Finite Group Databasebeta

← #13148714

Subgroups — #13148714

Order 1728.

1341 conjugacy classes of subgroups.

The subgroup lattice has 1051 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88677C211yesmaximal, characteristic, complemented
2C2×#88654C211yesmaximal, characteristic, complemented
3#11721738C211yesmaximal, characteristic, complemented
4#64093⋊C3C211yesmaximal, characteristic, complemented
5#64092⋊C3C211yesmaximal, characteristic, complemented
6#11721324C211yesmaximal, characteristic, complemented
7#11721323C211yesmaximal, characteristic, complemented
8#11721312C211yesmaximal, characteristic, complemented
9#11721163C211yesmaximal, characteristic, complemented
10#11721160C211yesmaximal, characteristic, complemented
11#11721156C211yesmaximal, characteristic, complemented
12#11721151C211yesmaximal, characteristic, complemented
13#11721127C211yesmaximal, characteristic, complemented
14#11721102C211yesmaximal, characteristic, complemented
15#11721100C211yesmaximal, characteristic, complemented
16#10594263—31nomaximal
17#10594262—31nomaximal
18C23×#272C2211yescharacteristic, complemented
19C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
20C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic, complemented
21C2×#6235C2211yescharacteristic, complemented
22C2×C4⋊#272C2211yescharacteristic
23C2×C4⋊#272C2211yescharacteristic, complemented
24C2×#638⋊C3C2211yescharacteristic
25C2×#638⋊C3C2211yescharacteristic, complemented
26C2×#638⋊C3C2211yescharacteristic, complemented
27C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
28C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
29C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
30#88677—24no—
31C2×#6200C2211yescharacteristic
32C2×#6200C2211yescharacteristic
33C2×#6200C2211yescharacteristic, complemented
34C2×#6200C2211yescharacteristic, complemented
35C2×#6200C2211yescharacteristic, complemented
36C2×#6199C2211yescharacteristic, complemented
37C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
38#88654—24no—
39C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
40#88542C2211yescharacteristic, complemented
41#88542C2211yescharacteristic, complemented
42#3757⋊C3C2211yescharacteristic, complemented
43#3752⋊C3C2211yescharacteristic, complemented
44#3752⋊C3C2211yescharacteristic, complemented
45C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
46#3750⋊C3C2211yescharacteristic, complemented
47#3750⋊C3C2211yescharacteristic, complemented
48#88451C2211yescharacteristic, complemented
49#88451C2211yescharacteristic, complemented
50#88451C2211yescharacteristic, complemented
51#88451C2211yescharacteristic, complemented
52#88450C2211yescharacteristic, complemented
53#88450C2211yescharacteristic, complemented
54#88449C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×D3×#67—31no—
57C2×#3802—31no—
58C2×D3×D12—31no—
59#64093D311yescharacteristic, complemented
60#64092D311yescharacteristic, complemented
