Finite Group Databasebeta

← C2×#13091474 #72244060

Subgroups — C2×#13091474 #72244060

Order 2916.

901 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13091474C212yesmaximal, direct product factor
2C2×#10624882C211yesmaximal, characteristic, complemented
3C2×C3⋊#4208C311yesmaximal, characteristic, complemented
4C2×C3⋊D3×3−1+2—31nomaximal
5C2×#92305C311yesmaximal, characteristic, complemented
6C2×#92305C311yesmaximal, characteristic, complemented
7C2×#92300C311yesmaximal, characteristic
8C2×#92262—31nomaximal
9C2×#92262—31nomaximal
10C2×#92262—31nomaximal
11#10624882C2211yescharacteristic, complemented, Sylow
12C2×C3×#737—21no—
13C2×C3×#737C2×C311yescharacteristic, complemented
14C2×C32×3−1+2D311yescharacteristic, complemented
15C3⋊#4208C2×C312yescomplemented
16C3⋊D3×3−1+2—32no—
17C2×#6893—21no—
18C2×#6893—21no—
19C2×#6893C2×C311yescharacteristic, complemented
20C2×#6893C2×C311yescharacteristic, complemented
21C2×C9⋊H(3,𝔽3)—21no—
22C2×C9⋊H(3,𝔽3)—21no—
23C2×C9⋊H(3,𝔽3)—21no—
24C2×C9⋊H(3,𝔽3)—21no—
25C2×C9⋊H(3,𝔽3)—21no—
26C2×C9⋊H(3,𝔽3)—21no—
27C2×C9⋊H(3,𝔽3)—21no—
28C2×C9⋊H(3,𝔽3)—21no—
29C2×C9⋊H(3,𝔽3)—21no—
30C2×C9⋊H(3,𝔽3)—21no—
31C2×C9⋊H(3,𝔽3)—21no—
32C2×C9⋊H(3,𝔽3)—21no—
33C2×C9⋊H(3,𝔽3)D311yescharacteristic, complemented
34C2×C9⋊H(3,𝔽3)D311yescharacteristic, complemented
35C2×C9⋊H(3,𝔽3)D311yescharacteristic, complemented
36C2×#6891—21no—
37C2×C32⋊H(3,𝔽3)C2×C311yescharacteristic
38#92305C2×C312yescomplemented
39#92305C2×C312yescomplemented
40#92300C2×C312yes—
41#92262—32no—
42#92262—32no—
43#92262—32no—
44C2×C32×C3⋊D3—31no—
45C2×C3⋊#272C3211yescharacteristic
46C2×#4208—91no—
47C2×#4208—91no—
48C2×#4208—91no—
49C2×C9×C3⋊D3—31no—
50C2×C9×C3⋊D3—31no—
51C2×C9×C3⋊D3—31no—
52C2×C9×C3⋊D3—31no—
53C2×C9×C3⋊D3—31no—
54C2×C9×C3⋊D3—31no—
55C2×D3×3−1+2—91no—
56C2×D3×3−1+2—91no—
57C2×D3×3−1+2—91no—
58C2×D3×3−1+2—91no—
59C2×C3×(C3⋊D3)⋊C3—31no—
60C2×C3×(C3⋊D3)⋊C3—31no—
61C2×C3×(C3⋊D3)⋊C3—31no—
62C2×(C3⋊D3)⋊C9—31no—
63C2×(C3⋊D3)⋊C9—31no—
64C2×(C3⋊D3)⋊C9—31no—
65C2×(C3⋊D3)⋊C9—31no—
66C2×(C3⋊D3)⋊C9—31no—
67C2×(C3⋊D3)⋊C9—31no—
68C3×#737—21no—
69C3×#737C22×C311yescharacteristic, complemented
70C32×3−1+2C2×D311yescharacteristic, complemented
71#6893—21no—
72#6893—21no—
73#6893C22×C311yescharacteristic, complemented
74#6893C22×C311yescharacteristic, complemented
