Finite Group Databasebeta

← C2×#13091660 #72243933

Subgroups — C2×#13091660 #72243933

Order 2916.

858 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13091660C212yesmaximal, direct product factor
2C2×#10624934C211yesmaximal, characteristic, complemented
3C2×C3⋊(C3⋊AGL(1,ℤ/9))C311yesmaximal, characteristic, complemented
4C2×#4207⋊C3—31nomaximal
5C2×#92330C311yesmaximal, characteristic, complemented
6C2×#92330C311yesmaximal, characteristic, complemented
7C2×#92330C311yesmaximal, characteristic, complemented
8C2×#4179⋊C3—31nomaximal
9C2×#4177⋊C3—31nomaximal
10C2×C3×#4175—31nomaximal
11#10624934C2211yescharacteristic, complemented, Sylow
12C2×3−1+4—21no—
13C2×3−1+4D311yescharacteristic, complemented
14C2×C32×3−1+2C2×C311yescharacteristic, complemented
15C3⋊(C3⋊AGL(1,ℤ/9))C2×C312yescomplemented
16#4207⋊C3—32no—
17C2×#6913—21no—
18C2×#6913—21no—
19C2×#6913—21no—
20C2×#6913—21no—
21C2×#6913—21no—
22C2×#6913—21no—
23C2×#6913—21no—
24C2×#6913—21no—
25C2×#6913—21no—
26C2×#6912—21no—
27C2×#6911D311yescharacteristic, complemented
28C2×#6910—21no—
29C2×#6910D311yescharacteristic, complemented
30C2×#6908—21no—
31C2×#6908—21no—
32C2×#6908—21no—
33C2×#6908C2×C311yescharacteristic, complemented
34C2×#6908C2×C311yescharacteristic, complemented
35C2×#6908C2×C311yescharacteristic, complemented
36C2×C3×AΣL(1,𝔽27)—21no—
37C2×C3×AΣL(1,𝔽27)D311yescharacteristic
38#92330C2×C312yescomplemented
39#92330C2×C312yescomplemented
40#92330C2×C312yescomplemented
41#4179⋊C3—32no—
42#4177⋊C3—32no—
43C3×#4175—32no—
44C2×C3×C3⋊(C3⋊D3)—31no—
45C2×C3⋊(C3⋊D9)C3211yescharacteristic, complemented
46C2×#4207—31no—
47C2×#4207—31no—
48C2×#4207—31no—
49C2×C3⋊AGL(1,ℤ/9)—31no—
50C2×C3⋊AGL(1,ℤ/9)—31no—
51C2×C3⋊AGL(1,ℤ/9)—31no—
52C2×C3⋊AGL(1,ℤ/9)—91no—
53C2×C3⋊AGL(1,ℤ/9)—91no—
54C2×C3⋊AGL(1,ℤ/9)—91no—
55C2×C3×AGL(1,ℤ/9)—91no—
56C2×C3×AGL(1,ℤ/9)—91no—
57C2×C3×AGL(1,ℤ/9)—91no—
58C2×C3×(C3⋊D3)⋊C3—91no—
59C2×#4179—31no—
60C2×#4179—31no—
61C2×#4179—31no—
62C2×#4177—31no—
63C2×#4177—31no—
64C2×#4177—31no—
65C2×#4175—31no—
66C2×#4175—31no—
67C2×#4175—31no—
683−1+4—21no—
693−1+4C2×D311yescharacteristic, complemented
70C32×3−1+2C22×C311yescharacteristic, complemented
71#6913—21no—
72#6913—21no—
73#6913—21no—
74#6913—21no—
75#6913—21no—
76#6913—21no—
77#6913—21no—
78#6913—21no—
79#6913—21no—
80#6912—21no—
81#6911C2×D311yescharacteristic, complemented
82#6910—21no—
83#6910C2×D311yescharacteristic, complemented
84#6908—21no—
85#6908—21no—
86#6908—21no—
87#6908C22×C311yescharacteristic, complemented
88#6908C22×C311yescharacteristic, complemented
89#6908C22×C311yescharacteristic, complemented
90C3×AΣL(1,𝔽27)—21no—
91C3×AΣL(1,𝔽27)C2×D311yescharacteristic
92C2×C34C3×D311yescharacteristic
