Finite Group Databasebeta

← #13178630

Subgroups — #13178630

Order 1728.

1798 conjugacy classes of subgroups.

The subgroup lattice has 1340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#89046C211yesmaximal, characteristic, complemented
3C3×#64148C211yesmaximal, characteristic, complemented
4C3×#64144C211yesmaximal, characteristic, complemented
5#11723727C211yesmaximal, characteristic, complemented
6#11723727C211yesmaximal, characteristic, complemented
7#11723726C211yesmaximal, characteristic, complemented
8#11723725C211yesmaximal, characteristic, complemented
9#11723723C211yesmaximal, characteristic, complemented
10C2×#88814C211yesmaximal, characteristic, complemented
11#11723718C211yesmaximal, characteristic, complemented
12#11723687C211yesmaximal, characteristic, complemented
13#11723686C211yesmaximal, characteristic, complemented
14#11723684C211yesmaximal, characteristic, complemented
15#11723671C211yesmaximal, characteristic, complemented
16#10595163—31nomaximal
17#10595150—31nomaximal
18#10595148—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C23×C3×C3⋊D3C2211yescharacteristic
21C2×C33×D4C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C2×C3×#638C2211yescharacteristic, complemented
25C2×C3×#638C2211yescharacteristic, complemented
26C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
27C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
28C3×D4×C3⋊D3—24no—
29C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
30C2×C3×C4×C3⋊D3C2211yescharacteristic
31C2×#6296C2211yescharacteristic, complemented
32C2×#6295C2211yescharacteristic
33C2×#6295C2211yescharacteristic, complemented
34C2×#6295C2211yescharacteristic, complemented
35#89046—24no—
36C2×#6294C2211yescharacteristic, complemented
37C2×#6294C2211yescharacteristic, complemented
38C2×#6294C2211yescharacteristic, complemented
39C3×#3757C2211yescharacteristic, complemented
40C3×#3757C2211yescharacteristic, complemented
41C3×#3757C2211yescharacteristic, complemented
42C3×#3757C2211yescharacteristic, complemented
43C3×#3752C2211yescharacteristic, complemented
44C3×#3750C2211yescharacteristic, complemented
45C3×#3750C2211yescharacteristic, complemented
46C3×#3750C2211yescharacteristic, complemented
47#88815C2211yescharacteristic, complemented
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic, complemented
52#88814C2211yescharacteristic, complemented
53#88814C2211yescharacteristic, complemented
54#88814C2211yescharacteristic, complemented
55#88813C2211yescharacteristic, complemented
56C2×D4×C3⋊D3D311yescharacteristic, complemented
57C2×C3×D3×D4—31no—
58C2×C3×D3×D4—31no—
59C2×C3×D3×D4—61no—
60C2×#3805—31no—
61C2×#3804—31no—
62C2×#3804—31no—
63#64148D311yescharacteristic, complemented
64#64144D311yescharacteristic, complemented
65C3×#939—31no—
66C3×#939—31no—
67C3×#939—61no—
68C3×#935—31no—
69C3×#935—31no—
70C3×#935—61no—
71#63981—31no—
72#63981—31no—
73#63977—31no—
74#63977—31no—
75#63976—31no—
76#63976—31no—
77#63974—31no—
78#67⋊Dic3—31no—
79Dic3×#67—31no—
80#63971—31no—
81#63970—31no—
82D3×#217—31no—
83D3×#217—31no—
84C2×#3722—31no—
85C2×(C2×D3)⋊Dic3—31no—
86C2×(C2×D3)⋊Dic3—31no—
87#63959—31no—
88#63959—31no—
89#63958—31no—
90#63953—31no—
91#63952—31no—
92#63910—31no—
93#63904—31no—
94#63897—31no—
95#63886—31no—
96#63885—31no—
97#63884—31no—
98#63884—31no—
99#63881—31no—
100#63879—31no—
101#63865—31no—
102#63851—31no—
103#63851—31no—
104C23×C33C2311yescharacteristic
105C23×C33C2311yescharacteristic
106C22×C3×C3⋊D3—22no—
107C22×C3×C3⋊D3—22no—
108C22×C3×C3⋊D3—22no—
109C22×C3×C3⋊D3—22no—
110C22×C3×C3⋊D3—41no—
111C22×C3×C3⋊D3—41no—