75C9⋊H(3,𝔽3)—21no—
76C9⋊H(3,𝔽3)—21no—
77C9⋊H(3,𝔽3)—21no—
78C9⋊H(3,𝔽3)—21no—
79C9⋊H(3,𝔽3)—21no—
80C9⋊H(3,𝔽3)—21no—
81C9⋊H(3,𝔽3)—21no—
82C9⋊H(3,𝔽3)—21no—
83C9⋊H(3,𝔽3)—21no—
84C9⋊H(3,𝔽3)—21no—
85C9⋊H(3,𝔽3)—21no—
86C9⋊H(3,𝔽3)—21no—
87C9⋊H(3,𝔽3)C2×D311yescharacteristic, complemented
88C9⋊H(3,𝔽3)C2×D311yescharacteristic, complemented
89C9⋊H(3,𝔽3)C2×D311yescharacteristic, complemented
90#6891—21no—
91C32⋊H(3,𝔽3)C22×C311yescharacteristic
92C2×C34C3×D311yescharacteristic
93C32×C3⋊D3—32no—
94C2×#737—31no—
95C2×#737—31no—
96C2×#737—31no—
97C2×#737—61no—
98C2×#737—61no—
99C2×#737—61no—
100C2×#737—61no—
101C2×#737—61no—
102C2×#737—61no—
103C2×#737—61no—
104C2×#737—61no—
105C2×#737—61no—
106C2×#737—61no—
107C2×#737—61no—
108C2×#737—61no—
109C2×C3×3−1+2—21no—
110C2×C3×3−1+2—21no—
111C2×C3×3−1+2—21no—
112C2×C3×3−1+2—21no—
113C2×C3×3−1+2—21no—
114C2×C3×3−1+2—21no—
115C2×C3×3−1+2—21no—
116C2×C3×3−1+2—21no—
117C2×C3×3−1+2—21no—
118C2×C3×3−1+2—21no—
119C2×C3×3−1+2—21no—
120C2×C3×3−1+2—21no—
121C2×C3×3−1+2—21no—
122C2×C3×3−1+2—21no—
123C2×C3×3−1+2—21no—
124C2×C3×3−1+2—21no—
125C2×C3×3−1+2—31no—
126C2×C3×3−1+2—31no—
127C2×C3×3−1+2—61no—
128C2×C3×3−1+2—61no—
129C2×C3×3−1+2—61no—
130C2×C3×3−1+2—61no—
131C2×C3×3−1+2C3⋊D311yescharacteristic
132C2×C3×H(3,𝔽3)—21no—
133C2×C3×H(3,𝔽3)—21no—
134C2×C3×H(3,𝔽3)—21no—
135C2×C3×H(3,𝔽3)—21no—
136C2×C3×H(3,𝔽3)C3×D311yescharacteristic
137C2×C3×H(3,𝔽3)C3×D311yescharacteristic
138C2×C3×H(3,𝔽3)C3×D311yescharacteristic
139C2×C3×H(3,𝔽3)C2×C3211yescharacteristic
140C2×C32×C9—21no—
141C2×C32×C9—21no—
142C2×C32×C9—21no—
143C2×C32×C9C3×D311yescharacteristic
144C2×C32×C9C3×D311yescharacteristic
145C2×C32×C9C3×D311yescharacteristic
146C2×C32×C9C3×D311yescharacteristic, complemented
147C2×C32×C9C3×D311yescharacteristic, complemented
148C2×C32×C9C3×D311yescharacteristic, complemented
149C3⋊#272C2×C3212yes—
150#4208—92no—
151#4208—92no—
152#4208—92no—
153C9×C3⋊D3—32no—
154C9×C3⋊D3—32no—
155C9×C3⋊D3—32no—
156C9×C3⋊D3—32no—
157C9×C3⋊D3—32no—
158C9×C3⋊D3—32no—
159D3×3−1+2—92no—
160D3×3−1+2—92no—
161D3×3−1+2—92no—
162D3×3−1+2—92no—
163C3×(C3⋊D3)⋊C3—32no—
164C3×(C3⋊D3)⋊C3—32no—
165C3×(C3⋊D3)⋊C3—32no—
166C2×C32⋊C9—21no—
167C2×C32⋊C9—21no—
168C2×C32⋊C9—21no—
169C2×C32⋊C9—21no—
170C2×C32⋊C9—21no—
171C2×C32⋊C9—21no—
172C2×C32⋊C9—21no—
