Finite Group Databasebeta

← #13151355

Subgroups — #13151355

Order 1728.

962 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#1084C211yesmaximal, characteristic, complemented
2#64146⋊C3C211yesmaximal, characteristic
3#64144⋊C3C211yesmaximal, characteristic, complemented
4#11721315C211yesmaximal, characteristic, complemented
5#11721311C211yesmaximal, characteristic, complemented
6#11721310C211yesmaximal, characteristic, complemented
7#11721309C211yesmaximal, characteristic, complemented
8#11721307C211yesmaximal, characteristic, complemented
9C2×#88450C211yesmaximal, characteristic, complemented
10#11721304C211yesmaximal, characteristic, complemented
11#11721296C211yesmaximal, characteristic, complemented
12#11721133C211yesmaximal, characteristic, complemented
13#11721121C211yesmaximal, characteristic, complemented
14#11721112C211yesmaximal, characteristic, complemented
15#11721111C211yesmaximal, characteristic, complemented
16#10595175—31nomaximal
17#10595118—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C2×D4×H(3,𝔽3)C2211yescharacteristic
20C22×#1084C2211yescharacteristic
21C22×#1084C2211yescharacteristic, complemented
22C2×#638⋊C3C2211yescharacteristic
23C2×#638⋊C3C2211yescharacteristic
24C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
25C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
26C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
27C2×#6196C2211yescharacteristic, complemented
28#88552C2211yescharacteristic
29#88552C2211yescharacteristic, complemented
30C4⋊#1084C2211yescharacteristic, complemented
31C4×#1084C2211yescharacteristic, complemented
32#3757⋊C3C2211yescharacteristic
33#3757⋊C3C2211yescharacteristic
34#3757⋊C3C2211yescharacteristic, complemented
35#3757⋊C3C2211yescharacteristic, complemented
36#3752⋊C3C2211yescharacteristic
37#3752⋊C3C2211yescharacteristic
38#3750⋊C3C2211yescharacteristic, complemented
39#3750⋊C3C2211yescharacteristic, complemented
40#88450C2211yescharacteristic
41#88450C2211yescharacteristic
42#88450C2211yescharacteristic
43#88450C2211yescharacteristic
44#88450C2211yescharacteristic
45#88450C2211yescharacteristic
46#88449C2211yescharacteristic, complemented
47#88448C2211yescharacteristic, complemented
48#88448C2211yescharacteristic, complemented
49#88448C2211yescharacteristic, complemented
50#88448C2211yescharacteristic, complemented
51#88447C2211yescharacteristic, complemented
52#88447C2211yescharacteristic, complemented
53#64146D311yescharacteristic
54#64144D311yescharacteristic, complemented
55C3×#937—31no—
56C3×#935—31no—
57C3×D4×Dic3—31no—
58C3×D4×Dic3—31no—
59C3×D4×Dic3—61no—
60#63975—31no—