112C22×C3×C3⋊D3C2311yescharacteristic
113C22×C3×C3⋊D3C2311yescharacteristic
114C22×C3×C3⋊D3C2311yescharacteristic
115C22×C3×C3⋊D3C2311yescharacteristic
116C33×D4—22no—
117C2×C33×C4C2311yescharacteristic
118C3×#638—22no—
119C3×#638—22no—
120C3×#638—41no—
121C3×#638D414yescomplemented
122C2×C3×C3⋊Dic3—22no—
123C2×C3×C3⋊Dic3—41no—
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C2×C3×C3⋊Dic3C2311yescharacteristic
126C2×C3×C3⋊Dic3C2311yescharacteristic
127C2×C3×C3⋊Dic3C2311yescharacteristic
128C2×C3×C3⋊Dic3C2311yescharacteristic
129C2×C3×C3⋊Dic3C2311yescharacteristic
130C2×C3×C3⋊Dic3C2311yescharacteristic
131C2×C3×C3⋊Dic3C2311yescharacteristic
132C3×C4⋊(C3⋊D3)—22no—
133C3×C4×C3⋊D3—22no—
134#6296—22no—
135#6295—22no—
136#6295—22no—
137#6295—41no—
138#6294—22no—
139#6294—22no—
140#6294—41no—
141#5806—91no—
142#5654—91no—
143#5610—91no—
144C23×C3⋊D3C2×D311yescharacteristic
145C23×C3⋊D3C2×D311yescharacteristic
146C23×C3×D3—31no—
147C23×C3×D3—31no—
148C23×C3×D3—31no—
149C23×C3×D3—31no—
150C23×C3×D3—61no—
151C23×C3×D3—61no—
152C2×C32×D4—21no—
153C2×C32×D4—21no—
154C2×C32×D4—21no—
155C2×C32×D4—41no—
156C2×C32×D4C2×D311yescharacteristic
157C2×C32×D4C2×D311yescharacteristic
158C2×C32×D4C2×D311yescharacteristic
159C2×#638C2×D311yescharacteristic
160C2×#638C2×D311yescharacteristic
161C2×#638C2×D311yescharacteristic, complemented
162C2×#638C2×D311yescharacteristic, complemented
163C22×C3⋊Dic3C2×D311yescharacteristic, complemented
164C22×C3⋊Dic3C2×D311yescharacteristic, complemented
165D4×C3⋊D3—24no—
166C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
167C2×C4×C3⋊D3C2×D311yescharacteristic
168C2×C3×#67—31no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67—31no—
172C2×C3×#67—31no—
173C2×C3×#67—31no—
174C2×C3×#67—31no—
175C2×C3×#67—31no—
176C2×C3×#67—61no—
177C2×C3×#67—61no—
178C2×C3×#67—61no—
179C2×C3×#67—61no—
180C22×C3×Dic3—31no—
181C22×C3×Dic3—31no—
182C22×C3×Dic3—31no—
183C22×C3×Dic3—31no—
184C22×C3×Dic3—61no—
185C22×C3×Dic3—61no—
186C3×D3×D4—64no—
187C3×D3×D4—64no—
188C3×D3×D4—68no—
189C2×C3×D12—31no—
190C2×C3×D12—31no—
191C2×C3×D12—61no—
192C2×C3×C4×D3—31no—
193C2×C3×C4×D3—31no—
194C2×C3×C4×D3—61no—
195C2×#627—31no—
196C2×#627—31no—
197C2×#627—31no—
198C2×#626—31no—
199C2×#626—31no—
200C2×#626—31no—
201C2×#626—31no—
202C2×#626—31no—
203C2×#626—31no—
204C2×#625—31no—
205C2×#625—31no—
206C2×#625—31no—
207C2×#624—31no—
208C2×#624—31no—
209C2×#624—31no—
210#3805—64no—
211#3804—64no—
212#3804—64no—
213C2×D3×Dic3—31no—
214C2×D3×Dic3—31no—
215C2×D3×Dic3—31no—
216C2×D3×Dic3—31no—
217C2×D3×Dic3—31no—
218C2×D3×Dic3—31no—
219#3757C2×D311yescharacteristic, complemented
220#3757C2×D311yescharacteristic, complemented
221#3757C2×D311yescharacteristic, complemented
222#3757C2×D311yescharacteristic, complemented
223#3752C2×D311yescharacteristic, complemented
224#3750C2×D311yescharacteristic, complemented
225#3750C2×D311yescharacteristic, complemented
226#3750C2×D311yescharacteristic, complemented
227C3×#217—31no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—31no—
233C3×#217—31no—
234C3×#217—31no—
235C3×#217—61no—
236C3×#217—61no—
237C3×#217—61no—
238C3×#217—61no—
239C3×(C2×D3)⋊C4—31no—
240C3×(C2×D3)⋊C4—31no—
241C3×(C2×D3)⋊C4—61no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—31no—
244C3×Dic3⋊C4—31no—
245C3×Dic3⋊C4—31no—
246C3×Dic3⋊C4—31no—
247C3×Dic3⋊C4—31no—
248C3×Dic3⋊C4—61no—
249C3×Dic3⋊C4—61no—
250C3×Dic3⋊C4—61no—
251#3724—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254#3722—31no—
255#3722—31no—
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—31no—
260#3722—31no—
