Finite Group Databasebeta

← #13150882

Subgroups — #13150882

Order 1728.

1592 conjugacy classes of subgroups.

The subgroup lattice has 779 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic, complemented
2C2×#88676C212yesmaximal, complemented
3C2×#88655C211yesmaximal, characteristic, complemented
4C4×#6235C211yesmaximal, characteristic, complemented
5#64139⋊C3C211yesmaximal, characteristic, complemented
6#11721316C212yesmaximal, complemented
7#11721162C212yesmaximal, complemented
8#11721159C211yesmaximal, characteristic, complemented
9#11721144C211yesmaximal, characteristic, complemented
10#11721136C211yesmaximal, characteristic, complemented
11#11721126C212yesmaximal, complemented
12#10595074—31nomaximal
13D12×#67—31nomaximal
14C23×(C3⋊D3)⋊C3C2212yescomplemented
15C22×((C3⋊D3)⋊C3)⋊C2C2212yescomplemented
16C22×C4×H(3,𝔽3)C2211yescharacteristic, complemented
17C2×#6235C2211yescharacteristic
18C2×C4×#272C2211yescharacteristic, complemented
19C2×#638⋊C3C2212yescomplemented
20C2×C4⋊((C3⋊D3)⋊C3)—24no—
21C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
22C2×C4⋊((C3⋊D3)⋊C3)C2212yescomplemented
23C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
24C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
25#88676—28no—
26C2×#6200C2212yescomplemented
27C2×#6198C2212yescomplemented
28C2×#6198C2212yescomplemented
29C2×#6198C2212yescomplemented
30C2×((C3⋊D3)⋊C3)⋊C4C2212yescomplemented
31#88655—24no—
32#88552C2211yescharacteristic, complemented
33#88542C2211yescharacteristic, complemented
34#88540C2211yescharacteristic, complemented
35C4×#1084C2211yescharacteristic, complemented
36#3752⋊C3C2212yescomplemented
37C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
38#88450C2212yescomplemented
39#88450C2212yescomplemented
40C22×C4⋊(C3⋊D3)D311yescharacteristic, complemented
41C22×C3×D12—31no—
42C2×#3811—32no—
43C2×D3×#67—32no—
44C2×D3×D12—31no—
45C2×D3×D12—31no—
46#64139D311yescharacteristic, complemented
47C3×#930—31no—
48C3×C4×#67—31no—
49C3×C4×#67—31no—
50C3×C4×#67—61no—
51#63981—32no—
52#63977—32no—
53#63923—32no—
54#63922—32no—
55#63911—31no—
56#63911—31no—
57#63910—32no—
58#63909—31no—
59#63908—31no—
60#63894—31no—
61Dic3×D12—31no—
62#63886—32no—
63C23×H(3,𝔽3)C2311yescharacteristic
64C22×#272C2311yescharacteristic
65C22×(C3⋊D3)⋊C3—24no—
66C22×(C3⋊D3)⋊C3—24no—
67C22×(C3⋊D3)⋊C3—42no—
68C22×(C3⋊D3)⋊C3C2312yes—
69C22×(C3⋊D3)⋊C3C2312yes—
70C22×(C3⋊D3)⋊C3C2312yes—
71C2×((C3⋊D3)⋊C3)⋊C2—24no—
72C2×((C3⋊D3)⋊C3)⋊C2—24no—
73C2×((C3⋊D3)⋊C3)⋊C2—42no—
74C2×C4×H(3,𝔽3)—22no—
75C2×C4×H(3,𝔽3)C2311yescharacteristic