61C3×#884—31no—
62C3×#883—31no—
63C3×#882—31no—
64C3×#882—31no—
65C3×#882—61no—
66#63983—31no—
67#63983—31no—
68#63977—31no—
69#63976—31no—
70#63970—31no—
71#63958—31no—
72#63922—31no—
73#63922—31no—
74#63921—31no—
75D3×(C2×D3)⋊C4—31no—
76#63916—31no—
77#63910—31no—
78#63908—31no—
79#63905—31no—
80#63891—31no—
81#63890—31no—
82#63885—31no—
83#63884—31no—
84#63884—31no—
85#63853—31no—
86C23×H(3,𝔽3)C2311yescharacteristic
87C22×#272—22no—
88C22×#272—41no—
89C22×#272—41no—
90C22×#272C2311yescharacteristic
91C22×#272C2311yescharacteristic
92C22×#272C2311yescharacteristic
93C22×(C3⋊D3)⋊C3C2311yescharacteristic
94C22×(C3⋊D3)⋊C3C2311yescharacteristic
95C22×(C3⋊D3)⋊C3C2311yescharacteristic
96C2×((C3⋊D3)⋊C3)⋊C2—22no—
97C2×((C3⋊D3)⋊C3)⋊C2—41no—
98C2×((C3⋊D3)⋊C3)⋊C2—41no—
99C2×((C3⋊D3)⋊C3)⋊C2—41no—
100C2×((C3⋊D3)⋊C3)⋊C2—41no—
101C2×((C3⋊D3)⋊C3)⋊C2D414yescomplemented
102C2×C4×H(3,𝔽3)C2311yescharacteristic
103C2×C4×H(3,𝔽3)C2311yescharacteristic
104#6235—41no—
105C2×#1084C2311yescharacteristic
106C4⋊#272—22no—
107C4⋊#272—41no—
108#638⋊C3—22no—
109#638⋊C3—22no—
110#638⋊C3—41no—
111C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
112C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
113C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
114C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
115C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
116C4⋊((C3⋊D3)⋊C3)—22no—
117C4×(C3⋊D3)⋊C3—22no—
118C4×(C3⋊D3)⋊C3—41no—
119#6200—22no—
120#6200—22no—
121#6200—22no—
122#6200—22no—
123#6200—41no—
124#6199—22no—
125((C3⋊D3)⋊C3)⋊C4—41no—
126#5653—91no—
127#5605—91no—
128#5589—91no—
129C23×C3×D3—31no—
130C23×C3×D3—31no—
131C23×C3×D3—61no—
132C22×D32—31no—
133C22×D32—31no—
134C22×D32—31no—
135C22×D32—31no—
136C2×#638C2×D311yescharacteristic
137C2×#638C2×D311yescharacteristic, complemented
138C2×#638C2×D311yescharacteristic, complemented
139C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
140C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
141C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×#67—31no—
147C2×C3×#67—61no—
148C2×C3×D12—31no—
149C2×C3×D12—31no—
150C2×C3×D12—31no—
151C2×C3×D12—31no—
152C2×C3×D12—31no—
153C2×C3×D12—61no—
154C2×C3×D12—61no—
155C2×C3×C4×D3—31no—
156C2×C3×C4×D3—31no—
157D3×#67—64no—
158D3×#67—64no—
159C2×#626—31no—
160C2×#626—31no—
161C2×#626—31no—
162C2×#626—31no—
163C2×#626—31no—
164C2×#625—31no—
165C2×#625—31no—
166C2×#625—31no—
167C2×#625—31no—
168C2×#625—31no—
169C2×#624—31no—
170C2×D3×Dic3—31no—
171C2×D3×Dic3—31no—
172C2×D3×Dic3—31no—
173#3802—64no—
174D3×D12—64no—
175C32×C22⋊C4—21no—
176C32×C22⋊C4C2×D311yescharacteristic, complemented
177C32×C22⋊C4C2×D311yescharacteristic, complemented
178#3757C2×D311yescharacteristic, complemented
179#3752C2×D311yescharacteristic, complemented
180#3752C2×D311yescharacteristic, complemented
181C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
182#3750C2×D311yescharacteristic, complemented
183#3750C2×D311yescharacteristic, complemented
