Finite Group Databasebeta

← #13150887

Subgroups — #13150887

Order 1728.

1734 conjugacy classes of subgroups.

The subgroup lattice has 785 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊#272C211yesmaximal, characteristic, complemented
2C2×#88677C212yesmaximal, complemented
3C2×#88654C211yesmaximal, characteristic, complemented
4#64139⋊C3C211yesmaximal, characteristic, complemented
5C4×#638⋊C3C211yesmaximal, characteristic, complemented
6#11721323C212yesmaximal, complemented
7#11721163C212yesmaximal, complemented
8#11721158C211yesmaximal, characteristic, complemented
9#11721157C212yesmaximal, complemented
10#11721156C211yesmaximal, characteristic, complemented
11#11721149C211yesmaximal, characteristic, complemented
12#10595069—31nomaximal
13D12×#67—31nomaximal
14C23×#272C2212yescomplemented
15C22×((C3⋊D3)⋊C3)⋊C2C2212yescomplemented
16C22×C4×H(3,𝔽3)C2211yescharacteristic, complemented
17C2×C4⋊#272—24no—
18C2×C4⋊#272C2211yescharacteristic
19C2×C4⋊#272C2211yescharacteristic, complemented
20C2×C4⋊#272C2212yescomplemented
21C2×#638⋊C3C2211yescharacteristic
22C2×#638⋊C3C2212yescomplemented
23C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
24C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
25#88677—28no—
26C2×#6200C2212yescomplemented
27C2×#6200C2212yescomplemented
28C2×#6200C2212yescomplemented
29C2×#6200C2212yescomplemented
30C2×#6199C2212yescomplemented
31#88654—24no—
32#3757⋊C3C2211yescharacteristic, complemented
33#3752⋊C3C2211yescharacteristic, complemented
34#3752⋊C3C2212yescomplemented
35C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
36#3750⋊C3C2211yescharacteristic, complemented
37C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
38#88451C2212yescomplemented
39#88451C2212yescomplemented
40C22×C3×D12—31no—
41C22×C3×D12—31no—
42C22×C3×D12—61no—
43C2×D3×#67—32no—
44C2×D3×#67—32no—
45C2×#3802—31no—
46C2×D3×D12—31no—
47#64139D311yescharacteristic, complemented
48C4×#638D311yescharacteristic, complemented
49C3×#930—31no—
50C3×C4×#67—31no—
51#63977—32no—
52#63976—32no—
53#63922—32no—
54#63922—32no—
55#63916—31no—
56#63914—31no—
57#63911—31no—
58#63908—31no—
59#63898—31no—
60Dic3×D12—31no—
61#63886—32no—
62#63885—32no—
63C23×H(3,𝔽3)C2311yescharacteristic
64C22×#272—24no—
65C22×#272—24no—
66C22×#272—42no—
67C22×#272C2312yes—
68C22×#272C2312yes—
69C22×(C3⋊D3)⋊C3C2312yes—
70C22×(C3⋊D3)⋊C3C2311yescharacteristic
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
77C4⋊#272—24no—
78C4⋊#272—22no—
79C4⋊#272D414yescomplemented
80#638⋊C3—24no—
81#638⋊C3D414yescomplemented
82C2×(C3⋊Dic3)⋊C3C2312yes—
83C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
84C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
85C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
86C4⋊((C3⋊D3)⋊C3)—22no—
87C4×(C3⋊D3)⋊C3—22no—
88#6200—24no—
89#6200—24no—
90#6200—24no—
91#6200—42no—
92#6199—24no—
93D4×#67—91no—
94#5609—91no—
95D4×D12—91no—
96C23×C3×D3—32no—