61#63974—31no—
62Dic3×#67—31no—
63#63969—31no—
64D3×#217—31no—
65#63966—31no—
66#63964—31no—
67#63964—31no—
68C2×#3722—31no—
69#63961—31no—
70C2×(C2×D3)⋊Dic3—31no—
71#63959—31no—
72#63957—31no—
73#63955—31no—
74#63953—31no—
75#63952—31no—
76#63899—31no—
77#63895—31no—
78#63877—31no—
79#63868—31no—
80#63859—31no—
81#63858—31no—
82#63848—31no—
83#63836—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C23×H(3,𝔽3)C2311yescharacteristic
86C22×(C3⋊D3)⋊C3—22no—
87C22×(C3⋊D3)⋊C3—22no—
88C22×(C3⋊D3)⋊C3—41no—
89C22×(C3⋊D3)⋊C3C2311yescharacteristic
90C22×(C3⋊D3)⋊C3C2311yescharacteristic
91D4×H(3,𝔽3)—22no—
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93C2×#1084—41no—
94C2×#1084—41no—
95C2×#1084C2311yescharacteristic
96C2×#1084C2311yescharacteristic
97C2×#1084C2311yescharacteristic
98C2×#1084C2311yescharacteristic
99#638⋊C3—22no—
100#638⋊C3—41no—
101C2×(C3⋊Dic3)⋊C3—22no—
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
107C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
108((C3⋊D3)⋊C3)⋊C4—22no—
109((C3⋊D3)⋊C3)⋊C4—41no—
110#6196—41no—
111#5658—91no—
112#5587—91no—
113#5556—91no—
114C23×C3⋊D3C2×D311yescharacteristic
115C23×C3×D3—31no—
116C2×C32×D4—21no—
117C2×C32×D4C2×D311yescharacteristic
118C2×C32×D4C2×D311yescharacteristic
119C2×#638C2×D311yescharacteristic
120C2×#638C2×D311yescharacteristic
121C22×C3⋊Dic3C2×D311yescharacteristic
122C2×C3×#67—31no—
123C2×C3×#67—31no—
124C22×C3×Dic3—31no—
125C22×C3×Dic3—31no—
126C22×C3×Dic3—31no—
127C22×C3×Dic3—31no—
128C22×C3×Dic3—31no—
129C22×C3×Dic3—61no—
130C22×C3×Dic3—61no—
131C2×#627—31no—
132C2×#627—31no—
133C2×#624—31no—
134C2×#624—31no—
135C2×D3×Dic3—31no—
136C2×D3×Dic3—31no—
137#3757C2×D311yescharacteristic
138#3757C2×D311yescharacteristic
139#3757C2×D311yescharacteristic, complemented
140#3757C2×D311yescharacteristic, complemented
141#3752C2×D311yescharacteristic
142#3752C2×D311yescharacteristic
143#3750C2×D311yescharacteristic, complemented
144#3750C2×D311yescharacteristic, complemented
145C3×#217—31no—
146C3×#217—31no—
147C3×#217—31no—
148C3×#217—31no—
149C3×#217—31no—
150C3×#217—31no—
151C3×#217—31no—
152C3×#217—31no—
153C3×#217—61no—
154C3×#217—61no—
155C3×(C2×D3)⋊C4—31no—
156C3×(C2×D3)⋊C4—31no—
157C3×C4⋊Dic3—31no—
158C3×C4⋊Dic3—31no—
159C3×C4⋊Dic3—61no—
160C3×Dic3⋊C4—31no—
161C3×Dic3⋊C4—31no—
162C3×C4×Dic3—31no—
163C3×C4×Dic3—31no—
164C3×C4×Dic3—61no—
165#3724—31no—
166#3724—31no—
167#3724—31no—
168#3724—31no—
169Dic3⋊Dic3—31no—
170Dic3⋊Dic3—31no—
171Dic3⋊Dic3—31no—
172Dic3⋊Dic3—31no—
173Dic3⋊Dic3—31no—
174Dic3⋊Dic3—31no—
175#3722—31no—
176#3722—31no—
177#3722—31no—
178#3722—31no—
179#3722—31no—
