Finite Group Databasebeta

← #13140244

Subgroups — #13140244

Order 1728.

1077 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6198C211yesmaximal, characteristic
2C22×((C3⋊D3)⋊C3)⋊C4C211yesmaximal, characteristic, complemented
3C2×#3752⋊C3C211yesmaximal, characteristic, complemented
4C2×#3752⋊C3C211yesmaximal, characteristic, complemented
5C2×#88450C211yesmaximal, characteristic, complemented
6#11720574C211yesmaximal, characteristic, complemented
7#11720334C211yesmaximal, characteristic, complemented
8#10591364—31nomaximal
9#10591275—31nomaximal
10C23×(C3⋊D3)⋊C3C2211yescharacteristic
11C23×(C3⋊D3)⋊C3C2211yescharacteristic
12C22×C4×H(3,𝔽3)C2211yescharacteristic
13C22×#1084C2211yescharacteristic
14C22×#1084C2211yescharacteristic
15C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
16C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
17C2×#6198—22no—
18C2×#6198—22no—
19C2×#6198C414yescomplemented
20C2×((C3⋊D3)⋊C3)⋊C4—22no—
21C2×((C3⋊D3)⋊C3)⋊C4—22no—
22C2×((C3⋊D3)⋊C3)⋊C4—22no—
23#3752⋊C3—22no—
24#3752⋊C3—22no—
25#88450—22no—
26C22×#626—31no—
27C22×#626—31no—
28C22×#624—31no—
29C22×D3×Dic3—31no—
30C2×#3752D311yescharacteristic, complemented
31C2×#3752D311yescharacteristic, complemented
32C2×C3×(C2×D3)⋊C4—31no—
33C2×C3×(C2×D3)⋊C4—31no—
34C2×#3722—31no—
35C2×(C2×D3)⋊Dic3—31no—
36C3×C3⋊#95—31no—
37C3×C3⋊#95—31no—
38C3×C3⋊#95—61no—
39#63579—31no—
40#63579—31no—
41C23×H(3,𝔽3)C2311yescharacteristic
42C22×(C3⋊D3)⋊C3—21no—
43C22×(C3⋊D3)⋊C3—21no—
44C22×(C3⋊D3)⋊C3—21no—
45C22×(C3⋊D3)⋊C3—21no—
46C22×(C3⋊D3)⋊C3—21no—
47C22×(C3⋊D3)⋊C3—21no—
48C22×(C3⋊D3)⋊C3—21no—
49C22×(C3⋊D3)⋊C3—21no—
50C22×(C3⋊D3)⋊C3—21no—
51C22×(C3⋊D3)⋊C3—21no—
52C22×(C3⋊D3)⋊C3C2×C412yes—
53C22×(C3⋊D3)⋊C3C2×C412yescomplemented
54C22×(C3⋊D3)⋊C3D412yes—
55C22×(C3⋊D3)⋊C3D412yes—
56C2×C4×H(3,𝔽3)—21no—
57C2×C4×H(3,𝔽3)—21no—
58C2×C4×H(3,𝔽3)—21no—
59C2×#1084—21no—
60C2×#1084—21no—
61C2×#1084—21no—
62C2×#1084—21no—
63C2×#1084C2×C412yescomplemented
64C2×#1084D412yescomplemented
65C2×(C3⋊Dic3)⋊C3—21no—
66C2×(C3⋊Dic3)⋊C3—21no—
67C2×(C3⋊Dic3)⋊C3—21no—
68C2×(C3⋊Dic3)⋊C3—21no—
69C2×(C3⋊Dic3)⋊C3—21no—
70C2×(C3⋊Dic3)⋊C3D412yescomplemented
71#6198—28no—
72((C3⋊D3)⋊C3)⋊C4—28no—
73#4958—91no—
74#4956—91no—
75#4665—91no—
76C23×C3⋊D3C2×D311yescharacteristic
77C23×C3⋊D3C2×D311yescharacteristic
78C23×C3×D3—31no—
79C23×C3×D3—31no—
80C22×C32×C4—21no—
81C22×C32×C4C2×D311yescharacteristic
82C22×C32×C4C2×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—31no—
91C22×C3×Dic3—61no—