97C23×C3×D3—32no—
98C23×C3×D3—62no—
99C22×D32—32no—
100C22×D32—32no—
101C22×C32×C4—21no—
102C22×C32×C4C2×D311yescharacteristic, complemented
103C22×C32×C4C2×D311yescharacteristic, complemented
104C2×#638C2×D311yescharacteristic
105C2×#638C2×D312yescomplemented
106C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
107C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
108C2×C3×#67—31no—
109C2×C3×#67—32no—
110C2×C3×D12—31no—
111C2×C3×D12—31no—
112C2×C3×D12—31no—
113C2×C3×D12—32no—
114C2×C3×D12—32no—
115C2×C3×D12—31no—
116C2×C3×D12—31no—
117C2×C3×D12—64no—
118C2×C3×D12—64no—
119C2×C3×D12—61no—
120C2×C3×D12—62no—
121C2×C3×D12—61no—
122C2×C3×D12—68no—
123C2×C3×C4×D3—31no—
124D3×#67—68no—
125D3×#67—68no—
126C2×#626—32no—
127C2×#626—32no—
128C2×#626—32no—
129C2×#626—32no—
130C2×#625—32no—
131C2×#625—32no—
132C2×#625—32no—
133C2×#625—32no—
134C2×D3×Dic3—32no—
135C2×D3×Dic3—32no—
136#3802—64no—
137D3×D12—64no—
138#3757C2×D311yescharacteristic, complemented
139#3752C2×D311yescharacteristic, complemented
140#3752C2×D312yescomplemented
141C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
142#3750C2×D311yescharacteristic, complemented
143C4×C3⋊Dic3C2×D311yescharacteristic, complemented
144C3×#217—31no—
145C3×(C2×D3)⋊C4—31no—
146C3×(C2×D3)⋊C4—32no—
147C3×C4⋊Dic3—31no—
148C3×Dic3⋊C4—31no—
149C3×C4×Dic3—31no—
150(C2×D3)⋊Dic3—32no—
151(C2×D3)⋊Dic3—32no—
152(C2×D3)⋊Dic3—32no—
153(C2×D3)⋊Dic3—32no—
154C22×H(3,𝔽3)—21no—
155C22×H(3,𝔽3)—21no—
156C22×H(3,𝔽3)C2×D412yescomplemented
157C22×H(3,𝔽3)C2411yescharacteristic
158C2×#272—22no—
159C2×#272—22no—
160C2×#272—22no—
161C2×#272—22no—
162C2×#272—22no—
163C2×#272—48no—
164C2×#272C2×D414yescomplemented
165C2×(C3⋊D3)⋊C3—21no—
166C2×(C3⋊D3)⋊C3—21no—
167C2×(C3⋊D3)⋊C3—22no—
168C2×(C3⋊D3)⋊C3—22no—
169C2×(C3⋊D3)⋊C3—22no—
170C2×(C3⋊D3)⋊C3C2×D412yescomplemented
171((C3⋊D3)⋊C3)⋊C2—48no—
172C4×H(3,𝔽3)—21no—
173C4×H(3,𝔽3)C2×D412yescomplemented
174(C3⋊Dic3)⋊C3—22no—
175(C3⋊Dic3)⋊C3—21no—
176(C3⋊Dic3)⋊C3—21no—
177(C3⋊Dic3)⋊C3C2×D412yescomplemented
178C22×C3×D4—91no—
179C22×#67—92no—
180C2×D3×D4—91no—
181C2×D3×D4—91no—
182C2×D3×D4—92no—
183C2×D3×D4—92no—
184C22×D12—31no—
185C22×D12—31no—
186C22×D12—61no—
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—91no—
203#895—92no—
204#895—91no—
205#893—91no—
206#884—92no—
207#882—92no—
208#882—92no—
209#882—92no—
210#874—91no—
211C4×D12—91no—
212C23×C32—21no—
213C23×C32C22×D311yescharacteristic
214C23×C32C22×D311yescharacteristic
215C22×C3⋊D3C22×D312yes—
216C22×C3⋊D3C22×D311yescharacteristic
217C22×C3×D3—31no—
218C22×C3×D3—32no—
219C22×C3×D3—32no—
220C22×C3×D3—32no—
221C22×C3×D3—32no—
222C22×C3×D3—32no—
223C22×C3×D3—62no—
224C22×C3×D3—62no—
225C22×C3×D3—64no—
226C22×C3×D3—64no—
227C22×C3×D3—68no—
228C22×C3×D3—64no—
229C22×C3×D3—64no—
230C22×C3×D3—124no—
231C22×C3×D3—122no—
232C22×C3×D3—122no—
233C22×C3×D3—124no—
234C2×D32—64no—
235C2×D32—64no—
236C2×D32—64no—
237C2×D32—64no—
238C2×D32—122no—
239C2×D32—122no—