261(C2×D3)⋊Dic3—31no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3—31no—
272(C2×D3)⋊Dic3—31no—
273(C2×D3)⋊Dic3—31no—
274(C2×D3)⋊Dic3—31no—
275Dic32—31no—
276Dic32—31no—
277Dic32—31no—
278C22×C33—21no—
279C22×C33—21no—
280C22×C33—21no—
281C22×C33—21no—
282C22×C33—21no—
283C22×C33C2×D412yes—
284C22×C33C2411yescharacteristic
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3—21no—
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3—21no—
291C2×C3×C3⋊D3—21no—
292C2×C3×C3⋊D3—21no—
293C2×C3×C3⋊D3—21no—
294C2×C3×C3⋊D3—21no—
295C2×C3×C3⋊D3—44no—
296C2×C3×C3⋊D3—44no—
297C2×C3×C3⋊D3C2×D412yes—
298C2×C3×C3⋊D3#4112yescomplemented
299C33×C4—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3—21no—
304C3×C3⋊Dic3—21no—
305C3×C3⋊Dic3—21no—
306C3×C3⋊Dic3—21no—
307C3×C3⋊Dic3C2×D412yes—
308C22×C3×D4—91no—
309C2×#237—91no—
310C2×#237—91no—
311C2×D3×D4—31no—
312C2×D3×D4—31no—
313C2×D3×D4—61no—
314C2×#235—91no—
315C3×#123—91no—
316C3×#121—91no—
317#953—91no—
318#953—91no—
319C2×#217—91no—
320C2×#217—91no—
321#939—31no—
322#939—31no—
323#939—61no—
324#939—91no—
325#939—91no—
326#938—91no—
327#937—91no—
328#937—91no—
329#936—91no—
330#935—31no—
331#935—31no—
332#935—61no—
333#935—91no—
334D4×Dic3—91no—
335C4×#67—91no—
336C4×#67—91no—
337C2×(C2×D3)⋊C4—91no—
338C2×(C2×D3)⋊C4—91no—
339#924—91no—
340#896—91no—
341#896—91no—
342#895—91no—
343#894—91no—
344#894—91no—
345#893—91no—
346#885—91no—
347#885—91no—
348#884—91no—
349#884—91no—
350#882—91no—
351#882—91no—
352#67⋊C4—91no—
353#67⋊C4—91no—
354D3×C22⋊C4—91no—
355D3×C22⋊C4—91no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—21no—
360C23×C32—21no—
361C23×C32—21no—
362C23×C32—41no—
363C23×C32—41no—
364C23×C32C22×D311yescharacteristic
365C23×C32C22×D311yescharacteristic
366C23×C32C22×D311yescharacteristic
367C23×C32C22×D311yescharacteristic
368C23×C32C22×D311yescharacteristic
369C23×C32C22×D311yescharacteristic
370C22×C3⋊D3—22no—
371C22×C3⋊D3—22no—
372C22×C3⋊D3—22no—
373C22×C3⋊D3—22no—
374C22×C3⋊D3—41no—
375C22×C3⋊D3—41no—
376C22×C3⋊D3C22×D311yescharacteristic
377C22×C3⋊D3C22×D311yescharacteristic
378C22×C3⋊D3C22×D311yescharacteristic
379C22×C3⋊D3C22×D311yescharacteristic
380C22×C3×D3—31no—
381C22×C3×D3—31no—
382C22×C3×D3—31no—
383C22×C3×D3—31no—
384C22×C3×D3—31no—
385C22×C3×D3—31no—
386C22×C3×D3—31no—
387C22×C3×D3—31no—
388C22×C3×D3—61no—
389C22×C3×D3—61no—
390C22×C3×D3—61no—
391C22×C3×D3—61no—
392C22×C3×D3—62no—
393C22×C3×D3—62no—
394C22×C3×D3—62no—
395C22×C3×D3—62no—
396C22×C3×D3—62no—
397C22×C3×D3—62no—
398C22×C3×D3—64no—
399C22×C3×D3—64no—
400C22×C3×D3—62no—
401C22×C3×D3—62no—
402C22×C3×D3—122no—
403C22×C3×D3—122no—
404C22×C3×D3—121no—
405C22×C3×D3—121no—
406C22×C3×D3—121no—
407C22×C3×D3—121no—
408C22×C3×D3—122no—
409C22×C3×D3—122no—
410C32×D4—22no—
411C32×D4—24no—
412C32×D4—22no—
413C32×D4—22no—
414C32×D4—42no—
415C32×D4—42no—
416C32×D4—44no—
417C2×C32×C4—21no—
418C2×C32×C4—21no—
419C2×C32×C4—21no—
420C2×C32×C4—41no—
421C2×C32×C4C22×D311yescharacteristic
422C2×C32×C4C22×D311yescharacteristic
423C2×C32×C4C22×D311yescharacteristic
424#638—22no—
425#638—22no—
426#638—41no—
427#638#6714yescomplemented
428C2×C3⋊Dic3—22no—
429C2×C3⋊Dic3—41no—
430C2×C3⋊Dic3C22×D311yescharacteristic
431C2×C3⋊Dic3C22×D311yescharacteristic
432C2×C3⋊Dic3C22×D311yescharacteristic
433C2×C3⋊Dic3C22×D311yescharacteristic
434C2×C3⋊Dic3C22×D311yescharacteristic
435C2×C3⋊Dic3C22×D311yescharacteristic
436C2×C3⋊Dic3C22×D311yescharacteristic
437C2×C3⋊Dic3C22×D311yescharacteristic
438C4⋊(C3⋊D3)—22no—
439C4×C3⋊D3—22no—
440C3×#67—34no—
441C3×#67—34no—
442C3×#67—64no—
443C3×#67—62no—
444C3×#67—62no—
445C3×#67—64no—
446C3×#67—62no—