92C22×C3×Dic3—61no—
93C2×#626—34no—
94C2×#626—34no—
95C2×#626—62no—
96C2×#626—62no—
97C2×#626—62no—
98C2×#626—62no—
99C2×#624—62no—
100C2×#624—62no—
101C2×#624—62no—
102C2×D3×Dic3—62no—
103C2×D3×Dic3—62no—
104C2×D3×Dic3—62no—
105#3752—22no—
106#3752—22no—
107C3×(C2×D3)⋊C4—62no—
108C3×(C2×D3)⋊C4—62no—
109#3722—62no—
110(C2×D3)⋊Dic3—62no—
111C22×H(3,𝔽3)C22×C411yescharacteristic
112C22×H(3,𝔽3)C2×D411yescharacteristic
113C22×H(3,𝔽3)C2×D411yescharacteristic
114C22×H(3,𝔽3)C2×D411yescharacteristic
115C22×H(3,𝔽3)C2×D411yescharacteristic
116C22×H(3,𝔽3)#4111yescharacteristic
117C22×H(3,𝔽3)#4111yescharacteristic
118C2×(C3⋊D3)⋊C3—22no—
119C2×(C3⋊D3)⋊C3—22no—
120C2×(C3⋊D3)⋊C3—22no—
121C2×(C3⋊D3)⋊C3—22no—
122C2×(C3⋊D3)⋊C3—22no—
123C2×(C3⋊D3)⋊C3—22no—
124C2×(C3⋊D3)⋊C3—22no—
125C2×(C3⋊D3)⋊C3—22no—
126C2×(C3⋊D3)⋊C3—22no—
127C2×(C3⋊D3)⋊C3—41no—
128C2×(C3⋊D3)⋊C3—41no—
129C2×(C3⋊D3)⋊C3—41no—
130C2×(C3⋊D3)⋊C3—41no—
131C2×(C3⋊D3)⋊C3C22⋊C414yescomplemented
132C4×H(3,𝔽3)—41no—
133#1084—22no—
134#1084—22no—
135(C3⋊Dic3)⋊C3—22no—
136(C3⋊Dic3)⋊C3—41no—
137C22×#67—91no—
138C22×#67—91no—
139C23×Dic3—91no—
140C22×D12—91no—
141C22×C4×D3—91no—
142C22×C4×D3—91no—
143C2×C3×C22⋊C4—91no—
144C2×C3×C22⋊C4—91no—
145C2×#217—91no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—91no—
149C2×(C2×D3)⋊C4—91no—
150C2×(C2×D3)⋊C4—91no—
151C2×(C2×D3)⋊C4—91no—
152C3×#95—91no—
153C3⋊#95—31no—
154C3⋊#95—31no—
155C3⋊#95—61no—
156C3⋊#95—91no—
157C3⋊#95—91no—
158C3⋊#95—91no—
159C23×C32—21no—
160C23×C32C22×D311yescharacteristic
161C23×C32C22×D311yescharacteristic
162C22×C3⋊D3—21no—
163C22×C3⋊D3—21no—
164C22×C3⋊D3—21no—
165C22×C3⋊D3—21no—
166C22×C3⋊D3—21no—
167C22×C3⋊D3—21no—
168C22×C3⋊D3—21no—
169C22×C3⋊D3—21no—
170C22×C3⋊D3—21no—
171C22×C3⋊D3—21no—
172C22×C3⋊D3C4×D312yes—
173C22×C3⋊D3C4×D312yescomplemented
174C22×C3⋊D3D1212yes—
175C22×C3⋊D3#6712yes—
176C22×C3×D3—32no—
177C22×C3×D3—32no—
178C22×C3×D3—32no—
179C22×C3×D3—32no—
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—
190C2×C32×C4—22no—
191C2×C32×C4—21no—
192C2×C32×C4—21no—
193C2×C32×C4—21no—
194C2×C32×C4—21no—
195C2×C32×C4—21no—
196C2×C32×C4—21no—
197C2×C32×C4—41no—
198C2×C32×C4—41no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3—21no—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3#6712yescomplemented
205C2×C3×Dic3—32no—
206C2×C3×Dic3—32no—
207C2×C3×Dic3—32no—
208C2×C3×Dic3—32no—
209C2×C3×Dic3—32no—
210C2×C3×Dic3—62no—
211C2×C3×Dic3—62no—
212C2×C3×Dic3—61no—
213C2×C3×Dic3—61no—
