Finite Group Databasebeta

← #13140222

Subgroups — #13140222

Order 1728.

965 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6200C211yesmaximal, characteristic
2C2×#88542C211yesmaximal, characteristic, complemented
3C2×#3752⋊C3C211yesmaximal, characteristic, complemented
4C2×#88451C211yesmaximal, characteristic, complemented
5C2×#88450C211yesmaximal, characteristic, complemented
6C2×#88448C211yesmaximal, characteristic, complemented
7#63658⋊C3C211yesmaximal, characteristic, complemented
8#10591390—31nomaximal
9#10591292—31nomaximal
10C23×#272C2211yescharacteristic
11C23×(C3⋊D3)⋊C3C2211yescharacteristic
12C22×C4×H(3,𝔽3)C2211yescharacteristic
13C22×#1084C2211yescharacteristic
14C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
15C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
16C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
17C2×#6200—22no—
18C2×#6200—22no—
19C2×#6200—22no—
20#88542—22no—
21#3752⋊C3—22no—
22#88451—22no—
23#88450—22no—
24#88448—22no—
25C22×#626—31no—
26C22×#625—31no—
27C2×#3752D311yescharacteristic, complemented
28C2×C3×(C2×D3)⋊C4—31no—
29C2×C3×(C2×D3)⋊C4—31no—
30C2×C3×(C2×D3)⋊C4—31no—
31C2×C3×(C2×D3)⋊C4—61no—
32C2×#3724—31no—
33C2×Dic3⋊Dic3—31no—
34C2×#3722—31no—
35C2×(C2×D3)⋊Dic3—31no—
36C2×(C2×D3)⋊Dic3—31no—
37C2×(C2×D3)⋊Dic3—31no—
38#63658D311yescharacteristic, complemented
39C3×C3⋊#95—31no—
40C23×H(3,𝔽3)C2311yescharacteristic
41C22×#272—21no—
42C22×#272—21no—
43C22×#272—21no—
44C22×#272—21no—
45C22×#272—21no—
46C22×#272—21no—
47C22×#272D412yes—
48C22×(C3⋊D3)⋊C3—21no—
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)⋊C3D412yes—
55C2×C4×H(3,𝔽3)—21no—
56C2×C4×H(3,𝔽3)—21no—
57C2×C4×H(3,𝔽3)—21no—
58C2×#1084—21no—
59C2×#1084—21no—
60C2×#1084—21no—
61C2×(C3⋊Dic3)⋊C3—21no—
62C2×(C3⋊Dic3)⋊C3—21no—
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)⋊C3D412yes—
69C2×(C3⋊Dic3)⋊C3D412yescomplemented
70#6200—28no—
71#4961—91no—
72#4959—91no—
73#4672—91no—
74C23×C3⋊D3C2×D311yescharacteristic
75C23×C3×D3—31no—
76C23×C3×D3—31no—
77C23×C3×D3—31no—
78C23×C3×D3—61no—
79C22×C32×C4—21no—
80C22×C32×C4C2×D311yescharacteristic
81C22×C32×C4C2×D311yescharacteristic
82C22×C3⋊Dic3C2×D311yescharacteristic
83C22×C3⋊Dic3C2×D311yescharacteristic
84C22×C3⋊Dic3C2×D311yescharacteristic
85C22×C3×Dic3—31no—
86C22×C3×Dic3—31no—
87C22×C3×Dic3—31no—
88C22×C3×Dic3—31no—
89C22×C3×Dic3—31no—
90C22×C3×Dic3—61no—
91C2×#626—62no—
92C2×#626—62no—
93C2×#626—62no—
94C2×#625—62no—
95C2×#625—62no—
96C2×#625—62no—
97#3752—22no—
98C3×(C2×D3)⋊C4—62no—
99C3×(C2×D3)⋊C4—62no—
100C3×(C2×D3)⋊C4—62no—