184C3×#217—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—31no—
190C3×(C2×D3)⋊C4—31no—
191C3×(C2×D3)⋊C4—61no—
192C3×(C2×D3)⋊C4—61no—
193C3×C4⋊Dic3—31no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—31no—
196Dic3⋊Dic3—31no—
197Dic3⋊Dic3—31no—
198#3722—31no—
199#3722—31no—
200(C2×D3)⋊Dic3—31no—
201(C2×D3)⋊Dic3—31no—
202(C2×D3)⋊Dic3—31no—
203(C2×D3)⋊Dic3—31no—
204(C2×D3)⋊Dic3—31no—
205(C2×D3)⋊Dic3—31no—
206(C2×D3)⋊Dic3—31no—
207(C2×D3)⋊Dic3—31no—
208(C2×D3)⋊Dic3—31no—
209(C2×D3)⋊Dic3—31no—
210C22×H(3,𝔽3)—21no—
211C22×H(3,𝔽3)—21no—
212C22×H(3,𝔽3)—21no—
213C22×H(3,𝔽3)C2411yescharacteristic
214C2×#272—21no—
215C2×#272—21no—
216C2×#272—21no—
217C2×#272—21no—
218C2×#272—21no—
219C2×#272—21no—
220C2×#272—21no—
221C2×#272—21no—
222C2×#272—44no—
223C2×#272C2×D412yes—
224C2×(C3⋊D3)⋊C3—21no—
225C2×(C3⋊D3)⋊C3—21no—
226C2×(C3⋊D3)⋊C3—21no—
227C2×(C3⋊D3)⋊C3—21no—
228C2×(C3⋊D3)⋊C3—21no—
229C2×(C3⋊D3)⋊C3—21no—
230C2×(C3⋊D3)⋊C3—21no—
231C2×(C3⋊D3)⋊C3C2×D412yes—
232C2×(C3⋊D3)⋊C3C2×D412yes—
233((C3⋊D3)⋊C3)⋊C2—44no—
234((C3⋊D3)⋊C3)⋊C2—44no—
235C4×H(3,𝔽3)—21no—
236C4×H(3,𝔽3)—21no—
237#1084—21no—
238(C3⋊Dic3)⋊C3—21no—
239(C3⋊Dic3)⋊C3—21no—
240(C3⋊Dic3)⋊C3—21no—
241(C3⋊Dic3)⋊C3—21no—
242(C3⋊Dic3)⋊C3—21no—
243C22×#67—91no—
244C2×D3×D4—91no—
245C2×D3×D4—91no—
246C2×D3×D4—91no—
247C2×D3×D4—91no—
248C22×D12—91no—
249C3×#123—91no—
250C3×#121—91no—
251C3×#120—91no—
252#953—91no—
253#939—91no—
254#939—91no—
255#938—91no—
256#938—91no—
257#937—91no—
258#937—91no—
259#937—91no—
260#937—91no—
261#937—91no—
262#935—91no—
263#930—91no—
264#929—91no—
265C2×(C2×D3)⋊C4—91no—
266#895—91no—
267#895—91no—
268#894—91no—
269#894—91no—
270#894—91no—
271#894—91no—
272#886—91no—
273#884—31no—
274#884—91no—
275#884—91no—
276#884—91no—
277#883—31no—
278#883—91no—
279#883—91no—
280#883—91no—
281#882—31no—
282#882—31no—
283#882—61no—
284#882—91no—
285#882—91no—
286#882—91no—
287D3×C22⋊C4—91no—
288D3×C22⋊C4—91no—
289C23×C32—21no—
290C23×C32C22×D311yescharacteristic
291C23×C32C22×D311yescharacteristic
292C22×C3⋊D3C22×D311yescharacteristic
293C22×C3⋊D3C22×D311yescharacteristic
294C22×C3⋊D3C22×D311yescharacteristic
295C22×C3×D3—31no—
296C22×C3×D3—31no—
297C22×C3×D3—31no—
298C22×C3×D3—31no—
299C22×C3×D3—31no—
300C22×C3×D3—31no—
301C22×C3×D3—31no—
302C22×C3×D3—31no—
303C22×C3×D3—31no—
304C22×C3×D3—61no—
305C22×C3×D3—61no—
306C22×C3×D3—61no—
307C22×C3×D3—62no—
308C22×C3×D3—62no—
309C22×C3×D3—122no—
310C22×C3×D3—121no—
311C22×C3×D3—121no—
312C22×C3×D3—121no—
313C22×C3×D3—121no—
314C22×C3×D3—122no—
315C22×C3×D3—122no—
316C2×D32—34no—
317C2×D32—34no—
318C2×D32—62no—
319C2×D32—62no—
320C2×D32—121no—
321C2×D32—121no—
322C2×D32—121no—
323C2×D32—121no—
324C2×D32—121no—
325C2×D32—121no—
326C2×D32—121no—
327C2×D32—121no—
328C2×C32×C4—21no—
329C2×C32×C4—21no—
330C2×C32×C4C22×D311yescharacteristic
331C2×C32×C4C22×D311yescharacteristic
332C2×C32×C4C22×D311yescharacteristic
333C2×C32×C4C22×D311yescharacteristic
334#638—22no—
