Finite Group Databasebeta

← C2×#13091668 #72269388

Subgroups — C2×#13091668 #72269388

Order 2916.

1042 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13091668C212yesmaximal, direct product factor
2C2×#10624936C211yesmaximal, characteristic, complemented
3C2×#4207⋊C3—31nomaximal
4C2×#4207⋊C3—31nomaximal
5C2×#4207⋊C3—31nomaximal
6C2×C3×#4207—31nomaximal
7C2×#92344C311yesmaximal, characteristic, complemented
8C2×#4184⋊C3—31nomaximal
9C2×#4184⋊C3—31nomaximal
10C2×#4184⋊C3—31nomaximal
11C2×#4183⋊C3—31nomaximal
12C2×#4183⋊C3—31nomaximal
13C2×#4183⋊C3—31nomaximal
14C2×C3×#733⋊C2—31nomaximal
15C2×C3×#733⋊C2—31nomaximal
16C2×C3×#4185—31nomaximal
17#10624936C2211yescharacteristic, complemented, Sylow
18C2×3−1+4D311yescharacteristic, complemented
19C2×3−1+4D311yescharacteristic, complemented
20C2×3−1+4D311yescharacteristic, complemented
21C2×C3×#737D311yescharacteristic, complemented
22#4207⋊C3—32no—
23#4207⋊C3—32no—
24#4207⋊C3—32no—
25C3×#4207—32no—
26C2×#6913—21no—
27C2×#6913—21no—
28C2×#6913—21no—
29C2×#6913—21no—
30C2×#6913—21no—
31C2×#6913—21no—
32C2×#6913—21no—
33C2×#6913—21no—
34C2×#6913—21no—
35C2×#6910D311yescharacteristic, complemented
36C2×#6910D311yescharacteristic, complemented
37C2×#6910D311yescharacteristic, complemented
38C2×#6909D311yescharacteristic, complemented
39C2×#6909D311yescharacteristic, complemented
40C2×#6909D311yescharacteristic, complemented
41C2×#6908—21no—
42C2×#6908—21no—
43C2×#6908—21no—
44C2×#6908—21no—
45C2×#6908C2×C311yescharacteristic, complemented
46C2×C3×#733D311yescharacteristic, complemented
47C2×C3×#733D311yescharacteristic, complemented
48C2×C3×#732D311yescharacteristic, complemented
49#92344C2×C312yescomplemented
50#4184⋊C3—32no—
51#4184⋊C3—32no—
52#4184⋊C3—32no—
53#4183⋊C3—32no—
54#4183⋊C3—32no—
55#4183⋊C3—32no—
56C3×#733⋊C2—32no—
57C3×#733⋊C2—32no—
58C3×#4185—32no—
59C2×#4207—31no—
60C2×#4207—31no—
61C2×#4207—31no—
62C2×#4207—31no—
63C2×#4207—31no—
64C2×#4207—31no—
65C2×#4207—31no—
66C2×#4207—31no—
67C2×#4207—31no—
68C2×#4207—31no—
69C2×#4207—31no—
70C2×#4207—31no—
71C2×C3⋊AGL(1,ℤ/9)—31no—
72C2×C3⋊AGL(1,ℤ/9)—31no—
73C2×C3⋊AGL(1,ℤ/9)—31no—
74C2×C3×C3⋊D9—31no—
75C2×C3×AGL(1,ℤ/9)—91no—
76C2×C3×AGL(1,ℤ/9)—91no—
77C2×C3×AGL(1,ℤ/9)—91no—
78C2×C3×AGL(1,ℤ/9)—91no—
79C2×C3×AGL(1,ℤ/9)—91no—
80C2×C3×AGL(1,ℤ/9)—91no—
81C2×C3×AGL(1,ℤ/9)—91no—
82C2×C3×AGL(1,ℤ/9)—91no—
83C2×C3×(C3⋊D3)⋊C3—91no—
84C2×C3×(C3⋊D3)⋊C3—91no—
85C2×C3×(C3⋊D3)⋊C3—91no—
86C2×C3×(C3⋊D3)⋊C3—91no—
87C2×C32×D9—91no—
88C2×#733⋊C2—31no—
89C2×#733⋊C2—31no—
90C2×#4185—31no—
91C2×#4184—31no—
92C2×#4184—31no—
93C2×#4184—31no—
94C2×#4183—31no—
95C2×#4183—31no—
96C2×#4183—31no—
