Finite Group Databasebeta

← #11794065

Subgroups — #11794065

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic
2C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
3#10591320C211yesmaximal, characteristic
4#10591213C211yesmaximal, characteristic, complemented
5C2×#63567C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic
7C3×#4551C211yesmaximal, characteristic, complemented
8#70482—31nomaximal
9#68863—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×#3744—22no—
14C2×#3744—22no—
15C2×#3744—22no—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×#3722—21no—
21C2×#3722—21no—
22C3×Dic3⋊C8—22no—
23#63579—21no—
24#63579—21no—
25#63567—22no—
26#63564—22no—
27C22×#204—31no—
28C22×#204—31no—
29C22×#204—61no—
30C2×C3×C4⋊C8—31no—
31C2×#821—31no—
32C2×#816—31no—
33C2×Dic3⋊C8D311yescharacteristic, complemented
34#4988—31no—
35#4973—31no—
36C2×#810—31no—
37C2×#809—31no—
38#4939—31no—
39#4929—31no—
40C3×#340—31no—
41#4551D311yescharacteristic, complemented
42C23×C3⋊D3—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)D412yes—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634—21no—
54C2×#634—21no—
55C2×#634—21no—
56C2×#634D412yes—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61C2×C32×C8—21no—
62C2×C32×C8—21no—
63C2×C32×C8D412yes—
64#3744—28no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4×Dic3—21no—
70C3×C4×Dic3—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74#3722—42no—
75#3722—42no—
76#2055—91noSylow
77C22×D12—31no—
78C22×D12—31no—
79C22×D12—61no—
80C22×Dic6—31no—
81C22×Dic6—31no—
82C22×Dic6—61no—
83C22×C3×C8—21no—
84C22×C3×C8—31no—
85C22×C3×C8C2×D311yescharacteristic
86C22×C3×C8C2×D311yescharacteristic
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C42—31no—
90C2×(C2×D3)⋊C4—61no—
91C2×(C2×D3)⋊C4—61no—
92C2×(C2×D3)⋊C4—61no—
93C2×(C2×D3)⋊C4—61no—
94C2×C4⋊Dic3C2×D311yescharacteristic
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×C4×Dic3C2×D311yescharacteristic
97C22×C3⋊C8C2×D311yescharacteristic
98C2×#204—62no—
99C2×#204—62no—
100C2×#204—62no—
101C2×#204—62no—
102C2×#204—64no—
103C2×#204—64no—
104C2×#204—64no—
105C2×#204—62no—
106C2×#204—62no—
107C3×C4⋊C8—62no—
108C3⋊#95—61no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111C3⋊#95—61no—
112#821—62no—
113#816—62no—
114Dic3⋊C8—22no—
115#810—62no—
116#809—62no—
117C23×C32C2×D411yescharacteristic
118C22×C3⋊D3—22no—
119C22×C3⋊D3—41no—
120C22×C3⋊D3—41no—
121C22×C3⋊D3—41no—
122C22×C3⋊D3—41no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—41no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—41no—
134C4⋊(C3⋊D3)—22no—
135C4⋊(C3⋊D3)—22no—
136C4⋊(C3⋊D3)—41no—
137C4⋊(C3⋊D3)—41no—
138#634—22no—
139#634—22no—
140#634—41no—
141#634—41no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3SD1612yescomplemented
154C32×C8—22no—
155C3×C3⋊C8—41no—
156C22×SD16—91no—
157C2×C4⋊C8—31no—
158C2×#103—91no—
159C2×#102—91no—
160#391—91no—
161#390—91no—
162#340—31no—
163C23×D3—61no—
164C23×D3—61no—
165C23×D3—121no—
166C22×C3×C4—21no—
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4—61no—
