Finite Group Databasebeta

← C2×#13091523 #72244032

Subgroups — C2×#13091523 #72244032

Order 2916.

737 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13091523C212yesmaximal, direct product factor
2C2×#10624900C211yesmaximal, characteristic, complemented
3C2×C3×#4208C311yesmaximal, characteristic
4C2×C9×#272C311yesmaximal, characteristic
5C2×C9×#272C311yesmaximal, characteristic
6C2×C9×#272C311yesmaximal, characteristic
7C2×D3×C9⋊C9—31nomaximal
8C2×D3×C9⋊C9—31nomaximal
9C2×D3×C9⋊C9—31nomaximal
10C2×D3×C9⋊C9—31nomaximal
11#10624900C2211yescharacteristic, complemented, Sylow
12C2×C3×#737C2×C311yescharacteristic
13C3×#4208C2×C312yes—
14C2×#6895—21no—
15C2×#6895—21no—
16C2×#6895—21no—
17C2×#6895—21no—
18C2×#6894—21no—
19C2×#6894—21no—
20C2×#6894—21no—
21C2×#6894—21no—
22C2×#6894—21no—
23C2×#6894—21no—
24C2×#6894—21no—
25C2×#6894—21no—
26C2×#6894—21no—
27C2×#6894—21no—
28C2×#6894—21no—
29C2×#6894—21no—
30C2×C9×H(3,𝔽3)C2×C311yescharacteristic
31C2×C9×H(3,𝔽3)C2×C311yescharacteristic
32C2×C9×H(3,𝔽3)C2×C311yescharacteristic
33C2×C3×C9⋊C9D311yescharacteristic, complemented
34C2×C3×C9⋊C9D311yescharacteristic, complemented
35C2×C3×C9⋊C9D311yescharacteristic, complemented
36C2×C3×C9⋊C9D311yescharacteristic, complemented
37C9×#272C2×C312yes—
38C9×#272C2×C312yes—
39C9×#272C2×C312yes—
40D3×C9⋊C9—32no—
41D3×C9⋊C9—32no—
42D3×C9⋊C9—32no—
43D3×C9⋊C9—32no—
44C2×#4208—31no—
45C2×C3×#272C3211yescharacteristic
46C2×C3×D3×C9—31no—
47C2×C3×D3×C9—31no—
48C2×C3×D3×C9—31no—
49C2×C3×D3×C9—31no—
50C2×C3×D3×C9—31no—
51C2×C3×D3×C9—31no—
52C2×C3×D3×C9—31no—
53C2×C3×D3×C9—31no—
54C2×C3×D3×C9—31no—
55C2×C3×D3×C9—31no—
56C2×C3×D3×C9—31no—
57C2×C3×D3×C9—31no—
58C2×C3×D3×C9—31no—
59C2×C3×D3×C9—31no—
60C2×C3×D3×C9—31no—
61C2×C3×D3×C9—31no—
62C22×C9⋊C9—91no—
63C3×#737C22×C311yescharacteristic
64#6895—21no—
65#6895—21no—
66#6895—21no—
67#6895—21no—
68#6894—21no—
69#6894—21no—
70#6894—21no—
71#6894—21no—
72#6894—21no—
73#6894—21no—
74#6894—21no—
75#6894—21no—
76#6894—21no—
77#6894—21no—
78#6894—21no—
79#6894—21no—
80C9×H(3,𝔽3)C22×C311yescharacteristic
81C9×H(3,𝔽3)C22×C311yescharacteristic
82C9×H(3,𝔽3)C22×C311yescharacteristic
83C3×C9⋊C9C2×D311yescharacteristic, complemented
84C3×C9⋊C9C2×D311yescharacteristic, complemented
85C3×C9⋊C9C2×D311yescharacteristic, complemented
86C3×C9⋊C9C2×D311yescharacteristic, complemented