335#638—22no—
336#638—41no—
337C2×C3⋊Dic3C22×D311yescharacteristic
338C2×C3⋊Dic3C22×D311yescharacteristic
339C2×C3⋊Dic3C22×D311yescharacteristic
340C2×C3⋊Dic3C22×D311yescharacteristic
341C2×C3⋊Dic3C22×D311yescharacteristic
342C4⋊(C3⋊D3)—22no—
343C4×C3⋊D3—22no—
344C4×C3⋊D3—41no—
345C3×#67—62no—
346C3×#67—62no—
347C3×#67—121no—
348C3×#67—121no—
349C3×#67—121no—
350C3×#67—122no—
351C2×C3×Dic3—31no—
352C2×C3×Dic3—31no—
353C2×C3×Dic3—31no—
354C2×C3×Dic3—31no—
355C2×C3×Dic3—31no—
356C2×C3×Dic3—31no—
357C2×C3×Dic3—31no—
358C2×C3×Dic3—61no—
359C3×D12—62no—
360C3×D12—62no—
361C3×D12—62no—
362C3×D12—122no—
363C3×D12—121no—
364C3×D12—121no—
365C3×D12—122no—
366C3×C4×D3—62no—
367C3×C4×D3—121no—
368#626—62no—
369#626—62no—
370#626—62no—
371#626—62no—
372#626—121no—
373#625—62no—
374#625—62no—
375#625—62no—
376#625—62no—
377#625—121no—
378#624—121no—
379D3×Dic3—62no—
380D3×Dic3—62no—
381D3×Dic3—121no—
382#534—271noSylow
383C2×H(3,𝔽3)—41no—
384C2×H(3,𝔽3)C22×D411yescharacteristic
385C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
386C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
387#272—22no—
388#272—41no—
389#272—41no—
390(C3⋊D3)⋊C3—22no—
391(C3⋊D3)⋊C3—22no—
392(C3⋊D3)⋊C3—41no—
393C24×C3—91no—
394C23×D3—31no—
395C23×D3—31no—
396C23×D3—61no—
397C23×D3—91no—
398C23×D3—91no—
399C23×D3—91no—
400C23×D3—91no—
401C23×D3—91no—
402C23×D3—91no—
403C2×C3×D4—91no—
404C2×C3×D4—91no—
405C2×C3×D4—91no—
406C2×C3×D4—91no—
407C2×C3×D4—91no—
408C2×C3×D4—91no—
409C2×C3×D4—91no—
410C22×C3×C4—91no—
411C22×C3×C4—91no—
412C2×#67—31no—
413C2×#67—31no—
414C2×#67—31no—
415C2×#67—31no—
416C2×#67—31no—
417C2×#67—61no—
418C2×#67—91no—
419C2×#67—91no—
420C2×#67—91no—
421C2×#67—91no—
422C2×#67—91no—
423C2×#67—91no—
424C2×#67—91no—
425C2×#67—91no—
426C2×#67—91no—
427C2×#67—91no—
428C2×#67—91no—
429C2×#67—91no—
430C2×#67—91no—
431C2×#67—184no—
432C22×Dic3—91no—
433C22×Dic3—91no—
434D3×D4—184no—
435D3×D4—184no—
436D3×D4—184no—
437D3×D4—184no—
438C2×D12—31no—
439C2×D12—31no—
440C2×D12—31no—
441C2×D12—31no—
442C2×D12—31no—
443C2×D12—61no—
444C2×D12—61no—
445C2×D12—91no—
446C2×D12—91no—
447C2×D12—91no—
448C2×D12—91no—
449C2×D12—91no—
450C2×D12—91no—
451C2×D12—184no—
452C2×C4×D3—31no—
453C2×C4×D3—31no—
454C2×C4×D3—91no—
455C2×C4×D3—91no—
456C2×C4×D3—91no—
457C2×C4×D3—91no—
458C2×C4×D3—91no—
459C2×C4×D3—91no—
460C3×C4⋊C4—91no—
461C3×C4⋊C4—91no—
462C3×C4⋊C4—91no—
463C3×C22⋊C4—31no—
464C3×C22⋊C4—31no—
465C3×C22⋊C4—61no—
466C3×C22⋊C4—91no—
467C3×C22⋊C4—91no—
468C3×C22⋊C4—91no—
469C3×C22⋊C4—91no—
470C3×C22⋊C4—91no—
471C3×C22⋊C4D3211yescharacteristic
472#217—31no—
473#217—91no—
474#217—91no—
475#217—91no—
476#217—91no—
477#217—91no—
478#217—91no—
479#217—91no—
480(C2×D3)⋊C4—31no—
481(C2×D3)⋊C4—31no—
482(C2×D3)⋊C4—31no—
483(C2×D3)⋊C4—31no—
484(C2×D3)⋊C4—31no—
485(C2×D3)⋊C4—31no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—61no—
488(C2×D3)⋊C4—91no—
489(C2×D3)⋊C4—91no—
490(C2×D3)⋊C4—91no—
491(C2×D3)⋊C4—91no—
