Finite Group Databasebeta

← C2×#13091046 #72254030

Subgroups — C2×#13091046 #72254030

Order 2916.

872 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 872 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13091046C212yesmaximal, direct product factor
2C2×#10624731C211yesmaximal, characteristic, complemented
3C2×C32×C3⋊D9—31nomaximal
4C2×C3×#4184—31nomaximal
5C2×C3×#4184—31nomaximal
6C2×C3×#4184—31nomaximal
7C2×C3×#4184—31nomaximal
8C2×C3×#4184—31nomaximal
9C2×C3×#4184—31nomaximal
10C2×C3×#4184—31nomaximal
11C2×C3×#4184—31nomaximal
12C2×C3×#4184—31nomaximal
13C2×#92302—31nomaximal
14C2×#92302—31nomaximal
15C2×#92300—31nomaximal
16#10624731C2211yescharacteristic, complemented, Sylow
17C2×C33×C9D311yescharacteristic, complemented
18C32×C3⋊D9—32no—
19C2×C3×#731D311yescharacteristic, complemented
20C2×C3×#731D311yescharacteristic, complemented
21C2×C3×#731D311yescharacteristic, complemented
22C2×C3×#731D311yescharacteristic, complemented
23C2×C3×#731D311yescharacteristic, complemented
24C2×C3×#731D311yescharacteristic, complemented
25C2×C3×#731D311yescharacteristic, complemented
26C2×C3×#731D311yescharacteristic, complemented
27C2×C3×#731D311yescharacteristic, complemented
28C2×#6891D311yescharacteristic, complemented
29C2×#6891D311yescharacteristic, complemented
30C2×C32⋊H(3,𝔽3)D311yescharacteristic
31C3×#4184—32no—
32C3×#4184—32no—
33C3×#4184—32no—
34C3×#4184—32no—
35C3×#4184—32no—
36C3×#4184—32no—
37C3×#4184—32no—
38C3×#4184—32no—
39C3×#4184—32no—
40#92302—32no—
41#92302—32no—
42#92300—32no—
43C2×C32×C3⋊D3—91no—
44C2×C3⋊#272—31no—
45C2×C3×C3⋊D9—31no—
46C2×C3×C3⋊D9—31no—
47C2×C3×C3⋊D9—31no—
48C2×C3×C3⋊D9—31no—
49C2×C3×AGL(1,ℤ/9)—91no—
50C2×C3×AGL(1,ℤ/9)—91no—
51C2×C3×AGL(1,ℤ/9)—91no—
52C2×C3×AGL(1,ℤ/9)—91no—
53C2×C3×AGL(1,ℤ/9)—91no—
54C2×C3×AGL(1,ℤ/9)—91no—
55C2×C3×(C3⋊D3)⋊C3—91no—
56C2×C3×(C3⋊D3)⋊C3—91no—
57C2×C3×(C3⋊D3)⋊C3—91no—
58C2×C32×D9—91no—
59C2×C32×D9—91no—
60C2×C32×D9—91no—
61C2×#4184—31no—
62C2×#4184—31no—
63C2×#4184—31no—
64C2×#4184—31no—
65C2×#4184—31no—
66C2×#4184—31no—
67C2×#4184—31no—
68C2×#4184—31no—
69C2×#4184—31no—
70C2×#4181—31no—
71C2×#4181—31no—
72C33×C9C2×D311yescharacteristic, complemented
73C3×#731C2×D311yescharacteristic, complemented
74C3×#731C2×D311yescharacteristic, complemented
75C3×#731C2×D311yescharacteristic, complemented