214C2×C3×Dic3—61no—
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—61no—
222C2×C3×Dic3—61no—
223C2×C3×Dic3—61no—
224C2×C3×Dic3—61no—
225C2×C3×Dic3—121no—
226C2×C3×Dic3—121no—
227C2×C3×Dic3—121no—
228C2×C3×Dic3—121no—
229#626—68no—
230#626—68no—
231#624—68no—
232D3×Dic3—68no—
233#386—271noSylow
234C2×H(3,𝔽3)C2×C22⋊C411yescharacteristic
235C2×H(3,𝔽3)C4×D411yescharacteristic
236C2×H(3,𝔽3)C4×D411yescharacteristic
237C2×H(3,𝔽3)#12011yescharacteristic
238C2×H(3,𝔽3)#12111yescharacteristic
239C2×H(3,𝔽3)#12111yescharacteristic
240C2×H(3,𝔽3)#12311yescharacteristic
241(C3⋊D3)⋊C3—24no—
242(C3⋊D3)⋊C3—42no—
243C24×C3—91no—
244C24×C3—91no—
245C23×D3—31no—
246C23×D3—31no—
247C23×D3—91no—
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—94no—
258C2×#67—94no—
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—31no—
269C22×Dic3—61no—
270C22×Dic3—61no—
271C22×Dic3—91no—
272C22×Dic3—91no—
273C22×Dic3—182no—
274C22×Dic3—182no—
275C22×Dic3—182no—
276C2×D12—94no—
277C2×D12—182no—
278C2×D12—182no—
279C2×C4×D3—182no—
280C2×C4×D3—182no—
281C2×C4×D3—182no—
282C2×C4×D3—182no—
283C2×C4×D3—182no—
284C2×C4×D3—182no—
285C3×C22⋊C4—182no—
286C3×C22⋊C4—182no—
287#217—182no—
288(C2×D3)⋊C4—62no—
289(C2×D3)⋊C4—62no—
290(C2×D3)⋊C4—182no—
291(C2×D3)⋊C4—182no—
292(C2×D3)⋊C4—182no—
293(C2×D3)⋊C4—182no—
294C22×C32—21no—
295C22×C32—21no—
296C22×C32—21no—
297C22×C32—21no—
298C22×C32—21no—
299C22×C32—21no—
300C22×C32—21no—
301C22×C32C2×C4×D311yescharacteristic
302C22×C32C2×C4×D311yescharacteristic
303C22×C32C2×D1211yescharacteristic
304C22×C32#23511yescharacteristic
305C22×C32D3×D411yescharacteristic
306C22×C32D3×D411yescharacteristic
307C22×C32D3×D411yescharacteristic
308C22×C32D3×D411yescharacteristic
309C22×C32D3×D411yescharacteristic
310C22×C32#23711yescharacteristic
311C22×C32#23711yescharacteristic
312C22×C32#23711yescharacteristic
313C22×C32C2×#6711yescharacteristic
314C22×C32C2×#6711yescharacteristic
315C2×C3⋊D3—22no—
316C2×C3⋊D3—22no—
317C2×C3⋊D3—22no—
318C2×C3⋊D3—22no—
319C2×C3⋊D3—22no—
320C2×C3⋊D3—22no—
321C2×C3⋊D3—22no—
322C2×C3⋊D3—22no—
323C2×C3⋊D3—22no—
324C2×C3⋊D3—41no—
325C2×C3⋊D3—41no—
326C2×C3⋊D3—41no—
327C2×C3⋊D3—41no—
328C2×C3⋊D3(C2×D3)⋊C414yescomplemented
329C2×C3×D3—34no—
330C2×C3×D3—62no—
331C2×C3×D3—62no—
332C2×C3×D3—62no—
333C2×C3×D3—62no—
334C2×C3×D3—62no—
335C2×C3×D3—62no—
336C2×C3×D3—62no—
337C2×C3×D3—62no—
338C2×C3×D3—62no—
339C2×C3×D3—121no—
340C2×C3×D3—121no—
341C2×C3×D3—121no—
342C2×C3×D3—121no—
343C32×C4—42no—
344C32×C4—41no—