180#3722—31no—
181(C2×D3)⋊Dic3—31no—
182(C2×D3)⋊Dic3—31no—
183(C2×D3)⋊Dic3—31no—
184(C2×D3)⋊Dic3—31no—
185(C2×D3)⋊Dic3—31no—
186(C2×D3)⋊Dic3—31no—
187Dic32—31no—
188Dic32—31no—
189Dic32—31no—
190Dic32—31no—
191C22×H(3,𝔽3)—21no—
192C22×H(3,𝔽3)—21no—
193C22×H(3,𝔽3)—21no—
194C22×H(3,𝔽3)—21no—
195C22×H(3,𝔽3)—21no—
196C22×H(3,𝔽3)#4112yes—
197C22×H(3,𝔽3)C2411yescharacteristic
198C2×(C3⋊D3)⋊C3—21no—
199C2×(C3⋊D3)⋊C3—21no—
200C2×(C3⋊D3)⋊C3—21no—
201C2×(C3⋊D3)⋊C3—21no—
202C2×(C3⋊D3)⋊C3—21no—
203C2×(C3⋊D3)⋊C3—44no—
204C2×(C3⋊D3)⋊C3#4112yes—
205C4×H(3,𝔽3)—21no—
206#1084—21no—
207#1084—21no—
208#1084—21no—
209#1084—21no—
210(C3⋊Dic3)⋊C3—21no—
211(C3⋊Dic3)⋊C3—21no—
212(C3⋊Dic3)⋊C3—21no—
213(C3⋊Dic3)⋊C3—21no—
214(C3⋊Dic3)⋊C3—21no—
215(C3⋊Dic3)⋊C3—21no—
216C3×#123—91no—
217C3×#120—91no—
218C3×C4×D4—91no—
219C2×#217—91no—
220C2×#217—91no—
221#937—31no—
222#937—91no—
223#936—91no—
224#935—31no—
225#935—91no—
226#935—91no—
227#935—91no—
228D4×Dic3—31no—
229D4×Dic3—31no—
230D4×Dic3—61no—
231D4×Dic3—91no—
232#929—91no—
233C4×#67—91no—
234C2×(C2×D3)⋊C4—91no—
235C2×(C2×D3)⋊C4—91no—
236#926—91no—
237#924—91no—
238#898—91no—
239#898—91no—
240#898—91no—
241#897—91no—
242#896—91no—
243#892—91no—
244#886—91no—
245#885—91no—
246#885—91no—
247#883—91no—
248#883—91no—
249#67⋊C4—91no—
250D3×C22⋊C4—91no—
251D3×C22⋊C4—91no—
252#879—91no—
253#879—91no—
254#878—91no—
255#878—91no—
256#878—91no—
257#877—91no—
258#877—91no—
259#877—91no—
260#876—91no—
261#872—91no—
262C23×C32—21no—
263C23×C32—21no—
264C23×C32C22×D311yescharacteristic
265C23×C32C22×D311yescharacteristic
266C23×C32C22×D311yescharacteristic
267C23×C32C22×D311yescharacteristic
268C22×C3⋊D3—22no—
269C22×C3⋊D3—22no—
270C22×C3⋊D3—41no—
271C22×C3⋊D3C22×D311yescharacteristic
272C22×C3⋊D3C22×D311yescharacteristic
273C22×C3×D3—31no—
274C22×C3×D3—31no—
275C22×C3×D3—62no—
276C22×C3×D3—62no—
277C22×C3×D3—121no—
278C32×D4—24no—
279C32×D4—22no—
280C32×D4—22no—
281C2×C32×C4—21no—
282C2×C32×C4C22×D311yescharacteristic
283C2×C32×C4C22×D311yescharacteristic
284#638—22no—
285#638—41no—
286C2×C3⋊Dic3—22no—
287C2×C3⋊Dic3C22×D311yescharacteristic
288C2×C3⋊Dic3C22×D311yescharacteristic
289C2×C3⋊Dic3C22×D311yescharacteristic
290C2×C3⋊Dic3C22×D311yescharacteristic
291C2×C3⋊Dic3C22×D311yescharacteristic
292C2×C3⋊Dic3C22×D311yescharacteristic
293C3×#67—62no—
294C3×#67—121no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—31no—
298C2×C3×Dic3—31no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—31no—
305C2×C3×Dic3—31no—
306C2×C3×Dic3—31no—
307C2×C3×Dic3—31no—
308C2×C3×Dic3—31no—
309C2×C3×Dic3—61no—
310C2×C3×Dic3—61no—
311C2×C3×Dic3—61no—
312C2×C3×Dic3—61no—
