacteristic
580C2×C3#514511yescharacteristic
581D3—122no—
582D3—122no—
583D3—242no—
584C22—21no—
585C22—21no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—182no—
590C22—361no—
591C22—361no—
592C22#6395211yescharacteristic
593C22#6395811yescharacteristic
594C22#6397511yescharacteristic
595C4—41no—
596C4—122no—
597C4—182no—
598C4#6395211yescharacteristic
599C4#6395811yescharacteristic
600C4#6397411yescharacteristic
601C4#6398311yescharacteristic
602C3—21no—
603C3#7001111yescharacteristic, complemented
604C3#7039011yescharacteristic, complemented
605C2—21no—
606C2—21no—
607C2—81no—
608C2—362no—
609C2#1059166211yescharacteristic
610C2#1059166311yescharacteristic
611C2#1059172211yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32C4×D4
prime radicalC2×#64159C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1876
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#63817C2semidirect
3. C2×C3×#837C2semidirect
4. C3×#5234C2semidirect
5. C2×#63570C2semidirect
6. #10589165C2semidirect
7. #10589155C2semidirect
14. C2×#3756C4semidirect
15. C2×#3755C4semidirect
16. C2×#3754C4semidirect
17. C2×#3753C4semidirect
38. C2×#837D3semidirect
39. #5234D3semidirect
526. C32#1876semidirect
603. C3#70011semidirect
604. C3#70390semidirect

Maximal subgroups

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

subgroupindex
C2×#641592
C2×#638172
C2×C3×#8372
C3×#52342
C2×#635702
#105891652
#105891552
#703903
#700113