76C2×C4×H(3,𝔽3)C2311yescharacteristic
77#6235D414yescomplemented
78C2×#1084C2311yescharacteristic
79C2×#1084C2311yescharacteristic
80C2×#1084C2311yescharacteristic
81C4×#272—22no—
82#638⋊C3—24no—
83C2×(C3⋊Dic3)⋊C3C2312yes—
84C4⋊((C3⋊D3)⋊C3)—24no—
85C4⋊((C3⋊D3)⋊C3)—22no—
86C4⋊((C3⋊D3)⋊C3)—22no—
87C4⋊((C3⋊D3)⋊C3)D414yescomplemented
88#6200—24no—
89#6198—24no—
90#6198—24no—
91#6198—42no—
92((C3⋊D3)⋊C3)⋊C4—24no—
93D4×#67—91no—
94#5609—91no—
95D4×D12—91no—
96C23×C3⋊D3C2×D312yescomplemented
97C23×C3×D3—32no—
98C22×D32—32no—
99C22×D32—32no—
100C22×C32×C4—21no—
101C22×C32×C4C2×D311yescharacteristic, complemented
102C22×C32×C4C2×D311yescharacteristic, complemented
103C2×#638C2×D312yescomplemented
104C2×C4⋊(C3⋊D3)—24no—
105C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
106C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
107C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
108C2×C4⋊(C3⋊D3)C2×D312yescomplemented
109C2×C3×#67—31no—
110C2×C3×#67—31no—
111C2×C3×#67—32no—
112C2×C3×#67—61no—
113C2×C3×D12—31no—
114C2×C3×D12—31no—
115C2×C3×D12—32no—
116C2×C3×D12—31no—
117C2×C3×D12—64no—
118C2×C3×C4×D3—31no—
119C2×C3×C4×D3—31no—
120C2×C3×C4×D3—61no—
121#3811—68no—
122D3×#67—68no—
123C2×#626—32no—
124C2×#626—32no—
125C2×#626—32no—
126C2×#626—32no—
127C2×#626—32no—
128C2×#626—32no—
129C2×#626—32no—
130C2×#625—32no—
131C2×#624—32no—
132C2×D3×Dic3—32no—
133D3×D12—64no—
134D3×D12—64no—
135#3752C2×D312yescomplemented
136C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
137C3×#217—31no—
138C3×#217—31no—
139C3×#217—61no—
140C3×(C2×D3)⋊C4—31no—
141C3×(C2×D3)⋊C4—31no—
142C3×(C2×D3)⋊C4—32no—
143C3×(C2×D3)⋊C4—61no—
144C3×C4⋊Dic3—31no—
145C3×Dic3⋊C4—31no—
146C3×Dic3⋊C4—31no—
147C3×Dic3⋊C4—61no—
148C3×C4×Dic3—31no—
149C3×C4×Dic3—31no—
150C3×C4×Dic3—61no—
151#3722—32no—
152#3722—32no—
153(C2×D3)⋊Dic3—32no—
154(C2×D3)⋊Dic3—32no—
155C22×H(3,𝔽3)—21no—
156C22×H(3,𝔽3)—21no—
157C22×H(3,𝔽3)C2×D412yescomplemented
158C22×H(3,𝔽3)C2411yescharacteristic
159C2×#272—21no—
160C2×#272—21no—
161C2×#272C2×D412yescomplemented
162C2×(C3⋊D3)⋊C3—22no—
163C2×(C3⋊D3)⋊C3—22no—
164C2×(C3⋊D3)⋊C3—22no—
165C2×(C3⋊D3)⋊C3—22no—
166C2×(C3⋊D3)⋊C3—22no—
167C2×(C3⋊D3)⋊C3—22no—
168C2×(C3⋊D3)⋊C3—22no—
169C2×(C3⋊D3)⋊C3—22no—
170C2×(C3⋊D3)⋊C3—48no—
171C2×(C3⋊D3)⋊C3C2×D414yescomplemented
172((C3⋊D3)⋊C3)⋊C2—48no—
173C4×H(3,𝔽3)—21no—
174C4×H(3,𝔽3)C2×D412yescomplemented
175#1084—21no—
176#1084—21no—
177#1084C2×D412yescomplemented
178(C3⋊Dic3)⋊C3—22no—
179C22×C3×D4—91no—
180C22×#67—92no—
181C2×D3×D4—91no—
182C2×D3×D4—91no—
183C2×D3×D4—92no—