87C2×#737—31no—
88C2×#737—61no—
89C2×#737—61no—
90C2×#737—61no—
91C2×#737—61no—
92C2×C3×3−1+2—21no—
93C2×C3×3−1+2—21no—
94C2×C3×3−1+2—21no—
95C2×C3×3−1+2—21no—
96C2×C3×H(3,𝔽3)C2×C3211yescharacteristic
97C2×C32×C9C3×D311yescharacteristic
98C2×C32×C9C3×D311yescharacteristic
99C2×C32×C9C3×D311yescharacteristic
100C2×C32×C9C3×D311yescharacteristic
101C2×C32×C9C3×D311yescharacteristic
102C2×C32×C9C3×D311yescharacteristic
103C2×C32×C9C3×D311yescharacteristic
104C2×C32×C9C3×D311yescharacteristic
105C2×C32×C9C3×D311yescharacteristic
106C2×C32×C9C3×D311yescharacteristic
107C2×C32×C9C3×D311yescharacteristic
108C2×C32×C9C3×D311yescharacteristic
109C2×C32×C9C3×D311yescharacteristic
110C2×C32×C9C3×D311yescharacteristic
111C2×C32×C9C3×D311yescharacteristic
112C2×C32×C9C3×D311yescharacteristic
113#4208—32no—
114C3×#272C2×C3212yes—
115C3×D3×C9—32no—
116C3×D3×C9—32no—
117C3×D3×C9—32no—
118C3×D3×C9—32no—
119C3×D3×C9—32no—
120C3×D3×C9—32no—
121C3×D3×C9—32no—
122C3×D3×C9—32no—
123C3×D3×C9—32no—
124C3×D3×C9—32no—
125C3×D3×C9—32no—
126C3×D3×C9—32no—
127C3×D3×C9—32no—
128C3×D3×C9—32no—
129C3×D3×C9—32no—
130C3×D3×C9—32no—
131C2×C9⋊C9—21no—
132C2×C9⋊C9—21no—
133C2×C9⋊C9—21no—
134C2×C9⋊C9—21no—
135C2×C9⋊C9—21no—
136C2×C9⋊C9—21no—
137C2×C9⋊C9—21no—
138C2×C9⋊C9—21no—
139C2×C9⋊C9—21no—
140C2×C9⋊C9—21no—
141C2×C9⋊C9—21no—
142C2×C9⋊C9—21no—
143C2×C9⋊C9—21no—
144C2×C9⋊C9—21no—
145C2×C9⋊C9—21no—
146C2×C9⋊C9—21no—
147C2×C9⋊C9—21no—
148C2×C9⋊C9—21no—
149C2×C9⋊C9—21no—
150C2×C9⋊C9—21no—
151C2×C9⋊C9—21no—
152C2×C9⋊C9—21no—
153C2×C9⋊C9—21no—
154C2×C9⋊C9—21no—
155C2×C9⋊C9—21no—
156C2×C9⋊C9—21no—
157C2×C9⋊C9—21no—
158C2×C9⋊C9—21no—
159C2×C9⋊C9—21no—
160C2×C9⋊C9—21no—
161C2×C9⋊C9—21no—
162C2×C9⋊C9—21no—
163C2×C9⋊C9—21no—
164C2×C9⋊C9—21no—
165C2×C9⋊C9—21no—
166C2×C9⋊C9—21no—
167C2×C9⋊C9—21no—
168C2×C9⋊C9—21no—
169C2×C9⋊C9—21no—
170C2×C9⋊C9—21no—
171C2×C9⋊C9—92no—
172C2×C9⋊C9C3⋊D311yescharacteristic
173C2×C32⋊C9—21no—
174C2×C32⋊C9—21no—
175C2×C32⋊C9—21no—
176C2×C32⋊C9—21no—
177C2×C32⋊C9—21no—
178C2×C32⋊C9—21no—
179C2×C32⋊C9—21no—
180C2×C32⋊C9—21no—
181C2×C32⋊C9—21no—
182C2×C32⋊C9—21no—
183C2×C32⋊C9—21no—
184C2×C32⋊C9—21no—
185C2×C32×D3—31no—
186C2×C32×D3—31no—
187C2×C32×D3—31no—
188C2×C32×D3—31no—
189C22×C3×C9—91no—
190C22×C3×C9—91no—
191C22×C3×C9—91no—
192C22×C3×C9—91no—
