Finite Group Databasebeta

← #13151347

Subgroups — #13151347

Order 1728.

1405 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#272C211yesmaximal, characteristic, complemented
2C2×#88671C211yesmaximal, characteristic, complemented
3#64148⋊C3C211yesmaximal, characteristic, complemented
4#64144⋊C3C211yesmaximal, characteristic, complemented
5#11721323C211yesmaximal, characteristic, complemented
6#11721323C211yesmaximal, characteristic, complemented
7#11721320C211yesmaximal, characteristic, complemented
8#11721312C211yesmaximal, characteristic, complemented
9C2×#88451C211yesmaximal, characteristic, complemented
10#11721294C211yesmaximal, characteristic, complemented
11#11721293C211yesmaximal, characteristic, complemented
12#11721157C211yesmaximal, characteristic, complemented
13#11721151C211yesmaximal, characteristic, complemented
14#11721124C211yesmaximal, characteristic, complemented
15#11721096C211yesmaximal, characteristic, complemented
16#10595150—31nomaximal
17#10595148—31nomaximal
18C23×#272C2211yescharacteristic
19C23×#272C2211yescharacteristic
20C2×D4×H(3,𝔽3)C2211yescharacteristic
21C2×#6235C2211yescharacteristic
22C2×#6235C2211yescharacteristic
23D4×#272—24no—
24C2×C4⋊#272C2211yescharacteristic
25C2×C4×#272C2211yescharacteristic
26C2×#638⋊C3C2211yescharacteristic, complemented
27C2×#638⋊C3C2211yescharacteristic, complemented
28C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
29C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
30C2×#6200C2211yescharacteristic
31C2×#6200C2211yescharacteristic, complemented
32C2×#6200C2211yescharacteristic, complemented
33C2×#6199C2211yescharacteristic, complemented
34C2×#6199C2211yescharacteristic, complemented
35#88671—24no—
36C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
37C2×#6196C2211yescharacteristic, complemented
38#3757⋊C3C2211yescharacteristic, complemented
39#3757⋊C3C2211yescharacteristic, complemented
40#3757⋊C3C2211yescharacteristic, complemented
41#3757⋊C3C2211yescharacteristic, complemented
42#3752⋊C3C2211yescharacteristic, complemented
43#3750⋊C3C2211yescharacteristic, complemented
44#3750⋊C3C2211yescharacteristic, complemented
45#3750⋊C3C2211yescharacteristic, complemented
46#88451C2211yescharacteristic
47#88451C2211yescharacteristic
48#88451C2211yescharacteristic
49#88451C2211yescharacteristic, complemented
50#88451C2211yescharacteristic, complemented
51#88451C2211yescharacteristic, complemented
52#88451C2211yescharacteristic, complemented
53#88449C2211yescharacteristic, complemented
54#88447C2211yescharacteristic, complemented
55C2×C3×D3×D4—31no—
56C2×C3×D3×D4—31no—
57C2×C3×D3×D4—61no—
58C2×#3805—31no—
59C2×#3804—31no—
60#64148D311yescharacteristic, complemented
61#64144D311yescharacteristic, complemented
62C3×#939—31no—