76C3×#731C2×D311yescharacteristic, complemented
77C3×#731C2×D311yescharacteristic, complemented
78C3×#731C2×D311yescharacteristic, complemented
79C3×#731C2×D311yescharacteristic, complemented
80C3×#731C2×D311yescharacteristic, complemented
81C3×#731C2×D311yescharacteristic, complemented
82#6891C2×D311yescharacteristic, complemented
83#6891C2×D311yescharacteristic, complemented
84C32⋊H(3,𝔽3)C2×D311yescharacteristic
85C2×C34C3⋊D311yescharacteristic
86C32×C3⋊D3—92no—
87C2×C3×3−1+2C3⋊D311yescharacteristic
88C2×C3×3−1+2C3⋊D311yescharacteristic
89C2×C3×3−1+2C3⋊D311yescharacteristic
90C2×C3×3−1+2C3⋊D311yescharacteristic
91C2×C3×3−1+2C3⋊D311yescharacteristic
92C2×C3×3−1+2C3⋊D311yescharacteristic
93C2×C3×H(3,𝔽3)—31no—
94C2×C3×H(3,𝔽3)—61no—
95C2×C3×H(3,𝔽3)C3⋊D311yescharacteristic
96C2×C3×H(3,𝔽3)C3⋊D311yescharacteristic
97C2×C3×H(3,𝔽3)C3⋊D311yescharacteristic
98C2×C32×C9—31no—
99C2×C32×C9—61no—
100C2×C32×C9—61no—
101C2×C32×C9—61no—
102C2×C32×C9—61no—
103C2×C32×C9—61no—
104C2×C32×C9—61no—
105C2×C32×C9—61no—
106C2×C32×C9C3⋊D311yescharacteristic
107C2×C32×C9C3⋊D311yescharacteristic
108C2×C32×C9C3⋊D311yescharacteristic
109C3⋊#272—32no—
110C3×C3⋊D9—32no—
111C3×C3⋊D9—32no—
112C3×C3⋊D9—32no—
113C3×C3⋊D9—32no—
114C3×AGL(1,ℤ/9)—92no—
115C3×AGL(1,ℤ/9)—92no—
116C3×AGL(1,ℤ/9)—92no—
117C3×AGL(1,ℤ/9)—92no—
118C3×AGL(1,ℤ/9)—92no—
119C3×AGL(1,ℤ/9)—92no—
120C3×(C3⋊D3)⋊C3—92no—
121C3×(C3⋊D3)⋊C3—92no—
122C3×(C3⋊D3)⋊C3—92no—
123C32×D9—92no—
124C32×D9—92no—
125C32×D9—92no—
126C2×#731—31no—
127C2×#731—31no—
128C2×#731—31no—
129C2×#731—61no—
130C2×#731—61no—
131C2×#731—61no—
132C2×#731—61no—
133C2×#731—61no—
134C2×#731—61no—
135C2×#731—61no—
136C2×#731—61no—
137C2×#731—61no—
138C2×#731—61no—
139C2×#731—61no—
140C2×#731—61no—
141C2×#731—61no—
142C2×#731—61no—
143C2×#731—61no—
144C2×C32⋊C9—31no—
145C2×C32⋊C9—31no—
146C2×C32⋊C9—61no—
147C2×C32⋊C9—61no—
148#4184—32no—
149#4184—32no—
150#4184—32no—
151#4184—32no—
152#4184—32no—
153#4184—32no—
154#4184—32no—
155#4184—32no—
156#4184—32no—
157#4181—32no—
158#4181—32no—
159C2×C3×C3⋊D3—91no—
160C2×C3×C3⋊D3—91no—
161C2×C3×C3⋊D3—91no—
162C2×C3×C3⋊D3—91no—
163C2×C3×C3⋊D3—91no—
164C2×C3×C3⋊D3—91no—
165C2×C3×C3⋊D3—91no—
166C2×C32×D3—271no—
167C2×C32×D3—271no—
168C2×C32×D3—271no—
169C2×C32×D3—271no—
170C2×#272—271no—
171C2×#272—271no—