447C3×#67—62no—
448C3×#67—122no—
449C3×#67—121no—
450C3×#67—121no—
451C3×#67—122no—
452C2×C3×Dic3—31no—
453C2×C3×Dic3—31no—
454C2×C3×Dic3—31no—
455C2×C3×Dic3—31no—
456C2×C3×Dic3—31no—
457C2×C3×Dic3—31no—
458C2×C3×Dic3—31no—
459C2×C3×Dic3—31no—
460C2×C3×Dic3—31no—
461C2×C3×Dic3—31no—
462C2×C3×Dic3—31no—
463C2×C3×Dic3—31no—
464C2×C3×Dic3—31no—
465C2×C3×Dic3—31no—
466C2×C3×Dic3—31no—
467C2×C3×Dic3—31no—
468C2×C3×Dic3—61no—
469C2×C3×Dic3—61no—
470C2×C3×Dic3—61no—
471C2×C3×Dic3—61no—
472C2×C3×Dic3—61no—
473C2×C3×Dic3—61no—
474C2×C3×Dic3—61no—
475C2×C3×Dic3—61no—
476C2×C3×Dic3—62no—
477C2×C3×Dic3—62no—
478C2×C3×Dic3—122no—
479C2×C3×Dic3—121no—
480C2×C3×Dic3—121no—
481C2×C3×Dic3—122no—
482C3×D12—62no—
483C3×D12—62no—
484C3×D12—64no—
485C3×C4×D3—62no—
486C3×C4×D3—62no—
487C3×C4×D3—64no—
488#627—62no—
489#627—62no—
490#627—62no—
491#626—62no—
492#626—62no—
493#626—62no—
494#626—62no—
495#626—121no—
496#626—121no—
497#625—62no—
498#625—62no—
499#625—121no—
500#624—62no—
501#624—62no—
502#624—121no—
503D3×Dic3—62no—
504D3×Dic3—62no—
505D3×Dic3—62no—
506D3×Dic3—62no—
507D3×Dic3—121no—
508D3×Dic3—121no—
509#546—271noSylow
510C2×C33—22no—
511C2×C33—41no—
512C2×C33C22×D411yescharacteristic
513C2×C33C2×#4111yescharacteristic
514C2×C33H(5,𝔽2)11yescharacteristic
515C3×C3⋊D3—22no—
516C3×C3⋊D3—22no—
517C3×C3⋊D3—41no—
518C3×C3⋊D3—41no—
519C24×C3—91no—
520C24×C3—91no—
521C23×D3—31no—
522C23×D3—31no—
523C23×D3—31no—
524C23×D3—31no—
525C23×D3—61no—
526C23×D3—61no—
527C2×C3×D4—21no—
528C2×C3×D4—21no—
529C2×C3×D4—21no—
530C2×C3×D4—41no—
531C2×C3×D4—91no—
532C2×C3×D4—91no—
533C2×C3×D4—91no—
534C2×C3×D4—91no—
535C2×C3×D4—91no—
536C2×C3×D4—184no—
537C2×C3×D4D3211yescharacteristic
538C2×C3×D4D3211yescharacteristic
539C2×C3×D4D3211yescharacteristic
540C22×C3×C4—91no—
541C22×C3×C4—91no—
542C22×C3×C4—91no—
543C2×#67—31no—
544C2×#67—31no—
545C2×#67—31no—
546C2×#67—31no—
547C2×#67—31no—
548C2×#67—31no—
549C2×#67—31no—
550C2×#67—31no—
551C2×#67—61no—
552C2×#67—61no—
553C2×#67—61no—
554C2×#67—61no—
555C2×#67—91no—
556C2×#67—91no—
557C2×#67—91no—
558C2×#67—91no—
559C2×#67—91no—
560C2×#67—91no—
561C22×Dic3—31no—
562C22×Dic3—31no—
563C22×Dic3—31no—
564C22×Dic3—31no—
565C22×Dic3—61no—
566C22×Dic3—61no—
567C22×Dic3—91no—
568C22×Dic3—91no—
569C22×Dic3—91no—
570#237—184no—
571#237—184no—
572D3×D4—64no—
573D3×D4—64no—
574D3×D4—68no—
575#235—184no—
576C2×D12—31no—
577C2×D12—31no—
578C2×D12—61no—
579C2×D12—91no—
580C2×D12—91no—
581C2×D12—91no—
582C2×C4×D3—31no—
583C2×C4×D3—31no—
584C2×C4×D3—61no—
585C2×C4×D3—91no—
586C2×C4×D3—91no—
587C2×C4×D3—91no—
588C2×C4×D3—91no—
589C2×C4×D3—91no—
590C2×C4×D3—91no—
591C2×Dic6—91no—
592C2×Dic6—91no—
593C2×Dic6—91no—
594C3×C4⋊C4—91no—
595C3×C4⋊C4—91no—
596C3×C4⋊C4—91no—
597C3×C22⋊C4—91no—
598C3×C22⋊C4—91no—
599C3×C22⋊C4—91no—
600C3×C22⋊C4—91no—
601C3×C22⋊C4—91no—
602#217—31no—
603#217—31no—
604#217—31no—
605#217—31no—
606#217—31no—
607#217—31no—
608#217—31no—
609#217—31no—
610#217—61no—
611#217—61no—
612#217—61no—
613#217—61no—
614#217—91no—
615#217—91no—
616#217—91no—
617#217—91no—
618#217—91no—
619#217—91no—
620#217—91no—
621(C2×D3)⋊C4—31no—
622(C2×D3)⋊C4—31no—
623(C2×D3)⋊C4—61no—
624(C2×D3)⋊C4—91no—
625(C2×D3)⋊C4—91no—
626(C2×D3)⋊C4—91no—
627(C2×D3)⋊C4—91no—
628(C2×D3)⋊C4—91no—
629(C2×D3)⋊C4—91no—
630(C2×D3)⋊C4—91no—
631(C2×D3)⋊C4—91no—
632(C2×D3)⋊C4—91no—
633(C2×D3)⋊C4—91no—
634(C2×D3)⋊C4—91no—
635(C2×D3)⋊C4—91no—
636(C2×D3)⋊C4—91no—
637(C2×D3)⋊C4—91no—
638C4⋊Dic3—91no—
639Dic3⋊C4—31no—
640Dic3⋊C4—31no—
641Dic3⋊C4—31no—
642Dic3⋊C4—31no—
643Dic3⋊C4—31no—
644Dic3⋊C4—31no—
645Dic3⋊C4—61no—
646Dic3⋊C4—61no—
647Dic3⋊C4—61no—