240C2×C32×C4—24no—
241C2×C32×C4—22no—
242C2×C32×C4—22no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C22×D311yescharacteristic
246C2×C32×C4C22×D311yescharacteristic
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D311yescharacteristic
249#638—24no—
250#638D1214yescomplemented
251C2×C3⋊Dic3C22×D311yescharacteristic
252C2×C3⋊Dic3C22×D311yescharacteristic
253C2×C3⋊Dic3C22×D312yes—
254C2×C3⋊Dic3C22×D311yescharacteristic
255C4⋊(C3⋊D3)—22no—
256C4×C3⋊D3—22no—
257C3×#67—34no—
258C3×#67—64no—
259C2×C3×Dic3—31no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—32no—
263C3×D12—34no—
264C3×D12—34no—
265C3×D12—64no—
266C3×D12—64no—
267C3×D12—64no—
268C3×D12—68no—
269C3×D12—64no—
270C3×D12—62no—
271C3×D12—62no—
272C3×D12—62no—
273C3×C4×D3—62no—
274#626—64no—
275#626—64no—
276#626—64no—
277#626—122no—
278#625—64no—
279#625—64no—
280#625—64no—
281#625—122no—
282D3×Dic3—64no—
283D3×Dic3—64no—
284D42—271noSylow
285C2×H(3,𝔽3)—22no—
286C2×H(3,𝔽3)C22×D411yescharacteristic
287C2×H(3,𝔽3)C22×D411yescharacteristic
288C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
289#272—24no—
290#272—42no—
291(C3⋊D3)⋊C3—22no—
292(C3⋊D3)⋊C3—42no—
293C24×C3—92no—
294C23×D3—32no—
295C23×D3—32no—
296C23×D3—62no—
297C23×D3—92no—
298C23×D3—92no—
299C23×D3—92no—
300C2×C3×D4—91no—
301C2×C3×D4—91no—
302C2×C3×D4—92no—
303C2×C3×D4—91no—
304C2×C3×D4—92no—
305C2×C3×D4—91no—
306C2×C3×D4—184no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C22×C3×C4—91no—
311C22×C3×C4D3211yescharacteristic
312C2×#67—31no—
313C2×#67—32no—
314C2×#67—91no—
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—92no—
324C2×#67—188no—
325C22×Dic3—92no—
326D3×D4—184no—
327D3×D4—184no—
328D3×D4—188no—
329D3×D4—188no—
330C2×D12—31no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—32no—
334C2×D12—32no—
335C2×D12—31no—
336C2×D12—31no—
337C2×D12—61no—
338C2×D12—62no—
339C2×D12—61no—
340C2×D12—64no—
341C2×D12—64no—
342C2×D12—68no—
343C2×D12—91no—
344C2×D12—92no—
345C2×D12—92no—
346C2×D12—92no—
347C2×D12—92no—
348C2×D12—184no—
349C2×C4×D3—31no—
350C2×C4×D3—91no—
351C2×C4×D3—92no—
352C2×C4×D3—92no—
353C3×C4⋊C4—91no—
354C3×C4⋊C4—91no—
355C3×C22⋊C4—91no—
356C3×C22⋊C4—92no—
357C3×C22⋊C4—91no—
358C3×C42—91no—
359#217—31no—
360#217—91no—
361#217—92no—
362#217—92no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—32no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4—92no—
367(C2×D3)⋊C4—92no—
368(C2×D3)⋊C4—92no—
369(C2×D3)⋊C4—92no—
370(C2×D3)⋊C4—92no—
371C4⋊Dic3—31no—
372C4⋊Dic3—91no—
373Dic3⋊C4—31no—
374Dic3⋊C4—91no—
375C4×Dic3—31no—
376C4×Dic3—91no—
377C22×C32—22no—
378C22×C32—22no—
379C22×C32—21no—
380C22×C32—21no—
381C22×C32—21no—
382C22×C32—21no—
383C22×C32—21no—
384C22×C32—22no—
385C22×C32C2×D1212yescomplemented
386C22×C32D3×D412yescomplemented
387C22×C32C23×D311yescharacteristic
388C22×C32C23×D311yescharacteristic
389C2×C3⋊D3—21no—
390C2×C3⋊D3—21no—
391C2×C3⋊D3—22no—
392C2×C3⋊D3—22no—
393C2×C3⋊D3—22no—