973−1+4C2×D311yescharacteristic, complemented
983−1+4C2×D311yescharacteristic, complemented
993−1+4C2×D311yescharacteristic, complemented
100C3×#737C2×D311yescharacteristic, complemented
101#6913—21no—
102#6913—21no—
103#6913—21no—
104#6913—21no—
105#6913—21no—
106#6913—21no—
107#6913—21no—
108#6913—21no—
109#6913—21no—
110#6910C2×D311yescharacteristic, complemented
111#6910C2×D311yescharacteristic, complemented
112#6910C2×D311yescharacteristic, complemented
113#6909C2×D311yescharacteristic, complemented
114#6909C2×D311yescharacteristic, complemented
115#6909C2×D311yescharacteristic, complemented
116#6908—21no—
117#6908—21no—
118#6908—21no—
119#6908—21no—
120#6908C22×C311yescharacteristic, complemented
121C3×#733C2×D311yescharacteristic, complemented
122C3×#733C2×D311yescharacteristic, complemented
123C3×#732C2×D311yescharacteristic, complemented
124C2×#737—21no—
125C2×#737—21no—
126C2×#737—21no—
127C2×#737—21no—
128C2×#737—21no—
129C2×#737—21no—
130C2×#737—21no—
131C2×#737—21no—
132C2×#737—21no—
133C2×#737—21no—
134C2×#737—21no—
135C2×#737—21no—
136C2×#737—31no—
137C2×#737—31no—
138C2×#737—61no—
139C2×#737—61no—
140C2×#737—61no—
141C2×#737—61no—
142C2×#737—61no—
143C2×#737—61no—
144C2×#737—61no—
145C2×#737—61no—
146C2×#737—61no—
147C2×#737—61no—
148C2×#737—61no—
149C2×#737—61no—
150C2×#737—61no—
151C2×#737—61no—
152C2×#737—61no—
153C2×#737—61no—
154C2×#737C3×D311yescharacteristic, complemented
155C2×#737C3×D311yescharacteristic, complemented
156C2×#737C3×D311yescharacteristic, complemented
157C2×C3×3−1+2—21no—
158C2×C3×3−1+2—21no—
159C2×C3×3−1+2—21no—
160C2×C3×3−1+2—31no—
161C2×C3×3−1+2—61no—
162C2×C3×3−1+2—61no—
163C2×C3×3−1+2—61no—
164C2×C3×3−1+2—61no—
165C2×C3×3−1+2—61no—
166C2×C3×3−1+2C3⋊D311yescharacteristic
167C2×C3×3−1+2C3⋊D311yescharacteristic
168C2×C3×3−1+2C3⋊D311yescharacteristic
169C2×C3×3−1+2C3⋊D311yescharacteristic
170C2×C3×3−1+2C3⋊D311yescharacteristic
171C2×C3×3−1+2C3⋊D311yescharacteristic
172C2×C3×3−1+2C3⋊D311yescharacteristic
173C2×C3×3−1+2C3⋊D311yescharacteristic
174C2×C3×H(3,𝔽3)C3⋊D311yescharacteristic
175C2×C3×H(3,𝔽3)C3⋊D311yescharacteristic
176C2×C3×H(3,𝔽3)C3⋊D311yescharacteristic
177C2×C3×H(3,𝔽3)C3⋊D311yescharacteristic
178C2×C32×C9—21no—
179C2×C32×C9C3×D311yescharacteristic, complemented
180C2×C32×C9C3⋊D311yescharacteristic
181#4207—32no—
182#4207—32no—
183#4207—32no—
184#4207—32no—
185#4207—32no—
186#4207—32no—
187#4207—32no—
188#4207—32no—
189#4207—32no—
190#4207—32no—
191#4207—32no—
192#4207—32no—
193C3⋊AGL(1,ℤ/9)—32no—
194C3⋊AGL(1,ℤ/9)—32no—
195C3⋊AGL(1,ℤ/9)—32no—
196C3×C3⋊D9—32no—
197C3×AGL(1,ℤ/9)—92no—
198C3×AGL(1,ℤ/9)—92no—
199C3×AGL(1,ℤ/9)—92no—
200C3×AGL(1,ℤ/9)—92no—