648Dic3⋊C4—91no—
649Dic3⋊C4—91no—
650C4×Dic3—91no—
651C4×Dic3—91no—
652C4×Dic3—91no—
653C22×C32—21no—
654C22×C32—21no—
655C22×C32—21no—
656C22×C32—21no—
657C22×C32—21no—
658C22×C32—21no—
659C22×C32—21no—
660C22×C32—22no—
661C22×C32—21no—
662C22×C32—21no—
663C22×C32—21no—
664C22×C32—21no—
665C22×C32—21no—
666C22×C32—21no—
667C22×C32—21no—
668C22×C32—21no—
669C22×C32—21no—
670C22×C32—21no—
671C22×C32—21no—
672C22×C32—22no—
673C22×C32—22no—
674C22×C32—22no—
675C22×C32—41no—
676C22×C32—42no—
677C22×C32—41no—
678C22×C32—41no—
679C22×C32—42no—
680C22×C32—41no—
681C22×C32—41no—
682C22×C32—41no—
683C22×C32—41no—
684C22×C32—41no—
685C22×C32—41no—
686C22×C32—41no—
687C22×C32—41no—
688C22×C32—41no—
689C22×C32—41no—
690C22×C32—41no—
691C22×C32—41no—
692C22×C32—81no—
693C22×C32—81no—
694C22×C32—81no—
695C22×C32—81no—
696C22×C32D3×D412yes—
697C22×C32D3×D412yes—
698C22×C32C2×#6712yes—
699C22×C32C23×D311yescharacteristic
700C22×C32C23×D311yescharacteristic
701C22×C32C23×D311yescharacteristic
702C2×C3⋊D3—21no—
703C2×C3⋊D3—21no—
704C2×C3⋊D3—21no—
705C2×C3⋊D3—21no—
706C2×C3⋊D3—21no—
707C2×C3⋊D3—21no—
708C2×C3⋊D3—21no—
709C2×C3⋊D3—21no—
710C2×C3⋊D3—21no—
711C2×C3⋊D3—21no—
712C2×C3⋊D3—44no—
713C2×C3⋊D3—44no—
714C2×C3⋊D3#23712yescomplemented
715C2×C3⋊D3C2×#6712yes—
716C2×C3×D3—32no—
717C2×C3×D3—32no—
718C2×C3×D3—32no—
719C2×C3×D3—32no—
720C2×C3×D3—62no—
721C2×C3×D3—62no—
722C2×C3×D3—62no—
723C2×C3×D3—62no—
724C2×C3×D3—61no—
725C2×C3×D3—61no—
726C2×C3×D3—61no—
727C2×C3×D3—61no—
728C2×C3×D3—61no—
729C2×C3×D3—61no—
730C2×C3×D3—61no—
731C2×C3×D3—61no—
732C2×C3×D3—62no—
733C2×C3×D3—61no—
734C2×C3×D3—61no—
735C2×C3×D3—61no—
736C2×C3×D3—61no—
737C2×C3×D3—61no—
738C2×C3×D3—61no—
739C2×C3×D3—61no—
740C2×C3×D3—61no—
741C2×C3×D3—61no—
742C2×C3×D3—61no—
743C2×C3×D3—61no—
744C2×C3×D3—61no—
745C2×C3×D3—121no—
746C2×C3×D3—121no—
747C2×C3×D3—121no—
748C2×C3×D3—121no—
749C2×C3×D3—121no—
750C2×C3×D3—121no—
751C2×C3×D3—121no—
752C2×C3×D3—124no—
753C2×C3×D3—124no—
754C2×C3×D3—124no—
755C2×C3×D3—124no—
756C2×C3×D3—128no—
757C2×C3×D3—128no—
758C32×C4—21no—
759C32×C4—22no—
760C32×C4—21no—
761C32×C4—21no—
762C32×C4—41no—
763C32×C4—41no—
764C32×C4—42no—
765C3⋊Dic3—21no—
766C3⋊Dic3—21no—
767C3⋊Dic3—21no—
768C3⋊Dic3—21no—
769C3⋊Dic3—21no—
770C3⋊Dic3—21no—
771C3⋊Dic3—21no—
772C3⋊Dic3C2×#6712yes—
773C3×Dic3—32no—
774C3×Dic3—32no—
775C3×Dic3—62no—
776C3×Dic3—62no—
777C3×Dic3—61no—
778C3×Dic3—61no—
779C3×Dic3—61no—
780C3×Dic3—61no—
781C3×Dic3—61no—
782C3×Dic3—61no—
783C3×Dic3—61no—
784C3×Dic3—61no—
785C3×Dic3—61no—
786C3×Dic3—61no—
787C3×Dic3—61no—
788C3×Dic3—61no—
789C3×Dic3—61no—
790C3×Dic3—61no—
791C3×Dic3—121no—
792C3×Dic3—121no—
793C3×Dic3—121no—
794C3×Dic3—121no—
795C3×Dic3—121no—
796C3×Dic3—121no—
797C2×#41—271no—
798C22×D4—91no—
799#124—271no—
800#123—91no—
801#123—271no—
802C22⋊Q8—271no—
803#121—91no—
804#121—271no—
805#121—271no—
806#120—271no—
807#120—271no—
808C4×D4—271no—
809C4×D4—271no—
810C2×C22⋊C4—271no—
811C2×C22⋊C4—271no—
812C33#54611yescharacteristic, complemented, Sylow
813C23×C3—21no—
814C23×C3—21no—
815C23×C3—21no—
816C23×C3—21no—
817C23×C3—21no—
818C23×C3—21no—
819C23×C3—41no—
820C23×C3—41no—
821C23×C3—91no—
822C23×C3—91no—
823C23×C3—91no—
824C23×C3—91no—
825C23×C3—182no—
826C23×C3—182no—
827C23×C3—182no—
828C23×C3—182no—
829C23×C3—361no—
830C23×C3—361no—
831C23×C3C2×D3211yescharacteristic
832C23×C3C2×D3211yescharacteristic
833C23×C3C2×D3211yescharacteristic
834C23×C3C2×D3211yescharacteristic
835C23×C3C2×D3211yescharacteristic
836C23×C3C2×D3211yescharacteristic
837C22×D3—31no—
838C22×D3—31no—
839C22×D3—31no—
840C22×D3—31no—
841C22×D3—31no—