63C3×#935—31no—
64#63977—31no—
65#63977—31no—
66#63976—31no—
67#63976—31no—
68#67⋊Dic3—31no—
69Dic3×#67—31no—
70#63970—31no—
71D3×#217—31no—
72D3×#217—31no—
73C2×(C2×D3)⋊Dic3—31no—
74C2×(C2×D3)⋊Dic3—31no—
75#63959—31no—
76#63959—31no—
77#63958—31no—
78#63904—31no—
79#63886—31no—
80#63885—31no—
81#63884—31no—
82#63884—31no—
83#63879—31no—
84#63851—31no—
85#63851—31no—
86C23×H(3,𝔽3)C2311yescharacteristic
87C23×H(3,𝔽3)C2311yescharacteristic
88C22×#272—22no—
89C22×#272—22no—
90C22×#272—22no—
91C22×#272—22no—
92C22×#272—41no—
93C22×#272—41no—
94C22×#272C2311yescharacteristic
95C22×#272C2311yescharacteristic
96C22×#272C2311yescharacteristic
97C22×(C3⋊D3)⋊C3C2311yescharacteristic
98D4×H(3,𝔽3)—22no—
99C2×C4×H(3,𝔽3)C2311yescharacteristic
100#6235—22no—
101#6235D414yescomplemented
102C2×#1084C2311yescharacteristic
103C4⋊#272—22no—
104C4×#272—22no—
105#638⋊C3—22no—
106#638⋊C3—41no—
107C2×(C3⋊Dic3)⋊C3—22no—
108C2×(C3⋊Dic3)⋊C3—41no—
109C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
110C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
111C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
112C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
113C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
114C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
115C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
116#6200—22no—
117#6200—22no—
118#6200—41no—
119#6199—22no—
120#6199—41no—
121((C3⋊D3)⋊C3)⋊C4—22no—
122#6196—22no—
123#5806—91no—
124#5654—91no—
125#5610—91no—
126C23×C3×D3—31no—
127C23×C3×D3—31no—
128C23×C3×D3—31no—
129C23×C3×D3—31no—
130C23×C3×D3—61no—
131C23×C3×D3—61no—
132C2×C32×D4—21no—
133C2×C32×D4C2×D311yescharacteristic
134C2×C32×D4C2×D311yescharacteristic
135C2×#638C2×D311yescharacteristic, complemented
136C2×#638C2×D311yescharacteristic, complemented
137C22×C3⋊Dic3C2×D311yescharacteristic, complemented
138C22×C3⋊Dic3C2×D311yescharacteristic, complemented
139C2×C3×#67—31no—
140C2×C3×#67—31no—
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—61no—
146C2×C3×#67—61no—
147C22×C3×Dic3—31no—
148C22×C3×Dic3—31no—
149C3×D3×D4—64no—
150C3×D3×D4—64no—
151C3×D3×D4—68no—
152C2×C3×D12—31no—
153C2×C3×D12—31no—
154C2×C3×D12—61no—
155C2×C3×C4×D3—31no—
156C2×C3×C4×D3—31no—
157C2×C3×C4×D3—61no—
158C2×#627—31no—
159C2×#627—31no—
160C2×#626—31no—
161C2×#626—31no—
162C2×#626—31no—
163C2×#625—31no—
164C2×#625—31no—
165C2×#625—31no—
166C2×#624—31no—
167#3805—64no—
168#3804—64no—
169C2×D3×Dic3—31no—
170C2×D3×Dic3—31no—
171C2×D3×Dic3—31no—
172C2×D3×Dic3—31no—
173C2×D3×Dic3—31no—
174#3757C2×D311yescharacteristic, complemented
175#3757C2×D311yescharacteristic, complemented
176#3757C2×D311yescharacteristic, complemented
177#3757C2×D311yescharacteristic, complemented
178#3752C2×D311yescharacteristic, complemented