201C3×AGL(1,ℤ/9)—92no—
202C3×AGL(1,ℤ/9)—92no—
203C3×AGL(1,ℤ/9)—92no—
204C3×AGL(1,ℤ/9)—92no—
205C3×(C3⋊D3)⋊C3—92no—
206C3×(C3⋊D3)⋊C3—92no—
207C3×(C3⋊D3)⋊C3—92no—
208C3×(C3⋊D3)⋊C3—92no—
209C32×D9—92no—
210C2×#733—21no—
211C2×#733—21no—
212C2×#733—21no—
213C2×#733—21no—
214C2×#733—21no—
215C2×#733—21no—
216C2×#733—21no—
217C2×#733—21no—
218C2×#733C3×D311yescharacteristic, complemented
219C2×#733C3×D311yescharacteristic, complemented
220C2×#732—21no—
221C2×#732—21no—
222C2×#732—21no—
223C2×#732—21no—
224C2×#732C3×D311yescharacteristic
225C2×#731—21no—
226C2×#731—21no—
227C2×#731—21no—
228C2×#731—21no—
229C2×#731—21no—
230C2×#731—21no—
231C2×#731—21no—
232C2×#731—21no—
233C2×#731—21no—
234C2×#731—21no—
235C2×#731—21no—
236C2×#731—21no—
237C2×#731C3×D311yescharacteristic, complemented
238C2×#731C3×D311yescharacteristic, complemented
239C2×#731C3×D311yescharacteristic, complemented
240C2×AΣL(1,𝔽27)—21no—
241C2×AΣL(1,𝔽27)—21no—
242C2×AΣL(1,𝔽27)—21no—
243C2×AΣL(1,𝔽27)—21no—
244C2×AΣL(1,𝔽27)—21no—
245C2×AΣL(1,𝔽27)—21no—
246C2×AΣL(1,𝔽27)—21no—
247C2×AΣL(1,𝔽27)—21no—
248C2×AΣL(1,𝔽27)—21no—
249C2×AΣL(1,𝔽27)—21no—
250C2×AΣL(1,𝔽27)—21no—
251C2×AΣL(1,𝔽27)—21no—
252C2×AΣL(1,𝔽27)C3×D311yescharacteristic, complemented
253C2×AΣL(1,𝔽27)C3×D311yescharacteristic, complemented
254C2×AΣL(1,𝔽27)C3×D311yescharacteristic, complemented
255#733⋊C2—32no—
256#733⋊C2—32no—
257#4185—32no—
258#4184—32no—
259#4184—32no—
260#4184—32no—
261#4183—32no—
262#4183—32no—
263#4183—32no—
264C2×C3×C3⋊D3—91no—
265C2×C3×C3⋊D3—91no—
266C2×C3×C3⋊D3—91no—
267C2×C3×C3⋊D3—91no—
268C2×C32×D3—271no—
269C2×C3⋊D9—31no—
270C2×C3⋊D9—31no—
271C2×C3⋊D9—31no—
272C2×C3⋊D9—31no—
273C2×AGL(1,ℤ/9)—91no—
274C2×AGL(1,ℤ/9)—91no—
275C2×AGL(1,ℤ/9)—91no—
276C2×AGL(1,ℤ/9)—91no—
277C2×AGL(1,ℤ/9)—91no—
278C2×AGL(1,ℤ/9)—91no—
279C2×AGL(1,ℤ/9)—91no—
280C2×AGL(1,ℤ/9)—91no—
281C2×AGL(1,ℤ/9)—91no—
282C2×AGL(1,ℤ/9)—91no—
283C2×AGL(1,ℤ/9)—91no—
284C2×AGL(1,ℤ/9)—91no—
285C2×AGL(1,ℤ/9)—91no—
286C2×AGL(1,ℤ/9)—91no—
287C2×AGL(1,ℤ/9)—91no—
288C2×AGL(1,ℤ/9)—91no—
289C2×AGL(1,ℤ/9)—91no—
290C2×AGL(1,ℤ/9)—91no—
291C2×AGL(1,ℤ/9)—91no—
292C2×AGL(1,ℤ/9)—91no—
293C2×AGL(1,ℤ/9)—91no—
294C2×AGL(1,ℤ/9)—91no—
295C2×AGL(1,ℤ/9)—91no—
296C2×AGL(1,ℤ/9)—91no—
297C2×(C3⋊D3)⋊C3—91no—
298C2×(C3⋊D3)⋊C3—91no—
299C2×(C3⋊D3)⋊C3—91no—
300C2×(C3⋊D3)⋊C3—91no—
301C2×(C3⋊D3)⋊C3—91no—
302C2×(C3⋊D3)⋊C3—91no—
303C2×(C3⋊D3)⋊C3—91no—
304C2×(C3⋊D3)⋊C3—91no—
305C2×(C3⋊D3)⋊C3—91no—
306C2×(C3⋊D3)⋊C3—91no—
307C2×(C3⋊D3)⋊C3—91no—
308C2×(C3⋊D3)⋊C3—91no—
309C2×C3×D9—91no—
310C2×C3×D9—91no—
311C2×C3×D9—91no—
312C2×C3×D9—91no—
313C2×C3×D9—91no—
314C2×C3×D9—91no—
315C2×C3×D9—91no—
316C2×C3×D9—91no—