492(C2×D3)⋊C4—91no—
493(C2×D3)⋊C4—91no—
494(C2×D3)⋊C4—91no—
495(C2×D3)⋊C4—91no—
496(C2×D3)⋊C4—91no—
497(C2×D3)⋊C4—91no—
498(C2×D3)⋊C4—91no—
499(C2×D3)⋊C4—91no—
500(C2×D3)⋊C4—91no—
501(C2×D3)⋊C4—91no—
502C4⋊Dic3—31no—
503C4⋊Dic3—91no—
504C4⋊Dic3—91no—
505Dic3⋊C4—31no—
506Dic3⋊C4—31no—
507Dic3⋊C4—91no—
508Dic3⋊C4—91no—
509Dic3⋊C4—91no—
510Dic3⋊C4—91no—
511C22×C32—22no—
512C22×C32—21no—
513C22×C32—21no—
514C22×C32—21no—
515C22×C32—21no—
516C22×C32—21no—
517C22×C32—21no—
518C22×C32—21no—
519C22×C32—41no—
520C22×C32—41no—
521C22×C32C23×D311yescharacteristic
522C22×C32C23×D311yescharacteristic
523C2×C3⋊D3—21no—
524C2×C3⋊D3—21no—
525C2×C3⋊D3—21no—
526C2×C3⋊D3—21no—
527C2×C3⋊D3—21no—
528C2×C3⋊D3—21no—
529C2×C3⋊D3—21no—
530C2×C3⋊D3D3×D412yes—
531C2×C3⋊D3D3×D412yes—
532C2×C3×D3—32no—
533C2×C3×D3—32no—
534C2×C3×D3—32no—
535C2×C3×D3—32no—
536C2×C3×D3—62no—
537C2×C3×D3—61no—
538C2×C3×D3—61no—
539C2×C3×D3—61no—
540C2×C3×D3—61no—
541C2×C3×D3—61no—
542C2×C3×D3—61no—
543C2×C3×D3—61no—
544C2×C3×D3—61no—
545C2×C3×D3—62no—
546C2×C3×D3—61no—
547C2×C3×D3—61no—
548C2×C3×D3—61no—
549C2×C3×D3—61no—
550C2×C3×D3—61no—
551C2×C3×D3—61no—
552C2×C3×D3—61no—
553C2×C3×D3—61no—
554C2×C3×D3—61no—
555C2×C3×D3—61no—
556C2×C3×D3—61no—
557C2×C3×D3—61no—
558C2×C3×D3—61no—
559C2×C3×D3—61no—
560C2×C3×D3—61no—
561C2×C3×D3—121no—
562C2×C3×D3—121no—
563C2×C3×D3—121no—
564C2×C3×D3—121no—
565C2×C3×D3—121no—
566C2×C3×D3—121no—
567C2×C3×D3—121no—
568C2×C3×D3—124no—
569C2×C3×D3—124no—
570C2×C3×D3—128no—
571D32—124no—
572D32—124no—
573D32—124no—
574D32—124no—
575C32×C4—21no—
576C32×C4—21no—
577C32×C4—21no—
578C32×C4—21no—
579C32×C4—41no—
580C32×C4—41no—
581C3⋊Dic3—21no—
582C3⋊Dic3—21no—
583C3⋊Dic3—21no—
584C3⋊Dic3—21no—
585C3⋊Dic3—21no—
586C3×Dic3—61no—
587C3×Dic3—61no—
588C3×Dic3—61no—
589C3×Dic3—61no—
590C3×Dic3—61no—
591C3×Dic3—61no—
592C3×Dic3—61no—
593C3×Dic3—121no—
594C22×D4—271no—
595C22×D4—271no—
596#123—91no—
597#123—271no—
598#123—271no—
599#123—271no—
600#121—91no—
601#121—271no—
602#121—271no—
603#121—271no—
604#120—91no—
605#120—271no—
606#120—271no—
607#120—271no—
608C2×C22⋊C4—271no—
609H(3,𝔽3)#53411yescharacteristic, complemented, Sylow
610C23×C3—31no—
611C23×C3—31no—
612C23×C3—61no—
613C23×C3—91no—
614C23×C3—91no—
615C23×C3—91no—
616C23×C3—91no—
617C23×C3—91no—
618C23×C3—91no—
619C23×C3—182no—
620C23×C3—361no—
621C23×C3—361no—
622C23×C3C2×D3211yescharacteristic
623C22×D3—31no—
624C22×D3—31no—
625C22×D3—31no—
626C22×D3—31no—
627C22×D3—31no—
628C22×D3—31no—
629C22×D3—31no—
630C22×D3—31no—
631C22×D3—31no—
632C22×D3—61no—
633C22×D3—61no—
634C22×D3—61no—
635C22×D3—62no—
636C22×D3—62no—
637C22×D3—91no—
638C22×D3—91no—
639C22×D3—91no—
640C22×D3—94no—
641C22×D3—94no—
642C22×D3—94no—
643C22×D3—122no—
644C22×D3—121no—
645C22×D3—121no—
646C22×D3—121no—
647C22×D3—121no—
648C22×D3—122no—
649C22×D3—122no—
650C22×D3—182no—
651C22×D3—182no—
652C22×D3—182no—
653C22×D3—361no—
654C22×D3—361no—
655C22×D3—361no—
656C22×D3—361no—
657C22×D3—361no—