842C22×D3—31no—
843C22×D3—31no—
844C22×D3—31no—
845C22×D3—61no—
846C22×D3—61no—
847C22×D3—61no—
848C22×D3—61no—
849C22×D3—62no—
850C22×D3—62no—
851C22×D3—62no—
852C22×D3—62no—
853C22×D3—62no—
854C22×D3—62no—
855C22×D3—64no—
856C22×D3—64no—
857C22×D3—62no—
858C22×D3—62no—
859C22×D3—122no—
860C22×D3—122no—
861C22×D3—121no—
862C22×D3—121no—
863C22×D3—121no—
864C22×D3—121no—
865C22×D3—122no—
866C22×D3—122no—
867C3×D4—24no—
868C3×D4—22no—
869C3×D4—22no—
870C3×D4—22no—
871C3×D4—42no—
872C3×D4—42no—
873C3×D4—44no—
874C3×D4—94no—
875C3×D4—182no—
876C3×D4—182no—
877C3×D4—182no—
878C3×D4—361no—
879C2×C3×C4—21no—
880C2×C3×C4—21no—
881C2×C3×C4—21no—
882C2×C3×C4—41no—
883C2×C3×C4—91no—
884C2×C3×C4—91no—
885C2×C3×C4—91no—
886C2×C3×C4—91no—
887C2×C3×C4—91no—
888C2×C3×C4—91no—
889C2×C3×C4—91no—
890C2×C3×C4—91no—
891C2×C3×C4—182no—
892C2×C3×C4—182no—
893C2×C3×C4—361no—
894C2×C3×C4C2×D3211yescharacteristic
895C2×C3×C4C2×D3211yescharacteristic
896C2×C3×C4C2×D3211yescharacteristic
897#67—34no—
898#67—34no—
899#67—64no—
900#67—62no—
901#67—62no—
902#67—64no—
903#67—62no—
904#67—62no—
905#67—122no—
906#67—121no—
907#67—121no—
908#67—122no—
909#67—182no—
910#67—182no—
911#67—182no—
912#67—182no—
913#67—361no—
914#67—361no—
915C2×Dic3—31no—
916C2×Dic3—31no—
917C2×Dic3—31no—
918C2×Dic3—31no—
919C2×Dic3—31no—
920C2×Dic3—31no—
921C2×Dic3—31no—
922C2×Dic3—31no—
923C2×Dic3—31no—
924C2×Dic3—31no—
925C2×Dic3—31no—
926C2×Dic3—31no—
927C2×Dic3—31no—
928C2×Dic3—31no—
929C2×Dic3—31no—
930C2×Dic3—31no—
931C2×Dic3—61no—
932C2×Dic3—61no—
933C2×Dic3—61no—
934C2×Dic3—61no—
935C2×Dic3—61no—
936C2×Dic3—61no—
937C2×Dic3—61no—
938C2×Dic3—61no—
939C2×Dic3—62no—
940C2×Dic3—62no—
941C2×Dic3—122no—
942C2×Dic3—121no—
943C2×Dic3—121no—
944C2×Dic3—122no—
945C2×Dic3—182no—
946C2×Dic3—182no—
947C2×Dic3—361no—
948D12—62no—
949D12—62no—
950D12—64no—
951D12—182no—
952D12—182no—
953D12—361no—
954C4×D3—62no—
955C4×D3—62no—
956C4×D3—64no—
957C4×D3—182no—
958C4×D3—182no—
959C4×D3—182no—
960C4×D3—182no—
961C4×D3—361no—
962C4×D3—361no—
963Dic6—182no—
964Dic6—182no—
965Dic6—182no—
966C2×C32—22no—
967C2×C32—22no—
968C2×C32—22no—
969C2×C32—21no—
970C2×C32—21no—
971C2×C32—21no—
972C2×C32—21no—
973C2×C32—21no—
974C2×C32—21no—
975C2×C32—21no—
976C2×C32—21no—
977C2×C32—21no—
978C2×C32—41no—
979C2×C32—41no—
980C2×C32—41no—
981C2×C32—42no—
982C2×C32—42no—
983C2×C32—42no—
984C2×C32—41no—
985C2×C32—42no—
986C2×C32—41no—
987C2×C32—41no—
988C2×C32—82no—
989C2×C32—81no—
990C2×C32—81no—
991C2×C32—82no—
992C2×C32C2×D3×D411yescharacteristic
993C2×C32C2×D3×D411yescharacteristic
994C2×C32C2×#23711yescharacteristic
995C2×C32#100411yescharacteristic
996C2×C32#100411yescharacteristic
997C2×C32D3×#4111yescharacteristic
998C2×C32D3×#4111yescharacteristic
999C2×C32#100911yescharacteristic
1000C2×C32C22×#6711yescharacteristic
1001C3⋊D3—22no—
1002C3⋊D3—22no—
1003C3⋊D3—41no—
1004C3⋊D3—41no—
1005C3×D3—64no—
1006C3×D3—62no—
1007C3×D3—62no—
1008C3×D3—62no—
1009C3×D3—62no—
1010C3×D3—122no—
1011C3×D3—122no—
1012C3×D3—121no—
1013C3×D3—121no—
1014C3×D3—121no—
1015C3×D3—121no—
1016C3×D3—241no—
1017C24—91no—
1018C24—91no—
1019#41—544no—
1020C2×Q8—271no—
1021C2×D4—91no—
1022C2×D4—91no—
1023C2×D4—91no—
1024C2×D4—91no—
1025C2×D4—91no—
1026C2×D4—184no—
1027C2×D4—271no—
1028C2×D4—271no—
1029C2×D4—271no—
1030C2×D4#111311yescharacteristic
1031C22×C4—91no—
1032C22×C4—91no—
1033C22×C4—91no—
1034C22×C4—271no—
1035C22×C4—271no—
1036C22×C4—271no—
1037C4⋊C4—91no—
1038C4⋊C4—91no—
1039C4⋊C4—91no—
1040C4⋊C4—271no—
1041C22⋊C4—91no—
1042C22⋊C4—91no—
1043C22⋊C4—91no—
1044C22⋊C4—91no—
1045C22⋊C4—91no—
1046C22⋊C4—271no—
1047C22⋊C4—271no—