394C2×C3⋊D3C2×D1212yescomplemented
395C2×C3×D3—32no—
396C2×C3×D3—34no—
397C2×C3×D3—34no—
398C2×C3×D3—64no—
399C2×C3×D3—62no—
400C2×C3×D3—61no—
401C2×C3×D3—62no—
402C2×C3×D3—61no—
403C2×C3×D3—62no—
404C2×C3×D3—62no—
405C2×C3×D3—64no—
406C2×C3×D3—62no—
407C2×C3×D3—62no—
408C2×C3×D3—62no—
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—122no—
416C2×C3×D3—122no—
417C2×C3×D3—122no—
418C2×C3×D3—122no—
419C2×C3×D3—128no—
420C2×C3×D3—128no—
421C2×C3×D3—1216no—
422D32—128no—
423D32—128no—
424C32×C4—22no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—22no—
428C32×C4D3×D412yescomplemented
429C32×C4D3×D412yescomplemented
430C3⋊Dic3—22no—
431C3⋊Dic3—21no—
432C3⋊Dic3—21no—
433C3⋊Dic3C2×D1212yescomplemented
434C3×Dic3—32no—
435C3×Dic3—62no—
436C3×Dic3—61no—
437C3×Dic3—61no—
438C22×D4—91no—
439C22×D4—271no—
440C22×D4—272no—
441#127—271no—
442#121—91no—
443#121—272no—
444#121—271no—
445#120—272no—
446#120—272no—
447C4×D4—91no—
448C4×D4—271no—
449H(3,𝔽3)D4211yescharacteristic, complemented, Sylow
450C23×C3—31no—
451C23×C3—31no—
452C23×C3—61no—
453C23×C3—91no—
454C23×C3—92no—
455C23×C3—92no—
456C23×C3—92no—
457C23×C3—184no—
458C23×C3—184no—
459C23×C3—362no—
460C23×C3C2×D3211yescharacteristic
461C22×D3—32no—
462C22×D3—32no—
463C22×D3—31no—
464C22×D3—32no—
465C22×D3—32no—
466C22×D3—32no—
467C22×D3—62no—
468C22×D3—62no—
469C22×D3—64no—
470C22×D3—64no—
471C22×D3—64no—
472C22×D3—64no—
473C22×D3—68no—
474C22×D3—91no—
475C22×D3—92no—
476C22×D3—124no—
477C22×D3—122no—
478C22×D3—122no—
479C22×D3—124no—
480C22×D3—184no—
481C22×D3—184no—
482C22×D3—184no—
483C22×D3—184no—
484C22×D3—184no—
485C22×D3—184no—
486C22×D3—362no—
487C22×D3—362no—
488C22×D3—362no—
489C3×D4—94no—
490C3×D4—94no—
491C3×D4—184no—
492C3×D4—182no—
493C3×D4—184no—
494C3×D4—182no—
495C2×C3×C4—22no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4—64no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—91no—
506C2×C3×C4—91no—
507C2×C3×C4—92no—
508C2×C3×C4—91no—
509C2×C3×C4—182no—
510C2×C3×C4C2×D3211yescharacteristic
511C2×C3×C4C2×D3211yescharacteristic
512#67—34no—
513#67—64no—
514#67—94no—
515#67—184no—
516#67—184no—
517#67—184no—
518#67—184no—
519#67—184no—
520#67—184no—
521#67—184no—
522#67—362no—
523#67—362no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—32no—
528C2×Dic3—91no—
529C2×Dic3—91no—
530C2×Dic3—91no—
531C2×Dic3—92no—
532C2×Dic3—184no—
533D12—34no—
534D12—34no—
535D12—64no—
536D12—62no—
537D12—62no—
538D12—64no—
539D12—64no—
540D12—68no—
541D12—64no—
542D12—62no—
543D12—182no—
544D12—184no—
545D12—184no—
546D12—184no—
547D12—362no—
548C4×D3—62no—
549C4×D3—182no—
550C4×D3—184no—
551C4×D3—184no—
552C2×C32—24no—
553C2×C32—22no—
554C2×C32—22no—
555C2×C32—21no—
556C2×C32—21no—
557C2×C32—21no—
558C2×C32C22×D1211yescharacteristic
559C2×C32C2×D3×D411yescharacteristic
560C2×C32C2×D3×D411yescharacteristic
561C2×C32C2×D3×D411yescharacteristic
562C2×C32#100911yescharacteristic
563C2×C32#100911yescharacteristic
564C3⋊D3—22no—