313C2×C3×Dic3—62no—
314C2×C3×Dic3—121no—
315C2×C3×Dic3—121no—
316C2×C3×Dic3—121no—
317C2×C3×Dic3—121no—
318C2×C3×Dic3—122no—
319C2×C3×Dic3—122no—
320#627—121no—
321#627—121no—
322#624—62no—
323#624—121no—
324D3×Dic3—62no—
325D3×Dic3—121no—
326#551—271noSylow
327C2×H(3,𝔽3)—22no—
328C2×H(3,𝔽3)—41no—
329C2×H(3,𝔽3)C2×#4111yescharacteristic
330C2×H(3,𝔽3)C2×#4111yescharacteristic
331C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
332(C3⋊D3)⋊C3—22no—
333(C3⋊D3)⋊C3—41no—
334C24×C3—91no—
335C23×D3—31no—
336C23×D3—91no—
337C2×C3×D4—31no—
338C2×C3×D4—31no—
339C2×C3×D4—61no—
340C2×C3×D4—91no—
341C2×C3×D4—91no—
342C2×C3×D4D3211yescharacteristic
343C22×C3×C4—91no—
344C22×C3×C4—91no—
345C22×C3×C4—91no—
346C2×#67—31no—
347C2×#67—31no—
348C2×#67—91no—
349C2×#67—91no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357C22×Dic3—91no—
358C22×Dic3—91no—
359C22×Dic3—91no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×C4×D3—91no—
363C2×C4×D3—91no—
364C2×Dic6—91no—
365C2×Dic6—91no—
366C2×Dic6—91no—
367C3×C4⋊C4—91no—
368C3×C4⋊C4—91no—
369C3×C4⋊C4—91no—
370C3×C22⋊C4—91no—
371C3×C22⋊C4—91no—
372C3×C22⋊C4—91no—
373C3×C22⋊C4—91no—
374C3×C22⋊C4—91no—
375C3×C22⋊C4—91no—
376C3×C22⋊C4—91no—
377C3×C22⋊C4—91no—
378C3×C42—91no—
379#217—31no—
380#217—31no—
381#217—31no—
382#217—31no—
383#217—31no—
384#217—31no—
385#217—31no—
386#217—31no—
387#217—61no—
388#217—61no—
389#217—91no—
390#217—91no—
391#217—91no—
392#217—91no—
393#217—91no—
394#217—91no—
395#217—91no—
396#217—91no—
397#217—91no—
398#217—91no—
399(C2×D3)⋊C4—31no—
400(C2×D3)⋊C4—31no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—91no—
414(C2×D3)⋊C4—91no—
415C4⋊Dic3—31no—
416C4⋊Dic3—31no—
417C4⋊Dic3—61no—
418C4⋊Dic3—91no—
419C4⋊Dic3—91no—
420C4⋊Dic3—91no—
421C4⋊Dic3—91no—
422C4⋊Dic3—91no—
423Dic3⋊C4—31no—
424Dic3⋊C4—31no—
425Dic3⋊C4—91no—
426Dic3⋊C4—91no—
427Dic3⋊C4—91no—
428Dic3⋊C4—91no—
429Dic3⋊C4—91no—
430Dic3⋊C4—91no—
431Dic3⋊C4—91no—
432Dic3⋊C4—91no—
433Dic3⋊C4—91no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437C4×Dic3—31no—
438C4×Dic3—31no—
439C4×Dic3—61no—
440C4×Dic3—91no—
441C4×Dic3—91no—
442C4×Dic3—91no—
443C4×Dic3—91no—
444C4×Dic3—91no—
445C4×Dic3—91no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—22no—
451C22×C32—21no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—22no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32#23712yes—
464C22×C32#23712yes—
465C22×C32C23×D311yescharacteristic
466C22×C32C23×D311yescharacteristic
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3—21no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3—21no—
472C2×C3⋊D3—44no—
473C2×C3⋊D3#23712yes—