1048C22⋊C4—271no—
1049C22⋊C4—271no—
1050C22⋊C4—271no—
1051C22⋊C4—271no—
1052C22⋊C4—271no—
1053C42—271no—
1054C22×C3—21no—
1055C22×C3—21no—
1056C22×C3—21no—
1057C22×C3—21no—
1058C22×C3—21no—
1059C22×C3—21no—
1060C22×C3—22no—
1061C22×C3—21no—
1062C22×C3—21no—
1063C22×C3—21no—
1064C22×C3—21no—
1065C22×C3—21no—
1066C22×C3—21no—
1067C22×C3—21no—
1068C22×C3—21no—
1069C22×C3—21no—
1070C22×C3—21no—
1071C22×C3—21no—
1072C22×C3—21no—
1073C22×C3—22no—
1074C22×C3—22no—
1075C22×C3—22no—
1076C22×C3—41no—
1077C22×C3—41no—
1078C22×C3—41no—
1079C22×C3—41no—
1080C22×C3—41no—
1081C22×C3—41no—
1082C22×C3—41no—
1083C22×C3—41no—
1084C22×C3—41no—
1085C22×C3—41no—
1086C22×C3—41no—
1087C22×C3—41no—
1088C22×C3—41no—
1089C22×C3—41no—
1090C22×C3—42no—
1091C22×C3—41no—
1092C22×C3—42no—
1093C22×C3—81no—
1094C22×C3—81no—
1095C22×C3—81no—
1096C22×C3—81no—
1097C22×C3—92no—
1098C22×C3—92no—
1099C22×C3—181no—
1100C22×C3—181no—
1101C22×C3—181no—
1102C22×C3—181no—
1103C22×C3—181no—
1104C22×C3—181no—
1105C22×C3—181no—
1106C22×C3—181no—
1107C22×C3—181no—
1108C22×C3—181no—
1109C22×C3—364no—
1110C22×C3—364no—
1111C22×C3D3×#6712yes—
1112C22×C3D3×#6712yes—
1113C22×C3#381112yes—
1114C22×C3C22×D3211yescharacteristic
1115C22×C3C22×D3211yescharacteristic
1116C22×C3C22×D3211yescharacteristic
1117C2×D3—32no—
1118C2×D3—32no—
1119C2×D3—32no—
1120C2×D3—32no—
1121C2×D3—62no—
1122C2×D3—62no—
1123C2×D3—62no—
1124C2×D3—62no—
1125C2×D3—61no—
1126C2×D3—61no—
1127C2×D3—61no—
1128C2×D3—61no—
1129C2×D3—61no—
1130C2×D3—61no—
1131C2×D3—61no—
1132C2×D3—61no—
1133C2×D3—62no—
1134C2×D3—61no—
1135C2×D3—61no—
1136C2×D3—61no—
1137C2×D3—61no—
1138C2×D3—61no—
1139C2×D3—61no—
1140C2×D3—61no—
1141C2×D3—61no—
1142C2×D3—61no—
1143C2×D3—61no—
1144C2×D3—61no—
1145C2×D3—61no—
1146C2×D3—121no—
1147C2×D3—121no—
1148C2×D3—121no—
1149C2×D3—121no—
1150C2×D3—121no—
1151C2×D3—121no—
1152C2×D3—121no—
1153C2×D3—124no—
1154C2×D3—124no—
1155C2×D3—124no—
1156C2×D3—124no—
1157C2×D3—128no—
1158C2×D3—128no—
1159C3×C4—22no—
1160C3×C4—21no—
1161C3×C4—21no—
1162C3×C4—21no—
1163C3×C4—41no—
1164C3×C4—41no—
1165C3×C4—42no—
1166C3×C4—92no—
1167C3×C4—181no—
1168C3×C4—181no—
1169C3×C4—181no—
1170C3×C4—181no—
1171C3×C4—181no—
1172C3×C4—181no—
1173C3×C4—181no—
1174Dic3—32no—
1175Dic3—32no—
1176Dic3—62no—
1177Dic3—62no—
1178Dic3—61no—
1179Dic3—61no—
1180Dic3—61no—
1181Dic3—61no—
1182Dic3—61no—
1183Dic3—61no—
1184Dic3—61no—
1185Dic3—61no—
1186Dic3—61no—
1187Dic3—61no—
1188Dic3—61no—
1189Dic3—61no—
1190Dic3—61no—
1191Dic3—61no—
1192Dic3—121no—
1193Dic3—121no—
1194Dic3—121no—
1195Dic3—121no—
1196Dic3—121no—
1197Dic3—121no—
1198C32—21no—
1199C32—21no—
1200C32—21no—
1201C32—41no—
1202C32#561011yescharacteristic, complemented
1203C32#565411yescharacteristic, complemented
1204C32#580611yescharacteristic, complemented
1205C23—91no—
1206C23—91no—
1207C23—91no—
1208C23—91no—
1209C23—182no—
1210C23—182no—
1211C23—182no—
1212C23—182no—
1213C23—361no—
1214C23—361no—
1215C23C2×#111311yescharacteristic
1216C23C2×#111311yescharacteristic
1217Q8—542no—
1218D4—22no—
1219D4—94no—
1220D4—182no—
1221D4—182no—
1222D4—182no—
1223D4—361no—
1224D4—542no—
1225D4—542no—
1226D4—1081no—
1227C2×C4—91no—
1228C2×C4—91no—
1229C2×C4—91no—
1230C2×C4—91no—
1231C2×C4—91no—
1232C2×C4—91no—
1233C2×C4—91no—
1234C2×C4—91no—
1235C2×C4—182no—
1236C2×C4—182no—
1237C2×C4—361no—
1238C2×C4—542no—
1239C2×C4—542no—
1240C2×C4—1081no—
1241C2×C4C2×#111311yescharacteristic
1242C2×C3—22no—
1243C2×C3—22no—
1244C2×C3—22no—
1245C2×C3—21no—
1246C2×C3—21no—
1247C2×C3—21no—
1248C2×C3—21no—
1249C2×C3—21no—
1250C2×C3—21no—
1251C2×C3—21no—
1252C2×C3—21no—
1253C2×C3—21no—