179#3750C2×D311yescharacteristic, complemented
180#3750C2×D311yescharacteristic, complemented
181#3750C2×D311yescharacteristic, complemented
182C3×#217—31no—
183C3×#217—31no—
184C3×#217—31no—
185C3×#217—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—31no—
190Dic3⋊Dic3—31no—
191Dic3⋊Dic3—31no—
192(C2×D3)⋊Dic3—31no—
193(C2×D3)⋊Dic3—31no—
194(C2×D3)⋊Dic3—31no—
195(C2×D3)⋊Dic3—31no—
196(C2×D3)⋊Dic3—31no—
197(C2×D3)⋊Dic3—31no—
198(C2×D3)⋊Dic3—31no—
199(C2×D3)⋊Dic3—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—
206Dic32—31no—
207Dic32—31no—
208C22×H(3,𝔽3)—21no—
209C22×H(3,𝔽3)—21no—
210C22×H(3,𝔽3)—21no—
211C22×H(3,𝔽3)—21no—
212C22×H(3,𝔽3)—21no—
213C22×H(3,𝔽3)C2×D412yes—
214C22×H(3,𝔽3)C2411yescharacteristic
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×#272—44no—
224C2×#272C2×D412yes—
225C2×#272#4112yescomplemented
226C2×(C3⋊D3)⋊C3—21no—
227C2×(C3⋊D3)⋊C3—21no—
228C2×(C3⋊D3)⋊C3—21no—
229C4×H(3,𝔽3)—21no—
230#1084C2×D412yes—
231(C3⋊Dic3)⋊C3—21no—
232(C3⋊Dic3)⋊C3—21no—
233(C3⋊Dic3)⋊C3—21no—
234(C3⋊Dic3)⋊C3—21no—
235(C3⋊Dic3)⋊C3—21no—
236(C3⋊Dic3)⋊C3—21no—
237(C3⋊Dic3)⋊C3—21no—
238C22×C3×D4—91no—
239C2×#237—91no—
240C2×#237—91no—
241C2×D3×D4—31no—
242C2×D3×D4—31no—
243C2×D3×D4—61no—
244C2×#235—91no—
245C3×#123—91no—
246C3×#121—91no—
247#953—91no—
248#953—91no—
249C2×#217—91no—
250C2×#217—91no—
251#939—31no—
252#939—91no—
253#939—91no—
254#939—91no—
255#938—91no—
256#937—91no—
257#937—91no—
258#936—91no—
259#935—31no—
260#935—91no—
261#935—91no—
262D4×Dic3—91no—
263C4×#67—91no—
264C4×#67—91no—
265C2×(C2×D3)⋊C4—91no—
266C2×(C2×D3)⋊C4—91no—
267#924—91no—
268#896—91no—
269#896—91no—
270#895—91no—
271#894—91no—
272#894—91no—
273#893—91no—
274#885—91no—
275#885—91no—
276#884—91no—
277#884—91no—
278#882—91no—
279#882—91no—
280#67⋊C4—91no—
281#67⋊C4—91no—
282D3×C22⋊C4—91no—
283D3×C22⋊C4—91no—
284C23×C32—21no—
285C23×C32—21no—
286C23×C32C22×D311yescharacteristic
287C23×C32C22×D311yescharacteristic
288C23×C32C22×D311yescharacteristic
289C23×C32C22×D311yescharacteristic
290C22×C3⋊D3C22×D311yescharacteristic
291C22×C3×D3—31no—
292C22×C3×D3—31no—
293C22×C3×D3—31no—
294C22×C3×D3—31no—
295C22×C3×D3—31no—
296C22×C3×D3—31no—
297C22×C3×D3—31no—
298C22×C3×D3—61no—
299C22×C3×D3—61no—
300C22×C3×D3—61no—
301C22×C3×D3—62no—
302C22×C3×D3—62no—
303C22×C3×D3—62no—
304C22×C3×D3—62no—
305C22×C3×D3—62no—
306C22×C3×D3—62no—
307C22×C3×D3—64no—
308C22×C3×D3—64no—
309C22×C3×D3—62no—
310C22×C3×D3—62no—
311C22×C3×D3—122no—
312C22×C3×D3—122no—
313C22×C3×D3—121no—
314C22×C3×D3—121no—
315C22×C3×D3—121no—
316C22×C3×D3—121no—
317C22×C3×D3—122no—
318C22×C3×D3—122no—
319C32×D4—24no—
320C32×D4—22no—
321C32×D4—22no—
322C2×C32×C4—21no—
323C2×C32×C4C22×D311yescharacteristic
324C2×C32×C4C22×D311yescharacteristic