101C3×(C2×D3)⋊C4—64no—
102#3724—62no—
103Dic3⋊Dic3—62no—
104#3722—62no—
105(C2×D3)⋊Dic3—62no—
106(C2×D3)⋊Dic3—62no—
107(C2×D3)⋊Dic3—62no—
108C22×H(3,𝔽3)C2×D411yescharacteristic
109C22×H(3,𝔽3)C2×D411yescharacteristic
110C22×H(3,𝔽3)C2×D411yescharacteristic
111C22×H(3,𝔽3)C2×D411yescharacteristic
112C22×H(3,𝔽3)#4111yescharacteristic
113C22×H(3,𝔽3)#4111yescharacteristic
114C22×H(3,𝔽3)#4111yescharacteristic
115C2×#272—22no—
116C2×#272—22no—
117C2×#272—22no—
118C2×#272—41no—
119C2×#272—41no—
120C2×#272—41no—
121C2×#272—41no—
122C2×(C3⋊D3)⋊C3—22no—
123C2×(C3⋊D3)⋊C3—22no—
124C2×(C3⋊D3)⋊C3—22no—
125C2×(C3⋊D3)⋊C3—41no—
126C2×(C3⋊D3)⋊C3—41no—
127C2×(C3⋊D3)⋊C3—41no—
128C2×(C3⋊D3)⋊C3—41no—
129C4×H(3,𝔽3)—41no—
130#1084—41no—
131(C3⋊Dic3)⋊C3—22no—
132(C3⋊Dic3)⋊C3—22no—
133(C3⋊Dic3)⋊C3—41no—
134C22×#67—91no—
135C22×#67—91no—
136C22×D12—91no—
137C2×C3×C22⋊C4—91no—
138C2×C3×C22⋊C4—91no—
139C2×#217—91no—
140C2×#217—91no—
141C2×(C2×D3)⋊C4—31no—
142C2×(C2×D3)⋊C4—31no—
143C2×(C2×D3)⋊C4—31no—
144C2×(C2×D3)⋊C4—61no—
145C2×(C2×D3)⋊C4—91no—
146C2×(C2×D3)⋊C4—91no—
147C2×(C2×D3)⋊C4—91no—
148C2×(C2×D3)⋊C4—91no—
149C2×(C2×D3)⋊C4—91no—
150C2×C4⋊Dic3—91no—
151C2×Dic3⋊C4—91no—
152C2×Dic3⋊C4—91no—
153C3×#95—91no—
154C3⋊#95—31no—
155C3⋊#95—91no—
156C23×C32—21no—
157C23×C32C22×D311yescharacteristic
158C23×C32C22×D311yescharacteristic
159C22×C3⋊D3—21no—
160C22×C3⋊D3—21no—
161C22×C3⋊D3—21no—
162C22×C3⋊D3—21no—
163C22×C3⋊D3—21no—
164C22×C3⋊D3—21no—
165C22×C3⋊D3D1212yes—
166C22×C3×D3—32no—
167C22×C3×D3—32no—
168C22×C3×D3—32no—
169C22×C3×D3—62no—
170C22×C3×D3—62no—
171C22×C3×D3—62no—
172C22×C3×D3—61no—
173C22×C3×D3—61no—
174C22×C3×D3—61no—
175C22×C3×D3—61no—
176C22×C3×D3—61no—
177C22×C3×D3—61no—
178C22×C3×D3—61no—
179C22×C3×D3—61no—
180C22×C3×D3—61no—
181C22×C3×D3—61no—
182C22×C3×D3—61no—
183C22×C3×D3—61no—
184C22×C3×D3—61no—
185C22×C3×D3—61no—
186C22×C3×D3—61no—
187C22×C3×D3—61no—
188C22×C3×D3—61no—
189C22×C3×D3—61no—
190C22×C3×D3—121no—
191C22×C3×D3—121no—
192C22×C3×D3—121no—
193C22×C3×D3—121no—
194C2×C32×C4—22no—
195C2×C32×C4—21no—
196C2×C32×C4—21no—
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—41no—
202C2×C32×C4—41no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3—21no—
205C2×C3⋊Dic3—21no—
206C2×C3⋊Dic3—21no—
207C2×C3⋊Dic3—21no—
208C2×C3⋊Dic3—21no—
209C2×C3⋊Dic3—21no—
210C2×C3⋊Dic3D1212yes—
211C2×C3⋊Dic3#6712yescomplemented
212C2×C3×Dic3—32no—
213C2×C3×Dic3—32no—
214C2×C3×Dic3—61no—
215C2×C3×Dic3—61no—
216C2×C3×Dic3—61no—
217C2×C3×Dic3—61no—
218C2×C3×Dic3—62no—
219C2×C3×Dic3—61no—
220C2×C3×Dic3—61no—
221C2×C3×Dic3—61no—