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⋊C9—21no—
186C2×C32⋊C9—21no—
187C2×C32⋊C9—21no—
188C2×C32⋊C9—21no—
189C2×C32⋊C9—21no—
190C2×C32⋊C9—21no—
191C2×C32⋊C9—21no—
192C2×C32⋊C9—21no—
193C2×C32⋊C9—21no—
194C2×C32⋊C9—21no—
195C2×C32⋊C9—21no—
196C2×C32⋊C9—21no—
197C2×C32⋊C9—21no—
198C2×C32⋊C9—21no—
199C2×C32⋊C9C3×D311yescharacteristic, complemented
200C2×C32⋊C9C3×D311yescharacteristic, complemented
201C2×C32⋊C9C3×D311yescharacteristic, complemented
202C2×C32⋊C9C3×D311yescharacteristic, complemented
203C2×C32⋊C9C3×D311yescharacteristic, complemented
204C2×C32⋊C9C3×D311yescharacteristic, complemented
205(C3⋊D3)⋊C9—32no—
206(C3⋊D3)⋊C9—32no—
207(C3⋊D3)⋊C9—32no—
208(C3⋊D3)⋊C9—32no—
209(C3⋊D3)⋊C9—32no—
210(C3⋊D3)⋊C9—32no—
211C2×C3×C3⋊D3—31no—
212C2×C3×C3⋊D3—31no—
213C2×C3×C3⋊D3—31no—
214C2×C3×C3⋊D3—31no—
215C2×C3×C3⋊D3—91no—
216C2×C32×D3—91no—
217C2×C32×D3—91no—
218C2×C32×D3—91no—
219C2×C32×D3—91no—
220C22×3−1+2—271no—
221C2×#272—91no—
222C2×#272—91no—
223C2×#272—91no—
224C2×(C3⋊D3)⋊C3—91no—
225C2×(C3⋊D3)⋊C3—91no—
226C2×(C3⋊D3)⋊C3—91no—
227C2×D3×C9—91no—
228C2×D3×C9—91no—
229C2×D3×C9—91no—
230C2×D3×C9—91no—
231C2×D3×C9—91no—
232C2×D3×C9—91no—
233C2×D3×C9—91no—
234C2×D3×C9—91no—
235C2×D3×C9—91no—
236C2×D3×C9—91no—
237C2×D3×C9—91no—
238C2×D3×C9—91no—
239C2×D3×C9—271no—
240C2×D3×C9—271no—
241C2×D3×C9—271no—
242C34C2×C3×D311yescharacteristic
243#737—31no—
244#737—31no—
245#737—31no—
246#737—61no—
247#737—61no—
248#737—61no—
249#737—61no—
250#737—61no—
251#737—61no—
252#737—61no—
253#737—61no—
254#737—61no—
255#737—61no—
256#737—61no—
257#737—61no—
258C3×3−1+2—21no—
259C3×3−1+2—21no—
260C3×3−1+2—21no—
261C3×3−1+2—21no—
262C3×3−1+2—21no—
263C3×3−1+2—21no—
264C3×3−1+2—21no—
265C3×3−1+2—21no—
266C3×3−1+2—21no—
267C3×3−1+2—21no—
268C3×3−1+2—21no—
269C3×3−1+2—21no—
270C3×3−1+2—21no—
271C3×3−1+2—21no—
272C3×3−1+2—21no—
273C3×3−1+2—21no—
274C3×3−1+2—31no—
275C3×3−1+2—31no—
276C3×3−1+2—61no—
277C3×3−1+2—61no—
278C3×3−1+2—61no—
279C3×3−1+2—61no—
280C3×3−1+2C2×C3⋊D311yescharacteristic
281C3×H(3,𝔽3)—21no—
282C3×H(3,𝔽3)—21no—
283C3×H(3,𝔽3)—21no—
284C3×H(3,𝔽3)—21no—
285C3×H(3,𝔽3)C2×C3×D311yescharacteristic
286C3×H(3,𝔽3)C2×C3×D311yescharacteristic
287C3×H(3,𝔽3)C2×C3×D311yescharacteristic
288C3×H(3,𝔽3)C22×C3211yescharacteristic
289C32×C9—21no—
290C32×C9—21no—
291C32×C9—21no—
