Finite Group Databasebeta

← #11787409

Subgroups — #11787409

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×#64113C211yesmaximal, characteristic
2C2×#63817C211yesmaximal, characteristic, complemented
3C2×#63570C211yesmaximal, characteristic, complemented
4C2×#63570C211yesmaximal, characteristic, complemented
5#10591073C211yesmaximal, characteristic, complemented
6C3×#4552C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8#68946—31nomaximal
9#68695—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×#3746C411yescharacteristic, complemented
14#64113—22no—
15#64113—22no—
16C2×#3745C411yescharacteristic, complemented
17C2×#3744C411yescharacteristic, complemented
18C2×#3744C411yescharacteristic, complemented
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—
27#63570—22no—
28#63570—22no—
29#63557—21no—
30#63557—21no—
31C2×#907—31no—
32C2×#904—31no—
33C2×#904—31no—
34C2×#904—61no—
35C2×#901—31no—
36C2×#825—31no—
37C2×#825—31no—
38#5129—31no—
39#5110—31no—
40C2×#805—31no—
41C2×#805—31no—
42C3×#341—31no—
43C3×#336—31no—
44#4552D311yescharacteristic, complemented
45#4550D311yescharacteristic, complemented
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48C2×#638—21no—
49#3828—21no—
50#3828—21no—
51#3828—21no—
52#3828—21no—
53#3828—21no—
54#3828—21no—
55#3828D412yes—
56#3828D412yes—
57C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
58C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—21no—
61C2×#634C2×C411yescharacteristic
62C2×#634C2×C411yescharacteristic
63C22×C3×Dic3—21no—
64C2×C32×C8—21no—
65C2×C32×C8—21no—
66C2×C32×C8C2×C411yescharacteristic
67C2×C32×C8C2×C411yescharacteristic
68#3746—22no—
69#3745—22no—
70#3744—22no—
71#3744—22no—
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×#235—31no—
88C2×#235—31no—
89C2×#235—31no—
90C2×#235—31no—
91C2×#235—61no—
92C2×#235—61no—
93C2×C3×M16—31no—
94C2×C3×M16—31no—
95C22×C3×C8—21no—
96C22×C3×C8—31no—
97C22×C3×C8C2×D311yescharacteristic
98C22×C3×C8C2×D311yescharacteristic
99C2×C3×C42—31no—
100C2×C4×Dic3C2×D311yescharacteristic
101C2×#208C2×D311yescharacteristic
102C2×#208C2×D311yescharacteristic
103C22×C3⋊C8C2×D311yescharacteristic
104#907—62no—
105#907—62no—
106C2×Dic12—31no—
107C2×Dic12—31no—
108C2×Dic12—61no—
109#904—62no—
110#904—62no—
111#904—62no—
112#904—62no—
113#904—64no—
114#904—64no—
115C2×D24—31no—
116C2×D24—31no—
117C2×D24—61no—
118C2×#204—31no—
119C2×#204—31no—
120C2×#204—31no—
121C2×#204—31no—
122C2×#204—61no—
123C2×#204—61no—
124#901—62no—
125#901—62no—
126C2×ΓL(1,𝔽25)—61no—
127C2×ΓL(1,𝔽25)—61no—
128C2×D3×C8—61no—
129C2×D3×C8—61no—
130#825—62no—
131#825—62no—
132(C2×D3)⋊C8—61no—
133(C2×D3)⋊C8—61no—
134(C2×D3)⋊C8—61no—
135(C2×D3)⋊C8—61no—
136#805—62no—
137#805—62no—
138C23×C32#4111yescharacteristic
139C22×C3⋊D3—21no—
140C22×C3⋊D3—21no—
141C2×C32×C4C22×C411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4111yescharacteristic