184C2×D3×D4—92no—
185C22×D12—31no—
186C22×D12—91no—
187C22×D12—91no—
188C3×#121—91no—
189C3×C4×D4—91no—
190#953—92no—
191#940—91no—
192#940—91no—
193#939—92no—
194#938—91no—
195#937—92no—
196#937—92no—
197D4×Dic3—91no—
198#930—31no—
199#930—91no—
200#930—91no—
201C4×#67—31no—
202C4×#67—31no—
203C4×#67—61no—
204#895—92no—
205#895—91no—
206#893—91no—
207#884—92no—
208#882—92no—
209#882—92no—
210#882—92no—
211#874—91no—
212C4×D12—91no—
213C23×C32—21no—
214C23×C32C22×D311yescharacteristic
215C23×C32C22×D311yescharacteristic
216C22×C3⋊D3—24no—
217C22×C3⋊D3—24no—
218C22×C3⋊D3—42no—
219C22×C3⋊D3C22×D312yes—
220C22×C3⋊D3C22×D312yes—
221C22×C3⋊D3C22×D312yes—
222C22×C3×D3—31no—
223C22×C3×D3—31no—
224C22×C3×D3—32no—
225C22×C3×D3—32no—
226C22×C3×D3—32no—
227C22×C3×D3—61no—
228C22×C3×D3—64no—
229C22×C3×D3—64no—
230C22×C3×D3—122no—
231C2×D32—64no—
232C2×D32—64no—
233C2×D32—64no—
234C2×D32—64no—
235C2×D32—122no—
236C2×D32—122no—
237C2×C32×C4—22no—
238C2×C32×C4—22no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—42no—
242C2×C32×C4C22×D311yescharacteristic
243C2×C32×C4C22×D311yescharacteristic
244C2×C32×C4C22×D311yescharacteristic
245C2×C32×C4C22×D311yescharacteristic
246#638—24no—
247C2×C3⋊Dic3C22×D312yes—
248C4⋊(C3⋊D3)—24no—
249C4⋊(C3⋊D3)—22no—
250C4⋊(C3⋊D3)—22no—
251C4⋊(C3⋊D3)#6714yescomplemented
252C3×#67—34no—
253C3×#67—34no—
254C3×#67—64no—
255C3×#67—64no—
256C2×C3×Dic3—31no—
257C2×C3×Dic3—31no—
258C2×C3×Dic3—32no—
259C2×C3×Dic3—31no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—61no—
264C2×C3×Dic3—61no—
265C2×C3×Dic3—61no—
266C3×D12—34no—
267C3×D12—64no—
268C3×D12—62no—
269C3×D12—62no—
270C3×C4×D3—62no—
271C3×C4×D3—62no—
272C3×C4×D3—122no—
273#626—64no—
274#626—64no—
275#626—64no—
276#626—64no—
277#626—64no—
278#626—122no—
279#626—122no—
280#625—64no—
281#624—64no—
282D3×Dic3—64no—
283D42—271noSylow
284C2×H(3,𝔽3)—22no—
285C2×H(3,𝔽3)C22×D411yescharacteristic
286C2×H(3,𝔽3)C22×D411yescharacteristic
287C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
288#272—22no—
289(C3⋊D3)⋊C3—24no—
290(C3⋊D3)⋊C3—42no—
291(C3⋊D3)⋊C3—42no—
292C24×C3—92no—
293C23×D3—32no—
294C23×D3—92no—
295C23×D3—92no—
296C23×D3—92no—
297C23×D3—92no—
298C2×C3×D4—91no—
299C2×C3×D4—92no—
300C2×C3×D4—91no—
301C2×C3×D4—91no—
302C2×C3×D4—91no—
303C2×C3×D4—92no—
304C2×C3×D4—184no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—91no—
309C22×C3×C4D3211yescharacteristic
310C2×#67—31no—
311C2×#67—31no—
312C2×#67—32no—
313C2×#67—61no—
314C2×#67—92no—
315C2×#67—92no—
316C2×#67—92no—
317C2×#67—92no—
318C2×#67—92no—
319C2×#67—92no—
320C2×#67—92no—