658C22×D3—361no—
659C22×D3—361no—
660C22×D3—361no—
661C22×D3—361no—
662C22×D3—361no—
663C22×D3—361no—
664C22×D3—361no—
665C3×D4—182no—
666C3×D4—182no—
667C3×D4—182no—
668C3×D4—182no—
669C3×D4—361no—
670C3×D4—361no—
671C3×D4—361no—
672C2×C3×C4—31no—
673C2×C3×C4—31no—
674C2×C3×C4—31no—
675C2×C3×C4—31no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—91no—
679C2×C3×C4—91no—
680C2×C3×C4—91no—
681C2×C3×C4—91no—
682C2×C3×C4—91no—
683C2×C3×C4—91no—
684C2×C3×C4—182no—
685C2×C3×C4—361no—
686C2×C3×C4C2×D3211yescharacteristic
687C2×C3×C4C2×D3211yescharacteristic
688#67—62no—
689#67—62no—
690#67—121no—
691#67—121no—
692#67—121no—
693#67—122no—
694#67—182no—
695#67—182no—
696#67—182no—
697#67—182no—
698#67—182no—
699#67—182no—
700#67—182no—
701#67—182no—
702#67—182no—
703#67—182no—
704#67—361no—
705#67—361no—
706#67—361no—
707C2×Dic3—31no—
708C2×Dic3—31no—
709C2×Dic3—31no—
710C2×Dic3—31no—
711C2×Dic3—31no—
712C2×Dic3—31no—
713C2×Dic3—31no—
714C2×Dic3—61no—
715C2×Dic3—91no—
716C2×Dic3—91no—
717C2×Dic3—91no—
718C2×Dic3—91no—
719C2×Dic3—91no—
720C2×Dic3—182no—
721C2×Dic3—361no—
722D12—62no—
723D12—62no—
724D12—62no—
725D12—122no—
726D12—121no—
727D12—121no—
728D12—122no—
729D12—182no—
730D12—182no—
731D12—182no—
732D12—182no—
733D12—182no—
734D12—361no—
735C4×D3—62no—
736C4×D3—121no—
737C4×D3—182no—
738C4×D3—182no—
739C4×D3—182no—
740C4×D3—361no—
741C4×D3—361no—
742C4×D3—361no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—42no—
747C2×C32—41no—
748C2×C32—41no—
749C2×C32C2×D3×D411yescharacteristic
750C2×C32C2×D3×D411yescharacteristic
751C2×C32#100411yescharacteristic
752C2×C32#100911yescharacteristic
753C2×C32#100911yescharacteristic
754C2×C32#100911yescharacteristic
755C3⋊D3—22no—
756C3⋊D3—22no—
757C3⋊D3—41no—
758C3×D3—62no—
759C3×D3—62no—
760C3×D3—62no—
761C3×D3—62no—
762C3×D3—122no—
763C3×D3—122no—
764C3×D3—121no—
765C3×D3—121no—
766C3×D3—121no—
767C3×D3—121no—
768C3×D3—121no—
769C3×D3—241no—
770C24—91no—
771C24—271no—
772C24—271no—
773C2×D4—91no—
774C2×D4—91no—
775C2×D4—91no—
776C2×D4—91no—
777C2×D4—91no—
778C2×D4—91no—
779C2×D4—91no—
780C2×D4—271no—
781C2×D4—271no—
782C2×D4—271no—
783C2×D4—271no—
784C2×D4—271no—
785C2×D4—544no—
786C2×D4—544no—
787C22×C4—91no—
788C22×C4—91no—
789C22×C4—271no—
790C22×C4—271no—
791C4⋊C4—91no—
792C4⋊C4—91no—
793C4⋊C4—91no—
794C4⋊C4—271no—
795C22⋊C4—91no—
796C22⋊C4—91no—
797C22⋊C4—91no—
798C22⋊C4—91no—
799C22⋊C4—91no—
800C22⋊C4—271no—
801C22⋊C4—271no—
802C22⋊C4—271no—
803C22⋊C4—271no—
804C22⋊C4—271no—
805C22⋊C4—271no—
806C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—31no—
811C22×C3—31no—
812C22×C3—61no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—61no—
818C22×C3—62no—
819C22×C3—61no—
820C22×C3—92no—
821C22×C3—92no—
822C22×C3—92no—
823C22×C3—121no—
824C22×C3—121no—
825C22×C3—181no—
826C22×C3—181no—
827C22×C3—181no—
828C22×C3—181no—
829C22×C3—181no—
830C22×C3—181no—
831C22×C3—181no—
832C22×C3—181no—
833C22×C3—181no—
834C22×C3—181no—
835C22×C3—181no—