147#638—22no—
148#638—22no—
149#638—41no—
150#638—41no—
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3—21no—
153C4⋊(C3⋊D3)—21no—
154C4⋊(C3⋊D3)—21no—
155C4⋊(C3⋊D3)—21no—
156C4⋊(C3⋊D3)C22⋊C412yes—
157C4×C3⋊D3—22no—
158C4×C3⋊D3—22no—
159C4×C3⋊D3—41no—
160C4×C3⋊D3—41no—
161#634—21no—
162#634—21no—
163#634—21no—
164#634C22⋊C412yes—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—41no—
167C2×C3×Dic3—41no—
168C32×C8—21no—
169C32×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—91no—
177C2×#104—91no—
178#408—91no—
179#341—31no—
180#336—31no—
181C22×C3×C4—21no—
182C22×C3×C4—61no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C2×#67—61no—
186C2×#67—61no—
187C2×#67—61no—
188C2×#67—61no—
189C2×#67—121no—
190C2×#67—121no—
191C22×Dic3—21no—
192#235—32no—
193#235—32no—
194#235—32no—
195#235—32no—
196#235—62no—
197#235—62no—
198#235—61no—
199#235—61no—
200#235—61no—
201#235—61no—
202#235—62no—
203#235—62no—
204#235—61no—
205#235—61no—
206#235—61no—
207#235—61no—
208#235—61no—
209#235—61no—
210#235—61no—
211#235—61no—
212#235—121no—
213#235—121no—
214#235—121no—
215#235—121no—
216C2×D12—31no—
217C2×D12—31no—
218C2×D12—31no—
219C2×D12—31no—
220C2×D12—61no—
221C2×D12—61no—
222C2×C4×D3—61no—
223C2×C4×D3—61no—
224C2×C4×D3—61no—
225C2×C4×D3—61no—
226C2×C4×D3—121no—
227C2×C4×D3—121no—
228C2×Dic6—31no—
229C2×Dic6—31no—
230C2×Dic6—31no—
231C2×Dic6—31no—
232C2×Dic6—61no—
233C2×Dic6—61no—
234C3×M16—32no—
235C3×M16—61no—
236C3×M16—61no—
237C3×M16—61no—
238C2×C3×C8—22no—
239C2×C3×C8—22no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—21no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C2×C3×C8—31no—
247C2×C3×C8—31no—
248C2×C3×C8—61no—
249C2×C3×C8—61no—
250C2×C3×C8—61no—
251C2×C3×C8—61no—
252C2×C3×C8C4×D311yescharacteristic
253C2×C3×C8C4×D311yescharacteristic
254C2×C3×C8C4×D311yescharacteristic
255C2×C3×C8C4×D311yescharacteristic
256C3×C42—61no—
257C3×C42—61no—
258C4×Dic3—21no—
259C4×Dic3—21no—
260#208—21no—
261#208—21no—
262#208—21no—
263#208D1212yes—
264C2×C3⋊C8—21no—
265C2×C3⋊C8—21no—
266C2×C3⋊C8—21no—
267C2×C3⋊C8—21no—
268C2×C3⋊C8D1211yescharacteristic
269C2×C3⋊C8D1211yescharacteristic
270Dic12—62no—
271Dic12—62no—
272Dic12—64no—
273D24—62no—
274D24—62no—
275D24—64no—
276#204—62no—
277#204—62no—
278#204—62no—
279#204—62no—
280#204—64no—
281#204—64no—
282ΓL(1,𝔽25)—64no—
283ΓL(1,𝔽25)—64no—
284D3×C8—64no—
285D3×C8—64no—
286C22×C32—21no—
287C22×C32—21no—
288C22×C32C4×D411yescharacteristic
289C22×C32#12111yescharacteristic
290C22×C32#12311yescharacteristic
291C2×C3⋊D3—22no—
292C2×C3⋊D3—41no—
293C2×C3⋊D3—41no—
294C2×C3⋊D3—41no—
295C2×C3⋊D3—41no—
296C2×C3⋊D3—41no—
297C32×C4C2×C22⋊C411yescharacteristic
298C32×C4C4×D411yescharacteristic
299C32×C4#12011yescharacteristic
300C32×C4#12111yescharacteristic
301C3⋊Dic3—22no—
302C3⋊Dic3—41no—
303C3×Dic3—42no—
