Finite Group Databasebeta

← #13147856

Subgroups — #13147856

Order 1728.

913 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊#272C211yesmaximal, characteristic, complemented
2#64081⋊C3C211yesmaximal, characteristic, complemented
3C4×#634⋊C3C211yesmaximal, characteristic, complemented
4#11721157C211yesmaximal, characteristic
5#11721155C211yesmaximal, characteristic, complemented
6C4×#6200C211yesmaximal, characteristic, complemented
7C4×#6200C211yesmaximal, characteristic, complemented
8#11721151C211yesmaximal, characteristic, complemented
9#11721148C211yesmaximal, characteristic, complemented
10C4×#6199C211yesmaximal, characteristic, complemented
11#11721111C211yesmaximal, characteristic, complemented
12#11721102C211yesmaximal, characteristic, complemented
13#11721097C211yesmaximal, characteristic, complemented
14#11721088C211yesmaximal, characteristic, complemented
15#11721085C211yesmaximal, characteristic, complemented
16#10593911—31nomaximal
17#10593910—31nomaximal
18C2×C4⋊#272C2211yescharacteristic
19C2×C4×#272C2211yescharacteristic
20C2×C4×#272C2211yescharacteristic
21C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
22C2×#634⋊C3C2211yescharacteristic
23C2×#6200C2211yescharacteristic
24C2×#6200C2211yescharacteristic
25C2×#6199C2211yescharacteristic
26C2×#6199C2211yescharacteristic
27C42×H(3,𝔽3)C2211yescharacteristic
28#88542C2211yescharacteristic
29#88542C2211yescharacteristic
30C4⋊#1084C2211yescharacteristic
31#3752⋊C3C2211yescharacteristic
32#3752⋊C3C2211yescharacteristic
33C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
34#3750⋊C3C2211yescharacteristic
35#3750⋊C3C2211yescharacteristic
36#3750⋊C3C2211yescharacteristic
37#3750⋊C3C2211yescharacteristic
38C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
39C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
40C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
41#88451C2211yescharacteristic
42#88451C2211yescharacteristic
43#88451C2211yescharacteristic
44#88451C2211yescharacteristic
45#88450C2211yescharacteristic
46#88450C2211yescharacteristic
47#88449C2211yescharacteristic
48#88449C2211yescharacteristic
49#88448C2211yescharacteristic
50#88448C2211yescharacteristic
51#88447C2211yescharacteristic
52#88447C2211yescharacteristic
53#64081D311yescharacteristic, complemented
54C4×#634D311yescharacteristic, complemented
55C3×C4×D12—31no—
56C3×C4×D12—31no—
57C3×C4×D12—61no—
58C3×#872—31no—
59C3×C4×Dic6—31no—
60#63913—31no—
61#63907—31no—
62C4×#626—31no—
63C4×#626—31no—
64C4×#625—31no—
65C4×#625—31no—
66#63896—31no—
67#63891—31no—
68#63890—31no—
69#63887—31no—
70#63886—31no—
71#63885—31no—
72#63884—31no—
73#63884—31no—
74C4×D3×Dic3—31no—
75C4×D3×Dic3—31no—
76#63861—31no—
77#63858—31no—
78#63858—31no—
79#63855—31no—
80#63855—31no—