172C2×#272—271no—
173C2×C3⋊D9—31no—
174C2×AGL(1,ℤ/9)—91no—
175C2×AGL(1,ℤ/9)—91no—
176C2×AGL(1,ℤ/9)—91no—
177C2×AGL(1,ℤ/9)—91no—
178C2×AGL(1,ℤ/9)—91no—
179C2×AGL(1,ℤ/9)—91no—
180C2×AGL(1,ℤ/9)—91no—
181C2×AGL(1,ℤ/9)—91no—
182C2×AGL(1,ℤ/9)—91no—
183C2×AGL(1,ℤ/9)—91no—
184C2×AGL(1,ℤ/9)—91no—
185C2×AGL(1,ℤ/9)—91no—
186C2×AGL(1,ℤ/9)—91no—
187C2×AGL(1,ℤ/9)—91no—
188C2×AGL(1,ℤ/9)—91no—
189C2×AGL(1,ℤ/9)—91no—
190C2×AGL(1,ℤ/9)—91no—
191C2×AGL(1,ℤ/9)—91no—
192C2×(C3⋊D3)⋊C3—91no—
193C2×(C3⋊D3)⋊C3—91no—
194C2×(C3⋊D3)⋊C3—91no—
195C2×(C3⋊D3)⋊C3—91no—
196C2×(C3⋊D3)⋊C3—91no—
197C2×(C3⋊D3)⋊C3—91no—
198C2×(C3⋊D3)⋊C3—91no—
199C2×(C3⋊D3)⋊C3—91no—
200C2×(C3⋊D3)⋊C3—91no—
201C2×C3×D9—91no—
202C2×C3×D9—91no—
203C2×C3×D9—91no—
204C2×C3×D9—91no—
205C2×C3×D9—91no—
206C2×C3×D9—91no—
207C2×C3×D9—91no—
208C2×C3×D9—91no—
209C2×C3×D9—91no—
210C2×C3×D9—91no—
211C2×C3×D9—91no—
212C2×C3×D9—91no—
213C2×C3×D9—91no—
214C2×C3×D9—91no—
215C2×C3×D9—91no—
216C2×C3×D9—91no—
217C2×C3×D9—91no—
218C2×C3×D9—91no—
219C34C2×C3⋊D311yescharacteristic
220C3×3−1+2C2×C3⋊D311yescharacteristic
221C3×3−1+2C2×C3⋊D311yescharacteristic
222C3×3−1+2C2×C3⋊D311yescharacteristic
223C3×3−1+2C2×C3⋊D311yescharacteristic
224C3×3−1+2C2×C3⋊D311yescharacteristic
225C3×3−1+2C2×C3⋊D311yescharacteristic
226C3×H(3,𝔽3)—31no—
227C3×H(3,𝔽3)—61no—
228C3×H(3,𝔽3)C2×C3⋊D311yescharacteristic
229C3×H(3,𝔽3)C2×C3⋊D311yescharacteristic
230C3×H(3,𝔽3)C2×C3⋊D311yescharacteristic
231C32×C9—31no—
232C32×C9—61no—
233C32×C9—61no—
234C32×C9—61no—
235C32×C9—61no—
236C32×C9—61no—
237C32×C9—61no—
238C32×C9—61no—
239C32×C9C2×C3⋊D311yescharacteristic
240C32×C9C2×C3⋊D311yescharacteristic
241C32×C9C2×C3⋊D311yescharacteristic
242#731—31no—
243#731—31no—
244#731—31no—
245#731—61no—
246#731—61no—
247#731—61no—
248#731—61no—
249#731—61no—
250#731—61no—
251#731—61no—
252#731—61no—
253#731—61no—
254#731—61no—
255#731—61no—
256#731—61no—
257#731—61no—
258#731—61no—
259#731—61no—
260C32⋊C9—31no—
261C32⋊C9—31no—
262C32⋊C9—61no—
263C32⋊C9—61no—
264C2×C33—21no—
265C2×C33—31no—
266C2×C33—31no—
267C2×C33—31no—
268C2×C33—31no—
269C2×C33—61no—
270C2×C33—61no—
271C2×C33—61no—
272C2×C33—61no—
273C2×C33—61no—
274C2×C33—61no—
275C2×C33—61no—
276C2×C33—61no—
277C2×C33#27211yescharacteristic
278C2×C33C3⋊(C3⋊D3)11yescharacteristic
279C3×C3⋊D3—92no—
280C3×C3⋊D3—92no—