170C22×C3×C4—61no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C22×Dic3—21no—
174C22×Dic3—21no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3—121no—
178C22×Dic3D1211yescharacteristic
179C22×Dic3D1211yescharacteristic
180C2×D12—32no—
181C2×D12—32no—
182C2×D12—62no—
183C2×D12—62no—
184C2×D12—62no—
185C2×D12—61no—
186C2×D12—61no—
187C2×D12—61no—
188C2×D12—61no—
189C2×D12—61no—
190C2×D12—61no—
191C2×D12—61no—
192C2×D12—61no—
193C2×D12—61no—
194C2×D12—61no—
195C2×D12—121no—
196C2×D12—121no—
197C2×D12—121no—
198C2×Dic6—32no—
199C2×Dic6—32no—
200C2×Dic6—62no—
201C2×Dic6—62no—
202C2×Dic6—62no—
203C2×Dic6—61no—
204C2×Dic6—61no—
205C2×Dic6—61no—
206C2×Dic6—61no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C2×Dic6—61no—
210C2×Dic6—61no—
211C2×Dic6—61no—
212C2×Dic6—61no—
213C2×Dic6—121no—
214C2×Dic6—121no—
215C2×Dic6—121no—
216C2×C3×C8—22no—
217C2×C3×C8—22no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8—22no—
223C2×C3×C8—61no—
224C2×C3×C8—61no—
225C2×C3×C8—61no—
226C2×C3×C8D1212yes—
227C2×C3×C8#6712yes—
228C3×C4⋊C4—61no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—61no—
232C3×C42—61no—
233C3×C42—61no—
234(C2×D3)⋊C4—122no—
235(C2×D3)⋊C4—122no—
236(C2×D3)⋊C4—122no—
237(C2×D3)⋊C4—122no—
238C4⋊Dic3—21no—
239C4⋊Dic3—21no—
240C4⋊Dic3—21no—
241C4⋊Dic3—21no—
242C4×Dic3—21no—
243C4×Dic3—21no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—21no—
246C2×C3⋊C8—21no—
247#204—616no—
248#204—68no—
249#204—68no—
250C22×C32#12111yescharacteristic
251C22×C32#12111yescharacteristic
252C22×C32#12111yescharacteristic
253C22×C32C2×SD1611yescharacteristic
254C22×C32#13511yescharacteristic
255C22×C32AGL(1,ℤ/8)11yescharacteristic
256C22×C32#13711yescharacteristic
257C2×C3⋊D3—42no—
258C2×C3⋊D3—42no—
259C2×C3⋊D3—42no—
260C2×C3⋊D3—81no—
261C2×C3⋊D3—81no—
262C2×C3⋊D3—81no—
263C2×C3⋊D3—81no—
264C32×C4#12011yescharacteristic
265C32×C4#12311yescharacteristic
266C32×C4#12311yescharacteristic
267C32×C4#12411yescharacteristic
268C3⋊Dic3—42no—
269C3×Dic3—22no—
270C3×Dic3—41no—
271C3×Dic3—81no—
272C3×Dic3—81no—
273C22×Q8—91no—
274C22×D4—91no—
275C2×SD16—182no—
276C2×SD16—182no—
277C2×SD16—182no—
278C22×C8—31no—
279C22×C8D3211yescharacteristic
280C2×C4⋊C4—31no—
281C2×C4⋊C4—31no—
282C2×C22⋊C4—181no—
283C2×C22⋊C4—181no—
284C2×C42—31no—
285C4⋊C8—62no—
286#103—182no—
287#102—182no—
288#95—181no—
289#95—181no—
290C23×C3—21no—
291C23×C3C2×D1211yescharacteristic
292C23×C3D3×D411yescharacteristic
293C22×D3—62no—
294C22×D3—62no—
295C22×D3—122no—
296C22×D3—122no—
297C22×D3—122no—
298C22×D3—121no—
299C22×D3—121no—
300C22×D3—121no—
301C22×D3—121no—
302C22×D3—121no—
303C22×D3—121no—
304C22×D3—121no—
305C22×D3—121no—
306C22×D3—121no—
307C22×D3—121no—
308C22×D3—121no—
309C22×D3—121no—
310C22×D3—241no—
311C22×D3—241no—
312C22×D3—241no—
313C22×D3—241no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—32no—
321C2×C3×C4—61no—
322C2×C3×C4—61no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—61no—
326C2×C3×C4—121no—
327C2×C3×C4—121no—
328C2×C3×C4—121no—