321C2×#67—92no—
322C2×#67—92no—
323C2×#67—188no—
324C22×Dic3—92no—
325D3×D4—184no—
326D3×D4—184no—
327D3×D4—188no—
328D3×D4—188no—
329C2×D12—31no—
330C2×D12—31no—
331C2×D12—31no—
332C2×D12—32no—
333C2×D12—64no—
334C2×D12—91no—
335C2×D12—92no—
336C2×D12—91no—
337C2×D12—91no—
338C2×D12—92no—
339C2×D12—92no—
340C2×D12—92no—
341C2×D12—92no—
342C2×D12—184no—
343C2×D12—184no—
344C2×C4×D3—31no—
345C2×C4×D3—31no—
346C2×C4×D3—61no—
347C2×C4×D3—92no—
348C2×C4×D3—92no—
349C3×C4⋊C4—91no—
350C3×C4⋊C4—91no—
351C3×C22⋊C4—92no—
352C3×C22⋊C4—91no—
353C3×C22⋊C4—91no—
354C3×C42—91no—
355#217—31no—
356#217—31no—
357#217—61no—
358#217—92no—
359#217—92no—
360(C2×D3)⋊C4—31no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—32no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—92no—
365(C2×D3)⋊C4—92no—
366(C2×D3)⋊C4—92no—
367(C2×D3)⋊C4—92no—
368(C2×D3)⋊C4—92no—
369C4⋊Dic3—31no—
370C4⋊Dic3—91no—
371Dic3⋊C4—31no—
372Dic3⋊C4—31no—
373Dic3⋊C4—61no—
374C4×Dic3—31no—
375C4×Dic3—31no—
376C4×Dic3—61no—
377C22×C32—21no—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—21no—
381C22×C32—21no—
382C22×C32—22no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32D3×D412yescomplemented
386C22×C32D3×D412yescomplemented
387C22×C32C23×D311yescharacteristic
388C22×C32C23×D311yescharacteristic
389C2×C3⋊D3—22no—
390C2×C3⋊D3—22no—
391C2×C3⋊D3—22no—
392C2×C3⋊D3—22no—
393C2×C3⋊D3—22no—
394C2×C3⋊D3—22no—
395C2×C3⋊D3—22no—
396C2×C3⋊D3—22no—
397C2×C3⋊D3—48no—
398C2×C3⋊D3C2×#6714yescomplemented
399C2×C3×D3—34no—
400C2×C3×D3—32no—
401C2×C3×D3—32no—
402C2×C3×D3—62no—
403C2×C3×D3—62no—
404C2×C3×D3—61no—
405C2×C3×D3—61no—
406C2×C3×D3—62no—
407C2×C3×D3—61no—
408C2×C3×D3—61no—
409C2×C3×D3—62no—
410C2×C3×D3—62no—
411C2×C3×D3—62no—
412C2×C3×D3—62no—
413C2×C3×D3—62no—
414C2×C3×D3—62no—
415C2×C3×D3—121no—
416C2×C3×D3—121no—
417C2×C3×D3—128no—
418D32—128no—
419D32—128no—
420C32×C4—21no—
421C32×C4—21no—
422C32×C4—22no—
423C32×C4—41no—
424C32×C4D3×D412yescomplemented
425C32×C4C2×#6712yescomplemented
426C3⋊Dic3—22no—
427C3×Dic3—32no—
428C3×Dic3—32no—
429C3×Dic3—62no—
430C3×Dic3—62no—
431C3×Dic3—61no—
432C3×Dic3—61no—
433C3×Dic3—61no—
434C3×Dic3—61no—
435C3×Dic3—121no—
436C3×Dic3—121no—
437C22×D4—91no—
438C22×D4—271no—
439C22×D4—272no—
440#127—271no—
441#121—91no—
442#121—272no—
443#121—271no—
444#120—272no—
445#120—272no—
446C4×D4—91no—
447C4×D4—271no—
448H(3,𝔽3)D4211yescharacteristic, complemented, Sylow
449C23×C3—31no—
450C23×C3—31no—
451C23×C3—61no—
452C23×C3—92no—
453C23×C3—92no—
454C23×C3—92no—
455C23×C3—91no—
456C23×C3—184no—
457C23×C3—184no—