474C2×C3×D3—32no—
475C2×C3×D3—61no—
476C2×C3×D3—61no—
477C2×C3×D3—61no—
478C2×C3×D3—61no—
479C2×C3×D3—61no—
480C2×C3×D3—124no—
481C32×C4—22no—
482C32×C4—21no—
483C32×C4—21no—
484C3⋊Dic3—21no—
485C3⋊Dic3—21no—
486C3⋊Dic3—21no—
487C3⋊Dic3—21no—
488C3⋊Dic3—21no—
489C3⋊Dic3—21no—
490C3×Dic3—62no—
491C3×Dic3—61no—
492C3×Dic3—61no—
493C3×Dic3—61no—
494C3×Dic3—61no—
495C3×Dic3—61no—
496C3×Dic3—61no—
497C3×Dic3—61no—
498C3×Dic3—61no—
499C3×Dic3—61no—
500C3×Dic3—61no—
501C3×Dic3—61no—
502C3×Dic3—61no—
503C3×Dic3—61no—
504C3×Dic3—61no—
505C3×Dic3—121no—
506C3×Dic3—121no—
507C3×Dic3—121no—
508#126—271no—
509#126—271no—
510#124—271no—
511#123—91no—
512#123—271no—
513#123—271no—
514C22⋊Q8—271no—
515C22⋊Q8—271no—
516#120—91no—
517C4×D4—91no—
518C4×D4—271no—
519#117—271no—
520#117—271no—
521C2×C22⋊C4—271no—
522C2×C22⋊C4—271no—
523H(3,𝔽3)#55111yescharacteristic, complemented, Sylow
524C23×C3—31no—
525C23×C3—31no—
526C23×C3—31no—
527C23×C3—31no—
528C23×C3—61no—
529C23×C3—61no—
530C23×C3—91no—
531C23×C3—91no—
532C23×C3—182no—
533C23×C3—182no—
534C23×C3—361no—
535C23×C3C2×D3211yescharacteristic
536C23×C3C2×D3211yescharacteristic
537C22×D3—31no—
538C22×D3—31no—
539C22×D3—62no—
540C22×D3—62no—
541C22×D3—91no—
542C22×D3—91no—
543C22×D3—121no—
544C22×D3—182no—
545C22×D3—182no—
546C22×D3—361no—
547C3×D4—22no—
548C3×D4—62no—
549C3×D4—62no—
550C3×D4—64no—
551C3×D4—182no—
552C3×D4—361no—
553C2×C3×C4—31no—
554C2×C3×C4—31no—
555C2×C3×C4—61no—
556C2×C3×C4—91no—
557C2×C3×C4—91no—
558C2×C3×C4—91no—
559C2×C3×C4—91no—
560C2×C3×C4—91no—
561C2×C3×C4—91no—
562C2×C3×C4—91no—
563C2×C3×C4—91no—
564C2×C3×C4—91no—
565C2×C3×C4—91no—
566C2×C3×C4—182no—
567C2×C3×C4—361no—
568C2×C3×C4—361no—
569C2×C3×C4C2×D3211yescharacteristic
570#67—62no—
571#67—121no—
572#67—182no—
573#67—361no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—31no—
578C2×Dic3—31no—
579C2×Dic3—31no—
580C2×Dic3—31no—
581C2×Dic3—31no—
582C2×Dic3—31no—
583C2×Dic3—31no—
584C2×Dic3—31no—
585C2×Dic3—31no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—62no—
593C2×Dic3—91no—
594C2×Dic3—91no—
595C2×Dic3—91no—
596C2×Dic3—91no—
597C2×Dic3—91no—
598C2×Dic3—91no—
599C2×Dic3—121no—
600C2×Dic3—121no—
601C2×Dic3—121no—
602C2×Dic3—121no—
603C2×Dic3—122no—
604C2×Dic3—122no—
605C2×Dic3—182no—
606C2×Dic3—182no—
607C2×Dic3—361no—
608C4×D3—182no—
609C4×D3—182no—
610C4×D3—361no—
611C4×D3—361no—
612Dic6—361no—
613Dic6—361no—
614Dic6—361no—
615C2×C32—22no—
616C2×C32—22no—
617C2×C32—21no—
618C2×C32—21no—
619C2×C32—21no—
620C2×C32—42no—
621C2×C32—42no—
622C2×C32—41no—
623C2×C32—41no—
624C2×C32C2×#23711yescharacteristic
625C2×C32C2×#23711yescharacteristic