325#638—22no—
326#638—41no—
327C2×C3⋊Dic3—22no—
328C2×C3⋊Dic3—41no—
329C2×C3⋊Dic3C22×D311yescharacteristic
330C2×C3⋊Dic3C22×D311yescharacteristic
331C2×C3⋊Dic3C22×D311yescharacteristic
332C2×C3⋊Dic3C22×D311yescharacteristic
333C2×C3⋊Dic3C22×D311yescharacteristic
334C2×C3⋊Dic3C22×D311yescharacteristic
335C2×C3⋊Dic3C22×D311yescharacteristic
336C3×#67—34no—
337C3×#67—34no—
338C3×#67—64no—
339C3×#67—62no—
340C3×#67—62no—
341C3×#67—64no—
342C3×#67—62no—
343C3×#67—121no—
344C2×C3×Dic3—31no—
345C2×C3×Dic3—31no—
346C2×C3×Dic3—31no—
347C2×C3×Dic3—31no—
348C2×C3×Dic3—31no—
349C2×C3×Dic3—31no—
350C2×C3×Dic3—31no—
351C2×C3×Dic3—31no—
352C2×C3×Dic3—31no—
353C2×C3×Dic3—61no—
354C2×C3×Dic3—62no—
355C2×C3×Dic3—121no—
356C3×D12—62no—
357C3×D12—62no—
358C3×D12—64no—
359C3×C4×D3—62no—
360C3×C4×D3—62no—
361C3×C4×D3—64no—
362#627—62no—
363#627—62no—
364#626—62no—
365#626—62no—
366#626—121no—
367#625—62no—
368#625—62no—
369#625—121no—
370#624—62no—
371D3×Dic3—62no—
372D3×Dic3—62no—
373D3×Dic3—62no—
374D3×Dic3—121no—
375D3×Dic3—121no—
376#546—271noSylow
377C2×H(3,𝔽3)—22no—
378C2×H(3,𝔽3)—41no—
379C2×H(3,𝔽3)C22×D411yescharacteristic
380C2×H(3,𝔽3)C2×#4111yescharacteristic
381C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
382#272—22no—
383#272—22no—
384#272—41no—
385(C3⋊D3)⋊C3—41no—
386C24×C3—91no—
387C24×C3—91no—
388C23×D3—31no—
389C23×D3—31no—
390C23×D3—31no—
391C23×D3—31no—
392C23×D3—61no—
393C23×D3—61no—
394C2×C3×D4—31no—
395C2×C3×D4—31no—
396C2×C3×D4—61no—
397C2×C3×D4—91no—
398C2×C3×D4—91no—
399C2×C3×D4—91no—
400C2×C3×D4—91no—
401C2×C3×D4—91no—
402C2×C3×D4—184no—
403C2×C3×D4D3211yescharacteristic
404C22×C3×C4—91no—
405C22×C3×C4—91no—
406C22×C3×C4—91no—
407C2×#67—31no—
408C2×#67—31no—
409C2×#67—31no—
410C2×#67—31no—
411C2×#67—31no—
412C2×#67—31no—
413C2×#67—61no—
414C2×#67—61no—
415C2×#67—91no—
416C2×#67—91no—
417C2×#67—91no—
418C2×#67—91no—
419C2×#67—91no—
420C2×#67—91no—
421C2×#67—91no—
422C2×#67—91no—
423C22×Dic3—31no—
424C22×Dic3—31no—
425C22×Dic3—91no—
426C22×Dic3—91no—
427C22×Dic3—91no—
428C22×Dic3—91no—
429C22×Dic3—91no—
430#237—184no—
431#237—184no—
432D3×D4—64no—
433D3×D4—64no—
434D3×D4—68no—
435#235—184no—
436C2×D12—31no—
437C2×D12—31no—
438C2×D12—61no—
439C2×D12—91no—
440C2×D12—91no—
441C2×D12—91no—
442C2×C4×D3—31no—
443C2×C4×D3—31no—
444C2×C4×D3—61no—
445C2×C4×D3—91no—
446C2×C4×D3—91no—
447C2×C4×D3—91no—
448C2×C4×D3—91no—
449C2×C4×D3—91no—
450C2×C4×D3—91no—
451C2×Dic6—91no—
452C2×Dic6—91no—
453C2×Dic6—91no—
454C3×C4⋊C4—91no—
455C3×C4⋊C4—91no—
456C3×C4⋊C4—91no—
457C3×C22⋊C4—91no—
458C3×C22⋊C4—91no—
459C3×C22⋊C4—91no—
460C3×C22⋊C4—91no—
461C3×C22⋊C4—91no—
462#217—31no—
463#217—31no—
464#217—31no—
465#217—31no—
466#217—91no—
467#217—91no—
468#217—91no—
469#217—91no—
470#217—91no—
471#217—91no—
472#217—91no—