329C2×C3×C4—121no—
330C2×C3×C4—121no—
331C2×C3×C4—121no—
332C2×C3×C4C2×D1211yescharacteristic
333C2×C3×C4#23511yescharacteristic
334C2×C3×C4#23511yescharacteristic
335C2×C3×C4#23511yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4#23911yescharacteristic
341C2×C3×C4#23911yescharacteristic
342C2×C3×C4#23911yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×Dic3—21no—
345C2×Dic3—21no—
346C2×Dic3—21no—
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—41no—
350C2×Dic3—41no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354C2×Dic3—41no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—122no—
358C2×Dic3—122no—
359C2×Dic3—122no—
360C2×Dic3—121no—
361C2×Dic3—121no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3#20412yescomplemented
365D12—64no—
366D12—62no—
367D12—62no—
368D12—62no—
369D12—62no—
370D12—122no—
371D12—122no—
372D12—122no—
373D12—121no—
374D12—121no—
375D12—121no—
376D12—121no—
377Dic6—64no—
378Dic6—62no—
379Dic6—62no—
380Dic6—62no—
381Dic6—62no—
382Dic6—122no—
383Dic6—122no—
384Dic6—122no—
385Dic6—121no—
386Dic6—121no—
387Dic6—121no—
388Dic6—121no—
389C3×C8—24no—
390C3×C8—22no—
391C3×C8—22no—
392C3×C8—121no—
393C3⋊C8—41no—
394C2×C32#39411yescharacteristic
395C2×C32#46011yescharacteristic
396C2×C32#46111yescharacteristic
397C2×C32#46311yescharacteristic
398C2×C32#46411yescharacteristic
399C2×C32#46511yescharacteristic
400C2×C32#46811yescharacteristic
401C3⋊D3—82no—
402C24—181no—
403C2×Q8—92no—
404C2×Q8—181no—
405C2×Q8—181no—
406C2×Q8—181no—
407C2×Q8—181no—
408C2×Q8—181no—
409C2×D4—92no—
410C2×D4—181no—
411C2×D4—181no—
412C2×D4—181no—
413C2×D4—181no—
414C2×D4—181no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—61no—
418C22×C4—61no—
419C22×C4—181no—
420C22×C4C2×D3211yescharacteristic
421SD16—188no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—61no—
425C2×C8—61no—
426C2×C8—61no—
427C2×C8#62612yes—
428C4⋊C4—61no—
429C4⋊C4—61no—
430C4⋊C4—61no—
431C4⋊C4—61no—
432C22⋊C4—362no—
433C22⋊C4—362no—
434C42—61no—
435C42—61no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3#88411yescharacteristic
444C22×C3#88411yescharacteristic
445C22×C3#89511yescharacteristic
446C22×C3#89511yescharacteristic
447C22×C3#89511yescharacteristic
448C22×C3C2×#20411yescharacteristic
449C22×C3#90411yescharacteristic
450C22×C3#90811yescharacteristic
451C22×C3#90911yescharacteristic
452C22×C3#91111yescharacteristic
453C22×C3D3×SD1611yescharacteristic
454C22×C3#91611yescharacteristic
455C22×C3#91811yescharacteristic
456C22×C3#93011yescharacteristic
457C2×D3—124no—
458C2×D3—122no—
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—122no—
463C2×D3—122no—
464C2×D3—242no—
465C2×D3—242no—
466C2×D3—242no—
467C2×D3—242no—
468C2×D3—242no—
469C2×D3—242no—
470C2×D3—241no—
471C2×D3—241no—
472C2×D3—241no—
473C2×D3—241no—
474C2×D3—241no—
475C2×D3—241no—
476C2×D3—241no—
477C2×D3—241no—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—62no—
483C3×C4—121no—
484C3×C4—241no—
485C3×C4—241no—
486C3×C4#87511yescharacteristic
487C3×C4#88211yescharacteristic