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—121no—
229C2×C3×Dic3—121no—
230#626—68no—
231#625—68no—
232#394—271noSylow
233C2×H(3,𝔽3)#12011yescharacteristic
234C2×H(3,𝔽3)#12111yescharacteristic
235C2×H(3,𝔽3)#12111yescharacteristic
236C2×H(3,𝔽3)#12111yescharacteristic
237C2×H(3,𝔽3)#12311yescharacteristic
238C2×H(3,𝔽3)#12311yescharacteristic
239C2×H(3,𝔽3)#12411yescharacteristic
240#272—42no—
241(C3⋊D3)⋊C3—42no—
242C24×C3—91no—
243C24×C3—91no—
244C23×D3—31no—
245C23×D3—31no—
246C23×D3—31no—
247C23×D3—61no—
248C23×D3—91no—
249C22×C3×C4—31no—
250C22×C3×C4—31no—
251C22×C3×C4—61no—
252C22×C3×C4—91no—
253C22×C3×C4—91no—
254C22×C3×C4—91no—
255C22×C3×C4—91no—
256C22×C3×C4D3211yescharacteristic
257C2×#67—182no—
258C2×#67—182no—
259C2×#67—182no—
260C2×#67—182no—
261C2×#67—182no—
262C2×#67—182no—
263C22×Dic3—31no—
264C22×Dic3—31no—
265C22×Dic3—31no—
266C22×Dic3—31no—
267C22×Dic3—31no—
268C22×Dic3—61no—
269C22×Dic3—91no—
270C22×Dic3—91no—
271C22×Dic3—91no—
272C2×D12—182no—
273C2×D12—182no—
274C2×D12—182no—
275C3×C22⋊C4—182no—
276C3×C22⋊C4—182no—
277#217—182no—
278#217—182no—
279(C2×D3)⋊C4—62no—
280(C2×D3)⋊C4—62no—
281(C2×D3)⋊C4—62no—
282(C2×D3)⋊C4—64no—
283(C2×D3)⋊C4—182no—
284(C2×D3)⋊C4—182no—
285(C2×D3)⋊C4—182no—
286(C2×D3)⋊C4—182no—
287(C2×D3)⋊C4—182no—
288C4⋊Dic3—182no—
289Dic3⋊C4—182no—
290Dic3⋊C4—182no—
291C22×C32—21no—
292C22×C32—21no—
293C22×C32—21no—
294C22×C32—21no—
295C22×C32—21no—
296C22×C32—21no—
297C22×C32—21no—
298C22×C32C2×D1211yescharacteristic
299C22×C32C2×D1211yescharacteristic
300C22×C32#23511yescharacteristic
301C22×C32#23511yescharacteristic
302C22×C32#23511yescharacteristic
303C22×C32D3×D411yescharacteristic
304C22×C32D3×D411yescharacteristic
305C22×C32D3×D411yescharacteristic
306C22×C32D3×D411yescharacteristic
307C22×C32D3×D411yescharacteristic
308C22×C32#23711yescharacteristic
309C22×C32#23711yescharacteristic
310C22×C32#23911yescharacteristic
311C22×C32C2×#6711yescharacteristic
312C2×C3⋊D3—22no—
313C2×C3⋊D3—22no—
314C2×C3⋊D3—22no—
315C2×C3⋊D3—41no—
316C2×C3⋊D3—41no—
317C2×C3⋊D3—41no—
318C2×C3⋊D3—41no—
319C2×C3×D3—64no—
320C2×C3×D3—62no—
321C2×C3×D3—62no—
322C2×C3×D3—62no—
323C2×C3×D3—62no—
324C2×C3×D3—62no—
325C2×C3×D3—62no—
326C2×C3×D3—62no—
327C2×C3×D3—62no—
328C2×C3×D3—62no—
329C2×C3×D3—122no—
330C2×C3×D3—122no—
331C2×C3×D3—122no—
332C2×C3×D3—122no—
333C2×C3×D3—122no—
334C2×C3×D3—122no—
335C2×C3×D3—121no—
336C2×C3×D3—121no—
337C2×C3×D3—121no—
338C2×C3×D3—121no—
339C2×C3×D3—121no—
340C2×C3×D3—121no—
341C2×C3×D3—121no—
342C2×C3×D3—121no—
343C2×C3×D3—121no—
344C2×C3×D3—121no—