473#217—91no—
474#217—91no—
475#217—91no—
476#217—91no—
477(C2×D3)⋊C4—31no—
478(C2×D3)⋊C4—91no—
479(C2×D3)⋊C4—91no—
480(C2×D3)⋊C4—91no—
481(C2×D3)⋊C4—91no—
482(C2×D3)⋊C4—91no—
483(C2×D3)⋊C4—91no—
484(C2×D3)⋊C4—91no—
485(C2×D3)⋊C4—91no—
486(C2×D3)⋊C4—91no—
487(C2×D3)⋊C4—91no—
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—
493C4⋊Dic3—91no—
494Dic3⋊C4—31no—
495Dic3⋊C4—31no—
496Dic3⋊C4—31no—
497Dic3⋊C4—91no—
498Dic3⋊C4—91no—
499Dic3⋊C4—91no—
500Dic3⋊C4—91no—
501Dic3⋊C4—91no—
502C4×Dic3—91no—
503C4×Dic3—91no—
504C4×Dic3—91no—
505C22×C32—21no—
506C22×C32—21no—
507C22×C32—21no—
508C22×C32—21no—
509C22×C32—22no—
510C22×C32—21no—
511C22×C32—21no—
512C22×C32—21no—
513C22×C32—21no—
514C22×C32—21no—
515C22×C32—21no—
516C22×C32—21no—
517C22×C32—22no—
518C22×C32—41no—
519C22×C32—41no—
520C22×C32—41no—
521C22×C32—41no—
522C22×C32D3×D412yes—
523C22×C32D3×D412yes—
524C22×C32C23×D311yescharacteristic
525C22×C32C23×D311yescharacteristic
526C2×C3⋊D3—21no—
527C2×C3⋊D3—21no—
528C2×C3⋊D3—21no—
529C2×C3×D3—32no—
530C2×C3×D3—32no—
531C2×C3×D3—32no—
532C2×C3×D3—32no—
533C2×C3×D3—62no—
534C2×C3×D3—62no—
535C2×C3×D3—62no—
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—121no—
556C2×C3×D3—121no—
557C2×C3×D3—121no—
558C2×C3×D3—121no—
559C2×C3×D3—124no—
560C2×C3×D3—124no—
561C2×C3×D3—124no—
562C2×C3×D3—124no—
563C2×C3×D3—128no—
564C2×C3×D3—128no—
565C32×C4—22no—
566C32×C4—21no—
567C32×C4—21no—
568C3⋊Dic3—21no—
569C3⋊Dic3—21no—
570C3⋊Dic3—21no—
571C3⋊Dic3—21no—
572C3⋊Dic3—21no—
573C3⋊Dic3—21no—
574C3⋊Dic3—21no—
575C3×Dic3—32no—
576C3×Dic3—32no—
577C3×Dic3—62no—
578C3×Dic3—61no—
579C3×Dic3—61no—
580C3×Dic3—61no—
581C3×Dic3—61no—
582C3×Dic3—61no—
583C3×Dic3—61no—
584C3×Dic3—61no—
585C2×#41—271no—
586C22×D4—91no—
587#124—271no—
588#123—91no—
589#123—271no—
590C22⋊Q8—271no—
591#121—91no—
592#121—271no—
593#121—271no—
594#120—271no—
595#120—271no—
596C4×D4—271no—
597C4×D4—271no—
598C2×C22⋊C4—271no—
599C2×C22⋊C4—271no—
600H(3,𝔽3)#54611yescharacteristic, complemented, Sylow
601C23×C3—31no—
602C23×C3—31no—
603C23×C3—31no—
604C23×C3—31no—
605C23×C3—61no—
606C23×C3—61no—
607C23×C3—91no—
608C23×C3—91no—
609C23×C3—91no—
610C23×C3—91no—
611C23×C3—182no—
612C23×C3—182no—
613C23×C3—182no—
614C23×C3—182no—
615C23×C3—361no—
616C23×C3—361no—
617C23×C3C2×D3211yescharacteristic
618C23×C3C2×D3211yescharacteristic
619C22×D3—31no—
620C22×D3—31no—
621C22×D3—31no—
622C22×D3—31no—
623C22×D3—31no—
624C22×D3—31no—
625C22×D3—31no—
626C22×D3—61no—
627C22×D3—61no—
628C22×D3—61no—
629C22×D3—62no—
630C22×D3—62no—
631C22×D3—62no—
632C22×D3—62no—
633C22×D3—62no—
634C22×D3—62no—
635C22×D3—62no—
636C22×D3—62no—
637C22×D3—64no—
638C22×D3—64no—
639C22×D3—91no—
640C22×D3—122no—
641C22×D3—122no—
642C22×D3—121no—
643C22×D3—121no—
644C22×D3—121no—
645C22×D3—121no—