626C2×C32C2×#23711yescharacteristic
627C2×C32#100411yescharacteristic
628C2×C32D3×#4111yescharacteristic
629C2×C32#100911yescharacteristic
630C3⋊D3—22no—
631C3⋊D3—41no—
632C3×D3—62no—
633C3×D3—121no—
634C24—91no—
635C2×Q8—271no—
636C2×D4—91no—
637C2×D4—91no—
638C2×D4((C3⋊D3)⋊C3)⋊C211yescharacteristic
639C22×C4—91no—
640C22×C4—91no—
641C22×C4—91no—
642C22×C4—271no—
643C22×C4—271no—
644C4⋊C4—91no—
645C4⋊C4—91no—
646C4⋊C4—91no—
647C4⋊C4—271no—
648C4⋊C4—271no—
649C4⋊C4—271no—
650C4⋊C4—271no—
651C4⋊C4—271no—
652C22⋊C4—91no—
653C22⋊C4—91no—
654C22⋊C4—91no—
655C22⋊C4—91no—
656C22⋊C4—91no—
657C22⋊C4—91no—
658C22⋊C4—91no—
659C22⋊C4—91no—
660C22⋊C4—271no—
661C22⋊C4—271no—
662C22⋊C4—271no—
663C22⋊C4—271no—
664C22⋊C4—271no—
665C22⋊C4—271no—
666C42—91no—
667C42—271no—
668C42—271no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—31no—
675C22×C3—31no—
676C22×C3—32no—
677C22×C3—32no—
678C22×C3—61no—
679C22×C3—61no—
680C22×C3—61no—
681C22×C3—61no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—61no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—61no—
688C22×C3—62no—
689C22×C3—61no—
690C22×C3—62no—
691C22×C3—92no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—121no—
695C22×C3—121no—
696C22×C3—181no—
697C22×C3—181no—
698C22×C3—181no—
699C22×C3—181no—
700C22×C3—181no—
701C22×C3—364no—
702C22×C3#380512yes—
703C22×C3C22×D3211yescharacteristic
704C2×D3—32no—
705C2×D3—61no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—92no—
711C2×D3—124no—
712C2×D3—181no—
713C2×D3—181no—
714C2×D3—181no—
715C2×D3—181no—
716C2×D3—181no—
717C2×D3—364no—
718C3×C4—21no—
719C3×C4—61no—
720C3×C4—61no—
721C3×C4—62no—
722C3×C4—181no—
723C3×C4—181no—
724C3×C4—181no—
725C3×C4—181no—
726C3×C4—181no—
727C3×C4—181no—
728C3×C4—181no—
729C3×C4—181no—
730C3×C4—181no—
731C3×C4—181no—
732Dic3—61no—
733Dic3—61no—
734Dic3—61no—
735Dic3—61no—
736Dic3—61no—
737Dic3—61no—
738Dic3—61no—
739Dic3—61no—
740Dic3—62no—
741Dic3—61no—
742Dic3—61no—
743Dic3—61no—
744Dic3—61no—
745Dic3—61no—
746Dic3—61no—
747Dic3—121no—
748Dic3—121no—
749Dic3—121no—
750Dic3—181no—
751Dic3—181no—
752Dic3—181no—
753Dic3—181no—
754Dic3—181no—
755Dic3—181no—
756C32—21no—
757C32#558711yescharacteristic, complemented
758C32#565811yescharacteristic, complemented
759C23—91no—
760C23—91no—
761C23—182no—
762C23—182no—
763C23—361no—
764C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
765C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
766Q8—1081no—
767D4—22no—
768D4—182no—
769D4—361no—
770C2×C4—91no—
771C2×C4—91no—
772C2×C4—91no—
773C2×C4—91no—
774C2×C4—91no—
775C2×C4—91no—
776C2×C4—91no—
777C2×C4—91no—
778C2×C4—91no—
779C2×C4—91no—
