Finite Group Databasebeta

← #13141153

Subgroups — #13141153

Order 1728.

1035 conjugacy classes of subgroups.

The subgroup lattice has 725 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#638⋊C3C211yesmaximal, characteristic
2C2×#88552C211yesmaximal, characteristic, complemented
3C2×#3757⋊C3C211yesmaximal, characteristic, complemented
4C2×#88450C211yesmaximal, characteristic, complemented
5C2×#88450C211yesmaximal, characteristic, complemented
6C2×#88448C211yesmaximal, characteristic, complemented
7C2×#88447C211yesmaximal, characteristic, complemented
8#10591707—31nomaximal
9#10591704—31nomaximal
10C24×H(3,𝔽3)C2211yescharacteristic
11C23×(C3⋊D3)⋊C3C2211yescharacteristic
12C22×#1084C2211yescharacteristic
13C22×#1084C2211yescharacteristic
14C2×#638⋊C3—22no—
15C2×#638⋊C3—22no—
16C2×#638⋊C3C414yescomplemented
17C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
18C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
19C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
20#88552—22no—
21#3757⋊C3—22no—
22#88450—22no—
23#88450—22no—
24#88448—22no—
25#88447—22no—
26C22×#638D311yescharacteristic
27C22×C3×#67—31no—
28C2×#3757D311yescharacteristic, complemented
29C2×C3×#217—31no—
30C2×C3×#217—31no—
31C2×C3×#217—31no—
32C2×C3×#217—61no—
33C2×#3724—31no—
34C2×Dic3⋊Dic3—31no—
35C2×#3722—31no—
36C2×#3722—31no—
37C2×(C2×D3)⋊Dic3—31no—
38C2×(C2×D3)⋊Dic3—31no—
39C2×Dic32—31no—
40C2×Dic32—31no—
41C23×H(3,𝔽3)—21no—
42C23×H(3,𝔽3)—21no—
43C23×H(3,𝔽3)—21no—
44C23×H(3,𝔽3)—21no—
45C23×H(3,𝔽3)—21no—
46C23×H(3,𝔽3)—21no—
47C23×H(3,𝔽3)C2×C412yes—
48C23×H(3,𝔽3)C2311yescharacteristic
49C22×(C3⋊D3)⋊C3—21no—
50C22×(C3⋊D3)⋊C3—21no—
51C22×(C3⋊D3)⋊C3—21no—
52C22×(C3⋊D3)⋊C3—21no—
53C22×(C3⋊D3)⋊C3—21no—
54C22×(C3⋊D3)⋊C3—21no—
55C22×(C3⋊D3)⋊C3C2×C412yes—
56C2×#1084—21no—
57C2×#1084—21no—
58C2×#1084—21no—
59C2×#1084—21no—
60C2×#1084—21no—
61C2×#1084D412yescomplemented
62#638⋊C3—28no—
63C2×(C3⋊Dic3)⋊C3—21no—
64C2×(C3⋊Dic3)⋊C3—21no—
65C2×(C3⋊Dic3)⋊C3—21no—
66C2×(C3⋊Dic3)⋊C3—21no—
67C2×(C3⋊Dic3)⋊C3—21no—
68C2×(C3⋊Dic3)⋊C3C2×C412yes—
69C2×(C3⋊Dic3)⋊C3D412yes—
70C2×(C3⋊Dic3)⋊C3D412yes—
71C2×(C3⋊Dic3)⋊C3D412yescomplemented
72#5221—91no—
73#4957—91no—
74#4957—91no—
75C24×C32—21no—
76C24×C32C2×D311yescharacteristic
77C24×C32C2×D311yescharacteristic
78C23×C3⋊D3C2×D311yescharacteristic
79C23×C3×D3—31no—
80C2×#638—22no—
81C2×#638—22no—
82C2×#638Dic314yescomplemented
83C22×C3⋊Dic3C2×D311yescharacteristic
84C22×C3⋊Dic3C2×D311yescharacteristic
85C22×C3⋊Dic3C2×D311yescharacteristic
86C2×C3×#67—34no—
87C2×C3×#67—62no—
88C2×C3×#67—62no—
89C22×C3×Dic3—31no—
90C22×C3×Dic3—31no—
91C22×C3×Dic3—31no—
92C22×C3×Dic3—31no—