836C22×C3—181no—
837C22×C3—181no—
838C22×C3—181no—
839C22×C3—181no—
840C22×C3—364no—
841C22×C3C22×D3211yescharacteristic
842C2×D3—32no—
843C2×D3—32no—
844C2×D3—32no—
845C2×D3—32no—
846C2×D3—62no—
847C2×D3—61no—
848C2×D3—61no—
849C2×D3—61no—
850C2×D3—61no—
851C2×D3—61no—
852C2×D3—61no—
853C2×D3—61no—
854C2×D3—61no—
855C2×D3—61no—
856C2×D3—61no—
857C2×D3—61no—
858C2×D3—61no—
859C2×D3—61no—
860C2×D3—61no—
861C2×D3—61no—
862C2×D3—61no—
863C2×D3—61no—
864C2×D3—61no—
865C2×D3—61no—
866C2×D3—61no—
867C2×D3—62no—
868C2×D3—61no—
869C2×D3—61no—
870C2×D3—61no—
871C2×D3—92no—
872C2×D3—92no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—121no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—124no—
881C2×D3—124no—
882C2×D3—128no—
883C2×D3—181no—
884C2×D3—181no—
885C2×D3—181no—
886C2×D3—181no—
887C2×D3—181no—
888C2×D3—181no—
889C2×D3—181no—
890C2×D3—364no—
891C2×D3—364no—
892C2×D3—364no—
893C2×D3—364no—
894C2×D3—364no—
895C2×D3—364no—
896C3×C4—21no—
897C3×C4—21no—
898C3×C4—61no—
899C3×C4—61no—
900C3×C4—61no—
901C3×C4—61no—
902C3×C4—121no—
903C3×C4—121no—
904C3×C4—181no—
905C3×C4—181no—
906C3×C4—181no—
907C3×C4—181no—
908C3×C4—181no—
909C3×C4—181no—
910Dic3—61no—
911Dic3—61no—
912Dic3—61no—
913Dic3—61no—
914Dic3—61no—
915Dic3—61no—
916Dic3—61no—
917Dic3—121no—
918Dic3—181no—
919Dic3—181no—
920Dic3—181no—
921Dic3—181no—
922Dic3—181no—
923C32—21no—
924C32#560511yescharacteristic, complemented
925C32#565311yescharacteristic, complemented
926C23—91no—
927C23—91no—
928C23—91no—
929C23—91no—
930C23—91no—
931C23—91no—
932C23—182no—
933C23—274no—
934C23—361no—
935C23—361no—
936C23—542no—
937C23—1081no—
938C23—1081no—
939C23—1081no—
940C23—1081no—
941C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
942D4—182no—
943D4—182no—
944D4—182no—
945D4—182no—
946D4—361no—
947D4—361no—
948D4—361no—
949D4—542no—
950D4—542no—
951D4—542no—
952D4—542no—
953D4—1081no—
954C2×C4—91no—
955C2×C4—91no—
956C2×C4—91no—
957C2×C4—91no—
958C2×C4—91no—
959C2×C4—91no—
960C2×C4—182no—
961C2×C4—361no—
962C2×C4—542no—
963C2×C4—1081no—
964C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
965C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
966C2×C3—31no—
967C2×C3—31no—
968C2×C3—31no—
969C2×C3—31no—
970C2×C3—31no—
971C2×C3—31no—
972C2×C3—41no—
973C2×C3—61no—
974C2×C3—61no—
975C2×C3—61no—
976C2×C3—121no—
977C2×C3—121no—
978C2×C3—122no—
979C2×C3—182no—
980C2×C3—182no—
981C2×C3—182no—
982C2×C3—361no—
983C2×C3—361no—
984C2×C3—361no—
985C2×C3#6430811yescharacteristic
986C2×C3D32×D411yescharacteristic
987C2×C3#6431411yescharacteristic
988D3—62no—
989D3—62no—
990D3—62no—
991D3—62no—
992D3—122no—
993D3—121no—
994D3—121no—
995D3—121no—
996D3—121no—
997D3—122no—
998D3—121no—
999D3—182no—
1000D3—182no—
1001D3—241no—
1002D3—361no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—92no—
1007C22—92no—
1008C22—92no—
1009C22—181no—
1010C22—181no—
1011C22—181no—
1012C22—181no—
1013C22—181no—
1014C22—181no—
1015C22—181no—