345C2×C3×D3—121no—
346C2×C3×D3—121no—
347C32×C4—42no—
348C32×C4—41no—
349C32×C4—41no—
350C3⋊Dic3—22no—
351C3⋊Dic3—22no—
352C3⋊Dic3—41no—
353C3×Dic3—62no—
354C3×Dic3—62no—
355C3×Dic3—122no—
356C3×Dic3—121no—
357C3×Dic3—121no—
358C3×Dic3—121no—
359C22×D4—271no—
360C2×C4⋊C4—271no—
361C2×C22⋊C4—91no—
362C2×C22⋊C4—91no—
363C2×C22⋊C4—271no—
364C2×C22⋊C4—271no—
365#95—91no—
366H(3,𝔽3)#39411yescharacteristic, complemented, Sylow
367C23×C3—31no—
368C23×C3—31no—
369C23×C3—61no—
370C23×C3—92no—
371C23×C3—92no—
372C23×C3—181no—
373C23×C3—181no—
374C23×C3—181no—
375C23×C3—181no—
376C23×C3—181no—
377C23×C3—181no—
378C23×C3—181no—
379C23×C3—181no—
380C23×C3—181no—
381C23×C3—181no—
382C23×C3—181no—
383C23×C3—181no—
384C23×C3C2×D3211yescharacteristic
385C22×D3—32no—
386C22×D3—32no—
387C22×D3—32no—
388C22×D3—62no—
389C22×D3—61no—
390C22×D3—61no—
391C22×D3—61no—
392C22×D3—61no—
393C22×D3—61no—
394C22×D3—61no—
395C22×D3—61no—
396C22×D3—61no—
397C22×D3—61no—
398C22×D3—61no—
399C22×D3—61no—
400C22×D3—61no—
401C22×D3—62no—
402C22×D3—62no—
403C22×D3—61no—
404C22×D3—61no—
405C22×D3—61no—
406C22×D3—61no—
407C22×D3—61no—
408C22×D3—61no—
409C22×D3—92no—
410C22×D3—121no—
411C22×D3—121no—
412C22×D3—121no—
413C22×D3—121no—
414C22×D3—181no—
415C22×D3—181no—
416C22×D3—181no—
417C22×D3—181no—
418C22×D3—181no—
419C22×D3—181no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—61no—
424C2×C3×C4—61no—
425C2×C3×C4—61no—
426C2×C3×C4—61no—
427C2×C3×C4—61no—
428C2×C3×C4—61no—
429C2×C3×C4—62no—
430C2×C3×C4—92no—
431C2×C3×C4—92no—
432C2×C3×C4—121no—
433C2×C3×C4—121no—
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—
442C2×C3×C4—181no—
443C2×C3×C4—181no—
444#67—188no—
445#67—188no—
446C2×Dic3—32no—
447C2×Dic3—32no—
448C2×Dic3—61no—
449C2×Dic3—61no—
450C2×Dic3—61no—
451C2×Dic3—61no—
452C2×Dic3—61no—
453C2×Dic3—61no—
454C2×Dic3—61no—
455C2×Dic3—61no—
456C2×Dic3—61no—
457C2×Dic3—61no—
458C2×Dic3—62no—
459C2×Dic3—61no—
460C2×Dic3—61no—
461C2×Dic3—61no—
462C2×Dic3—92no—
463C2×Dic3—92no—
464C2×Dic3—121no—
465C2×Dic3—121no—
466C2×Dic3—181no—
467C2×Dic3—181no—
468C2×Dic3—181no—
469C2×Dic3—181no—
470C2×Dic3—181no—
471C2×Dic3—181no—
472C2×Dic3—181no—
473D12—188no—
474C2×C32—21no—
475C2×C32—21no—
476C2×C32—21no—
477C2×C32—21no—
478C2×C32—21no—
479C2×C32—21no—
480C2×C32—21no—
481C2×C32#87511yescharacteristic
482C2×C32#88211yescharacteristic
483C2×C32#88211yescharacteristic
484C2×C32#88311yescharacteristic
485C2×C32#88411yescharacteristic
486C2×C32#88411yescharacteristic
487C2×C32#88511yescharacteristic
488C2×C32#88611yescharacteristic