458C23×C3—362no—
459C23×C3C2×D3211yescharacteristic
460C22×D3—31no—
461C22×D3—31no—
462C22×D3—32no—
463C22×D3—32no—
464C22×D3—32no—
465C22×D3—61no—
466C22×D3—64no—
467C22×D3—64no—
468C22×D3—92no—
469C22×D3—92no—
470C22×D3—92no—
471C22×D3—122no—
472C22×D3—184no—
473C22×D3—184no—
474C22×D3—184no—
475C22×D3—184no—
476C22×D3—184no—
477C22×D3—184no—
478C22×D3—184no—
479C22×D3—184no—
480C22×D3—362no—
481C22×D3—362no—
482C22×D3—362no—
483C22×D3—362no—
484C3×D4—94no—
485C3×D4—94no—
486C3×D4—182no—
487C3×D4—182no—
488C3×D4—184no—
489C3×D4—184no—
490C2×C3×C4—22no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—62no—
496C2×C3×C4—62no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—91no—
500C2×C3×C4—92no—
501C2×C3×C4—91no—
502C2×C3×C4—91no—
503C2×C3×C4—122no—
504C2×C3×C4—182no—
505C2×C3×C4C2×D3211yescharacteristic
506C2×C3×C4C2×D3211yescharacteristic
507#67—34no—
508#67—34no—
509#67—64no—
510#67—64no—
511#67—184no—
512#67—184no—
513#67—184no—
514#67—184no—
515#67—184no—
516#67—184no—
517#67—184no—
518#67—362no—
519#67—362no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—32no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—92no—
531C2×Dic3—184no—
532D12—34no—
533D12—64no—
534D12—62no—
535D12—62no—
536D12—94no—
537D12—182no—
538D12—182no—
539D12—184no—
540D12—184no—
541D12—184no—
542D12—184no—
543D12—362no—
544C4×D3—62no—
545C4×D3—62no—
546C4×D3—122no—
547C4×D3—184no—
548C4×D3—184no—
549C2×C32—22no—
550C2×C32—22no—
551C2×C32—21no—
552C2×C32—21no—
553C2×C32—21no—
554C2×C32—42no—
555C2×C32C2×D3×D411yescharacteristic
556C2×C32C2×D3×D411yescharacteristic
557C2×C32C2×D3×D411yescharacteristic
558C2×C32#100411yescharacteristic
559C2×C32#100911yescharacteristic
560C2×C32C22×#6711yescharacteristic
561C3⋊D3—24no—
562C3⋊D3—42no—
563C3⋊D3—42no—
564C3×D3—62no—
565C3×D3—64no—
566C3×D3—62no—
567C3×D3—122no—
568C3×D3—122no—
569C3×D3—122no—
570C24—92no—
571C24—272no—
572C2×D4—91no—
573C2×D4—92no—
574C2×D4—91no—
575C2×D4—92no—
576C2×D4—91no—
577C2×D4—91no—
578C2×D4—184no—
579C2×D4—272no—
580C2×D4—272no—
581C2×D4—272no—
582C2×D4—272no—
583C2×D4—544no—
584C2×D4—548no—
585C22×C4—91no—
586C22×C4—272no—
587C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
588C4⋊C4—91no—
589C4⋊C4—91no—
590C22⋊C4—91no—
591C22⋊C4—91no—
592C22⋊C4—92no—
593C22⋊C4—272no—
594C22⋊C4—272no—
595C42—91no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—31no—
599C22×C3—31no—
600C22×C3—32no—
601C22×C3—32no—
602C22×C3—61no—
603C22×C3—61no—
604C22×C3—61no—
605C22×C3—61no—
606C22×C3—61no—
607C22×C3—62no—
608C22×C3—94no—
609C22×C3—92no—