81#63848—31no—
82#63847—31no—
83#63846—31no—
84C22×#272C2311yescharacteristic
85C22×#272C2311yescharacteristic
86C22×(C3⋊D3)⋊C3C2311yescharacteristic
87C2×C4×H(3,𝔽3)C2311yescharacteristic
88C2×C4×H(3,𝔽3)C2311yescharacteristic
89C2×C4×H(3,𝔽3)C2311yescharacteristic
90C2×#1084C2311yescharacteristic
91C2×#1084C2311yescharacteristic
92C4⋊#272—22no—
93C4×#272—22no—
94C4×#272—22no—
95C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
96C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
97C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
98C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C4×(C3⋊D3)⋊C3—22no—
103#634⋊C3—22no—
104#6200—22no—
105#6200—22no—
106#6199—22no—
107#6199—22no—
108#5580—91no—
109#5538—91no—
110#5528—91no—
111C2×C4×C3⋊D3C2×D311yescharacteristic
112C2×#634C2×D311yescharacteristic
113C2×C3×D12—31no—
114C2×C3×D12—31no—
115C2×C3×D12—61no—
116C2×C3×C4×D3—31no—
117C2×C3×C4×D3—31no—
118C2×C3×C4×D3—31no—
119C2×C3×C4×D3—31no—
120C2×C3×C4×D3—31no—
121C2×C3×C4×D3—61no—
122C2×C3×C4×D3—61no—
123C2×C3×Dic6—31no—
124C2×#626—31no—
125C2×#626—31no—
126C2×#625—31no—
127C2×#625—31no—
128C2×D3×Dic3—31no—
129C2×D3×Dic3—31no—
130C2×D3×Dic3—31no—
131C2×D3×Dic3—31no—
132C32×C42—21no—
133C32×C42C2×D311yescharacteristic
134C32×C42C2×D311yescharacteristic
135#3752C2×D311yescharacteristic
136#3752C2×D311yescharacteristic
137C4⋊(C3⋊Dic3)C2×D311yescharacteristic
138#3750C2×D311yescharacteristic
139#3750C2×D311yescharacteristic
140#3750C2×D311yescharacteristic
141#3750C2×D311yescharacteristic
142C4×C3⋊Dic3C2×D311yescharacteristic
143C4×C3⋊Dic3C2×D311yescharacteristic
144C4×C3⋊Dic3C2×D311yescharacteristic
145C3×(C2×D3)⋊C4—31no—
146C3×(C2×D3)⋊C4—31no—
147C3×(C2×D3)⋊C4—31no—
148C3×(C2×D3)⋊C4—31no—
149C3×(C2×D3)⋊C4—31no—
150C3×(C2×D3)⋊C4—31no—
151C3×(C2×D3)⋊C4—61no—
152C3×(C2×D3)⋊C4—61no—
153C3×C4⋊Dic3—31no—
154C3×C4⋊Dic3—31no—
155C3×C4⋊Dic3—31no—
156C3×C4⋊Dic3—61no—
157C3×Dic3⋊C4—31no—
158C3×Dic3⋊C4—31no—
159C3×Dic3⋊C4—31no—
160C3×Dic3⋊C4—31no—
161C3×C4×Dic3—31no—
162C3×C4×Dic3—31no—
163C3×C4×Dic3—31no—
164#3724—31no—
165#3724—31no—
166Dic3⋊Dic3—31no—
167Dic3⋊Dic3—31no—
168Dic3⋊Dic3—31no—
169Dic3⋊Dic3—31no—
170Dic3⋊Dic3—31no—
171Dic3⋊Dic3—31no—
172#3722—31no—
173#3722—31no—
174(C2×D3)⋊Dic3—31no—
175(C2×D3)⋊Dic3—31no—
176(C2×D3)⋊Dic3—31no—
177(C2×D3)⋊Dic3—31no—
178(C2×D3)⋊Dic3—31no—
179(C2×D3)⋊Dic3—31no—
180(C2×D3)⋊Dic3—31no—
181(C2×D3)⋊Dic3—31no—
182(C2×D3)⋊Dic3—31no—
183(C2×D3)⋊Dic3—31no—
184Dic32—31no—
185Dic32—31no—
186Dic32—31no—
187Dic32—31no—
188C22×H(3,𝔽3)C2411yescharacteristic
189C2×#272—21no—
190C2×#272—21no—
191C2×#272—21no—
192C2×#272—21no—
193C2×#272—21no—
194C2×#272#4112yes—
195C2×(C3⋊D3)⋊C3—21no—
196C2×(C3⋊D3)⋊C3—21no—
197C2×(C3⋊D3)⋊C3—21no—
198C4×H(3,𝔽3)—21no—
199C4×H(3,𝔽3)—21no—