281C3×C3⋊D3—92no—
282C3×C3⋊D3—92no—
283C3×C3⋊D3—92no—
284C3×C3⋊D3—92no—
285C3×C3⋊D3—92no—
286C32×D3—272no—
287C32×D3—272no—
288C32×D3—272no—
289C32×D3—272no—
290C2×3−1+2—31no—
291C2×3−1+2—31no—
292C2×3−1+2—31no—
293C2×3−1+2—31no—
294C2×3−1+2—31no—
295C2×3−1+2—31no—
296C2×3−1+2—31no—
297C2×3−1+2—61no—
298C2×3−1+2—61no—
299C2×3−1+2—61no—
300C2×3−1+2—61no—
301C2×3−1+2—61no—
302C2×3−1+2—61no—
303C2×3−1+2—61no—
304C2×3−1+2—61no—
305C2×3−1+2—61no—
306C2×3−1+2—61no—
307C2×3−1+2—61no—
308C2×H(3,𝔽3)—31no—
309C2×H(3,𝔽3)—31no—
310C2×H(3,𝔽3)—31no—
311C2×H(3,𝔽3)—31no—
312C2×H(3,𝔽3)—61no—
313C2×H(3,𝔽3)—61no—
314C2×H(3,𝔽3)—61no—
315C2×H(3,𝔽3)—61no—
316C2×H(3,𝔽3)—61no—
317C2×H(3,𝔽3)—91no—
318C2×H(3,𝔽3)—181no—
319C2×H(3,𝔽3)—181no—
320C2×H(3,𝔽3)—181no—
321C2×H(3,𝔽3)—181no—
322C2×H(3,𝔽3)—181no—
323C2×C3×C9—21no—
324C2×C3×C9—21no—
325C2×C3×C9—21no—
326C2×C3×C9—31no—
327C2×C3×C9—31no—
328C2×C3×C9—31no—
329C2×C3×C9—31no—
330C2×C3×C9—61no—
331C2×C3×C9—61no—
332C2×C3×C9—61no—
333C2×C3×C9—61no—
334C2×C3×C9—61no—
335C2×C3×C9—61no—
336C2×C3×C9—61no—
337C2×C3×C9—61no—
338C2×C3×C9—61no—
339C2×C3×C9—61no—
340C2×C3×C9—63no—
341C2×C3×C9—61no—
342C2×C3×C9—61no—
343C2×C3×C9—61no—
344C2×C3×C9—61no—
345C2×C3×C9—61no—
346C2×C3×C9—61no—
347C2×C3×C9—61no—
348C2×C3×C9—61no—
349C2×C3×C9—61no—
350C2×C3×C9—61no—
351C2×C3×C9—61no—
352C2×C3×C9—61no—
353C2×C3×C9#27211yescharacteristic, complemented
354C2×C3×C9#27211yescharacteristic, complemented
355C2×C3×C9#27211yescharacteristic, complemented
356#272—272no—
357#272—272no—
358#272—272no—
359C3⋊D9—32no—
360AGL(1,ℤ/9)—92no—
361AGL(1,ℤ/9)—92no—
362AGL(1,ℤ/9)—92no—
363AGL(1,ℤ/9)—92no—
364AGL(1,ℤ/9)—92no—
365AGL(1,ℤ/9)—92no—
366AGL(1,ℤ/9)—92no—
367AGL(1,ℤ/9)—92no—
368AGL(1,ℤ/9)—92no—
369AGL(1,ℤ/9)—92no—
370AGL(1,ℤ/9)—92no—
371AGL(1,ℤ/9)—92no—
372AGL(1,ℤ/9)—92no—
373AGL(1,ℤ/9)—92no—
374AGL(1,ℤ/9)—92no—
375AGL(1,ℤ/9)—92no—
376AGL(1,ℤ/9)—92no—
377AGL(1,ℤ/9)—92no—
378(C3⋊D3)⋊C3—92no—
379(C3⋊D3)⋊C3—92no—
380(C3⋊D3)⋊C3—92no—
381(C3⋊D3)⋊C3—92no—
382(C3⋊D3)⋊C3—92no—
383(C3⋊D3)⋊C3—92no—
384(C3⋊D3)⋊C3—92no—
385(C3⋊D3)⋊C3—92no—
386(C3⋊D3)⋊C3—92no—
387C3×D9—92no—
388C3×D9—92no—
389C3×D9—92no—
390C3×D9—92no—
391C3×D9—92no—
392C3×D9—92no—
393C3×D9—92no—
394C3×D9—92no—
395C3×D9—92no—
396C3×D9—92no—
397C3×D9—92no—
398C3×D9—92no—
399C3×D9—92no—
400C3×D9—92no—