292C32×C9C2×C3×D311yescharacteristic
293C32×C9C2×C3×D311yescharacteristic
294C32×C9C2×C3×D311yescharacteristic
295C32×C9C2×C3×D311yescharacteristic, complemented
296C32×C9C2×C3×D311yescharacteristic, complemented
297C32×C9C2×C3×D311yescharacteristic, complemented
298C32⋊C9—21no—
299C32⋊C9—21no—
300C32⋊C9—21no—
301C32⋊C9—21no—
302C32⋊C9—21no—
303C32⋊C9—21no—
304C32⋊C9—21no—
305C32⋊C9—21no—
306C32⋊C9—21no—
307C32⋊C9—21no—
308C32⋊C9—21no—
309C32⋊C9—21no—
310C32⋊C9—21no—
311C32⋊C9—21no—
312C32⋊C9—21no—
313C32⋊C9—21no—
314C32⋊C9—21no—
315C32⋊C9—21no—
316C32⋊C9—21no—
317C32⋊C9—21no—
318C32⋊C9—21no—
319C32⋊C9—21no—
320C32⋊C9—21no—
321C32⋊C9—21no—
322C32⋊C9—21no—
323C32⋊C9—21no—
324C32⋊C9—21no—
325C32⋊C9—21no—
326C32⋊C9—21no—
327C32⋊C9—21no—
328C32⋊C9—21no—
329C32⋊C9—21no—
330C32⋊C9—21no—
331C32⋊C9C2×C3×D311yescharacteristic, complemented
332C32⋊C9C2×C3×D311yescharacteristic, complemented
333C32⋊C9C2×C3×D311yescharacteristic, complemented
334C32⋊C9C2×C3×D311yescharacteristic, complemented
335C32⋊C9C2×C3×D311yescharacteristic, complemented
336C32⋊C9C2×C3×D311yescharacteristic, complemented
337C2×C33—21no—
338C2×C33—21no—
339C2×C33—21no—
340C2×C33—21no—
341C2×C33—61no—
342C2×C33—61no—
343C2×C33—61no—
344C2×C33—91no—
345C2×C33—181no—
346C2×C33C32×D311yescharacteristic
347C2×C33C32×D311yescharacteristic
348C2×C33C32×D311yescharacteristic
349C2×C33C32×D311yescharacteristic
350C2×C33C3×C3⋊D311yescharacteristic
351C3×C3⋊D3—32no—
352C3×C3⋊D3—32no—
353C3×C3⋊D3—32no—
354C3×C3⋊D3—32no—
355C3×C3⋊D3—92no—
356C32×D3—92no—
357C32×D3—92no—
358C32×D3—92no—
359C32×D3—92no—
360C2×3−1+2—61no—
361C2×3−1+2—61no—
362C2×3−1+2—61no—
363C2×3−1+2—61no—
364C2×3−1+2—61no—
365C2×3−1+2—61no—
366C2×3−1+2—61no—
367C2×3−1+2—61no—
368C2×3−1+2—61no—
369C2×3−1+2—61no—
370C2×3−1+2—61no—
371C2×3−1+2—61no—
372C2×3−1+2—61no—
373C2×3−1+2—61no—
374C2×3−1+2—61no—
375C2×3−1+2—61no—
376C2×3−1+2—61no—
377C2×3−1+2—61no—
378C2×3−1+2—61no—
379C2×3−1+2—62no—
380C2×3−1+2—61no—
381C2×3−1+2—61no—
382C2×3−1+2—61no—
383C2×3−1+2—61no—
384C2×3−1+2—61no—
385C2×3−1+2—61no—
386C2×3−1+2—61no—
387C2×3−1+2—61no—
388C2×3−1+2—61no—
389C2×3−1+2—61no—
390C2×3−1+2—61no—
391C2×3−1+2—61no—
392C2×3−1+2—61no—
393C2×3−1+2—61no—
394C2×3−1+2—61no—
395C2×3−1+2—61no—
396C2×3−1+2—61no—
397C2×3−1+2—61no—
398C2×3−1+2—61no—
399C2×3−1+2—61no—