200C4×H(3,𝔽3)#4112yes—
201#1084—21no—
202#1084—21no—
203(C3⋊Dic3)⋊C3—21no—
204(C3⋊Dic3)⋊C3—21no—
205(C3⋊Dic3)⋊C3—21no—
206(C3⋊Dic3)⋊C3—21no—
207(C3⋊Dic3)⋊C3—21no—
208(C3⋊Dic3)⋊C3—21no—
209(C3⋊Dic3)⋊C3#4112yes—
210C3×C4×Q8—91no—
211C3×C4×D4—91no—
212C3×#117—91no—
213#947—91no—
214#946—91no—
215#939—91no—
216#935—91no—
217C4×#67—91no—
218C4×#67—91no—
219C4×#67—91no—
220C4×#67—91no—
221#926—91no—
222C2×C4×Dic3—91no—
223#898—91no—
224#898—91no—
225#898—91no—
226#898—91no—
227#896—91no—
228#895—91no—
229#894—91no—
230#894—91no—
231#894—91no—
232#890—91no—
233#889—91no—
234#889—91no—
235#886—91no—
236#885—91no—
237#885—91no—
238#884—91no—
239#883—91no—
240#879—91no—
241#879—91no—
242#878—91no—
243C4×D12—31no—
244C4×D12—31no—
245C4×D12—61no—
246C4×D12—91no—
247C4×D12—91no—
248#872—31no—
249#872—91no—
250#872—91no—
251#872—91no—
252C42×D3—91no—
253C42×D3—91no—
254C4×Dic6—31no—
255C4×Dic6—91no—
256C22×C3⋊D3C22×D311yescharacteristic
257C22×C3×D3—31no—
258C22×C3×D3—31no—
259C22×C3×D3—31no—
260C22×C3×D3—31no—
261C22×C3×D3—31no—
262C22×C3×D3—61no—
263C22×C3×D3—61no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C22×D311yescharacteristic
268C2×C32×C4C22×D311yescharacteristic
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C22×D311yescharacteristic
272C2×C32×C4C22×D311yescharacteristic
273C2×C3⋊Dic3C22×D311yescharacteristic
274C2×C3⋊Dic3C22×D311yescharacteristic
275C2×C3⋊Dic3C22×D311yescharacteristic
276C2×C3⋊Dic3C22×D311yescharacteristic
277C2×C3⋊Dic3C22×D311yescharacteristic
278C2×C3⋊Dic3C22×D311yescharacteristic
279C2×C3⋊Dic3C22×D311yescharacteristic
280C4×C3⋊D3—22no—
281#634—22no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—31no—
286C2×C3×Dic3—31no—
287C2×C3×Dic3—31no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—61no—
294C2×C3×Dic3—61no—
295C3×D12—62no—
296C3×D12—62no—
297C3×D12—64no—
298C3×C4×D3—62no—
299C3×C4×D3—62no—
300C3×C4×D3—62no—
301C3×C4×D3—62no—
302C3×C4×D3—62no—
303C3×C4×D3—122no—
304C3×C4×D3—122no—
305C3×Dic6—62no—
306#626—62no—
307#626—62no—
308#625—62no—
309#625—62no—
310D3×Dic3—62no—
311D3×Dic3—62no—
312D3×Dic3—62no—
313D3×Dic3—62no—
314#529—271noSylow
315C2×H(3,𝔽3)C2×#4111yescharacteristic
316C2×H(3,𝔽3)C2×#4111yescharacteristic
317C2×H(3,𝔽3)C2×#4111yescharacteristic
318#272—22no—
319#272—41no—
320(C3⋊D3)⋊C3—41no—
321C2×C3×Q8—91no—
322C2×C3×D4—91no—
323C22×C3×C4—91no—
324C22×C3×C4—91no—
325C22×C3×C4—91no—
326C2×#67—91no—
327C2×#67—91no—
328C2×#67—91no—
329C2×#67—91no—
330C22×Dic3—91no—
331C22×Dic3—91no—
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—61no—
335C2×D12—91no—
336C2×D12—91no—
337C2×C4×D3—31no—
338C2×C4×D3—31no—
339C2×C4×D3—31no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—91no—
345C2×C4×D3—91no—
346C2×C4×D3—91no—
347C2×C4×D3—91no—
348C2×C4×D3—91no—