489C2×C32#89411yescharacteristic
490C2×C32#89411yescharacteristic
491C2×C32#89511yescharacteristic
492C2×C32#93011yescharacteristic
493C2×C32#93811yescharacteristic
494C2×C32#93911yescharacteristic
495C3⋊D3—42no—
496C3×D3—124no—
497C3×D3—122no—
498C3×D3—122no—
499C3×D3—122no—
500C24—91no—
501C24—91no—
502C2×D4—542no—
503C2×D4—542no—
504C2×D4—542no—
505C22×C4—91no—
506C22×C4—91no—
507C22×C4—91no—
508C22×C4—91no—
509C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
510C4⋊C4—542no—
511C22⋊C4—182no—
512C22⋊C4—182no—
513C22⋊C4—542no—
514C22⋊C4—542no—
515C22×C3—31no—
516C22×C3—31no—
517C22×C3—31no—
518C22×C3—31no—
519C22×C3—31no—
520C22×C3—31no—
521C22×C3—31no—
522C22×C3—31no—
523C22×C3—31no—
524C22×C3—31no—
525C22×C3—31no—
526C22×C3—31no—
527C22×C3—31no—
528C22×C3—31no—
529C22×C3—61no—
530C22×C3—61no—
531C22×C3—61no—
532C22×C3—61no—
533C22×C3—61no—
534C22×C3—61no—
535C22×C3—61no—
536C22×C3—182no—
537C22×C3—182no—
538C22×C3—182no—
539C22×C3—182no—
540C22×C3—182no—
541C22×C3—182no—
542C22×C3—361no—
543C22×C3—361no—
544C22×C3—361no—
545C22×C3—361no—
546C22×C3—361no—
547C22×C3—361no—
548C22×C3—361no—
549C22×C3—361no—
550C22×C3#379611yescharacteristic
551C22×C3#379811yescharacteristic
552C22×C3D3×D1211yescharacteristic
553C22×C3D3×D1211yescharacteristic
554C22×C3#380411yescharacteristic
555C22×C3D3×#6711yescharacteristic
556C22×C3#381111yescharacteristic
557C2×D3—62no—
558C2×D3—62no—
559C2×D3—62no—
560C2×D3—62no—
561C2×D3—62no—
562C2×D3—62no—
563C2×D3—64no—
564C2×D3—62no—
565C2×D3—62no—
566C2×D3—62no—
567C2×D3—122no—
568C2×D3—122no—
569C2×D3—121no—
570C2×D3—121no—
571C2×D3—121no—
572C2×D3—121no—
573C2×D3—121no—
574C2×D3—121no—
575C2×D3—121no—
576C2×D3—121no—
577C2×D3—122no—
578C2×D3—122no—
579C2×D3—122no—
580C2×D3—122no—
581C2×D3—121no—
582C2×D3—121no—
583C2×D3—121no—
584C2×D3—121no—
585C2×D3—182no—
586C2×D3—182no—
587C2×D3—182no—
588C2×D3—361no—
589C2×D3—361no—
590C2×D3—361no—
591C2×D3—361no—
592C3×C4—41no—
593C3×C4—121no—
594C3×C4—121no—
595C3×C4—122no—
596C3×C4—182no—
597C3×C4—182no—
598C3×C4—361no—
599C3×C4—361no—
600Dic3—62no—
601Dic3—62no—
602Dic3—121no—
603Dic3—121no—
604Dic3—122no—
605Dic3—121no—
606Dic3—182no—
607Dic3—182no—
608Dic3—361no—
609C32—21no—
610C32#467211yescharacteristic, complemented
611C32#496111yescharacteristic, complemented
612C23—92no—
613C23—92no—
614C23—181no—
615C23—181no—
616C23—181no—
617C23—181no—
618C23—181no—
619C23—181no—
620C23—181no—
621C23—181no—
622C23—181no—
623C23—181no—
624C23—181no—
625C23—181no—
626C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