646C22×D3—122no—
647C22×D3—122no—
648C3×D4—22no—
649C3×D4—62no—
650C3×D4—62no—
651C3×D4—64no—
652C3×D4—94no—
653C3×D4—182no—
654C3×D4—182no—
655C3×D4—182no—
656C3×D4—361no—
657C2×C3×C4—31no—
658C2×C3×C4—31no—
659C2×C3×C4—61no—
660C2×C3×C4—91no—
661C2×C3×C4—91no—
662C2×C3×C4—91no—
663C2×C3×C4—91no—
664C2×C3×C4—91no—
665C2×C3×C4—91no—
666C2×C3×C4—91no—
667C2×C3×C4—91no—
668C2×C3×C4—182no—
669C2×C3×C4—182no—
670C2×C3×C4—361no—
671C2×C3×C4C2×D3211yescharacteristic
672#67—34no—
673#67—34no—
674#67—64no—
675#67—62no—
676#67—62no—
677#67—64no—
678#67—62no—
679#67—121no—
680#67—182no—
681#67—182no—
682#67—182no—
683#67—182no—
684#67—182no—
685#67—361no—
686#67—361no—
687#67—361no—
688C2×Dic3—31no—
689C2×Dic3—31no—
690C2×Dic3—31no—
691C2×Dic3—31no—
692C2×Dic3—31no—
693C2×Dic3—31no—
694C2×Dic3—31no—
695C2×Dic3—31no—
696C2×Dic3—31no—
697C2×Dic3—61no—
698C2×Dic3—62no—
699C2×Dic3—91no—
700C2×Dic3—91no—
701C2×Dic3—91no—
702C2×Dic3—91no—
703C2×Dic3—91no—
704C2×Dic3—91no—
705C2×Dic3—91no—
706C2×Dic3—121no—
707C2×Dic3—182no—
708C2×Dic3—182no—
709C2×Dic3—182no—
710C2×Dic3—361no—
711C2×Dic3—361no—
712D12—62no—
713D12—62no—
714D12—64no—
715D12—182no—
716D12—182no—
717D12—361no—
718C4×D3—62no—
719C4×D3—62no—
720C4×D3—64no—
721C4×D3—182no—
722C4×D3—182no—
723C4×D3—182no—
724C4×D3—182no—
725C4×D3—361no—
726C4×D3—361no—
727Dic6—182no—
728Dic6—182no—
729Dic6—182no—
730C2×C32—22no—
731C2×C32—22no—
732C2×C32—21no—
733C2×C32—21no—
734C2×C32—21no—
735C2×C32—42no—
736C2×C32—42no—
737C2×C32—41no—
738C2×C32—41no—
739C2×C32C2×D3×D411yescharacteristic
740C2×C32C2×D3×D411yescharacteristic
741C2×C32#100411yescharacteristic
742C2×C32D3×#4111yescharacteristic
743C2×C32D3×#4111yescharacteristic
744C2×C32#100911yescharacteristic
745C3⋊D3—41no—
746C3×D3—64no—
747C3×D3—62no—
748C3×D3—62no—
749C3×D3—62no—
750C3×D3—62no—
751C3×D3—122no—
752C3×D3—122no—
753C3×D3—121no—
754C3×D3—121no—
755C3×D3—121no—
756C24—91no—
757C24—91no—
758#41—544no—
759C2×Q8—271no—
760C2×D4—91no—
761C2×D4—91no—
762C2×D4—91no—
763C2×D4—91no—
764C2×D4—91no—
765C2×D4—184no—
766C2×D4—271no—
767C2×D4—271no—
768C2×D4—271no—
769C2×D4((C3⋊D3)⋊C3)⋊C211yescharacteristic
770C22×C4—91no—
771C22×C4—91no—
772C22×C4—91no—
773C22×C4—271no—
774C22×C4—271no—
775C22×C4—271no—
776C4⋊C4—91no—
777C4⋊C4—91no—
778C4⋊C4—91no—
779C4⋊C4—271no—
780C22⋊C4—91no—
781C22⋊C4—91no—
782C22⋊C4—91no—
783C22⋊C4—91no—
784C22⋊C4—91no—
785C22⋊C4—271no—
786C22⋊C4—271no—
787C22⋊C4—271no—
788C22⋊C4—271no—
789C22⋊C4—271no—
790C22⋊C4—271no—
791C22⋊C4—271no—
792C42—271no—
793C22×C3—21no—
794C22×C3—21no—
795C22×C3—21no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—31no—
799C22×C3—31no—
800C22×C3—32no—
801C22×C3—32no—
802C22×C3—61no—
803C22×C3—61no—
804C22×C3—61no—
805C22×C3—61no—
806C22×C3—61no—