93C22×C3×Dic3—31no—
94C22×C3×Dic3—31no—
95C22×C3×Dic3—31no—
96C22×C3×Dic3—61no—
97C22×C3×Dic3—61no—
98#3757—22no—
99C3×#217—62no—
100C3×#217—62no—
101C3×#217—62no—
102C3×#217—64no—
103#3724—62no—
104Dic3⋊Dic3—62no—
105#3722—62no—
106#3722—62no—
107(C2×D3)⋊Dic3—62no—
108(C2×D3)⋊Dic3—62no—
109Dic32—62no—
110Dic32—62no—
111C22×H(3,𝔽3)—22no—
112C22×H(3,𝔽3)—22no—
113C22×H(3,𝔽3)—22no—
114C22×H(3,𝔽3)—41no—
115C22×H(3,𝔽3)—41no—
116C22×H(3,𝔽3)—41no—
117C22×H(3,𝔽3)—41no—
118C22×H(3,𝔽3)C22×C411yescharacteristic
119C22×H(3,𝔽3)C2×D411yescharacteristic
120C22×H(3,𝔽3)C2×D411yescharacteristic
121C22×H(3,𝔽3)C2×D411yescharacteristic
122C22×H(3,𝔽3)C2×D411yescharacteristic
123C22×H(3,𝔽3)#4111yescharacteristic
124C22×H(3,𝔽3)#4111yescharacteristic
125C2×(C3⋊D3)⋊C3—22no—
126C2×(C3⋊D3)⋊C3—22no—
127C2×(C3⋊D3)⋊C3—22no—
128C2×(C3⋊D3)⋊C3—41no—
129C2×(C3⋊D3)⋊C3—41no—
130C2×(C3⋊D3)⋊C3—41no—
131C2×(C3⋊D3)⋊C3—41no—
132#1084—22no—
133#1084—41no—
134(C3⋊Dic3)⋊C3—22no—
135(C3⋊Dic3)⋊C3—41no—
136(C3⋊Dic3)⋊C3C22⋊C414yescomplemented
137C22×C3×D4—91no—
138C22×#67—31no—
139C22×#67—91no—
140C2×C3×C22⋊C4—91no—
141C2×C3×C22⋊C4—91no—
142C2×#217—31no—
143C2×#217—31no—
144C2×#217—31no—
145C2×#217—61no—
146C2×#217—91no—
147C2×#217—91no—
148C2×#217—91no—
149C2×(C2×D3)⋊C4—91no—
150C2×(C2×D3)⋊C4—91no—
151C2×(C2×D3)⋊C4—91no—
152C2×(C2×D3)⋊C4—91no—
153C2×C4⋊Dic3—91no—
154C2×Dic3⋊C4—91no—
155C2×Dic3⋊C4—91no—
156C2×C4×Dic3—91no—
157C2×C4×Dic3—91no—
158C2×C4×Dic3—91no—
159C23×C32—22no—
160C23×C32—22no—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32—21no—
164C23×C32—21no—
165C23×C32—21no—
166C23×C32—21no—
167C23×C32—21no—
168C23×C32—21no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—21no—
172C23×C32—21no—
173C23×C32—22no—
174C23×C32—21no—
175C23×C32—41no—
176C23×C32—41no—
177C23×C32—41no—
178C23×C32—41no—
179C23×C32C4×D312yes—
180C23×C32C2×Dic312yes—
181C23×C32C22×D311yescharacteristic
182C23×C32C22×D311yescharacteristic
183C22×C3⋊D3—21no—
184C22×C3⋊D3—21no—
185C22×C3⋊D3—21no—
186C22×C3⋊D3—21no—
187C22×C3⋊D3—21no—
188C22×C3⋊D3—21no—
189C22×C3⋊D3C2×Dic312yes—
190C22×C3×D3—32no—
191C22×C3×D3—61no—
192C22×C3×D3—61no—
193C22×C3×D3—61no—
194C22×C3×D3—61no—
195C22×C3×D3—61no—
196C22×C3×D3—61no—
197#638—28no—
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3—21no—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3C2×Dic312yes—
204C2×C3⋊Dic3#6712yes—
205C2×C3⋊Dic3#6712yes—
206C2×C3⋊Dic3#6712yescomplemented
207C3×#67—68no—
208C2×C3×Dic3—32no—
209C2×C3×Dic3—32no—
210C2×C3×Dic3—32no—
211C2×C3×Dic3—32no—
212C2×C3×Dic3—32no—
213C2×C3×Dic3—32no—
214C2×C3×Dic3—62no—
215C2×C3×Dic3—61no—
216C2×C3×Dic3—61no—
217C2×C3×Dic3—61no—