401C3×D9—92no—
402C3×D9—92no—
403C3×D9—92no—
404C3×D9—92no—
405C22×C32—811no—
406C2×C3⋊D3—91no—
407C2×C3⋊D3—91no—
408C2×C3⋊D3—91no—
409C2×C3⋊D3—91no—
410C2×C3×D3—271no—
411C2×C3×D3—271no—
412C2×C3×D3—271no—
413C2×C3×D3—271no—
414C2×C3×D3—271no—
415C2×C3×D3—271no—
416C2×C3×D3—271no—
417C2×C3×D3—271no—
418C2×C3×D3—271no—
419C2×C3×D3—271no—
420C2×C3×D3—271no—
421C2×C3×D3—271no—
422C2×C3×D3—271no—
423C2×C3×D3—271no—
424C2×C3×D3—271no—
425C2×C3×D3—271no—
426C2×C3×D3—811no—
427C2×C3×D3—811no—
428C2×C3×D3—811no—
429C2×D9—91no—
430C2×D9—91no—
431C2×D9—91no—
432C2×D9—91no—
433C2×D9—91no—
434C2×D9—91no—
435C2×D9—91no—
436C2×D9—91no—
437C2×D9—91no—
438C33—21no—
439C33—31no—
440C33—31no—
441C33—31no—
442C33—31no—
443C33—61no—
444C33—61no—
445C33—61no—
446C33—61no—
447C33—61no—
448C33—61no—
449C33—61no—
450C33—61no—
451C33C2×#27211yescharacteristic
452C33C2×C3⋊(C3⋊D3)11yescharacteristic
4533−1+2—31no—
4543−1+2—31no—
4553−1+2—31no—
4563−1+2—31no—
4573−1+2—31no—
4583−1+2—31no—
4593−1+2—31no—
4603−1+2—61no—
4613−1+2—61no—
4623−1+2—61no—
4633−1+2—61no—
4643−1+2—61no—
4653−1+2—61no—
4663−1+2—61no—
4673−1+2—61no—
4683−1+2—61no—
4693−1+2—61no—
4703−1+2—61no—
471H(3,𝔽3)—31no—
472H(3,𝔽3)—31no—
473H(3,𝔽3)—31no—
474H(3,𝔽3)—31no—
475H(3,𝔽3)—61no—
476H(3,𝔽3)—61no—
477H(3,𝔽3)—61no—
478H(3,𝔽3)—61no—
479H(3,𝔽3)—61no—
480H(3,𝔽3)—91no—
481H(3,𝔽3)—181no—
482H(3,𝔽3)—181no—
483H(3,𝔽3)—181no—
484H(3,𝔽3)—181no—
485H(3,𝔽3)—181no—
486C3×C9—21no—
487C3×C9—21no—
488C3×C9—21no—
489C3×C9—31no—
490C3×C9—31no—
491C3×C9—31no—
492C3×C9—31no—
493C3×C9—61no—
494C3×C9—61no—
495C3×C9—61no—
496C3×C9—61no—
497C3×C9—61no—
498C3×C9—61no—
499C3×C9—61no—
500C3×C9—61no—
501C3×C9—61no—
502C3×C9—61no—
503C3×C9—61no—
504C3×C9—61no—
505C3×C9—61no—
506C3×C9—63no—
507C3×C9—61no—
508C3×C9—61no—
509C3×C9—61no—
510C3×C9—61no—
511C3×C9—61no—
512C3×C9—61no—
513C3×C9—61no—
514C3×C9—61no—
515C3×C9—61no—
516C3×C9C2×#27211yescharacteristic, complemented
517C3×C9C2×#27211yescharacteristic, complemented
518C3×C9C2×#27211yescharacteristic, complemented
519C2×C32—21no—
520C2×C32—21no—
521C2×C32—21no—
522C2×C32—31no—
523C2×C32—31no—
524C2×C32—31no—
525C2×C32—31no—
526C2×C32—61no—
527C2×C32—61no—
528C2×C32—61no—
529C2×C32—61no—
530C2×C32—61no—
531C2×C32—61no—
532C2×C32—61no—
533C2×C32—61no—
534C2×C32—61no—
535C2×C32—61no—