345C32×C4—41no—
346C3⋊Dic3—22no—
347C3⋊Dic3—41no—
348C3×Dic3—62no—
349C3×Dic3—62no—
350C3×Dic3—62no—
351C3×Dic3—62no—
352C3×Dic3—62no—
353C3×Dic3—122no—
354C3×Dic3—122no—
355C3×Dic3—121no—
356C22×D4—271no—
357C23×C4—271no—
358C2×C22⋊C4—91no—
359C2×C22⋊C4—91no—
360C2×C22⋊C4—271no—
361#95—91no—
362#95—271no—
363H(3,𝔽3)#38611yescharacteristic, complemented, Sylow
364C23×C3—31no—
365C23×C3—31no—
366C23×C3—61no—
367C23×C3—92no—
368C23×C3—92no—
369C23×C3—92no—
370C23×C3—92no—
371C23×C3—181no—
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×C3C2×D3211yescharacteristic
382C22×D3—32no—
383C22×D3—32no—
384C22×D3—32no—
385C22×D3—32no—
386C22×D3—61no—
387C22×D3—61no—
388C22×D3—61no—
389C22×D3—61no—
390C22×D3—61no—
391C22×D3—61no—
392C22×D3—61no—
393C22×D3—61no—
394C22×D3—61no—
395C22×D3—61no—
396C22×D3—92no—
397C22×D3—92no—
398C22×D3—92no—
399C22×D3—92no—
400C22×D3—181no—
401C22×D3—181no—
402C22×D3—181no—
403C22×D3—181no—
404C22×D3—181no—
405C22×D3—181no—
406C22×D3—181no—
407C22×D3—181no—
408C22×D3—181no—
409C22×D3—181no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—61no—
414C2×C3×C4—61no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4—61no—
418C2×C3×C4—61no—
419C2×C3×C4—62no—
420C2×C3×C4—92no—
421C2×C3×C4—92no—
422C2×C3×C4—92no—
423C2×C3×C4—121no—
424C2×C3×C4—121no—
425C2×C3×C4—181no—
426C2×C3×C4—181no—
427C2×C3×C4—181no—
428C2×C3×C4—181no—
429C2×C3×C4—181no—
430C2×C3×C4—181no—
431C2×C3×C4—181no—
432C2×C3×C4—181no—
433C2×C3×C4—181no—
434#67—188no—
435#67—188no—
436C2×Dic3—32no—
437C2×Dic3—32no—
438C2×Dic3—32no—
439C2×Dic3—32no—
440C2×Dic3—32no—
441C2×Dic3—62no—
442C2×Dic3—62no—
443C2×Dic3—61no—
444C2×Dic3—61no—
445C2×Dic3—61no—
446C2×Dic3—61no—
447C2×Dic3—61no—
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—92no—
457C2×Dic3—121no—
458C2×Dic3—121no—
459C2×Dic3—121no—
460C2×Dic3—121no—
461C2×Dic3—181no—
462C2×Dic3—181no—
463C2×Dic3—181no—
464C2×Dic3—181no—
465C2×Dic3—181no—
466C2×Dic3—188no—
467D12—188no—
468C4×D3—188no—
469C4×D3—188no—
470C2×C32—21no—
471C2×C32—21no—
472C2×C32—21no—
473C2×C32—21no—
474C2×C32—21no—
475C2×C32—21no—
476C2×C32—21no—
477C2×C32D3×C22⋊C411yescharacteristic
478C2×C32#67⋊C411yescharacteristic
479C2×C32#67⋊C411yescharacteristic
480C2×C32#67⋊C411yescharacteristic
481C2×C32#88211yescharacteristic
482C2×C32#88311yescharacteristic
483C2×C32#88411yescharacteristic
484C2×C32#88611yescharacteristic
485C2×C32C2×(C2×D3)⋊C411yescharacteristic
486C2×C32C4×#6711yescharacteristic