304C2×#41—91no—
305C2×#41—91no—
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—181no—
319C22×C8D3211yescharacteristic
320C2×C42—31no—
321#104—182no—
322#104—182no—
323C22⋊C8—181no—
324C22⋊C8—181no—
325C23×C3—21no—
326C23×C3#23511yescharacteristic
327C23×C3#23911yescharacteristic
328C22×D3—61no—
329C22×D3—61no—
330C22×D3—61no—
331C22×D3—61no—
332C22×D3—121no—
333C22×D3—121no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—62no—
341C2×C3×C4—121no—
342C2×C3×C4—121no—
343C2×C3×C4C2×C4×D311yescharacteristic
344C2×C3×C4C2×C4×D311yescharacteristic
345C2×C3×C4C2×D1211yescharacteristic
346C2×C3×C4C2×D1211yescharacteristic
347C2×C3×C4#23511yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4#23911yescharacteristic
355#67—62no—
356#67—62no—
357#67—62no—
358#67—62no—
359#67—122no—
360#67—122no—
361#67—122no—
362#67—122no—
363#67—121no—
364#67—121no—
365#67—121no—
366#67—121no—
367C2×Dic3—22no—
368C2×Dic3—41no—
369C2×Dic3—41no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—121no—
375C2×Dic3—121no—
376D12—32no—
377D12—32no—
378D12—62no—
379D12—62no—
380D12—61no—
381D12—61no—
382D12—61no—
383D12—61no—
384D12—61no—
385D12—61no—
386D12—121no—
387D12—121no—
388C4×D3—62no—
389C4×D3—62no—
390C4×D3—62no—
391C4×D3—62no—
392C4×D3—122no—
393C4×D3—122no—
394C4×D3—122no—
395C4×D3—122no—
396C4×D3—121no—
397C4×D3—121no—
398C4×D3—121no—
399C4×D3—121no—
400Dic6—32no—
401Dic6—32no—
402Dic6—62no—
403Dic6—61no—
404Dic6—61no—
405Dic6—62no—
406Dic6—61no—
407Dic6—61no—
408Dic6—61no—
409Dic6—61no—
410Dic6—121no—
411Dic6—121no—
412C3×C8—22no—
413C3×C8—22no—
414C3×C8—21no—
415C3×C8—21no—
416C3×C8—21no—
417C3×C8—21no—
418C3×C8—61no—
419C3×C8—62no—
420C3×C8—61no—
421C3×C8—121no—
422C3⋊C8—21no—
423C3⋊C8—22no—
424C3⋊C8—21no—
425C3⋊C8—41no—
426C2×C32—21no—
427C2×C32—21no—
428C2×C32#38611yescharacteristic
429C2×C32#44311yescharacteristic
430C2×C32#44411yescharacteristic
431C3⋊D3—42no—
432C3⋊D3—81no—
433#41—92no—
434#41—92no—
435#41—181no—
436#41—181no—
437#41—181no—
438#41—181no—
439#41—181no—
440#41—181no—
441C2×Q8—91no—
442C2×Q8—91no—
443C2×D4—91no—
444C2×D4—91no—
445C2×D4—181no—
446C2×D4—181no—
447C22×C4—61no—
448C22×C4—181no—
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—21no—
461C2×C8—21no—
462C2×C8—31no—
463C2×C8—31no—
464C2×C8—61no—
465C2×C8—61no—
466C2×C8—61no—
467C2×C8—61no—
468C2×C8—184no—
469C2×C8#62411yescharacteristic
470C2×C8#62411yescharacteristic
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×C3C4×D1211yescharacteristic
483C22×C3#88411yescharacteristic
484C22×C3#89311yescharacteristic
485C22×C3#89411yescharacteristic
486C22×C3#89411yescharacteristic
487C22×C3#89511yescharacteristic
488C2×D3—62no—
489C2×D3—62no—
490C2×D3—122no—
491C2×D3—121no—
492C2×D3—121no—
493C2×D3—121no—
494C2×D3—121no—
495C2×D3—122no—
496C2×D3—121no—
497C2×D3—121no—
498C2×D3—121no—
499C2×D3—121no—
500C2×D3—121no—