400C2×3−1+2—61no—
401C2×3−1+2—61no—
402C2×3−1+2—61no—
403C2×3−1+2—61no—
404C2×3−1+2—61no—
405C2×3−1+2—61no—
406C2×3−1+2—61no—
407C2×3−1+2—61no—
408C2×3−1+2—61no—
409C2×3−1+2—272no—
410C2×H(3,𝔽3)—31no—
411C2×H(3,𝔽3)—31no—
412C2×H(3,𝔽3)—31no—
413C2×H(3,𝔽3)—61no—
414C2×H(3,𝔽3)—61no—
415C2×H(3,𝔽3)—61no—
416C2×H(3,𝔽3)—91no—
417C2×H(3,𝔽3)—91no—
418C2×H(3,𝔽3)—181no—
419C2×H(3,𝔽3)—181no—
420C2×H(3,𝔽3)—181no—
421C2×H(3,𝔽3)—181no—
422C2×C3×C9—21no—
423C2×C3×C9—21no—
424C2×C3×C9—21no—
425C2×C3×C9—21no—
426C2×C3×C9—21no—
427C2×C3×C9—21no—
428C2×C3×C9—21no—
429C2×C3×C9—21no—
430C2×C3×C9—21no—
431C2×C3×C9—21no—
432C2×C3×C9—21no—
433C2×C3×C9—21no—
434C2×C3×C9—21no—
435C2×C3×C9—21no—
436C2×C3×C9—21no—
437C2×C3×C9—31no—
438C2×C3×C9—31no—
439C2×C3×C9—31no—
440C2×C3×C9—31no—
441C2×C3×C9—31no—
442C2×C3×C9—31no—
443C2×C3×C9—61no—
444C2×C3×C9—61no—
445C2×C3×C9—61no—
446C2×C3×C9—61no—
447C2×C3×C9—61no—
448C2×C3×C9—61no—
449C2×C3×C9—61no—
450C2×C3×C9—61no—
451C2×C3×C9—61no—
452C2×C3×C9—61no—
453C2×C3×C9—61no—
454C2×C3×C9—61no—
455C2×C3×C9—61no—
456C2×C3×C9—61no—
457C2×C3×C9—61no—
458C2×C3×C9(C3⋊D3)⋊C311yescharacteristic, complemented
459C2×C3×C9(C3⋊D3)⋊C311yescharacteristic, complemented
460C2×C3×C9(C3⋊D3)⋊C311yescharacteristic, complemented
461C2×C3×C9C3×C3⋊D311yescharacteristic
462C2×C3×C9C3×C3⋊D311yescharacteristic
463C2×C3×C9C3×C3⋊D311yescharacteristic
464#272—92no—
465#272—92no—
466#272—92no—
467(C3⋊D3)⋊C3—92no—
468(C3⋊D3)⋊C3—92no—
469(C3⋊D3)⋊C3—92no—
470D3×C9—92no—
471D3×C9—92no—
472D3×C9—92no—
473D3×C9—92no—
474D3×C9—92no—
475D3×C9—92no—
476D3×C9—92no—
477D3×C9—92no—
478D3×C9—92no—
479D3×C9—92no—
480D3×C9—92no—
481D3×C9—92no—
482D3×C9—272no—
483D3×C9—272no—
484D3×C9—272no—
485C22×C32—271no—
486C2×C3⋊D3—31no—
487C2×C3⋊D3—31no—
488C2×C3⋊D3—31no—
489C2×C3⋊D3—31no—
490C2×C3×D3—91no—
491C2×C3×D3—91no—
492C2×C3×D3—91no—
493C2×C3×D3—91no—
494C2×C3×D3—271no—
495C2×C3×D3—271no—
496C2×C3×D3—271no—
497C2×C3×D3—271no—
498C2×C3×D3—271no—
499C2×C3×D3—271no—
500C2×C3×D3—271no—
501C22×C9—271no—
502C22×C9—271no—
503C22×C9—271no—
504C33—21no—
505C33—21no—
506C33—21no—
507C33—21no—
508C33—61no—
509C33—61no—
510C33—61no—
511C33—91no—
512C33—181no—
513C33C2×C32×D311yescharacteristic
514C33C2×C32×D311yescharacteristic
515C33C2×C32×D311yescharacteristic
516C33C2×C32×D311yescharacteristic