317C2×C3×D9—91no—
318C2×C3×D9—91no—
319C2×C3×D9—91no—
320C2×C3×D9—91no—
321#737—21no—
322#737—21no—
323#737—21no—
324#737—21no—
325#737—21no—
326#737—21no—
327#737—21no—
328#737—21no—
329#737—21no—
330#737—21no—
331#737—21no—
332#737—21no—
333#737—31no—
334#737—31no—
335#737—61no—
336#737—61no—
337#737—61no—
338#737—61no—
339#737—61no—
340#737—61no—
341#737—61no—
342#737—61no—
343#737—61no—
344#737—61no—
345#737—61no—
346#737—61no—
347#737—61no—
348#737—61no—
349#737—61no—
350#737—61no—
351#737C2×C3×D311yescharacteristic, complemented
352#737C2×C3×D311yescharacteristic, complemented
353#737C2×C3×D311yescharacteristic, complemented
354C3×3−1+2—21no—
355C3×3−1+2—21no—
356C3×3−1+2—21no—
357C3×3−1+2—31no—
358C3×3−1+2—61no—
359C3×3−1+2—61no—
360C3×3−1+2—61no—
361C3×3−1+2—61no—
362C3×3−1+2—61no—
363C3×3−1+2C2×C3⋊D311yescharacteristic
364C3×3−1+2C2×C3⋊D311yescharacteristic
365C3×3−1+2C2×C3⋊D311yescharacteristic
366C3×3−1+2C2×C3⋊D311yescharacteristic
367C3×3−1+2C2×C3⋊D311yescharacteristic
368C3×3−1+2C2×C3⋊D311yescharacteristic
369C3×3−1+2C2×C3⋊D311yescharacteristic
370C3×3−1+2C2×C3⋊D311yescharacteristic
371C3×H(3,𝔽3)C2×C3⋊D311yescharacteristic
372C3×H(3,𝔽3)C2×C3⋊D311yescharacteristic
373C3×H(3,𝔽3)C2×C3⋊D311yescharacteristic
374C3×H(3,𝔽3)C2×C3⋊D311yescharacteristic
375C32×C9—21no—
376C32×C9C2×C3×D311yescharacteristic, complemented
377C32×C9C2×C3⋊D311yescharacteristic
378#733—21no—
379#733—21no—
380#733—21no—
381#733—21no—
382#733—21no—
383#733—21no—
384#733—21no—
385#733—21no—
386#733C2×C3×D311yescharacteristic, complemented
387#733C2×C3×D311yescharacteristic, complemented
388#732—21no—
389#732—21no—
390#732—21no—
391#732—21no—
392#732C2×C3×D311yescharacteristic
393#731—21no—
394#731—21no—
395#731—21no—
396#731—21no—
397#731—21no—
398#731—21no—
399#731—21no—
400#731—21no—
401#731—21no—
402#731—21no—
403#731—21no—
404#731—21no—
405#731C2×C3×D311yescharacteristic, complemented
406#731C2×C3×D311yescharacteristic, complemented
407#731C2×C3×D311yescharacteristic, complemented
408AΣL(1,𝔽27)—21no—
409AΣL(1,𝔽27)—21no—
410AΣL(1,𝔽27)—21no—
411AΣL(1,𝔽27)—21no—
412AΣL(1,𝔽27)—21no—
413AΣL(1,𝔽27)—21no—
414AΣL(1,𝔽27)—21no—
415AΣL(1,𝔽27)—21no—
416AΣL(1,𝔽27)—21no—
417AΣL(1,𝔽27)—21no—
418AΣL(1,𝔽27)—21no—
419AΣL(1,𝔽27)—21no—
420AΣL(1,𝔽27)C2×C3×D311yescharacteristic, complemented
421AΣL(1,𝔽27)C2×C3×D311yescharacteristic, complemented
422AΣL(1,𝔽27)C2×C3×D311yescharacteristic, complemented
423C2×C33—21no—
424C2×C33—31no—
425C2×C33—61no—
426C2×C33—61no—
427C2×C33C3×C3⋊D311yescharacteristic
428C2×C33C3⋊(C3⋊D3)11yescharacteristic
429C3×C3⋊D3—92no—
430C3×C3⋊D3—92no—
431C3×C3⋊D3—92no—
432C3×C3⋊D3—92no—
433C32×D3—272no—