610C22×C3—121no—
611C22×C3—121no—
612C22×C3—182no—
613C22×C3—182no—
614C22×C3—182no—
615C22×C3—182no—
616C22×C3—182no—
617C22×C3—182no—
618C22×C3—182no—
619C22×C3—182no—
620C22×C3—181no—
621C22×C3—181no—
622C22×C3—368no—
623C22×C3#380212yes—
624C22×C3C22×D3211yescharacteristic
625C2×D3—32no—
626C2×D3—32no—
627C2×D3—34no—
628C2×D3—62no—
629C2×D3—61no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—62no—
634C2×D3—62no—
635C2×D3—62no—
636C2×D3—62no—
637C2×D3—62no—
638C2×D3—62no—
639C2×D3—62no—
640C2×D3—62no—
641C2×D3—94no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—128no—
645C2×D3—182no—
646C2×D3—182no—
647C2×D3—182no—
648C2×D3—182no—
649C2×D3—182no—
650C2×D3—182no—
651C2×D3—182no—
652C2×D3—182no—
653C2×D3—368no—
654C2×D3—368no—
655C2×D3—368no—
656C2×D3—368no—
657C3×C4—21no—
658C3×C4—32no—
659C3×C4—32no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—62no—
663C3×C4—92no—
664C3×C4—121no—
665C3×C4—182no—
666C3×C4—181no—
667C3×C4—181no—
668C3×C4D3×#6712yes—
669Dic3—32no—
670Dic3—32no—
671Dic3—62no—
672Dic3—61no—
673Dic3—61no—
674Dic3—61no—
675Dic3—61no—
676Dic3—62no—
677Dic3—121no—
678Dic3—121no—
679Dic3—182no—
680C32—21no—
681C32#560911yescharacteristic, complemented
682C32D4×#6711yescharacteristic, complemented
683C23—91no—
684C23—92no—
685C23—92no—
686C23—92no—
687C23—184no—
688C23—184no—
689C23—362no—
690C23—544no—
691C23—544no—
692C23—1082no—
693C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
694D4—94no—
695D4—94no—
696D4—184no—
697D4—184no—
698D4—182no—
699D4—182no—
700D4—544no—
701D4—544no—
702D4—544no—
703D4—1082no—
704C2×C4—22no—
705C2×C4—91no—
706C2×C4—91no—
707C2×C4—91no—
708C2×C4—92no—
709C2×C4—182no—
710C2×C4—544no—
711C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
712C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
713C2×C3—22no—
714C2×C3—31no—
715C2×C3—31no—
716C2×C3—31no—
717C2×C3—31no—
718C2×C3—31no—
719C2×C3—31no—
720C2×C3—62no—
721C2×C3—62no—
722C2×C3—61no—
723C2×C3—61no—
724C2×C3—61no—
725C2×C3—122no—
726C2×C3—184no—
727C2×C3—182no—
728C2×C3—362no—
729C2×C3—362no—
730C2×C3C2×#380211yescharacteristic
731C2×C3#6430711yescharacteristic
732C2×C3C2×D3×#6711yescharacteristic
733D3—62no—
734D3—62no—
735D3—64no—
736D3—122no—
737D3—122no—
738D3—122no—
739D3—184no—
740D3—362no—
741D3—362no—
742C22—21no—
743C22—21no—
744C22—94no—
745C22—92no—
746C22—181no—
747C22—182no—
748C22—182no—
749C22—181no—
750C22—182no—
751C22—182no—
752C22—182no—
753C22—182no—
754C22—182no—
755C22—182no—
756C22—368no—
757C22—1088no—
758C22#8865512yescomplemented