501C2×D3—121no—
502C2×D3—241no—
503C2×D3—241no—
504C2×D3—241no—
505C2×D3—241no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—122no—
511C3×C4C4×D1211yescharacteristic
512C3×C4D3×C22⋊C411yescharacteristic
513C3×C4D3×C22⋊C411yescharacteristic
514C3×C4#88211yescharacteristic
515C3×C4#88211yescharacteristic
516C3×C4#88411yescharacteristic
517C3×C4#89311yescharacteristic
518C3×C4#89511yescharacteristic
519Dic3—42no—
520Dic3—62no—
521Dic3—62no—
522Dic3—122no—
523Dic3—122no—
524Dic3—121no—
525Dic3—121no—
526C32#187611yescharacteristic, complemented, Sylow
527C23—181no—
528C23—181no—
529C23#379911yescharacteristic
530Q8—92no—
531Q8—181no—
532Q8—181no—
533Q8—181no—
534D4—92no—
535D4—182no—
536D4—182no—
537D4—181no—
538D4—181no—
539D4—181no—
540D4—361no—
541D4—361no—
542C2×C4—62no—
543C2×C4—121no—
544C2×C4—121no—
545C2×C4—181no—
546C2×C4—182no—
547C2×C4—182no—
548C2×C4—181no—
549C2×C4—361no—
550C2×C4—361no—
551C2×C4#379911yescharacteristic
552C2×C4D3×D1211yescharacteristic
553C2×C4D3×D1211yescharacteristic
554C2×C4C2×#62411yescharacteristic
555C2×C4#381111yescharacteristic
556C2×C4#381111yescharacteristic
557C8—21no—
558C8—21no—
559C8—61no—
560C8—61no—
561C8—62no—
562C8—121no—
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#466511yescharacteristic
573C2×C3#466511yescharacteristic
574C2×C3#470011yescharacteristic
575C2×C3#471711yescharacteristic
576C2×C3#489411yescharacteristic
577C2×C3#489511yescharacteristic
578D3—122no—
579D3—122no—
580D3—242no—
581D3—242no—
582D3—241no—
583D3—241no—
584C22—21no—
585C22—21no—
586C22—182no—
587C22—361no—
588C22—361no—
589C22—361no—
590C22—361no—
591C22—361no—
592C22#6389411yescharacteristic
593C22#6389711yescharacteristic
594C22#6391011yescharacteristic
595C4—122no—
596C4—182no—
597C4—361no—
598C4#6389411yescharacteristic
599C4#6391011yescharacteristic
600C4#6392311yescharacteristic
601C4#6397411yescharacteristic
602C3—21no—
603C3#6869511yescharacteristic, complemented
604C3#6894611yescharacteristic, complemented
605C2—21no—
606C2—21no—
607C2—362no—
608C2—721no—
609C2#1059091711yescharacteristic
610C2#1059091811yescharacteristic
611C2#1059138011yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32C4×D4
prime radicalC2×#64113C2
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1876
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63817C2semidirect
3. C2×#63570C2semidirect
4. C2×#63570C2semidirect
5. #10591073C2semidirect
6. C3×#4552C2semidirect
7. C3×#4550C2semidirect
13. C2×#3746C4semidirect
16. C2×#3745C4semidirect
17. C2×#3744C4semidirect
18. C2×#3744C4semidirect
44. #4552D3semidirect
45. #4550D3semidirect
526. C32#1876semidirect
603. C3#68695semidirect
604. C3#68946semidirect

Maximal subgroups

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

subgroupindex
C2×#641132
C2×#638172
C2×#635702
#105910732
C3×#45522
C3×#45502
#689463
#686953