434C2×3−1+2—21no—
435C2×3−1+2—21no—
436C2×3−1+2—21no—
437C2×3−1+2—21no—
438C2×3−1+2—21no—
439C2×3−1+2—21no—
440C2×3−1+2—21no—
441C2×3−1+2—21no—
442C2×3−1+2—21no—
443C2×3−1+2—31no—
444C2×3−1+2—31no—
445C2×3−1+2—31no—
446C2×3−1+2—31no—
447C2×3−1+2—31no—
448C2×3−1+2—31no—
449C2×3−1+2—61no—
450C2×3−1+2—61no—
451C2×3−1+2—61no—
452C2×3−1+2—61no—
453C2×3−1+2—61no—
454C2×3−1+2—61no—
455C2×3−1+2—61no—
456C2×3−1+2—61no—
457C2×3−1+2—61no—
458C2×3−1+2—61no—
459C2×3−1+2—61no—
460C2×3−1+2—61no—
461C2×3−1+2—61no—
462C2×3−1+2—61no—
463C2×3−1+2—61no—
464C2×3−1+2—62no—
465C2×3−1+2—61no—
466C2×3−1+2—61no—
467C2×3−1+2—61no—
468C2×3−1+2—61no—
469C2×3−1+2—61no—
470C2×3−1+2—61no—
471C2×3−1+2—61no—
472C2×3−1+2—61no—
473C2×3−1+2—61no—
474C2×3−1+2—61no—
475C2×3−1+2—61no—
476C2×3−1+2—61no—
477C2×3−1+2—61no—
478C2×3−1+2—61no—
479C2×3−1+2—61no—
480C2×3−1+2—61no—
481C2×3−1+2—61no—
482C2×3−1+2—61no—
483C2×3−1+2—61no—
484C2×3−1+2—61no—
485C2×3−1+2—61no—
486C2×3−1+2—61no—
487C2×3−1+2—61no—
488C2×3−1+2—61no—
489C2×3−1+2—61no—
490C2×3−1+2—61no—
491C2×3−1+2—61no—
492C2×3−1+2—61no—
493C2×3−1+2#27211yescharacteristic
494C2×3−1+2#27211yescharacteristic
495C2×3−1+2#27211yescharacteristic
496C2×3−1+2C3×C3⋊D311yescharacteristic
497C2×3−1+2C3×C3⋊D311yescharacteristic
498C2×3−1+2C3×C3⋊D311yescharacteristic
499C2×3−1+2C3×C3⋊D311yescharacteristic
500C2×3−1+2C3×C3⋊D311yescharacteristic
501C2×3−1+2C3×C3⋊D311yescharacteristic
502C2×H(3,𝔽3)—21no—
503C2×H(3,𝔽3)—21no—
504C2×H(3,𝔽3)—21no—
505C2×H(3,𝔽3)—31no—
506C2×H(3,𝔽3)—31no—
507C2×H(3,𝔽3)—31no—
508C2×H(3,𝔽3)—61no—
509C2×H(3,𝔽3)—61no—
510C2×H(3,𝔽3)—61no—
511C2×H(3,𝔽3)—61no—
512C2×H(3,𝔽3)—61no—
513C2×H(3,𝔽3)—61no—
514C2×H(3,𝔽3)C3×C3⋊D311yescharacteristic
515C2×H(3,𝔽3)C3×C3⋊D311yescharacteristic
516C2×H(3,𝔽3)C3×C3⋊D311yescharacteristic
517C2×C3×C9—21no—
518C2×C3×C9—21no—
519C2×C3×C9—21no—
520C2×C3×C9—31no—
521C2×C3×C9—31no—
522C2×C3×C9—31no—
523C2×C3×C9—31no—
524C2×C3×C9—31no—
525C2×C3×C9—31no—
526C2×C3×C9—61no—
527C2×C3×C9—61no—
528C2×C3×C9—61no—
529C2×C3×C9—61no—
530C2×C3×C9—61no—
531C2×C3×C9—61no—
532C2×C3×C9—61no—
533C2×C3×C9—61no—
534C2×C3×C9—61no—
535C2×C3×C9—61no—
536C2×C3×C9—61no—
537C2×C3×C9—61no—
538C2×C3×C9—61no—
539C2×C3×C9—61no—
540C2×C3×C9—61no—
541C2×C3×C9—61no—
542C2×C3×C9—61no—
543C2×C3×C9—61no—
544C2×C3×C9—61no—
545C2×C3×C9—61no—
546C2×C3×C9—61no—
547C2×C3×C9—61no—
548C2×C3×C9—61no—
549C2×C3×C9C3×C3⋊D311yescharacteristic
550C2×C3×C9C3×C3⋊D311yescharacteristic
551C2×C3×C9C3×C3⋊D311yescharacteristic
552C3⋊D9—32no—
553C3⋊D9—32no—
554C3⋊D9—32no—
555C3⋊D9—32no—
556AGL(1,ℤ/9)—92no—
557AGL(1,ℤ/9)—92no—
558AGL(1,ℤ/9)—92no—
559AGL(1,ℤ/9)—92no—
560AGL(1,ℤ/9)—92no—