536C2×C32—61no—
537C2×C32—61no—
538C2×C32—61no—
539C2×C32—61no—
540C2×C32—61no—
541C2×C32—61no—
542C2×C32—61no—
543C2×C32—61no—
544C2×C32—61no—
545C2×C32—61no—
546C2×C32—61no—
547C2×C32—91no—
548C2×C32—91no—
549C2×C32—181no—
550C2×C32—181no—
551C2×C32—181no—
552C2×C32—181no—
553C2×C32—181no—
554C2×C32—181no—
555C2×C32—181no—
556C2×C32—812no—
557C2×C32#418411yescharacteristic, complemented
558C2×C32#418411yescharacteristic, complemented
559C2×C32#418411yescharacteristic, complemented
560C2×C32C3⋊#27211yescharacteristic
561C2×C32C3⋊#27211yescharacteristic
562C2×C32C3⋊#27211yescharacteristic
563C2×C32C3⋊#27211yescharacteristic
564C3⋊D3—92no—
565C3⋊D3—92no—
566C3⋊D3—92no—
567C3⋊D3—92no—
568C3×D3—272no—
569C3×D3—272no—
570C3×D3—272no—
571C3×D3—272no—
572C3×D3—272no—
573C3×D3—272no—
574C3×D3—272no—
575C3×D3—272no—
576C3×D3—272no—
577C3×D3—272no—
578C3×D3—272no—
579C3×D3—272no—
580C3×D3—272no—
581C3×D3—272no—
582C3×D3—272no—
583C3×D3—272no—
584C3×D3—812no—
585C3×D3—812no—
586C3×D3—812no—
587C2×C9—31no—
588C2×C9—61no—
589C2×C9—61no—
590C2×C9—61no—
591C2×C9—61no—
592C2×C9—61no—
593C2×C9—181no—
594C2×C9—181no—
595C2×C9—181no—
596C2×C9—181no—
597C2×C9—181no—
598C2×C9—181no—
599D9—92no—
600D9—92no—
601D9—92no—
602D9—92no—
603D9—92no—
604D9—92no—
605D9—92no—
606D9—92no—
607D9—92no—
608C22×C3—811no—
609C22×C3—811no—
610C22×C3—811no—
611C22×C3—811no—
612C2×D3—271no—
613C2×D3—271no—
614C2×D3—271no—
615C2×D3—271no—
616C2×D3—811no—
617C2×D3—811no—
618C2×D3—811no—
619C32—21no—
620C32—21no—
621C32—21no—
622C32—31no—
623C32—31no—
624C32—31no—
625C32—31no—
626C32—61no—
627C32—61no—
628C32—61no—
629C32—61no—
630C32—61no—
631C32—61no—
632C32—61no—
633C32—61no—
634C32—61no—
635C32—61no—
636C32—61no—
637C32—61no—
638C32—61no—
639C32—61no—
640C32—61no—
641C32—61no—
642C32—61no—
643C32—61no—
644C32—61no—
645C32—61no—
646C32—61no—
647C32—91no—
648C32—91no—
649C32—181no—
650C32—181no—
651C32—181no—
652C32—181no—
653C32—181no—
654C32—181no—
655C32—181no—
656C32C2×#418411yescharacteristic, complemented
657C32C2×#418411yescharacteristic, complemented
658C32C2×#418411yescharacteristic, complemented
659C32C2×C3⋊#27211yescharacteristic
660C32C2×C3⋊#27211yescharacteristic
661C32C2×C3⋊#27211yescharacteristic
662C32C2×C3⋊#27211yescharacteristic
663C9—31no—
664C9—61no—
665C9—61no—
666C9—61no—