517C33C2×C3×C3⋊D311yescharacteristic
5183−1+2—61no—
5193−1+2—61no—
5203−1+2—61no—
5213−1+2—61no—
5223−1+2—61no—
5233−1+2—61no—
5243−1+2—61no—
5253−1+2—61no—
5263−1+2—61no—
5273−1+2—61no—
5283−1+2—61no—
5293−1+2—61no—
5303−1+2—61no—
5313−1+2—61no—
5323−1+2—61no—
5333−1+2—61no—
5343−1+2—61no—
5353−1+2—61no—
5363−1+2—61no—
5373−1+2—62no—
5383−1+2—61no—
5393−1+2—61no—
5403−1+2—61no—
5413−1+2—61no—
5423−1+2—61no—
5433−1+2—61no—
5443−1+2—61no—
5453−1+2—61no—
5463−1+2—61no—
5473−1+2—61no—
5483−1+2—61no—
5493−1+2—61no—
5503−1+2—61no—
5513−1+2—61no—
5523−1+2—61no—
5533−1+2—61no—
5543−1+2—61no—
5553−1+2—61no—
5563−1+2—61no—
5573−1+2—61no—
5583−1+2—61no—
5593−1+2—61no—
5603−1+2—61no—
5613−1+2—61no—
5623−1+2—61no—
5633−1+2—61no—
5643−1+2—61no—
5653−1+2—61no—
5663−1+2—61no—
567H(3,𝔽3)—31no—
568H(3,𝔽3)—31no—
569H(3,𝔽3)—31no—
570H(3,𝔽3)—61no—
571H(3,𝔽3)—61no—
572H(3,𝔽3)—61no—
573H(3,𝔽3)—91no—
574H(3,𝔽3)—91no—
575H(3,𝔽3)—181no—
576H(3,𝔽3)—181no—
577H(3,𝔽3)—181no—
578H(3,𝔽3)—181no—
579C3×C9—21no—
580C3×C9—21no—
581C3×C9—21no—
582C3×C9—21no—
583C3×C9—21no—
584C3×C9—21no—
585C3×C9—21no—
586C3×C9—21no—
587C3×C9—21no—
588C3×C9—21no—
589C3×C9—21no—
590C3×C9—21no—
591C3×C9—21no—
592C3×C9—21no—
593C3×C9—21no—
594C3×C9—31no—
595C3×C9—31no—
596C3×C9—31no—
597C3×C9—31no—
598C3×C9—31no—
599C3×C9—31no—
600C3×C9—61no—
601C3×C9—61no—
602C3×C9—61no—
603C3×C9—61no—
604C3×C9—61no—
605C3×C9—61no—
606C3×C9—61no—
607C3×C9—61no—
608C3×C9—61no—
609C3×C9—61no—
610C3×C9—61no—
611C3×C9—61no—
612C3×C9—61no—
613C3×C9—61no—
614C3×C9—61no—
615C3×C9C2×(C3⋊D3)⋊C311yescharacteristic, complemented
616C3×C9C2×(C3⋊D3)⋊C311yescharacteristic, complemented
617C3×C9C2×(C3⋊D3)⋊C311yescharacteristic, complemented
618C3×C9C2×C3×C3⋊D311yescharacteristic
619C3×C9C2×C3×C3⋊D311yescharacteristic
620C3×C9C2×C3×C3⋊D311yescharacteristic
621C2×C32—31no—
622C2×C32—31no—
623C2×C32—31no—
624C2×C32—31no—
625C2×C32—31no—
626C2×C32—31no—
627C2×C32—31no—
628C2×C32—31no—
629C2×C32—61no—
630C2×C32—61no—
631C2×C32—61no—
632C2×C32—61no—
633C2×C32—61no—
634C2×C32—61no—
635C2×C32—61no—
636C2×C32—61no—
637C2×C32—61no—
638C2×C32—61no—
639C2×C32—61no—
640C2×C32—61no—
641C2×C32—61no—
642C2×C32—61no—
643C2×C32—61no—
644C2×C32—61no—
645C2×C32—61no—
646C2×C32—61no—
647C2×C32—61no—
648C2×C32—61no—
649C2×C32—61no—
650C2×C32—61no—