807C22×C3—61no—
808C22×C3—61no—
809C22×C3—61no—
810C22×C3—61no—
811C22×C3—61no—
812C22×C3—62no—
813C22×C3—61no—
814C22×C3—62no—
815C22×C3—92no—
816C22×C3—92no—
817C22×C3—121no—
818C22×C3—121no—
819C22×C3—121no—
820C22×C3—121no—
821C22×C3—181no—
822C22×C3—181no—
823C22×C3—181no—
824C22×C3—181no—
825C22×C3—181no—
826C22×C3—181no—
827C22×C3—181no—
828C22×C3—181no—
829C22×C3—181no—
830C22×C3—181no—
831C22×C3—364no—
832C22×C3—364no—
833C22×C3#381112yes—
834C22×C3C22×D3211yescharacteristic
835C2×D3—32no—
836C2×D3—32no—
837C2×D3—32no—
838C2×D3—32no—
839C2×D3—62no—
840C2×D3—62no—
841C2×D3—61no—
842C2×D3—61no—
843C2×D3—61no—
844C2×D3—61no—
845C2×D3—61no—
846C2×D3—61no—
847C2×D3—61no—
848C2×D3—61no—
849C2×D3—62no—
850C2×D3—62no—
851C2×D3—61no—
852C2×D3—61no—
853C2×D3—61no—
854C2×D3—61no—
855C2×D3—61no—
856C2×D3—61no—
857C2×D3—62no—
858C2×D3—61no—
859C2×D3—61no—
860C2×D3—61no—
861C2×D3—121no—
862C2×D3—121no—
863C2×D3—121no—
864C2×D3—121no—
865C2×D3—124no—
866C2×D3—124no—
867C2×D3—124no—
868C2×D3—124no—
869C2×D3—128no—
870C2×D3—128no—
871C2×D3—181no—
872C2×D3—181no—
873C2×D3—181no—
874C3×C4—21no—
875C3×C4—61no—
876C3×C4—61no—
877C3×C4—62no—
878C3×C4—92no—
879C3×C4—181no—
880C3×C4—181no—
881C3×C4—181no—
882C3×C4—181no—
883C3×C4—181no—
884C3×C4—181no—
885C3×C4—181no—
886Dic3—32no—
887Dic3—32no—
888Dic3—62no—
889Dic3—61no—
890Dic3—61no—
891Dic3—61no—
892Dic3—61no—
893Dic3—61no—
894Dic3—61no—
895Dic3—61no—
896Dic3—181no—
897Dic3—181no—
898Dic3—181no—
899Dic3—181no—
900Dic3—181no—
901Dic3—181no—
902Dic3—181no—
903C32—21no—
904C32#561011yescharacteristic, complemented
905C32#565411yescharacteristic, complemented
906C23—91no—
907C23—91no—
908C23—91no—
909C23—91no—
910C23—182no—
911C23—182no—
912C23—182no—
913C23—182no—
914C23—361no—
915C23—361no—
916C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
917C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
918Q8—542no—
919D4—22no—
920D4—94no—
921D4—182no—
922D4—182no—
923D4—182no—
924D4—361no—
925D4—542no—
926D4—542no—
927D4—1081no—
928C2×C4—91no—
929C2×C4—91no—
930C2×C4—91no—
931C2×C4—91no—
932C2×C4—91no—
933C2×C4—91no—
934C2×C4—91no—
935C2×C4—91no—
936C2×C4—182no—
937C2×C4—182no—
938C2×C4—361no—
939C2×C4—542no—
940C2×C4—542no—
941C2×C4—1081no—
942C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
943C2×C3—22no—
944C2×C3—31no—
945C2×C3—31no—
946C2×C3—31no—
947C2×C3—31no—
948C2×C3—31no—
949C2×C3—31no—
950C2×C3—41no—
951C2×C3—62no—
952C2×C3—62no—
953C2×C3—61no—
954C2×C3—61no—
955C2×C3—61no—
956C2×C3—122no—
957C2×C3—121no—
958C2×C3—121no—
959C2×C3—122no—
960C2×C3—182no—
961C2×C3—182no—
962C2×C3—361no—
963C2×C3—361no—
964C2×C3#6431211yescharacteristic
965C2×C3#6431411yescharacteristic
966C2×C3C2×#381111yescharacteristic
967D3—62no—
968D3—62no—
969D3—62no—
970D3—62no—