561AGL(1,ℤ/9)—92no—
562AGL(1,ℤ/9)—92no—
563AGL(1,ℤ/9)—92no—
564AGL(1,ℤ/9)—92no—
565AGL(1,ℤ/9)—92no—
566AGL(1,ℤ/9)—92no—
567AGL(1,ℤ/9)—92no—
568AGL(1,ℤ/9)—92no—
569AGL(1,ℤ/9)—92no—
570AGL(1,ℤ/9)—92no—
571AGL(1,ℤ/9)—92no—
572AGL(1,ℤ/9)—92no—
573AGL(1,ℤ/9)—92no—
574AGL(1,ℤ/9)—92no—
575AGL(1,ℤ/9)—92no—
576AGL(1,ℤ/9)—92no—
577AGL(1,ℤ/9)—92no—
578AGL(1,ℤ/9)—92no—
579AGL(1,ℤ/9)—92no—
580(C3⋊D3)⋊C3—92no—
581(C3⋊D3)⋊C3—92no—
582(C3⋊D3)⋊C3—92no—
583(C3⋊D3)⋊C3—92no—
584(C3⋊D3)⋊C3—92no—
585(C3⋊D3)⋊C3—92no—
586(C3⋊D3)⋊C3—92no—
587(C3⋊D3)⋊C3—92no—
588(C3⋊D3)⋊C3—92no—
589(C3⋊D3)⋊C3—92no—
590(C3⋊D3)⋊C3—92no—
591(C3⋊D3)⋊C3—92no—
592C3×D9—92no—
593C3×D9—92no—
594C3×D9—92no—
595C3×D9—92no—
596C3×D9—92no—
597C3×D9—92no—
598C3×D9—92no—
599C3×D9—92no—
600C3×D9—92no—
601C3×D9—92no—
602C3×D9—92no—
603C3×D9—92no—
604C22×C32—811no—
605C2×C3⋊D3—91no—
606C2×C3⋊D3—91no—
607C2×C3⋊D3—91no—
608C2×C3⋊D3—91no—
609C2×C3×D3—271no—
610C2×C3×D3—271no—
611C2×C3×D3—271no—
612C2×C3×D3—271no—
613C2×C3×D3—811no—
614C2×C3×D3—811no—
615C2×C3×D3—811no—
616C2×C3×D3—811no—
617C2×D9—91no—
618C2×D9—91no—
619C2×D9—91no—
620C2×D9—91no—
621C2×D9—91no—
622C2×D9—91no—
623C2×D9—91no—
624C2×D9—91no—
625C2×D9—91no—
626C33—21no—
627C33—31no—
628C33—61no—
629C33—61no—
630C33C2×C3×C3⋊D311yescharacteristic
631C33C2×C3⋊(C3⋊D3)11yescharacteristic
6323−1+2—21no—
6333−1+2—21no—
6343−1+2—21no—
6353−1+2—21no—
6363−1+2—21no—
6373−1+2—21no—
6383−1+2—21no—
6393−1+2—21no—
6403−1+2—21no—
6413−1+2—31no—
6423−1+2—31no—
6433−1+2—31no—
6443−1+2—31no—
6453−1+2—31no—
6463−1+2—31no—
6473−1+2—61no—
6483−1+2—61no—
6493−1+2—61no—
6503−1+2—61no—
6513−1+2—61no—
6523−1+2—61no—
6533−1+2—61no—
6543−1+2—61no—
6553−1+2—61no—
6563−1+2—61no—
6573−1+2—61no—
6583−1+2—61no—
6593−1+2—61no—
6603−1+2—61no—
6613−1+2—61no—
6623−1+2—62no—
6633−1+2—61no—
6643−1+2—61no—
6653−1+2—61no—
6663−1+2—61no—
6673−1+2—61no—
6683−1+2—61no—
6693−1+2—61no—
6703−1+2—61no—
6713−1+2—61no—
6723−1+2—61no—
6733−1+2—61no—
6743−1+2—61no—
6753−1+2—61no—
6763−1+2—61no—
6773−1+2—61no—
6783−1+2—61no—
6793−1+2—61no—
6803−1+2—61no—
6813−1+2—61no—
6823−1+2—61no—
6833−1+2—61no—
6843−1+2—61no—
6853−1+2—61no—
6863−1+2—61no—
6873−1+2—61no—
6883−1+2—61no—
6893−1+2—61no—
6903−1+2—61no—
6913−1+2C2×#27211yescharacteristic
6923−1+2C2×#27211yescharacteristic
6933−1+2C2×#27211yescharacteristic
6943−1+2C2×C3×C3⋊D311yescharacteristic
6953−1+2C2×C3×C3⋊D311yescharacteristic
6963−1+2C2×C3×C3⋊D311yescharacteristic
6973−1+2C2×C3×C3⋊D311yescharacteristic
6983−1+2C2×C3×C3⋊D311yescharacteristic
6993−1+2C2×C3×C3⋊D311yescharacteristic
700H(3,𝔽3)—21no—
701H(3,𝔽3)—21no—
702H(3,𝔽3)—21no—
703H(3,𝔽3)—31no—
704H(3,𝔽3)—31no—
705H(3,𝔽3)—31no—