651C2×C32—91no—
652C2×C32—181no—
653C2×C32—181no—
654C2×C32—181no—
655C2×C32—181no—
656C2×C32—181no—
657C2×C32—272no—
658C2×C32C3×(C3⋊D3)⋊C311yescharacteristic
659C2×C32C3×(C3⋊D3)⋊C311yescharacteristic
660C2×C32C3×(C3⋊D3)⋊C311yescharacteristic
661C2×C32C32×C3⋊D311yescharacteristic
662C3⋊D3—32no—
663C3⋊D3—32no—
664C3⋊D3—32no—
665C3⋊D3—32no—
666C3×D3—92no—
667C3×D3—92no—
668C3×D3—92no—
669C3×D3—92no—
670C3×D3—272no—
671C3×D3—272no—
672C3×D3—272no—
673C3×D3—272no—
674C3×D3—272no—
675C3×D3—272no—
676C3×D3—272no—
677C2×C9—21no—
678C2×C9—21no—
679C2×C9—21no—
680C2×C9—21no—
681C2×C9—61no—
682C2×C9—61no—
683C2×C9—61no—
684C2×C9—61no—
685C2×C9—61no—
686C2×C9—61no—
687C2×C9—61no—
688C2×C9—61no—
689C2×C9—61no—
690C2×C9—61no—
691C2×C9—61no—
692C2×C9—61no—
693C2×C9—61no—
694C2×C9—272no—
695C2×C9—272no—
696C2×C9—272no—
697C2×C9C3⋊((C3⋊D3)⋊C3)11yescharacteristic
698C22×C3—271no—
699C22×C3—811no—
700C2×D3—91no—
701C2×D3—91no—
702C2×D3—91no—
703C2×D3—91no—
704C2×D3—271no—
705C2×D3—271no—
706C2×D3—271no—
707C32—31no—
708C32—31no—
709C32—31no—
710C32—31no—
711C32—31no—
712C32—31no—
713C32—31no—
714C32—31no—
715C32—61no—
716C32—61no—
717C32—61no—
718C32—61no—
719C32—61no—
720C32—61no—
721C32—61no—
722C32—61no—
723C32—61no—
724C32—61no—
725C32—61no—
726C32—61no—
727C32—61no—
728C32—61no—
729C32—61no—
730C32—61no—
731C32—61no—
732C32—61no—
733C32—61no—
734C32—61no—
735C32—61no—
736C32—61no—
737C32—91no—
738C32—181no—
739C32—181no—
740C32—181no—
741C32—181no—
742C32—181no—
743C32C2×C3×(C3⋊D3)⋊C311yescharacteristic
744C32C2×C3×(C3⋊D3)⋊C311yescharacteristic
745C32C2×C3×(C3⋊D3)⋊C311yescharacteristic
746C32C2×C32×C3⋊D311yescharacteristic
747C9—21no—
748C9—21no—
749C9—21no—
750C9—21no—
751C9—61no—
752C9—61no—
753C9—61no—
754C9—61no—
755C9—61no—
756C9—61no—
757C9—61no—
758C9—61no—
759C9—61no—
760C9—61no—
761C9—61no—
762C9—61no—
763C9—61no—
764C9C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
765C2×C3—21no—
766C2×C3—61no—
767C2×C3—61no—
768C2×C3—61no—
769C2×C3—91no—
770C2×C3—181no—
771C2×C3—181no—
772C2×C3—181no—
773C2×C3—181no—
774C2×C3—181no—
775C2×C3—181no—
776C2×C3—181no—
777C2×C3—272no—
778C2×C3—812no—
779C2×C3C3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
780C2×C3#9239411yescharacteristic
781D3—92no—
782D3—92no—
783D3—92no—
784D3—92no—
785D3—272no—
786D3—272no—