1016C22—181no—
1017C22—181no—
1018C22—181no—
1019C22—181no—
1020C22—181no—
1021C22—181no—
1022C22—181no—
1023C22—181no—
1024C22—364no—
1025C22—1084no—
1026C22—1084no—
1027C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
1028C4—21no—
1029C4—21no—
1030C4—181no—
1031C4—181no—
1032C4—181no—
1033C4—181no—
1034C4—181no—
1035C4—181no—
1036C3—31no—
1037C3—31no—
1038C3—61no—
1039C3#1059426411yescharacteristic
1040C2—41no—
1041C2—182no—
1042C2—182no—
1043C2—182no—
1044C2—361no—
1045C2—361no—
1046C2—361no—
1047C2#1172249311yescharacteristic
1048C2D4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
1049C2#1172250711yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC22⋊C4×H(3,𝔽3)C22
hypercenterC22⋊C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#534
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#88677C2semidirect
2. C2×#88654C2semidirect
3. #11721738C2semidirect
4. #64093⋊C3C2semidirect
5. #64092⋊C3C2semidirect
6. #11721324C2semidirect
7. #11721323C2semidirect
8. #11721312C2semidirect
9. #11721163C2semidirect
10. #11721160C2semidirect
11. #11721156C2semidirect
12. #11721151C2semidirect
13. #11721127C2semidirect
14. #11721102C2semidirect
15. #11721100C2semidirect
18. C23×#272C22semidirect
20. C22×((C3⋊D3)⋊C3)⋊C2C22semidirect
21. C2×#6235C22semidirect
23. C2×C4⋊#272C22semidirect
25. C2×#638⋊C3C22semidirect
26. C2×#638⋊C3C22semidirect
27. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
28. C2×C4×(C3⋊D3)⋊C3C22semidirect
29. C2×C4×(C3⋊D3)⋊C3C22semidirect
33. C2×#6200C22semidirect
34. C2×#6200C22semidirect
35. C2×#6200C22semidirect
36. C2×#6199C22semidirect
37. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
39. C22⋊C4×H(3,𝔽3)C22semidirect
40. #88542C22semidirect
41. #88542C22semidirect
42. #3757⋊C3C22semidirect
43. #3752⋊C3C22semidirect
44. #3752⋊C3C22semidirect
45. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
46. #3750⋊C3C22semidirect
47. #3750⋊C3C22semidirect
48. #88451C22semidirect
49. #88451C22semidirect
50. #88451C22semidirect
51. #88451C22semidirect
52. #88450C22semidirect
53. #88450C22semidirect
54. #88449C22semidirect
59. #64093D3semidirect
60. #64092D3semidirect
101. C2×((C3⋊D3)⋊C3)⋊C2D4semidirect
137. C2×#638C2×D3semidirect
138. C2×#638C2×D3semidirect
139. C2×C4⋊(C3⋊D3)C2×D3semidirect
140. C2×C4×C3⋊D3C2×D3semidirect
141. C2×C4×C3⋊D3C2×D3semidirect
176. C32×C22⋊C4C2×D3semidirect
177. C32×C22⋊C4C2×D3semidirect
178. #3757C2×D3semidirect
179. #3752C2×D3semidirect
180. #3752C2×D3semidirect
181. C4⋊(C3⋊Dic3)C2×D3semidirect
182. #3750C2×D3semidirect
183. #3750C2×D3semidirect
609. H(3,𝔽3)#534semidirect
806. C22⋊C4((C3⋊D3)⋊C3)⋊C2semidirect
924. C32#5605semidirect
925. C32#5653semidirect

Maximal subgroups

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

subgroupindex
C2×#886772
C2×#886542
#117217382
#64093⋊C32
#64092⋊C32
#117213242
#117213232
#117213122
#117211632
#117211602
#117211562
#117211512
#117211272
#117211022
#117211002
#105942633
#105942623