193C2×#2723−1+211yescharacteristic
194C2×D3×C9—31no—
195C2×D3×C9—31no—
196C2×D3×C9—31no—
197C2×D3×C9—31no—
198C2×D3×C9—31no—
199C2×D3×C9—31no—
200C2×D3×C9—31no—
201C2×D3×C9—31no—
202C2×D3×C9—31no—
203C2×D3×C9—31no—
204C2×D3×C9—31no—
205C2×D3×C9—31no—
206C2×D3×C9—91no—
207C2×D3×C9—91no—
208C2×D3×C9—91no—
209C2×D3×C9—91no—
210C2×D3×C9—91no—
211C2×D3×C9—91no—
212C2×D3×C9—91no—
213C2×D3×C9—91no—
214C2×D3×C9—91no—
215C2×D3×C9—91no—
216C2×D3×C9—91no—
217C2×D3×C9—91no—
218#737—31no—
219#737—61no—
220#737—61no—
221#737—61no—
222#737—61no—
223C3×3−1+2—21no—
224C3×3−1+2—21no—
225C3×3−1+2—21no—
226C3×3−1+2—21no—
227C3×H(3,𝔽3)C22×C3211yescharacteristic
228C32×C9C2×C3×D311yescharacteristic
229C32×C9C2×C3×D311yescharacteristic
230C32×C9C2×C3×D311yescharacteristic
231C32×C9C2×C3×D311yescharacteristic
232C32×C9C2×C3×D311yescharacteristic
233C32×C9C2×C3×D311yescharacteristic
234C32×C9C2×C3×D311yescharacteristic
235C32×C9C2×C3×D311yescharacteristic
236C32×C9C2×C3×D311yescharacteristic
237C32×C9C2×C3×D311yescharacteristic
238C32×C9C2×C3×D311yescharacteristic
239C32×C9C2×C3×D311yescharacteristic
240C32×C9C2×C3×D311yescharacteristic
241C32×C9C2×C3×D311yescharacteristic
242C32×C9C2×C3×D311yescharacteristic
243C32×C9C2×C3×D311yescharacteristic
244C9⋊C9—21no—
245C9⋊C9—21no—
246C9⋊C9—21no—
247C9⋊C9—21no—
248C9⋊C9—21no—
249C9⋊C9—21no—
250C9⋊C9—21no—
251C9⋊C9—21no—
252C9⋊C9—21no—
253C9⋊C9—21no—
254C9⋊C9—21no—
255C9⋊C9—21no—
256C9⋊C9—21no—
257C9⋊C9—21no—
258C9⋊C9—21no—
259C9⋊C9—21no—
260C9⋊C9—21no—
261C9⋊C9—21no—
262C9⋊C9—21no—
263C9⋊C9—21no—
264C9⋊C9—21no—
265C9⋊C9—21no—
266C9⋊C9—21no—
267C9⋊C9—21no—
268C9⋊C9—21no—
269C9⋊C9—21no—
270C9⋊C9—21no—
271C9⋊C9—21no—
272C9⋊C9—21no—
273C9⋊C9—21no—
274C9⋊C9—21no—
275C9⋊C9—21no—
276C9⋊C9—21no—
277C9⋊C9—21no—
278C9⋊C9—21no—
279C9⋊C9—21no—
280C9⋊C9—21no—
281C9⋊C9—21no—
282C9⋊C9—21no—
283C9⋊C9—21no—
284C9⋊C9C2×C3⋊D311yescharacteristic
285C32⋊C9—21no—
286C32⋊C9—21no—
287C32⋊C9—21no—
288C32⋊C9—21no—
289C32⋊C9—21no—
290C32⋊C9—21no—
291C32⋊C9—21no—
292C32⋊C9—21no—
293C32⋊C9—21no—
294C32⋊C9—21no—
295C32⋊C9—21no—
296C32⋊C9—21no—
297C2×C33C32×D311yescharacteristic
298C2×C33C32×D311yescharacteristic
299C2×C33C32×D311yescharacteristic
300C2×C33C32×D311yescharacteristic
301C32×D3—32no—
302C32×D3—32no—
303C32×D3—32no—
304C32×D3—32no—
305C2×3−1+2—62no—
306C2×3−1+2—62no—