218C2×C3×Dic3—61no—
219C2×C3×Dic3—61no—
220C2×C3×Dic3—61no—
221C2×C3×Dic3—62no—
222C2×C3×Dic3—61no—
223C2×C3×Dic3—61no—
224C2×C3×Dic3—61no—
225C2×C3×Dic3—61no—
226C2×C3×Dic3—61no—
227C2×C3×Dic3—61no—
228C2×C3×Dic3—61no—
229C2×C3×Dic3—61no—
230C2×C3×Dic3—61no—
231C2×C3×Dic3—121no—
232C2×C3×Dic3—121no—
233C2×C3×Dic3—121no—
234C2×C3×Dic3—121no—
235#390—271noSylow
236C2×H(3,𝔽3)—42no—
237C2×H(3,𝔽3)C2×C22⋊C411yescharacteristic
238C2×H(3,𝔽3)C4×D411yescharacteristic
239C2×H(3,𝔽3)C4×D411yescharacteristic
240C2×H(3,𝔽3)#12111yescharacteristic
241C2×H(3,𝔽3)#12111yescharacteristic
242C2×H(3,𝔽3)#12411yescharacteristic
243C2×H(3,𝔽3)#12711yescharacteristic
244(C3⋊D3)⋊C3—42no—
245C24×C3—31no—
246C24×C3—31no—
247C24×C3—61no—
248C24×C3—91no—
249C24×C3D3211yescharacteristic
250C23×D3—31no—
251C23×D3—91no—
252C2×C3×D4—94no—
253C2×C3×D4—182no—
254C2×C3×D4—182no—
255C22×C3×C4—91no—
256C22×C3×C4—91no—
257C22×C3×C4—91no—
258C22×C3×C4—91no—
259C22×C3×C4—91no—
260C2×#67—34no—
261C2×#67—62no—
262C2×#67—62no—
263C2×#67—94no—
264C2×#67—182no—
265C2×#67—182no—
266C22×Dic3—31no—
267C22×Dic3—31no—
268C22×Dic3—31no—
269C22×Dic3—31no—
270C22×Dic3—31no—
271C22×Dic3—31no—
272C22×Dic3—31no—
273C22×Dic3—61no—
274C22×Dic3—61no—
275C22×Dic3—91no—
276C22×Dic3—91no—
277C22×Dic3—91no—
278C3×C22⋊C4—182no—
279C3×C22⋊C4—182no—
280#217—62no—
281#217—62no—
282#217—62no—
283#217—64no—
284#217—182no—
285#217—182no—
286#217—182no—
287(C2×D3)⋊C4—182no—
288(C2×D3)⋊C4—182no—
289(C2×D3)⋊C4—182no—
290(C2×D3)⋊C4—182no—
291C4⋊Dic3—182no—
292Dic3⋊C4—182no—
293Dic3⋊C4—182no—
294C4×Dic3—182no—
295C4×Dic3—182no—
296C4×Dic3—182no—
297C22×C32—24no—
298C22×C32—22no—
299C22×C32—22no—
300C22×C32—22no—
301C22×C32—22no—
302C22×C32—22no—
303C22×C32—22no—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32—21no—
311C22×C32—42no—
312C22×C32—42no—
313C22×C32—42no—
314C22×C32—42no—
315C22×C32—42no—
316C22×C32—42no—
317C22×C32—41no—
318C22×C32—41no—
319C22×C32—41no—
320C22×C32—41no—
321C22×C32—41no—
322C22×C32—41no—
323C22×C32—41no—
324C22×C32—41no—
325C22×C32C2×C4×D311yescharacteristic
326C22×C32#23511yescharacteristic
327C22×C32D3×D411yescharacteristic
328C22×C32D3×D411yescharacteristic
329C22×C32D3×D411yescharacteristic
330C22×C32D3×D411yescharacteristic
331C22×C32D3×D411yescharacteristic
332C22×C32#23711yescharacteristic
333C22×C32#23711yescharacteristic
334C22×C32#23711yescharacteristic
335C22×C32C22×Dic311yescharacteristic
336C22×C32C2×#6711yescharacteristic
337C22×C32C2×#6711yescharacteristic
338C22×C32C2×#6711yescharacteristic
339C2×C3⋊D3—22no—
340C2×C3⋊D3—22no—
341C2×C3⋊D3—22no—
342C2×C3⋊D3—41no—
343C2×C3⋊D3—41no—
344C2×C3⋊D3—41no—