971D3—64no—
972D3—122no—
973D3—121no—
974D3—121no—
975D3—122no—
976D3—121no—
977D3—361no—
978C22—21no—
979C22—21no—
980C22—21no—
981C22—21no—
982C22—21no—
983C22—92no—
984C22—92no—
985C22—181no—
986C22—181no—
987C22—181no—
988C22—181no—
989C22—181no—
990C22—181no—
991C22—181no—
992C22—181no—
993C22—181no—
994C22—181no—
995C22—364no—
996C22—364no—
997C22#8867712yes—
998C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
999C4—21no—
1000C4—92no—
1001C4—181no—
1002C4—181no—
1003C4—181no—
1004C4—181no—
1005C4—181no—
1006C4—181no—
1007C4—181no—
1008C3—31no—
1009C3—31no—
1010C3—61no—
1011C3#1059516311yescharacteristic
1012C2—22no—
1013C2—41no—
1014C2—182no—
1015C2—182no—
1016C2—361no—
1017C2—361no—
1018C2#1172250511yescharacteristic
1019C2#1172250711yescharacteristic
1020C2C2×#8867711yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC2×D4×H(3,𝔽3)C22
hypercenterC2×D4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#546
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. C2×D4×#272C2semidirect
2. C2×#88671C2semidirect
3. #64148⋊C3C2semidirect
4. #64144⋊C3C2semidirect
5. #11721323C2semidirect
6. #11721323C2semidirect
7. #11721320C2semidirect
8. #11721312C2semidirect
9. C2×#88451C2semidirect
10. #11721294C2semidirect
11. #11721293C2semidirect
12. #11721157C2semidirect
13. #11721151C2semidirect
14. #11721124C2semidirect
15. #11721096C2semidirect
26. C2×#638⋊C3C22semidirect
27. C2×#638⋊C3C22semidirect
28. C22×(C3⋊Dic3)⋊C3C22semidirect
29. C22×(C3⋊Dic3)⋊C3C22semidirect
31. C2×#6200C22semidirect
32. C2×#6200C22semidirect
33. C2×#6199C22semidirect
34. C2×#6199C22semidirect
36. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
37. C2×#6196C22semidirect
38. #3757⋊C3C22semidirect
39. #3757⋊C3C22semidirect
40. #3757⋊C3C22semidirect
41. #3757⋊C3C22semidirect
42. #3752⋊C3C22semidirect
43. #3750⋊C3C22semidirect
44. #3750⋊C3C22semidirect
45. #3750⋊C3C22semidirect
49. #88451C22semidirect
50. #88451C22semidirect
51. #88451C22semidirect
52. #88451C22semidirect
53. #88449C22semidirect
54. #88447C22semidirect
60. #64148D3semidirect
61. #64144D3semidirect
101. #6235D4semidirect
135. C2×#638C2×D3semidirect
136. C2×#638C2×D3semidirect
137. C22×C3⋊Dic3C2×D3semidirect
138. C22×C3⋊Dic3C2×D3semidirect
174. #3757C2×D3semidirect
175. #3757C2×D3semidirect
176. #3757C2×D3semidirect
177. #3757C2×D3semidirect
178. #3752C2×D3semidirect
179. #3750C2×D3semidirect
180. #3750C2×D3semidirect
181. #3750C2×D3semidirect
225. C2×#272#41semidirect
600. H(3,𝔽3)#546semidirect
904. C32#5610semidirect
905. C32#5654semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#2722
C2×#886712
#64148⋊C32
#64144⋊C32
#117213232
#117213202
#117213122
C2×#884512
#117212942
#117212932
#117211572
#117211512
#117211242
#117210962
#105951503
#105951483