627D4—548no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—92no—
632C2×C4—92no—
633C2×C4—181no—
634C2×C4—181no—
635C2×C4—181no—
636C2×C4—181no—
637C2×C4—181no—
638C2×C4—181no—
639C2×C4—181no—
640C2×C4—181no—
641C2×C4—181no—
642C2×C4—181no—
643C2×C3—31no—
644C2×C3—31no—
645C2×C3—31no—
646C2×C3—31no—
647C2×C3—31no—
648C2×C3—31no—
649C2×C3—31no—
650C2×C3—31no—
651C2×C3—31no—
652C2×C3—31no—
653C2×C3—31no—
654C2×C3—31no—
655C2×C3—31no—
656C2×C3—31no—
657C2×C3—61no—
658C2×C3—61no—
659C2×C3—61no—
660C2×C3—61no—
661C2×C3—61no—
662C2×C3—61no—
663C2×C3—61no—
664C2×C3—362no—
665C2×C3—362no—
666C2×C3#6385211yescharacteristic
667C2×C3#6385311yescharacteristic
668C2×C3#6388611yescharacteristic
669C2×C3#6389011yescharacteristic
670C2×C3#6390611yescharacteristic
671C2×C3#6392311yescharacteristic
672C2×C3#6395811yescharacteristic
673D3—122no—
674D3—122no—
675D3—124no—
676D3—122no—
677D3—362no—
678C22—182no—
679C22—182no—
680C22—182no—
681C22—182no—
682C22—182no—
683C22—182no—
684C22—361no—
685C22—361no—
686C22—361no—
687C22—361no—
688C22—361no—
689C22—361no—
690C22—361no—
691C22—361no—
692C22#8864911yescharacteristic
693C22#8865011yescharacteristic
694C22#8865411yescharacteristic
695C22#8865411yescharacteristic
696C22#8867111yescharacteristic
697C22#8867611yescharacteristic
698C22#8867711yescharacteristic
699C4—41no—
700C4—182no—
701C4—182no—
702C4—361no—
703C4—361no—
704C3—31no—
705C3—31no—
706C3—61no—
707C3#1059131211yescharacteristic
708C2—362no—
709C2—362no—
710C2#1172110311yescharacteristic
711C2#1172110411yescharacteristic
712C2#1172112711yescharacteristic
713C2#1172113011yescharacteristic
714C2#1172114011yescharacteristic
715C2#1172116311yescharacteristic
716C2#1172130311yescharacteristic
subgroupG/H
centerC23C2×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC23×H(3,𝔽3)C23
Frattini, socleC23×C3C2×D32
FittingC22×C4×H(3,𝔽3)C22
prime radicalC22×#6200C2
hypercenterC22×C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#394
LCSG ▷ C23×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#88542C2semidirect
3. C2×#3752⋊C3C2semidirect
4. C2×#88451C2semidirect
5. C2×#88450C2semidirect
6. C2×#88448C2semidirect
7. #63658⋊C3C2semidirect
27. C2×#3752D3semidirect
38. #63658D3semidirect
69. C2×(C3⋊Dic3)⋊C3D4semidirect
211. C2×C3⋊Dic3#67semidirect
366. H(3,𝔽3)#394semidirect
610. C32#4672semidirect
611. C32#4961semidirect

Maximal subgroups

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

subgroupindex
C22×#62002
C2×#885422
C2×#3752⋊C32
C2×#884512
C2×#884502
C2×#884482
#63658⋊C32
#105913903
#105912923