787D3—272no—
788C22—271noSylow
789C3—21no—
790C3—61no—
791C3—61no—
792C3—61no—
793C3—91no—
794C3—181no—
795C3—181no—
796C3—181no—
797C3—181no—
798C3—181no—
799C3—181no—
800C3—181no—
801C3C2×C3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
802C3C2×#9239411yescharacteristic
803C2—272no—
804C2#1309147411yescharacteristic, direct product factor
subgroupG/H
centerC2×C3C3×C3⋊((C3⋊D3)⋊C3)
commutator, cosocle, hypocenterC3×H(3,𝔽3)C22×C32
FrattiniC32C2×C32×C3⋊D3
FittingC2×#10624882C2
socleC2×C32C32×C3⋊D3
prime radicalC2×#92300C3
hypercenterC2×C9C3⋊((C3⋊D3)⋊C3)
LCSG ▷ C3×H(3,𝔽3)
UCSC1 ◁ C2×C3 ◁ C2×C9

Complements

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

NH ≅ G/Ntype
1. #13091474C2direct (N × H)
2. C2×#10624882C2semidirect
3. C2×C3⋊#4208C3semidirect
5. C2×#92305C3semidirect
6. C2×#92305C3semidirect
11. #10624882C22semidirect
13. C2×C3×#737C2×C3semidirect
14. C2×C32×3−1+2D3semidirect
15. C3⋊#4208C2×C3semidirect
19. C2×#6893C2×C3semidirect
20. C2×#6893C2×C3semidirect
33. C2×C9⋊H(3,𝔽3)D3semidirect
34. C2×C9⋊H(3,𝔽3)D3semidirect
35. C2×C9⋊H(3,𝔽3)D3semidirect
38. #92305C2×C3semidirect
39. #92305C2×C3semidirect
69. C3×#737C22×C3semidirect
70. C32×3−1+2C2×D3semidirect
73. #6893C22×C3semidirect
74. #6893C22×C3semidirect
87. C9⋊H(3,𝔽3)C2×D3semidirect
88. C9⋊H(3,𝔽3)C2×D3semidirect
89. C9⋊H(3,𝔽3)C2×D3semidirect
146. C2×C32×C9C3×D3semidirect
147. C2×C32×C9C3×D3semidirect
148. C2×C32×C9C3×D3semidirect
199. C2×C32⋊C9C3×D3semidirect
200. C2×C32⋊C9C3×D3semidirect
201. C2×C32⋊C9C3×D3semidirect
202. C2×C32⋊C9C3×D3semidirect
203. C2×C32⋊C9C3×D3semidirect
204. C2×C32⋊C9C3×D3semidirect
295. C32×C9C2×C3×D3semidirect
296. C32×C9C2×C3×D3semidirect
297. C32×C9C2×C3×D3semidirect
331. C32⋊C9C2×C3×D3semidirect
332. C32⋊C9C2×C3×D3semidirect
333. C32⋊C9C2×C3×D3semidirect
334. C32⋊C9C2×C3×D3semidirect
335. C32⋊C9C2×C3×D3semidirect
336. C32⋊C9C2×C3×D3semidirect
458. C2×C3×C9(C3⋊D3)⋊C3semidirect
459. C2×C3×C9(C3⋊D3)⋊C3semidirect
460. C2×C3×C9(C3⋊D3)⋊C3semidirect
615. C3×C9C2×(C3⋊D3)⋊C3semidirect
616. C3×C9C2×(C3⋊D3)⋊C3semidirect
617. C3×C9C2×(C3⋊D3)⋊C3semidirect
804. C2#13091474direct (N × H)

Maximal subgroups

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

subgroupindex
#130914742
C2×#106248822
C2×C3⋊#42083
C2×C3⋊D3×3−1+23
C2×#923053
C2×#923003
C2×#922623