706H(3,𝔽3)—61no—
707H(3,𝔽3)—61no—
708H(3,𝔽3)—61no—
709H(3,𝔽3)—61no—
710H(3,𝔽3)—61no—
711H(3,𝔽3)—61no—
712H(3,𝔽3)C2×C3×C3⋊D311yescharacteristic
713H(3,𝔽3)C2×C3×C3⋊D311yescharacteristic
714H(3,𝔽3)C2×C3×C3⋊D311yescharacteristic
715C3×C9—21no—
716C3×C9—21no—
717C3×C9—21no—
718C3×C9—31no—
719C3×C9—31no—
720C3×C9—31no—
721C3×C9—31no—
722C3×C9—31no—
723C3×C9—31no—
724C3×C9—61no—
725C3×C9—61no—
726C3×C9—61no—
727C3×C9—61no—
728C3×C9—61no—
729C3×C9—61no—
730C3×C9—61no—
731C3×C9—61no—
732C3×C9—61no—
733C3×C9—61no—
734C3×C9—61no—
735C3×C9—61no—
736C3×C9—61no—
737C3×C9—61no—
738C3×C9—61no—
739C3×C9—61no—
740C3×C9—61no—
741C3×C9—61no—
742C3×C9—61no—
743C3×C9—61no—
744C3×C9—61no—
745C3×C9—61no—
746C3×C9—61no—
747C3×C9C2×C3×C3⋊D311yescharacteristic
748C3×C9C2×C3×C3⋊D311yescharacteristic
749C3×C9C2×C3×C3⋊D311yescharacteristic
750C2×C32—31no—
751C2×C32—61no—
752C2×C32—61no—
753C2×C32—61no—
754C2×C32—61no—
755C2×C32—61no—
756C2×C32—61no—
757C2×C32—61no—
758C2×C32—181no—
759C2×C32—181no—
760C2×C32—181no—
761C2×C32—271no—
762C2×C32—541no—
763C2×C32—541no—
764C2×C32—812no—
765C2×C32C3⋊#27211yescharacteristic
766C2×C32C3⋊#27211yescharacteristic
767C2×C32C3⋊#27211yescharacteristic
768C2×C32C3×C3⋊(C3⋊D3)11yescharacteristic
769C3⋊D3—92no—
770C3⋊D3—92no—
771C3⋊D3—92no—
772C3⋊D3—92no—
773C3×D3—272no—
774C3×D3—272no—
775C3×D3—272no—
776C3×D3—272no—
777C3×D3—812no—
778C3×D3—812no—
779C3×D3—812no—
780C3×D3—812no—
781C2×C9—21no—
782C2×C9—21no—
783C2×C9—21no—
784C2×C9—21no—
785C2×C9—31no—
786C2×C9—31no—
787C2×C9—61no—
788C2×C9—61no—
789C2×C9—61no—
790C2×C9—61no—
791C2×C9—61no—
792C2×C9—61no—
793C2×C9—61no—
794C2×C9—61no—
795C2×C9—61no—
796C2×C9—61no—
797C2×C9—61no—
798C2×C9—61no—
799C2×C9—61no—
800C2×C9—61no—
801C2×C9C3×#27211yescharacteristic
802D9—92no—
803D9—92no—
804D9—92no—
805D9—92no—
806D9—92no—
807D9—92no—
808D9—92no—
809D9—92no—
810D9—92no—
811C22×C3—811no—
812C22×C3—811no—
813C22×C3—811no—
814C22×C3—811no—
815C2×D3—271no—
816C2×D3—811no—
817C2×D3—811no—
818C2×D3—811no—
819C2×D3—811no—
820C32—31no—
821C32—61no—
822C32—61no—
823C32—61no—
824C32—61no—
825C32—61no—
826C32—61no—
827C32—61no—
828C32—181no—
829C32—181no—
830C32—181no—
831C32—271no—
832C32—541no—
833C32—541no—
834C32C2×C3⋊#27211yescharacteristic
835C32C2×C3⋊#27211yescharacteristic
836C32C2×C3⋊#27211yescharacteristic
837C32C2×C3×C3⋊(C3⋊D3)11yescharacteristic
838C9—21no—
839C9—21no—
840C9—21no—
841C9—21no—
842C9—31no—
843C9—31no—
844C9—61no—
845C9—61no—
846C9—61no—
847C9—61no—
848C9—61no—
849C9—61no—
850C9—61no—
851C9—61no—
852C9—61no—
853C9—61no—
854C9—61no—
855C9—61no—
856C9—61no—
857C9—61no—
858C9C2×C3×#27211yescharacteristic
859C2×C3—31no—