780C2×C4—182no—
781C2×C4—361no—
782C2×C4—361no—
783C2×C4—542no—
784C2×C4—1081no—
785C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
786C2×C3—22no—
787C2×C3—31no—
788C2×C3—31no—
789C2×C3—31no—
790C2×C3—31no—
791C2×C3—31no—
792C2×C3—31no—
793C2×C3—41no—
794C2×C3—62no—
795C2×C3—62no—
796C2×C3—61no—
797C2×C3—61no—
798C2×C3—61no—
799C2×C3—122no—
800C2×C3—121no—
801C2×C3—121no—
802C2×C3—122no—
803C2×C3—182no—
804C2×C3—361no—
805C2×C3D3×#23711yescharacteristic
806C2×C3#6431411yescharacteristic
807C2×C3C2×#380511yescharacteristic
808D3—62no—
809D3—121no—
810D3—182no—
811D3—361no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—92no—
818C22—181no—
819C22—181no—
820C22—181no—
821C22—181no—
822C22—181no—
823C22—364no—
824C22#8867212yes—
825C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
826C4—21no—
827C4—181no—
828C4—181no—
829C4—181no—
830C4—181no—
831C4—181no—
832C4—181no—
833C4—181no—
834C4—181no—
835C4—181no—
836C4—181no—
837C3—31no—
838C3—31no—
839C3—61no—
840C3#1059517711yescharacteristic
841C2—22no—
842C2—41no—
843C2—182no—
844C2—361no—
845C2#1172250411yescharacteristic
846C2#1172250711yescharacteristic
847C2C2×#8867211yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC2×D4×H(3,𝔽3)C22
prime radical#64146⋊C3C2
hypercenterC2×D4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#551
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. D4×#1084C2semidirect
3. #64144⋊C3C2semidirect
4. #11721315C2semidirect
5. #11721311C2semidirect
6. #11721310C2semidirect
7. #11721309C2semidirect
8. #11721307C2semidirect
9. C2×#88450C2semidirect
10. #11721304C2semidirect
11. #11721296C2semidirect
12. #11721133C2semidirect
13. #11721121C2semidirect
14. #11721112C2semidirect
15. #11721111C2semidirect
21. C22×#1084C22semidirect
27. C2×#6196C22semidirect
29. #88552C22semidirect
30. C4⋊#1084C22semidirect
31. C4×#1084C22semidirect
34. #3757⋊C3C22semidirect
35. #3757⋊C3C22semidirect
38. #3750⋊C3C22semidirect
39. #3750⋊C3C22semidirect
46. #88449C22semidirect
47. #88448C22semidirect
48. #88448C22semidirect
49. #88448C22semidirect
50. #88448C22semidirect
51. #88447C22semidirect
52. #88447C22semidirect
54. #64144D3semidirect
139. #3757C2×D3semidirect
140. #3757C2×D3semidirect
143. #3750C2×D3semidirect
144. #3750C2×D3semidirect
523. H(3,𝔽3)#551semidirect
757. C32#5587semidirect
758. C32#5658semidirect

Maximal subgroups

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

subgroupindex
D4×#10842
#64146⋊C32
#64144⋊C32
#117213152
#117213112
#117213102
#117213092
#117213072
C2×#884502
#117213042
#117212962
#117211332
#117211212
#117211122
#117211112
#105951753
#105951183