349C2×Dic6—31no—
350C2×Dic6—91no—
351C3×C4⋊C4—91no—
352C3×C4⋊C4—91no—
353C3×C4⋊C4—91no—
354C3×C4⋊C4—91no—
355C3×C4⋊C4—91no—
356C3×C4⋊C4—91no—
357C3×C22⋊C4—91no—
358C3×C22⋊C4—91no—
359C3×C22⋊C4—91no—
360C3×C22⋊C4—91no—
361C3×C42—31no—
362C3×C42—31no—
363C3×C42—61no—
364C3×C42—91no—
365C3×C42—91no—
366C3×C42—91no—
367C3×C42D3211yescharacteristic
368#217—91no—
369#217—91no—
370#217—91no—
371#217—91no—
372#217—91no—
373#217—91no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—91no—
395(C2×D3)⋊C4—91no—
396C4⋊Dic3—31no—
397C4⋊Dic3—31no—
398C4⋊Dic3—31no—
399C4⋊Dic3—61no—
400C4⋊Dic3—91no—
401C4⋊Dic3—91no—
402C4⋊Dic3—91no—
403C4⋊Dic3—91no—
404C4⋊Dic3—91no—
405Dic3⋊C4—31no—
406Dic3⋊C4—31no—
407Dic3⋊C4—31no—
408Dic3⋊C4—31no—
409Dic3⋊C4—91no—
410Dic3⋊C4—91no—
411Dic3⋊C4—91no—
412Dic3⋊C4—91no—
413Dic3⋊C4—91no—
414Dic3⋊C4—91no—
415Dic3⋊C4—91no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
420Dic3⋊C4—91no—
421C4×Dic3—31no—
422C4×Dic3—31no—
423C4×Dic3—31no—
424C4×Dic3—91no—
425C4×Dic3—91no—
426C4×Dic3—91no—
427C4×Dic3—91no—
428C4×Dic3—91no—
429C4×Dic3—91no—
430C4×Dic3—91no—
431C4×Dic3—91no—
432C4×Dic3—91no—
433C22×C32—21no—
434C22×C32C23×D311yescharacteristic
435C22×C32C23×D311yescharacteristic
436C2×C3⋊D3—21no—
437C2×C3⋊D3—21no—
438C2×C3⋊D3—21no—
439C2×C3×D3—32no—
440C2×C3×D3—32no—
441C2×C3×D3—62no—
442C2×C3×D3—61no—
443C2×C3×D3—61no—
444C2×C3×D3—61no—
445C2×C3×D3—61no—
446C2×C3×D3—62no—
447C2×C3×D3—61no—
448C2×C3×D3—61no—
449C2×C3×D3—61no—
450C2×C3×D3—61no—
451C2×C3×D3—61no—
452C2×C3×D3—61no—
453C2×C3×D3—61no—
454C2×C3×D3—61no—
455C2×C3×D3—61no—
456C2×C3×D3—121no—
457C2×C3×D3—121no—
458C2×C3×D3—121no—
459C2×C3×D3—121no—
460C32×C4—22no—
461C32×C4—21no—
462C32×C4—21no—
463C32×C4—21no—
464C32×C4—21no—
465C32×C4—22no—
466C32×C4—41no—
467C32×C4#23512yes—
468C32×C4#23912yes—
469C3⋊Dic3—21no—
470C3⋊Dic3—21no—
471C3⋊Dic3—21no—
472C3⋊Dic3—21no—
473C3⋊Dic3—21no—
474C3⋊Dic3—21no—
475C3⋊Dic3#23512yes—
476C3×Dic3—32no—
477C3×Dic3—61no—
478C3×Dic3—61no—
479C3×Dic3—61no—
480C3×Dic3—61no—
481C3×Dic3—61no—
482C3×Dic3—61no—
483C3×Dic3—61no—
484C3×Dic3—61no—
485C3×Dic3—61no—
486C3×Dic3—61no—
487C3×Dic3—121no—
488C3×Dic3—121no—
489#126—271no—
490#126—271no—
491#125—271no—
492#124—271no—
493#123—271no—
494#123—271no—
495C22⋊Q8—271no—
496#121—271no—
497C4×Q8—91no—
498C4×D4—91no—
499C4×D4—271no—
500C4×D4—271no—
501#117—91no—
502#117—271no—
503C2×C42—271no—
504H(3,𝔽3)#52911yescharacteristic, complemented, Sylow
505C23×C3—91no—
506C23×C3—91no—
507C23×C3—91no—
508C22×D3—31no—
509C22×D3—31no—
510C22×D3—31no—
511C22×D3—31no—
512C22×D3—31no—
513C22×D3—61no—
514C22×D3—61no—
515C22×D3—91no—
516C3×Q8—182no—
517C3×D4—182no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—91no—
528C2×C3×C4—91no—
529C2×C3×C4—91no—