759C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
760C4—21no—
761C4—92no—
762C4—181no—
763C4—182no—
764C4—181no—
765C4#8867612yescomplemented
766C3—31no—
767C3—31no—
768C3—61no—
769C3#1059506911yescharacteristic
770C2—22no—
771C2—184no—
772C2—182no—
773C2—362no—
774C2—362no—
775C2C2×#8865511yescharacteristic
776C2#1172249211yescharacteristic
777C2C2×#8867611yescharacteristic
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)D42
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. C22×C4⋊((C3⋊D3)⋊C3)C2semidirect
2. C2×#88676C2semidirect
3. C2×#88655C2semidirect
4. C4×#6235C2semidirect
5. #64139⋊C3C2semidirect
6. #11721316C2semidirect
7. #11721162C2semidirect
8. #11721159C2semidirect
9. #11721144C2semidirect
10. #11721136C2semidirect
11. #11721126C2semidirect
14. C23×(C3⋊D3)⋊C3C22semidirect
15. C22×((C3⋊D3)⋊C3)⋊C2C22semidirect
16. C22×C4×H(3,𝔽3)C22semidirect
18. C2×C4×#272C22semidirect
19. C2×#638⋊C3C22semidirect
22. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
23. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
24. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
26. C2×#6200C22semidirect
27. C2×#6198C22semidirect
28. C2×#6198C22semidirect
29. C2×#6198C22semidirect
30. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
32. #88552C22semidirect
33. #88542C22semidirect
34. #88540C22semidirect
35. C4×#1084C22semidirect
36. #3752⋊C3C22semidirect
37. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
38. #88450C22semidirect
39. #88450C22semidirect
40. C22×C4⋊(C3⋊D3)D3semidirect
46. #64139D3semidirect
77. #6235D4semidirect
87. C4⋊((C3⋊D3)⋊C3)D4semidirect
96. C23×C3⋊D3C2×D3semidirect
101. C22×C32×C4C2×D3semidirect
102. C22×C32×C4C2×D3semidirect
103. C2×#638C2×D3semidirect
106. C2×C4⋊(C3⋊D3)C2×D3semidirect
107. C2×C4⋊(C3⋊D3)C2×D3semidirect
108. C2×C4⋊(C3⋊D3)C2×D3semidirect
135. #3752C2×D3semidirect
136. C4⋊(C3⋊Dic3)C2×D3semidirect
157. C22×H(3,𝔽3)C2×D4semidirect
161. C2×#272C2×D4semidirect
171. C2×(C3⋊D3)⋊C3C2×D4semidirect
174. C4×H(3,𝔽3)C2×D4semidirect
177. #1084C2×D4semidirect
251. C4⋊(C3⋊D3)#67semidirect
385. C22×C32D3×D4semidirect
386. C22×C32D3×D4semidirect
398. C2×C3⋊D3C2×#67semidirect
424. C32×C4D3×D4semidirect
425. C32×C4C2×#67semidirect
448. H(3,𝔽3)D42semidirect
587. C22×C4((C3⋊D3)⋊C3)⋊C2semidirect
681. C32#5609semidirect
682. C32D4×#67semidirect
758. C22#88655semidirect
765. C4#88676semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊((C3⋊D3)⋊C3)2
C2×#886762
C2×#886552
C4×#62352
#64139⋊C32
#117213162
#117211622
#117211592
#117211442
#117211362
#117211262
#105950743
D12×#673