345C2×C3⋊D3—41no—
346C2×C3×D3—62no—
347C2×C3×D3—62no—
348C2×C3×D3—62no—
349C2×C3×D3—121no—
350C2×C3×D3—121no—
351C2×C3×D3—121no—
352C2×C3×D3—121no—
353C3⋊Dic3—22no—
354C3⋊Dic3—41no—
355C3⋊Dic3#21714yescomplemented
356C3×Dic3—34no—
357C3×Dic3—62no—
358C3×Dic3—62no—
359C3×Dic3—62no—
360C3×Dic3—122no—
361C3×Dic3—122no—
362C3×Dic3—121no—
363C3×Dic3—121no—
364C3×Dic3—121no—
365C22×D4—91no—
366C2×C4⋊C4—271no—
367C2×C22⋊C4—91no—
368C2×C22⋊C4—91no—
369C2×C22⋊C4—271no—
370C2×C22⋊C4—271no—
371C2×C42—271no—
372H(3,𝔽3)#39011yescharacteristic, complemented, Sylow
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—32no—
380C23×C3—32no—
381C23×C3—31no—
382C23×C3—31no—
383C23×C3—61no—
384C23×C3—61no—
385C23×C3—61no—
386C23×C3—61no—
387C23×C3—61no—
388C23×C3—61no—
389C23×C3—61no—
390C23×C3—61no—
391C23×C3—61no—
392C23×C3—61no—
393C23×C3—61no—
394C23×C3—61no—
395C23×C3—62no—
396C23×C3—62no—
397C23×C3—62no—
398C23×C3—61no—
399C23×C3—92no—
400C23×C3—121no—
401C23×C3—121no—
402C23×C3—121no—
403C23×C3—121no—
404C23×C3—181no—
405C23×C3—181no—
406C23×C3—181no—
407C23×C3—181no—
408C23×C3—181no—
409C23×C3—181no—
410C23×C3D3×Dic312yes—
411C23×C3C2×D3211yescharacteristic
412C22×D3—32no—
413C22×D3—61no—
414C22×D3—61no—
415C22×D3—61no—
416C22×D3—61no—
417C22×D3—61no—
418C22×D3—61no—
419C22×D3—92no—
420C22×D3—181no—
421C22×D3—181no—
422C22×D3—181no—
423C22×D3—181no—
424C22×D3—181no—
425C22×D3—181no—
426C3×D4—188no—
427C2×C3×C4—92no—
428C2×C3×C4—92no—
429C2×C3×C4—92no—
430C2×C3×C4—92no—
431C2×C3×C4—92no—
432C2×C3×C4—181no—
433C2×C3×C4—181no—
434C2×C3×C4—181no—
435C2×C3×C4—181no—
436C2×C3×C4—181no—
437C2×C3×C4—181no—
438C2×C3×C4—181no—
439C2×C3×C4—181no—
440C2×C3×C4—181no—
441C2×C3×C4—181no—
442#67—68no—
443#67—188no—
444C2×Dic3—32no—
445C2×Dic3—32no—
446C2×Dic3—32no—
447C2×Dic3—32no—
448C2×Dic3—32no—
449C2×Dic3—32no—
450C2×Dic3—62no—
451C2×Dic3—61no—
452C2×Dic3—61no—
453C2×Dic3—61no—
454C2×Dic3—61no—
455C2×Dic3—61no—
456C2×Dic3—61no—
457C2×Dic3—61no—
458C2×Dic3—61no—
459C2×Dic3—61no—
460C2×Dic3—61no—
461C2×Dic3—61no—
462C2×Dic3—61no—
463C2×Dic3—62no—
464C2×Dic3—61no—
465C2×Dic3—61no—
466C2×Dic3—61no—
467C2×Dic3—92no—
468C2×Dic3—92no—
469C2×Dic3—92no—
470C2×Dic3—92no—
471C2×Dic3—121no—
472C2×Dic3—121no—
473C2×Dic3—121no—
474C2×Dic3—121no—
475C2×Dic3—181no—
476C2×Dic3—181no—
477C2×Dic3—181no—
478C2×Dic3—181no—
479C2×Dic3—181no—
480C2×C32—21no—
481C2×C32—21no—
482C2×C32—21no—
483C2×C32—21no—
484C2×C32—21no—
485C2×C32—21no—
486C2×C32—21no—
487C2×C32—44no—
488C2×C32—42no—
489C2×C32—42no—
490C2×C32D3×C22⋊C411yescharacteristic
491C2×C32#67⋊C411yescharacteristic
492C2×C32#88411yescharacteristic
493C2×C32#88511yescharacteristic