530C2×C3×C4—91no—
531C2×C3×C4—91no—
532C2×C3×C4—91no—
533C2×C3×C4—91no—
534C2×C3×C4—91no—
535C2×C3×C4—91no—
536C2×C3×C4—182no—
537C2×C3×C4—182no—
538C2×C3×C4—182no—
539C2×C3×C4C2×D3211yescharacteristic
540C2×C3×C4C2×D3211yescharacteristic
541C2×C3×C4C2×D3211yescharacteristic
542#67—182no—
543#67—182no—
544#67—182no—
545#67—182no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—31no—
550C2×Dic3—31no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—31no—
554C2×Dic3—31no—
555C2×Dic3—31no—
556C2×Dic3—31no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—91no—
560C2×Dic3—91no—
561C2×Dic3—91no—
562C2×Dic3—91no—
563C2×Dic3—91no—
564C2×Dic3—91no—
565C2×Dic3—91no—
566C2×Dic3—182no—
567C2×Dic3—182no—
568D12—62no—
569D12—62no—
570D12—64no—
571D12—182no—
572D12—182no—
573C4×D3—62no—
574C4×D3—62no—
575C4×D3—62no—
576C4×D3—62no—
577C4×D3—62no—
578C4×D3—122no—
579C4×D3—122no—
580C4×D3—182no—
581C4×D3—182no—
582C4×D3—182no—
583C4×D3—182no—
584C4×D3—182no—
585Dic6—62no—
586Dic6—182no—
587C2×C32—21no—
588C2×C32—21no—
589C2×C32—21no—
590C2×C32C2×#23511yescharacteristic
591C2×C32C2×#23511yescharacteristic
592C2×C32C2×#23911yescharacteristic
593C2×C32D3×#4111yescharacteristic
594C2×C32D3×#4111yescharacteristic
595C2×C32D3×#4111yescharacteristic
596C3⋊D3—41no—
597C3×D3—62no—
598C3×D3—62no—
599C3×D3—122no—
600C3×D3—122no—
601C3×D3—121no—
602C3×D3—121no—
603C3×D3—121no—
604C2×Q8—91no—
605C2×D4—91no—
606C2×D4—271no—
607C2×D4—271no—
608C22×C4—91no—
609C22×C4—91no—
610C22×C4—91no—
611C22×C4—271no—
612C22×C4—271no—
613C4⋊C4—91no—
614C4⋊C4—91no—
615C4⋊C4—91no—
616C4⋊C4—91no—
617C4⋊C4—91no—
618C4⋊C4—91no—
619C4⋊C4—271no—
620C4⋊C4—271no—
621C4⋊C4—271no—
622C4⋊C4—271no—
623C22⋊C4—91no—
624C22⋊C4—91no—
625C22⋊C4—91no—
626C22⋊C4—91no—
627C22⋊C4—271no—
628C22⋊C4—271no—
629C22⋊C4—271no—
630C22⋊C4—271no—
631C22⋊C4—271no—
632C22⋊C4—271no—
633C42—91no—
634C42—91no—
635C42—91no—
636C42—271no—
637C42—271no—
638C42((C3⋊D3)⋊C3)⋊C211yescharacteristic
639C22×C3—31no—
640C22×C3—31no—
641C22×C3—61no—
642C22×C3—92no—
643C22×C3—181no—
644C22×C3—181no—
645C22×C3—181no—
646C22×C3—181no—
647C22×C3—181no—
648C22×C3—181no—
649C22×C3—181no—
650C22×C3—181no—
651C22×C3C22×D3211yescharacteristic
652C2×D3—32no—
653C2×D3—32no—
654C2×D3—62no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—62no—
666C2×D3—61no—
667C2×D3—61no—
668C2×D3—61no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—181no—
674C2×D3—181no—
675C2×D3—181no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—32no—
679C3×C4—32no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—62no—
685C3×C4—62no—
686C3×C4—92no—
687C3×C4—121no—
688C3×C4—181no—
689C3×C4—181no—
690C3×C4—181no—
691C3×C4—181no—
692C3×C4—181no—
693C3×C4—181no—
694C3×C4—181no—
695C3×C4—181no—
696C3×C4#379912yes—