307C2×3−1+2—62no—
308C2×3−1+2—62no—
309C2×3−1+2—61no—
310C2×3−1+2—61no—
311C2×3−1+2—61no—
312C2×3−1+2—61no—
313C2×H(3,𝔽3)—21no—
314C2×H(3,𝔽3)—21no—
315C2×H(3,𝔽3)—21no—
316C2×H(3,𝔽3)—21no—
317C2×H(3,𝔽3)C2×3−1+211yescharacteristic
318C2×C3×C9—21no—
319C2×C3×C9—21no—
320C2×C3×C9—21no—
321C2×C3×C9—21no—
322C2×C3×C9—21no—
323C2×C3×C9—21no—
324C2×C3×C9—21no—
325C2×C3×C9—21no—
326C2×C3×C9—21no—
327C2×C3×C9—21no—
328C2×C3×C9—21no—
329C2×C3×C9—21no—
330C2×C3×C9—21no—
331C2×C3×C9—21no—
332C2×C3×C9—21no—
333C2×C3×C9—21no—
334C2×C3×C9—31no—
335C2×C3×C9—31no—
336C2×C3×C9—31no—
337C2×C3×C9—31no—
338C2×C3×C9—31no—
339C2×C3×C9—31no—
340C2×C3×C9—31no—
341C2×C3×C9—31no—
342C2×C3×C9—31no—
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—61no—
354C2×C3×C9—91no—
355C2×C3×C9—91no—
356C2×C3×C9—91no—
357C2×C3×C9—92no—
358C2×C3×C9—92no—
359C2×C3×C9—92no—
360C2×C3×C9—92no—
361C2×C3×C9—181no—
362C2×C3×C9—181no—
363C2×C3×C9—181no—
364C2×C3×C9—181no—
365C2×C3×C9—181no—
366C2×C3×C9C3×C3⋊D311yescharacteristic
367C2×C3×C9C3×C3⋊D311yescharacteristic
368C2×C3×C9C3×C3⋊D311yescharacteristic
369C2×C3×C9C3×C3⋊D311yescharacteristic
370#272C2×3−1+212yes—
371D3×C9—32no—
372D3×C9—32no—
373D3×C9—32no—
374D3×C9—32no—
375D3×C9—32no—
376D3×C9—32no—
377D3×C9—32no—
378D3×C9—32no—
379D3×C9—32no—
380D3×C9—32no—
381D3×C9—32no—
382D3×C9—32no—
383D3×C9—92no—
384D3×C9—92no—
385D3×C9—92no—
386D3×C9—92no—
387D3×C9—92no—
388D3×C9—92no—
389D3×C9—92no—
390D3×C9—92no—
391D3×C9—92no—
392D3×C9—92no—
393D3×C9—92no—
394D3×C9—92no—
395C22×C32—91no—
396C2×C3×D3—31no—
397C2×C3×D3—31no—
398C2×C3×D3—31no—
399C2×C3×D3—31no—
400C2×C3×D3—31no—
401C2×C3×D3—31no—
402C2×C3×D3—31no—
403C2×C3×D3—31no—
404C2×C3×D3—31no—
405C2×C3×D3—31no—
406C2×C3×D3—31no—
407C2×C3×D3—31no—
408C2×C3×D3—31no—
409C2×C3×D3—31no—
410C2×C3×D3—31no—
411C2×C3×D3—31no—
412C22×C9—91no—
413C22×C9—91no—
414C22×C9—91no—
415C22×C9—271no—
416C22×C9—271no—
417C22×C9—271no—
418C33C2×C32×D311yescharacteristic
419C33C2×C32×D311yescharacteristic
420C33C2×C32×D311yescharacteristic
421C33C2×C32×D311yescharacteristic
4223−1+2—62no—
4233−1+2—62no—
4243−1+2—62no—
4253−1+2—62no—
4263−1+2—61no—
4273−1+2—61no—
4283−1+2—61no—
4293−1+2—61no—
430H(3,𝔽3)—21no—
431H(3,𝔽3)—21no—
432H(3,𝔽3)—21no—
433H(3,𝔽3)—21no—
434H(3,𝔽3)C22×3−1+211yescharacteristic
435C3×C9—21no—
436C3×C9—21no—