494C2×C32C4×#6711yescharacteristic
495C2×C32D4×Dic311yescharacteristic
496C2×C32D4×Dic311yescharacteristic
497C2×C32#93611yescharacteristic
498C2×C32#93811yescharacteristic
499C2×C32#93811yescharacteristic
500C2×C32#93911yescharacteristic
501C2×C32#94011yescharacteristic
502C2×C32#94011yescharacteristic
503C2×C32C2×#21711yescharacteristic
504C3⋊D3—42no—
505C3×D3—122no—
506C24—91no—
507C24((C3⋊D3)⋊C3)⋊C211yescharacteristic
508C2×D4—94no—
509C2×D4—182no—
510C2×D4—182no—
511C22×C4—91no—
512C22×C4—91no—
513C22×C4—91no—
514C22×C4—91no—
515C22×C4—91no—
516C4⋊C4—542no—
517C22⋊C4—182no—
518C22⋊C4—182no—
519C22⋊C4—542no—
520C22⋊C4—542no—
521C42—542no—
522C22×C3—22no—
523C22×C3—22no—
524C22×C3—22no—
525C22×C3—31no—
526C22×C3—31no—
527C22×C3—31no—
528C22×C3—31no—
529C22×C3—31no—
530C22×C3—31no—
531C22×C3—31no—
532C22×C3—31no—
533C22×C3—31no—
534C22×C3—31no—
535C22×C3—31no—
536C22×C3—31no—
537C22×C3—31no—
538C22×C3—31no—
539C22×C3—41no—
540C22×C3—41no—
541C22×C3—41no—
542C22×C3—41no—
543C22×C3—62no—
544C22×C3—62no—
545C22×C3—62no—
546C22×C3—62no—
547C22×C3—62no—
548C22×C3—62no—
549C22×C3—64no—
550C22×C3—61no—
551C22×C3—61no—
552C22×C3—61no—
553C22×C3—61no—
554C22×C3—61no—
555C22×C3—61no—
556C22×C3—61no—
557C22×C3—122no—
558C22×C3—122no—
559C22×C3—121no—
560C22×C3—121no—
561C22×C3—121no—
562C22×C3—121no—
563C22×C3—121no—
564C22×C3—121no—
565C22×C3—121no—
566C22×C3—121no—
567C22×C3—122no—
568C22×C3—122no—
569C22×C3—122no—
570C22×C3—122no—
571C22×C3—182no—
572C22×C3—182no—
573C22×C3—182no—
574C22×C3—361no—
575C22×C3—361no—
576C22×C3—361no—
577C22×C3—361no—
578C22×C3C2×D3×Dic311yescharacteristic
579C22×C3#380411yescharacteristic
580C22×C3#380511yescharacteristic
581C22×C3D3×#6711yescharacteristic
582C22×C3D3×#6711yescharacteristic
583C22×C3D3×#6711yescharacteristic
584C22×C3#381111yescharacteristic
585C2×D3—62no—
586C2×D3—62no—
587C2×D3—62no—
588C2×D3—121no—
589C2×D3—121no—
590C2×D3—121no—
591C2×D3—121no—
592C2×D3—182no—
593C2×D3—182no—
594C2×D3—182no—
595C2×D3—361no—
596C2×D3—361no—
597C2×D3—361no—
598C2×D3—361no—
599C3×C4—94no—
600C3×C4—182no—
601C3×C4—182no—
602C3×C4—361no—
603C3×C4—361no—
604Dic3—34no—
605Dic3—62no—
606Dic3—62no—
607Dic3—62no—
608Dic3—94no—
609Dic3—122no—
610Dic3—121no—
611Dic3—121no—
612Dic3—122no—
613Dic3—121no—
614Dic3—182no—
615Dic3—361no—
616C32—21no—
617C32#495711yescharacteristic, complemented
618C32#522111yescharacteristic, complemented
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—92no—
626C23—181no—
627C23—181no—
628C23—181no—
629C23—181no—
630C23—181no—
631C23—181no—
632C23((C3⋊D3)⋊C3)⋊C412yes—
633C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