697Dic3—32no—
698Dic3—61no—
699Dic3—61no—
700Dic3—61no—
701Dic3—61no—
702Dic3—61no—
703Dic3—61no—
704Dic3—61no—
705Dic3—61no—
706Dic3—61no—
707Dic3—61no—
708Dic3—92no—
709Dic3—121no—
710Dic3—121no—
711Dic3—181no—
712Dic3—181no—
713Dic3—181no—
714Dic3—181no—
715Dic3—181no—
716Dic3—181no—
717C32—21no—
718C32#552811yescharacteristic, complemented
719C32#558011yescharacteristic, complemented
720C23—91no—
721C23—91no—
722C23—91no—
723Q8—182no—
724D4—182no—
725D4—542no—
726D4—542no—
727C2×C4—91no—
728C2×C4—91no—
729C2×C4—91no—
730C2×C4—91no—
731C2×C4—91no—
732C2×C4—91no—
733C2×C4—91no—
734C2×C4—91no—
735C2×C4—91no—
736C2×C4—182no—
737C2×C4—182no—
738C2×C4—182no—
739C2×C4—542no—
740C2×C4—542no—
741C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
742C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
743C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
744C2×C3—31no—
745C2×C3—31no—
746C2×C3—31no—
747C2×C3—31no—
748C2×C3—31no—
749C2×C3—31no—
750C2×C3—61no—
751C2×C3—61no—
752C2×C3—61no—
753C2×C3—182no—
754C2×C3—361no—
755C2×C3—361no—
756C2×C3C2×#379911yescharacteristic
757C2×C3D3×#23511yescharacteristic
758C2×C3#6430611yescharacteristic
759D3—62no—
760D3—62no—
761D3—122no—
762D3—121no—
763D3—121no—
764D3—122no—
765D3—121no—
766D3—361no—
767C22—92no—
768C22—181no—
769C22—181no—
770C22—181no—
771C22—181no—
772C22—181no—
773C22—181no—
774C22—181no—
775C22—181no—
776C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
777C4—21no—
778C4—21no—
779C4—92no—
780C4—181no—
781C4—181no—
782C4—181no—
783C4—181no—
784C4—181no—
785C4—181no—
786C4—181no—
787C4—181no—
788C4#8865212yes—
789C3—31no—
790C3—31no—
791C3—61no—
792C3#1059393411yescharacteristic
793C2—182no—
794C2—361no—
795C2—361no—
796C2C2×#8865211yescharacteristic
797C2#1172249011yescharacteristic
798C2#1172249111yescharacteristic
subgroupG/H
centerC2×C4C2×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC42×H(3,𝔽3)C22
prime radical#11721157C2
hypercenterC42((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#529
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C4×C4⋊#272C2semidirect
2. #64081⋊C3C2semidirect
3. C4×#634⋊C3C2semidirect
5. #11721155C2semidirect
6. C4×#6200C2semidirect
7. C4×#6200C2semidirect
8. #11721151C2semidirect
9. #11721148C2semidirect
10. C4×#6199C2semidirect
11. #11721111C2semidirect
12. #11721102C2semidirect
13. #11721097C2semidirect
14. #11721088C2semidirect
15. #11721085C2semidirect
53. #64081D3semidirect
54. C4×#634D3semidirect
504. H(3,𝔽3)#529semidirect
718. C32#5528semidirect
719. C32#5580semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊#2722
#64081⋊C32
C4×#634⋊C32
#117211572
#117211552
C4×#62002
#117211512
#117211482
C4×#61992
#117211112
#117211022
#117210972
#117210882
#117210852
#105939113
#105939103