487C2×C32#93711yescharacteristic
488C2×C32#93811yescharacteristic
489C2×C32#93911yescharacteristic
490C2×C32#93911yescharacteristic
491C3⋊D3—24no—
492C3⋊D3—42no—
493C3×D3—64no—
494C3×D3—122no—
495C24—91no—
496C24—91no—
497C2×D4—274no—
498C2×D4—542no—
499C2×D4—542no—
500C22×C4—91no—
501C22×C4—91no—
502C22×C4—91no—
503C22×C4—91no—
504C22×C4—542no—
505C22×C4—542no—
506C22×C4—542no—
507C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
508C22⋊C4—182no—
509C22⋊C4—182no—
510C22⋊C4—542no—
511C22×C3—31no—
512C22×C3—31no—
513C22×C3—31no—
514C22×C3—31no—
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—61no—
526C22×C3—61no—
527C22×C3—61no—
528C22×C3—61no—
529C22×C3—61no—
530C22×C3—61no—
531C22×C3—61no—
532C22×C3—94no—
533C22×C3—182no—
534C22×C3—182no—
535C22×C3—182no—
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#379511yescharacteristic
547C22×C3C4×D3211yescharacteristic
548C22×C3D3×D1211yescharacteristic
549C22×C3#380211yescharacteristic
550C22×C3#380511yescharacteristic
551C22×C3D3×#6711yescharacteristic
552C22×C3D3×#6711yescharacteristic
553C2×D3—34no—
554C2×D3—62no—
555C2×D3—62no—
556C2×D3—62no—
557C2×D3—62no—
558C2×D3—62no—
559C2×D3—62no—
560C2×D3—62no—
561C2×D3—62no—
562C2×D3—62no—
563C2×D3—94no—
564C2×D3—121no—
565C2×D3—121no—
566C2×D3—121no—
567C2×D3—121no—
568C2×D3—182no—
569C2×D3—182no—
570C2×D3—182no—
571C2×D3—182no—
572C2×D3—182no—
573C2×D3—182no—
574C2×D3—182no—
575C2×D3—182no—
576C2×D3—182no—
577C2×D3—361no—
578C2×D3—361no—
579C2×D3—361no—
580C2×D3—361no—
581C3×C4—41no—
582C3×C4—121no—
583C3×C4—121no—
584C3×C4—122no—
585C3×C4—182no—
586C3×C4—182no—
587C3×C4—182no—
588C3×C4—361no—
589Dic3—62no—
590Dic3—62no—
591Dic3—62no—
592Dic3—62no—
593Dic3—62no—
594Dic3—122no—
595Dic3—122no—
596Dic3—121no—
597Dic3—182no—
598Dic3—361no—
599C32—21no—
600C32#495611yescharacteristic, complemented
601C32#495811yescharacteristic, complemented
602C23—92no—
603C23—92no—
604C23—92no—
605C23—92no—
606C23—181no—
607C23—181no—
608C23—181no—
609C23—181no—
610C23—181no—
611C23—181no—
612C23—181no—
613C23—181no—
614C23—181no—
615C23—181no—
616C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
617D4—548no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—92no—
622C2×C4—92no—
623C2×C4—92no—
624C2×C4—181no—
625C2×C4—181no—
626C2×C4—181no—
627C2×C4—181no—
628C2×C4—181no—
629C2×C4—181no—
630C2×C4—181no—
631C2×C4—181no—
632C2×C4—181no—
633C2×C4—548no—
634C2×C3—31no—
635C2×C3—31no—
636C2×C3—31no—
637C2×C3—31no—
638C2×C3—31no—
639C2×C3—31no—