565C3⋊D3—42no—
566C3×D3—64no—
567C3×D3—62no—
568C3×D3—64no—
569C3×D3—124no—
570C3×D3—124no—
571C3×D3—122no—
572C3×D3—122no—
573C3×D3—122no—
574C24—92no—
575C24—272no—
576C2×D4—91no—
577C2×D4—92no—
578C2×D4—91no—
579C2×D4—92no—
580C2×D4—91no—
581C2×D4—91no—
582C2×D4—184no—
583C2×D4—272no—
584C2×D4—272no—
585C2×D4—272no—
586C2×D4—272no—
587C2×D4—544no—
588C2×D4—548no—
589C22×C4—91no—
590C22×C4—272no—
591C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
592C4⋊C4—91no—
593C4⋊C4—91no—
594C22⋊C4—91no—
595C22⋊C4—91no—
596C22⋊C4—92no—
597C22⋊C4—272no—
598C22⋊C4—272no—
599C42—91no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—31no—
603C22×C3—31no—
604C22×C3—32no—
605C22×C3—32no—
606C22×C3—61no—
607C22×C3—61no—
608C22×C3—61no—
609C22×C3—61no—
610C22×C3—62no—
611C22×C3—62no—
612C22×C3—61no—
613C22×C3—62no—
614C22×C3—92no—
615C22×C3—94no—
616C22×C3—181no—
617C22×C3—181no—
618C22×C3—182no—
619C22×C3—182no—
620C22×C3—182no—
621C22×C3—182no—
622C22×C3—182no—
623C22×C3—182no—
624C22×C3—182no—
625C22×C3—182no—
626C22×C3—368no—
627C22×C3D3×D1212yes—
628C22×C3C22×D3211yescharacteristic
629C2×D3—34no—
630C2×D3—34no—
631C2×D3—32no—
632C2×D3—64no—
633C2×D3—62no—
634C2×D3—62no—
635C2×D3—62no—
636C2×D3—62no—
637C2×D3—61no—
638C2×D3—61no—
639C2×D3—62no—
640C2×D3—62no—
641C2×D3—62no—
642C2×D3—62no—
643C2×D3—62no—
644C2×D3—62no—
645C2×D3—64no—
646C2×D3—62no—
647C2×D3—62no—
648C2×D3—62no—
649C2×D3—92no—
650C2×D3—122no—
651C2×D3—122no—
652C2×D3—122no—
653C2×D3—122no—
654C2×D3—128no—
655C2×D3—128no—
656C2×D3—1216no—
657C2×D3—181no—
658C2×D3—181no—
659C2×D3—182no—
660C2×D3—182no—
661C2×D3—182no—
662C2×D3—368no—
663C2×D3—368no—
664C2×D3—368no—
665C3×C4—21no—
666C3×C4—32no—
667C3×C4—32no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—62no—
671C3×C4—62no—
672C3×C4—92no—
673C3×C4—182no—
674C3×C4—181no—
675C3×C4—181no—
676C3×C4#381112yes—
677Dic3—32no—
678Dic3—62no—
679Dic3—61no—
680Dic3—61no—
681Dic3—92no—
682Dic3—181no—
683Dic3—182no—
684Dic3—181no—
685C32—21no—
686C32D4×D1211yescharacteristic, complemented
687C32#560911yescharacteristic, complemented
688C23—91no—
689C23—92no—
690C23—92no—
691C23—92no—
692C23—184no—
693C23—184no—
694C23—362no—
695C23—544no—
696C23—544no—
697C23—1082no—
698C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
699D4—94no—
700D4—94no—
701D4—184no—
702D4—184no—
703D4—182no—
704D4—182no—
705D4—544no—
706D4—544no—
707D4—544no—
708D4—1082no—
709C2×C4—22no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—91no—
713C2×C4—92no—
714C2×C4—182no—
715C2×C4—544no—
716C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
717C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
718C2×C3—22no—
719C2×C3—31no—
720C2×C3—31no—
721C2×C3—31no—
722C2×C3—31no—
723C2×C3—31no—
724C2×C3—31no—
725C2×C3—62no—
726C2×C3—62no—
727C2×C3—64no—
728C2×C3—61no—
729C2×C3—61no—
730C2×C3—61no—
731C2×C3—182no—
732C2×C3—184no—
733C2×C3—362no—
734C2×C3—362no—
735C2×C3C2×D3×D1211yescharacteristic