488C3×C4#89411yescharacteristic
489C3×C4#89411yescharacteristic
490C3×C4#89411yescharacteristic
491C3×C4#89411yescharacteristic
492C3×C4#93711yescharacteristic
493C3×C4#94711yescharacteristic
494Dic3—22no—
495Dic3—41no—
496Dic3—81no—
497Dic3—81no—
498Dic3—124no—
499Dic3—122no—
500Dic3—122no—
501C32#205511yescharacteristic, complemented, Sylow
502C23—182no—
503C23—361no—
504C23—361no—
505C23—361no—
506C23—361no—
507C23—361no—
508C23—361no—
509C23D3×D1211yescharacteristic
510Q8—182no—
511Q8—182no—
512Q8—361no—
513Q8—361no—
514D4—182no—
515D4—182no—
516D4—361no—
517D4—361no—
518C2×C4—32no—
519C2×C4—61no—
520C2×C4—61no—
521C2×C4—61no—
522C2×C4—61no—
523C2×C4—61no—
524C2×C4—121no—
525C2×C4—121no—
526C2×C4—121no—
527C2×C4—121no—
528C2×C4—121no—
529C2×C4—121no—
530C2×C4—182no—
531C2×C4—361no—
532C2×C4—361no—
533C2×C4#379911yescharacteristic
534C2×C4#379911yescharacteristic
535C2×C4#379911yescharacteristic
536C2×C4C2×#62611yescharacteristic
537C2×C4#381111yescharacteristic
538C2×C4#381111yescharacteristic
539C8—22no—
540C8—121no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3#467211yescharacteristic
549C2×C3#476211yescharacteristic
550C2×C3#478711yescharacteristic
551C2×C3#479811yescharacteristic
552C2×C3#481811yescharacteristic
553C2×C3#484111yescharacteristic
554C2×C3#484411yescharacteristic
555C2×C3#484511yescharacteristic
556C2×C3#484811yescharacteristic
557C2×C3#486411yescharacteristic
558C2×C3#488611yescharacteristic
559C2×C3#499111yescharacteristic
560C2×C3#511411yescharacteristic
561C2×C3#513411yescharacteristic
562D3—244no—
563D3—242no—
564D3—242no—
565C22—362no—
566C22—362no—
567C22—362no—
568C22—721no—
569C22—721no—
570C22—721no—
571C22—721no—
572C22D3×#20411yescharacteristic
573C22#6379511yescharacteristic
574C22#6380111yescharacteristic
575C22#6380611yescharacteristic
576C22#6390911yescharacteristic
577C22#6391011yescharacteristic
578C22#6391011yescharacteristic
579C4—62no—
580C4—121no—
581C4—241no—
582C4—241no—
583C4—362no—
584C4#6386411yescharacteristic
585C4#6389711yescharacteristic
586C4#6389711yescharacteristic
587C4#6398111yescharacteristic
588C3—21no—
589C3#6886311yescharacteristic, complemented
590C3#7048211yescharacteristic, complemented
591C2—722no—
592C2#1059076011yescharacteristic
593C2#1059081311yescharacteristic
594C2#1059083011yescharacteristic
595C2#1059083811yescharacteristic
596C2#1059086011yescharacteristic
597C2#1059087911yescharacteristic
598C2#1059132111yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22×C8D32
hypocenterC32#2055
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×Dic3⋊C8C2semidirect
4. #10591213C2semidirect
5. C2×#63567C2semidirect
7. C3×#4551C2semidirect
33. C2×Dic3⋊C8D3semidirect
41. #4551D3semidirect
153. C2×C3×Dic3SD16semidirect
364. C2×Dic3#204semidirect
501. C32#2055semidirect
589. C3#68863semidirect
590. C3#70482semidirect

Maximal subgroups

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

subgroupindex
C22×#37442
C2×C3×Dic3⋊C82
#105913202
#105912132
C2×#635672
C2×#635642
C3×#45512
#704823
#688633