437C3×C9—21no—
438C3×C9—21no—
439C3×C9—21no—
440C3×C9—21no—
441C3×C9—21no—
442C3×C9—21no—
443C3×C9—21no—
444C3×C9—21no—
445C3×C9—21no—
446C3×C9—21no—
447C3×C9—21no—
448C3×C9—21no—
449C3×C9—21no—
450C3×C9—21no—
451C3×C9—31no—
452C3×C9—31no—
453C3×C9—31no—
454C3×C9—31no—
455C3×C9—31no—
456C3×C9—31no—
457C3×C9—31no—
458C3×C9—31no—
459C3×C9—31no—
460C3×C9—61no—
461C3×C9—61no—
462C3×C9—61no—
463C3×C9—61no—
464C3×C9—61no—
465C3×C9—61no—
466C3×C9—61no—
467C3×C9—61no—
468C3×C9—61no—
469C3×C9—61no—
470C3×C9—61no—
471C3×C9—91no—
472C3×C9—91no—
473C3×C9—91no—
474C3×C9—181no—
475C3×C9—181no—
476C3×C9—181no—
477C3×C9—181no—
478C3×C9—181no—
479C3×C9C2×C3×C3⋊D311yescharacteristic
480C3×C9C2×C3×C3⋊D311yescharacteristic
481C3×C9C2×C3×C3⋊D311yescharacteristic
482C3×C9C2×C3×C3⋊D311yescharacteristic
483C2×C32—21no—
484C2×C32—21no—
485C2×C32—21no—
486C2×C32—21no—
487C2×C32—31no—
488C2×C32—31no—
489C2×C32—31no—
490C2×C32—61no—
491C2×C32—61no—
492C2×C32—61no—
493C2×C32—61no—
494C2×C32—61no—
495C2×C32—61no—
496C2×C32—61no—
497C2×C32—61no—
498C2×C32—61no—
499C2×C32—92no—
500C2×C32D3×3−1+211yescharacteristic
501C2×C32D3×3−1+211yescharacteristic
502C2×C32D3×3−1+211yescharacteristic
503C2×C32D3×3−1+211yescharacteristic
504C2×C32C32×C3⋊D311yescharacteristic
505C3×D3—32no—
506C3×D3—32no—
507C3×D3—32no—
508C3×D3—32no—
509C3×D3—32no—
510C3×D3—32no—
511C3×D3—32no—
512C3×D3—32no—
513C3×D3—32no—
514C3×D3—32no—
515C3×D3—32no—
516C3×D3—32no—
517C3×D3—32no—
518C3×D3—32no—
519C3×D3—32no—
520C3×D3—32no—
521C2×C9—31no—
522C2×C9—31no—
523C2×C9—31no—
524C2×C9—61no—
525C2×C9—61no—
526C2×C9—61no—
527C2×C9—61no—
528C2×C9—61no—
529C2×C9—61no—
530C2×C9—61no—
531C2×C9—61no—
532C2×C9—61no—
533C2×C9—61no—
534C2×C9—61no—
535C2×C9—61no—
536C2×C9—61no—
537C2×C9—61no—
538C2×C9—61no—
539C2×C9—61no—
540C2×C9—92no—
541C2×C9—92no—
542C2×C9—92no—
543C2×C9—272no—
544C2×C9—272no—
545C2×C9—272no—
546C2×C9#420811yescharacteristic, complemented
547C2×C9#420811yescharacteristic, complemented
548C2×C9#420811yescharacteristic, complemented
549C22×C3—91no—
550C22×C3—91no—
551C22×C3—91no—
552C22×C3—91no—
553C2×D3—31no—
554C2×D3—31no—
555C2×D3—31no—
556C2×D3—31no—
557C32—21no—
558C32—21no—
559C32—21no—
560C32—21no—
561C32—31no—
562C32—31no—
563C32—31no—
564C32—61no—
565C32—61no—
566C32—61no—
567C32—61no—
568C32—61no—
569C32—61no—