667C9—61no—
668C9—61no—
669C9—181no—
670C9—181no—
671C9—181no—
672C9—181no—
673C9—181no—
674C9—181no—
675C2×C3—21no—
676C2×C3—31no—
677C2×C3—31no—
678C2×C3—31no—
679C2×C3—31no—
680C2×C3—61no—
681C2×C3—61no—
682C2×C3—61no—
683C2×C3—61no—
684C2×C3—61no—
685C2×C3—541no—
686C2×C3—541no—
687C2×C3—541no—
688C2×C3—812no—
689C2×C3—812no—
690C2×C3—812no—
691C2×C3—812no—
692C2×C3#9233811yescharacteristic
693C2×C3C3⋊#418411yescharacteristic
694D3—272no—
695D3—272no—
696D3—272no—
697D3—272no—
698D3—812no—
699D3—812no—
700D3—812no—
701C22—811noSylow
702C3—21no—
703C3—31no—
704C3—31no—
705C3—31no—
706C3—31no—
707C3—61no—
708C3—61no—
709C3—61no—
710C3—61no—
711C3—61no—
712C3—541no—
713C3—541no—
714C3—541no—
715C3C2×#9233811yescharacteristic
716C3C2×C3⋊#418411yescharacteristic
717C2—812no—
718C2#1309104611yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3C3⋊#4184
commutator, cosocle, hypocenter#10624731C22
FrattiniC33C2×C3⋊(C3⋊D3)
FittingC2×#10624731C2
socleC2×C32C3⋊#272
LCSG ▷ #10624731
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. #13091046C2direct (N × H)
2. C2×#10624731C2semidirect
16. #10624731C22semidirect
17. C2×C33×C9D3semidirect
19. C2×C3×#731D3semidirect
20. C2×C3×#731D3semidirect
21. C2×C3×#731D3semidirect
22. C2×C3×#731D3semidirect
23. C2×C3×#731D3semidirect
24. C2×C3×#731D3semidirect
25. C2×C3×#731D3semidirect
26. C2×C3×#731D3semidirect
27. C2×C3×#731D3semidirect
28. C2×#6891D3semidirect
29. C2×#6891D3semidirect
72. C33×C9C2×D3semidirect
73. C3×#731C2×D3semidirect
74. C3×#731C2×D3semidirect
75. C3×#731C2×D3semidirect
76. C3×#731C2×D3semidirect
77. C3×#731C2×D3semidirect
78. C3×#731C2×D3semidirect
79. C3×#731C2×D3semidirect
80. C3×#731C2×D3semidirect
81. C3×#731C2×D3semidirect
82. #6891C2×D3semidirect
83. #6891C2×D3semidirect
353. C2×C3×C9#272semidirect
354. C2×C3×C9#272semidirect
355. C2×C3×C9#272semidirect
516. C3×C9C2×#272semidirect
517. C3×C9C2×#272semidirect
518. C3×C9C2×#272semidirect
557. C2×C32#4184semidirect
558. C2×C32#4184semidirect
559. C2×C32#4184semidirect
656. C32C2×#4184semidirect
657. C32C2×#4184semidirect
658. C32C2×#4184semidirect
718. C2#13091046direct (N × H)

Maximal subgroups

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

subgroupindex
#130910462
C2×#106247312
C2×C32×C3⋊D93
C2×C3×#41843
C2×#923023
C2×#923003