860C2×C3—31no—
861C2×C3—61no—
862C2×C3—61no—
863C2×C3—91no—
864C2×C3—91no—
865C2×C3—181no—
866C2×C3—181no—
867C2×C3—181no—
868C2×C3—181no—
869C2×C3—181no—
870C2×C3—181no—
871C2×C3—812no—
872C2×C3—812no—
873C2×C3—812no—
874C2×C3—812no—
875C2×C3C3×C3⋊#27211yescharacteristic
876D3—272no—
877D3—812no—
878D3—812no—
879D3—812no—
880D3—812no—
881C22—811noSylow
882C3—31no—
883C3—31no—
884C3—61no—
885C3—61no—
886C3—91no—
887C3—91no—
888C3—181no—
889C3—181no—
890C3—181no—
891C3—181no—
892C3—181no—
893C3—181no—
894C3C2×C3×C3⋊#27211yescharacteristic
895C2—812no—
896C2#1309166811yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#13091668
commutator, cosocle, hypocenter#6908C22×C3
FrattiniC32C2×C3×C3⋊(C3⋊D3)
FittingC2×#10624936C2
socleC2×C3C3×C3⋊#272
LCSG ▷ #6908
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #13091668C2direct (N × H)
2. C2×#10624936C2semidirect
7. C2×#92344C3semidirect
17. #10624936C22semidirect
18. C2×3−1+4D3semidirect
19. C2×3−1+4D3semidirect
20. C2×3−1+4D3semidirect
21. C2×C3×#737D3semidirect
35. C2×#6910D3semidirect
36. C2×#6910D3semidirect
37. C2×#6910D3semidirect
38. C2×#6909D3semidirect
39. C2×#6909D3semidirect
40. C2×#6909D3semidirect
45. C2×#6908C2×C3semidirect
46. C2×C3×#733D3semidirect
47. C2×C3×#733D3semidirect
48. C2×C3×#732D3semidirect
49. #92344C2×C3semidirect
97. 3−1+4C2×D3semidirect
98. 3−1+4C2×D3semidirect
99. 3−1+4C2×D3semidirect
100. C3×#737C2×D3semidirect
110. #6910C2×D3semidirect
111. #6910C2×D3semidirect
112. #6910C2×D3semidirect
113. #6909C2×D3semidirect
114. #6909C2×D3semidirect
115. #6909C2×D3semidirect
120. #6908C22×C3semidirect
121. C3×#733C2×D3semidirect
122. C3×#733C2×D3semidirect
123. C3×#732C2×D3semidirect
154. C2×#737C3×D3semidirect
155. C2×#737C3×D3semidirect
156. C2×#737C3×D3semidirect
179. C2×C32×C9C3×D3semidirect
218. C2×#733C3×D3semidirect
219. C2×#733C3×D3semidirect
237. C2×#731C3×D3semidirect
238. C2×#731C3×D3semidirect
239. C2×#731C3×D3semidirect
252. C2×AΣL(1,𝔽27)C3×D3semidirect
253. C2×AΣL(1,𝔽27)C3×D3semidirect
254. C2×AΣL(1,𝔽27)C3×D3semidirect
351. #737C2×C3×D3semidirect
352. #737C2×C3×D3semidirect
353. #737C2×C3×D3semidirect
376. C32×C9C2×C3×D3semidirect
386. #733C2×C3×D3semidirect
387. #733C2×C3×D3semidirect
405. #731C2×C3×D3semidirect
406. #731C2×C3×D3semidirect
407. #731C2×C3×D3semidirect
420. AΣL(1,𝔽27)C2×C3×D3semidirect
421. AΣL(1,𝔽27)C2×C3×D3semidirect
422. AΣL(1,𝔽27)C2×C3×D3semidirect
896. C2#13091668direct (N × H)

Maximal subgroups

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

subgroupindex
#130916682
C2×#106249362
C2×#4207⋊C33
C2×C3×#42073
C2×#923443
C2×#4184⋊C33
C2×#4183⋊C33
C2×C3×#733⋊C23
C2×C3×#41853