570C32—61no—
571C32—61no—
572C32—61no—
573C32C2×D3×3−1+211yescharacteristic
574C32C2×D3×3−1+211yescharacteristic
575C32C2×D3×3−1+211yescharacteristic
576C32C2×D3×3−1+211yescharacteristic
577C32C2×C32×C3⋊D311yescharacteristic
578C9—31no—
579C9—31no—
580C9—31no—
581C9—61no—
582C9—61no—
583C9—61no—
584C9—61no—
585C9—61no—
586C9—61no—
587C9—61no—
588C9—61no—
589C9—61no—
590C9—61no—
591C9—61no—
592C9—61no—
593C9—61no—
594C9—61no—
595C9—61no—
596C9—61no—
597C9C2×#420811yescharacteristic, complemented
598C9C2×#420811yescharacteristic, complemented
599C9C2×#420811yescharacteristic, complemented
600C2×C3—31no—
601C2×C3—61no—
602C2×C3—61no—
603C2×C3—61no—
604C2×C3—61no—
605C2×C3—61no—
606C2×C3—61no—
607C2×C3—61no—
608C2×C3—92no—
609C2×C3—92no—
610C2×C3—92no—
611C2×C3—92no—
612C2×C3C3⋊D3×3−1+211yescharacteristic
613C2×C3C3×#420811yescharacteristic
614C2×C3#9239411yescharacteristic
615C2×C3#9239411yescharacteristic
616D3—32no—
617D3—32no—
618D3—32no—
619D3—32no—
620C22—91noSylow
621C3—31no—
622C3—61no—
623C3—61no—
624C3—61no—
625C3—61no—
626C3—61no—
627C3—61no—
628C3—61no—
629C3C2×C3⋊D3×3−1+211yescharacteristic
630C3C2×C3×#420811yescharacteristic
631C3C2×#9239411yescharacteristic
632C3C2×#9239411yescharacteristic
633C2—92no—
634C2#1309152311yescharacteristic, direct product factor
subgroupG/H
center, socleC2×C32C32×C3⋊D3
commutator, cosocleC3×H(3,𝔽3)C22×C32
FrattiniC32C2×C32×C3⋊D3
FittingC2×#10624900C2
prime radicalC2×C3×#272C32
hypercenterC2×C9⋊C9C3⋊D3
hypocenterH(3,𝔽3)C22×3−1+2
LCSG ▷ C3×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C2×C32 ◁ C2×C9⋊C9

Complements

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

NH ≅ G/Ntype
1. #13091523C2direct (N × H)
2. C2×#10624900C2semidirect
11. #10624900C22semidirect
33. C2×C3×C9⋊C9D3semidirect
34. C2×C3×C9⋊C9D3semidirect
35. C2×C3×C9⋊C9D3semidirect
36. C2×C3×C9⋊C9D3semidirect
83. C3×C9⋊C9C2×D3semidirect
84. C3×C9⋊C9C2×D3semidirect
85. C3×C9⋊C9C2×D3semidirect
86. C3×C9⋊C9C2×D3semidirect
546. C2×C9#4208semidirect
547. C2×C9#4208semidirect
548. C2×C9#4208semidirect
597. C9C2×#4208semidirect
598. C9C2×#4208semidirect
599. C9C2×#4208semidirect
634. C2#13091523direct (N × H)

Maximal subgroups

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

subgroupindex
#130915232
C2×#106249002
C2×C3×#42083
C2×C9×#2723
C2×D3×C9⋊C93