640C2×C3—31no—
641C2×C3—31no—
642C2×C3—31no—
643C2×C3—31no—
644C2×C3—31no—
645C2×C3—31no—
646C2×C3—31no—
647C2×C3—31no—
648C2×C3—61no—
649C2×C3—61no—
650C2×C3—61no—
651C2×C3—61no—
652C2×C3—61no—
653C2×C3—61no—
654C2×C3—61no—
655C2×C3—184no—
656C2×C3—362no—
657C2×C3#6387911yescharacteristic
658C2×C3#6388511yescharacteristic
659C2×C3#6389111yescharacteristic
660C2×C3#6390211yescharacteristic
661C2×C3D3×(C2×D3)⋊C411yescharacteristic
662C2×C3#6392211yescharacteristic
663C2×C3#6397011yescharacteristic
664D3—64no—
665D3—122no—
666D3—184no—
667D3—362no—
668C22—94no—
669C22—182no—
670C22—182no—
671C22—182no—
672C22—182no—
673C22—182no—
674C22—182no—
675C22—182no—
676C22—182no—
677C22—182no—
678C22—361no—
679C22—361no—
680C22—361no—
681C22—361no—
682C22#8864811yescharacteristic
683C22C4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
684C22#8865411yescharacteristic
685C22#8865511yescharacteristic
686C22#8867211yescharacteristic
687C22#8867611yescharacteristic
688C22#8867611yescharacteristic
689C4—41no—
690C4—182no—
691C4—182no—
692C4—182no—
693C4—361no—
694C3—31no—
695C3—31no—
696C3—61no—
697C3#1059136311yescharacteristic
698C2—184no—
699C2—362no—
700C2#1172112211yescharacteristic
701C2#1172112611yescharacteristic
702C2#1172113111yescharacteristic
703C2#1172113811yescharacteristic
704C2#1172116011yescharacteristic
705C2#1172116211yescharacteristic
706C2#1172131311yescharacteristic
subgroupG/H
centerC23C2×((C3⋊D3)⋊C3)⋊C2
commutatorC22×H(3,𝔽3)C22×C4
Frattini, socleC23×C3C2×D32
FittingC22×C4×H(3,𝔽3)C22
prime radicalC22×#6198C2
cosocleC23×H(3,𝔽3)C23
hypercenterC22×C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#386
LCSG ▷ C22×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. C22×((C3⋊D3)⋊C3)⋊C4C2semidirect
3. C2×#3752⋊C3C2semidirect
4. C2×#3752⋊C3C2semidirect
5. C2×#88450C2semidirect
6. #11720574C2semidirect
7. #11720334C2semidirect
19. C2×#6198C4semidirect
30. C2×#3752D3semidirect
31. C2×#3752D3semidirect
53. C22×(C3⋊D3)⋊C3C2×C4semidirect
63. C2×#1084C2×C4semidirect
64. C2×#1084D4semidirect
70. C2×(C3⋊Dic3)⋊C3D4semidirect
131. C2×(C3⋊D3)⋊C3C22⋊C4semidirect
173. C22×C3⋊D3C4×D3semidirect
204. C2×C3⋊Dic3#67semidirect
328. C2×C3⋊D3(C2×D3)⋊C4semidirect
363. H(3,𝔽3)#386semidirect
600. C32#4956semidirect
601. C32#4958semidirect

Maximal subgroups

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

subgroupindex
C22×#61982
C22×((C3⋊D3)⋊C3)⋊C42
C2×#3752⋊C32
C2×#884502
#117205742
#117203342
#105913643
#105912753