736C2×C3#6430811yescharacteristic
737C2×C3C2×#381111yescharacteristic
738D3—64no—
739D3—64no—
740D3—62no—
741D3—124no—
742D3—122no—
743D3—122no—
744D3—124no—
745D3—122no—
746D3—182no—
747D3—362no—
748C22—21no—
749C22—21no—
750C22—94no—
751C22—92no—
752C22—181no—
753C22—182no—
754C22—182no—
755C22—181no—
756C22—182no—
757C22—182no—
758C22—182no—
759C22—182no—
760C22—182no—
761C22—182no—
762C22—368no—
763C22—1088no—
764C22#8865412yescomplemented
765C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
766C4—21no—
767C4—92no—
768C4—181no—
769C4—182no—
770C4—181no—
771C4#8867712yescomplemented
772C3—31no—
773C3—31no—
774C3—61no—
775C3#1059507411yescharacteristic
776C2—22no—
777C2—184no—
778C2—182no—
779C2—362no—
780C2—362no—
781C2C2×#8865411yescharacteristic
782C2#1172249311yescharacteristic
783C2C2×#8867711yescharacteristic
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⋊#272C2semidirect
2. C2×#88677C2semidirect
3. C2×#88654C2semidirect
4. #64139⋊C3C2semidirect
5. C4×#638⋊C3C2semidirect
6. #11721323C2semidirect
7. #11721163C2semidirect
8. #11721158C2semidirect
9. #11721157C2semidirect
10. #11721156C2semidirect
11. #11721149C2semidirect
14. C23×#272C22semidirect
15. C22×((C3⋊D3)⋊C3)⋊C2C22semidirect
16. C22×C4×H(3,𝔽3)C22semidirect
19. C2×C4⋊#272C22semidirect
20. C2×C4⋊#272C22semidirect
22. C2×#638⋊C3C22semidirect
23. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
24. C2×C4×(C3⋊D3)⋊C3C22semidirect
26. C2×#6200C22semidirect
27. C2×#6200C22semidirect
28. C2×#6200C22semidirect
29. C2×#6200C22semidirect
30. C2×#6199C22semidirect
32. #3757⋊C3C22semidirect
33. #3752⋊C3C22semidirect
34. #3752⋊C3C22semidirect
35. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
36. #3750⋊C3C22semidirect
37. C4×(C3⋊Dic3)⋊C3C22semidirect
38. #88451C22semidirect
39. #88451C22semidirect
47. #64139D3semidirect
48. C4×#638D3semidirect
79. C4⋊#272D4semidirect
81. #638⋊C3D4semidirect
102. C22×C32×C4C2×D3semidirect
103. C22×C32×C4C2×D3semidirect
105. C2×#638C2×D3semidirect
106. C2×C4⋊(C3⋊D3)C2×D3semidirect
107. C2×C4×C3⋊D3C2×D3semidirect
138. #3757C2×D3semidirect
139. #3752C2×D3semidirect
140. #3752C2×D3semidirect
141. C4⋊(C3⋊Dic3)C2×D3semidirect
142. #3750C2×D3semidirect
143. C4×C3⋊Dic3C2×D3semidirect
156. C22×H(3,𝔽3)C2×D4semidirect
164. C2×#272C2×D4semidirect
170. C2×(C3⋊D3)⋊C3C2×D4semidirect
173. C4×H(3,𝔽3)C2×D4semidirect
177. (C3⋊Dic3)⋊C3C2×D4semidirect
250. #638D12semidirect
385. C22×C32C2×D12semidirect
386. C22×C32D3×D4semidirect
394. C2×C3⋊D3C2×D12semidirect
428. C32×C4D3×D4semidirect
429. C32×C4D3×D4semidirect
433. C3⋊Dic3C2×D12semidirect
449. H(3,𝔽3)D42semidirect
591. C22×C4((C3⋊D3)⋊C3)⋊C2semidirect
686. C32D4×D12semidirect
687. C32#5609semidirect
764. C22#88654semidirect
771. C4#88677semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#2722
C2×#886772
C2×#886542
#64139⋊C32
C4×#638⋊C32
#117213232
#117211632
#117211582
#117211572
#117211562
#117211492
#105950693
D12×#673