1254C2×C3—42no—
1255C2×C3—42no—
1256C2×C3—42no—
1257C2×C3—42no—
1258C2×C3—41no—
1259C2×C3—41no—
1260C2×C3—41no—
1261C2×C3—41no—
1262C2×C3—41no—
1263C2×C3—41no—
1264C2×C3—82no—
1265C2×C3—81no—
1266C2×C3—81no—
1267C2×C3—82no—
1268C2×C3—182no—
1269C2×C3—182no—
1270C2×C3—361no—
1271C2×C3—361no—
1272C2×C3D3×#23711yescharacteristic
1273C2×C3D3×#23711yescharacteristic
1274C2×C3#6431211yescharacteristic
1275C2×C3#6431311yescharacteristic
1276C2×C3#6431411yescharacteristic
1277C2×C3#6431411yescharacteristic
1278C2×C3C2×D3×#6711yescharacteristic
1279C2×C3C2×D3×#6711yescharacteristic
1280C2×C3C2×#381111yescharacteristic
1281D3—64no—
1282D3—62no—
1283D3—62no—
1284D3—62no—
1285D3—62no—
1286D3—122no—
1287D3—122no—
1288D3—121no—
1289D3—121no—
1290D3—121no—
1291D3—121no—
1292D3—241no—
1293C22—21no—
1294C22—21no—
1295C22—21no—
1296C22—21no—
1297C22—21no—
1298C22—92no—
1299C22—92no—
1300C22—181no—
1301C22—181no—
1302C22—181no—
1303C22—181no—
1304C22—181no—
1305C22—181no—
1306C22—181no—
1307C22—181no—
1308C22—181no—
1309C22—181no—
1310C22—364no—
1311C22—364no—
1312C22#8904912yes—
1313C22C22×#111311yescharacteristic
1314C4—21no—
1315C4—92no—
1316C4—181no—
1317C4—181no—
1318C4—181no—
1319C4—181no—
1320C4—181no—
1321C4—181no—
1322C4—181no—
1323C3—21no—
1324C3—21no—
1325C3—21no—
1326C3—41no—
1327C3#1059514811yescharacteristic, complemented
1328C3#1059515011yescharacteristic, complemented
1329C3#1059516311yescharacteristic, complemented
1330C2—22no—
1331C2—41no—
1332C2—182no—
1333C2—182no—
1334C2—361no—
1335C2—361no—
1336C2#1172462211yescharacteristic
1337C2#1172462311yescharacteristic
1338C2C2×#8904911yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×C3⋊D3C2semidirect
2. C2×#89046C2semidirect
3. C3×#64148C2semidirect
4. C3×#64144C2semidirect
5. #11723727C2semidirect
6. #11723727C2semidirect
7. #11723726C2semidirect
8. #11723725C2semidirect
9. #11723723C2semidirect
10. C2×#88814C2semidirect
11. #11723718C2semidirect
12. #11723687C2semidirect
13. #11723686C2semidirect
14. #11723684C2semidirect
15. #11723671C2semidirect
24. C2×C3×#638C22semidirect
25. C2×C3×#638C22semidirect
26. C22×C3×C3⋊Dic3C22semidirect
27. C22×C3×C3⋊Dic3C22semidirect
31. C2×#6296C22semidirect
33. C2×#6295C22semidirect
34. C2×#6295C22semidirect
36. C2×#6294C22semidirect
37. C2×#6294C22semidirect
38. C2×#6294C22semidirect
39. C3×#3757C22semidirect
40. C3×#3757C22semidirect
41. C3×#3757C22semidirect
42. C3×#3757C22semidirect
43. C3×#3752C22semidirect
44. C3×#3750C22semidirect
45. C3×#3750C22semidirect
46. C3×#3750C22semidirect
47. #88815C22semidirect
51. #88814C22semidirect
52. #88814C22semidirect
53. #88814C22semidirect
54. #88814C22semidirect
55. #88813C22semidirect
56. C2×D4×C3⋊D3D3semidirect
63. #64148D3semidirect
64. #64144D3semidirect
121. C3×#638D4semidirect
161. C2×#638C2×D3semidirect
162. C2×#638C2×D3semidirect
163. C22×C3⋊Dic3C2×D3semidirect
164. C22×C3⋊Dic3C2×D3semidirect
219. #3757C2×D3semidirect
220. #3757C2×D3semidirect
221. #3757C2×D3semidirect
222. #3757C2×D3semidirect
223. #3752C2×D3semidirect
224. #3750C2×D3semidirect
225. #3750C2×D3semidirect
226. #3750C2×D3semidirect
298. C2×C3×C3⋊D3#41semidirect
427. #638#67semidirect
714. C2×C3⋊D3#237semidirect
812. C33#546semidirect
1202. C32#5610semidirect
1203. C32#5654semidirect
1204. C32#5806semidirect
1327. C3#10595148semidirect
1328. C3#10595150semidirect
1329. C3#10595163semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×C3⋊D32
C2×#890462
C3×#641482
C3×#641442
#117237272
#117237262
#117237252
#117237232
C2×#888142
#117237182
#117236872
#117236862
#117236842
#117236712
#105951633
#105951503
#105951483