634D4—188no—
635C2×C4—92no—
636C2×C4—92no—
637C2×C4—92no—
638C2×C4—92no—
639C2×C4—92no—
640C2×C4—181no—
641C2×C4—181no—
642C2×C4—181no—
643C2×C4—181no—
644C2×C4—181no—
645C2×C4—181no—
646C2×C4—181no—
647C2×C4—181no—
648C2×C4—181no—
649C2×C4—181no—
650C2×C3—31no—
651C2×C3—31no—
652C2×C3—31no—
653C2×C3—31no—
654C2×C3—31no—
655C2×C3—31no—
656C2×C3—31no—
657C2×C3—31no—
658C2×C3—31no—
659C2×C3—31no—
660C2×C3—31no—
661C2×C3—31no—
662C2×C3—31no—
663C2×C3—31no—
664C2×C3—42no—
665C2×C3—61no—
666C2×C3—61no—
667C2×C3—61no—
668C2×C3—61no—
669C2×C3—61no—
670C2×C3—61no—
671C2×C3—61no—
672C2×C3—122no—
673C2×C3—122no—
674C2×C3—124no—
675C2×C3—362no—
676C2×C3#6395811yescharacteristic
677C2×C3#6395911yescharacteristic
678C2×C3D3×#21711yescharacteristic
679C2×C3#6397011yescharacteristic
680C2×C3Dic3×#6711yescharacteristic
681C2×C3#67⋊Dic311yescharacteristic
682C2×C3#6397911yescharacteristic
683D3—122no—
684D3—362no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—182no—
693C22—182no—
694C22—182no—
695C22—361no—
696C22—361no—
697C22—361no—
698C22—361no—
699C22C2×((C3⋊D3)⋊C3)⋊C411yescharacteristic
700C22#8867111yescharacteristic
701C22#8867211yescharacteristic
702C22#8867611yescharacteristic
703C22#8867611yescharacteristic
704C22#8867611yescharacteristic
705C22#8867711yescharacteristic
706C4—94no—
707C4—182no—
708C4—182no—
709C4—361no—
710C4—361no—
711C3—31no—
712C3—31no—
713C3—61no—
714C3#1059170711yescharacteristic
715C2—42no—
716C2—362no—
717C2#1172130311yescharacteristic
718C2#1172130411yescharacteristic
719C2#1172131011yescharacteristic
720C2#1172131311yescharacteristic
721C2#1172131411yescharacteristic
722C2#1172131511yescharacteristic
723C2#1172131711yescharacteristic
subgroupG/H
centerC23C2×((C3⋊D3)⋊C3)⋊C2
commutatorC22×H(3,𝔽3)C22×C4
Frattini, socleC23×C3C2×D32
FittingC24×H(3,𝔽3)C22
prime radicalC22×#638⋊C3C2
cosocleC23×H(3,𝔽3)C23
hypercenterC24((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#390
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C2×#88552C2semidirect
3. C2×#3757⋊C3C2semidirect
4. C2×#88450C2semidirect
5. C2×#88450C2semidirect
6. C2×#88448C2semidirect
7. C2×#88447C2semidirect
16. C2×#638⋊C3C4semidirect
28. C2×#3757D3semidirect
61. C2×#1084D4semidirect
71. C2×(C3⋊Dic3)⋊C3D4semidirect
82. C2×#638Dic3semidirect
136. (C3⋊Dic3)⋊C3C22⋊C4semidirect
206. C2×C3⋊Dic3#67semidirect
355. C3⋊Dic3#217semidirect
372. H(3,𝔽3)#390semidirect
617. C32#4957semidirect
618. C32#5221semidirect

Maximal subgroups

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

subgroupindex
C22×#638⋊C32
C2×#885522
C2×#3757⋊C32
C2×#884502
C2×#884482
C2×#884472
#105917073
#105917043