93C3×C3⋊(C3⋊D3)—32no—
94C2×#737—21no—
95C2×#737—21no—
96C2×#737—21no—
97C2×#737—21no—
98C2×#737—21no—
99C2×#737—21no—
100C2×#737—21no—
101C2×#737—21no—
102C2×#737—21no—
103C2×#737—21no—
104C2×#737—21no—
105C2×#737—21no—
106C2×#737—61no—
107C2×#737—61no—
108C2×#737—61no—
109C2×#737—61no—
110C2×#737—61no—
111C2×#737—61no—
112C2×#737—61no—
113C2×#737—61no—
114C2×#737—61no—
115C2×#737C3×D311yescharacteristic, complemented
116C2×#737C3×D311yescharacteristic, complemented
117C2×#737C3×D311yescharacteristic, complemented
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—31no—
125C2×C3×3−1+2—31no—
126C2×C3×3−1+2—31no—
127C2×C3×3−1+2—31no—
128C2×C3×3−1+2—31no—
129C2×C3×3−1+2—61no—
130C2×C3×3−1+2—61no—
131C2×C3×3−1+2—61no—
132C2×C3×3−1+2—61no—
133C2×C3×3−1+2—61no—
134C2×C3×3−1+2—61no—
135C2×C3×3−1+2—61no—
136C2×C3×3−1+2C3×D311yescharacteristic
137C2×C3×3−1+2C3×D311yescharacteristic
138C2×C3×3−1+2C3×D311yescharacteristic
139C2×C3×H(3,𝔽3)—21no—
140C2×C3×H(3,𝔽3)C3⋊D311yescharacteristic
141C2×C32×C9—21no—
142C2×C32×C9C2×C3211yescharacteristic, complemented
143C3⋊(C3⋊D9)C2×C3212yescomplemented
144#4207—32no—
145#4207—32no—
146#4207—32no—
147C3⋊AGL(1,ℤ/9)—32no—
148C3⋊AGL(1,ℤ/9)—32no—
149C3⋊AGL(1,ℤ/9)—32no—
150C3⋊AGL(1,ℤ/9)—92no—
151C3⋊AGL(1,ℤ/9)—92no—
152C3⋊AGL(1,ℤ/9)—92no—
153C3×AGL(1,ℤ/9)—92no—
154C3×AGL(1,ℤ/9)—92no—
155C3×AGL(1,ℤ/9)—92no—
156C3×(C3⋊D3)⋊C3—92no—
157C2×#733—21no—
158C2×#733—21no—
159C2×#733—21no—
160C2×#733—21no—
161C2×#733—21no—
162C2×#733—21no—
163C2×#733—21no—
164C2×#733—21no—
165C2×#733—21no—
166C2×#732—21no—
167C2×#732—21no—
168C2×#732—21no—
169C2×#732C3×D311yescharacteristic, complemented
170C2×#732C3×D311yescharacteristic, complemented
171C2×#732C3×D311yescharacteristic, complemented
172C2×#731—21no—
173C2×#731—21no—
174C2×#731—21no—
175C2×#731—21no—
176C2×#731—21no—
177C2×#731—21no—
178C2×#731—21no—
179C2×#731—21no—
180C2×#731—21no—
181C2×#731—21no—
182C2×#731—21no—
183C2×#731—21no—
184C2×#731C3×D311yescharacteristic, complemented
185C2×#731C3×D311yescharacteristic, complemented
186C2×#731C3×D311yescharacteristic, complemented
187C2×AΣL(1,𝔽27)—21no—
188C2×AΣL(1,𝔽27)—21no—
189C2×AΣL(1,𝔽27)—21no—
190C2×AΣL(1,𝔽27)—21no—
191C2×AΣL(1,𝔽27)—21no—
192C2×AΣL(1,𝔽27)—21no—
193C2×AΣL(1,𝔽27)—21no—
194C2×AΣL(1,𝔽27)—21no—
195C2×AΣL(1,𝔽27)—21no—
196C2×AΣL(1,𝔽27)—21no—
197C2×AΣL(1,𝔽27)—21no—
198C2×AΣL(1,𝔽27)—21no—
199C2×AΣL(1,𝔽27)C3×D311yescharacteristic
200C2×AΣL(1,𝔽27)C3×D311yescharacteristic
201C2×AΣL(1,𝔽27)C3×D311yescharacteristic
202#4179—32no—
203#4179—32no—
204#4179—32no—
205#4177—32no—
206#4177—32no—
207#4177—32no—
208#4175—32no—
209#4175—32no—
210#4175—32no—
211C2×C3⋊(C3⋊D3)—31no—
212C2×C3×C3⋊D3—91no—
213C2×C3×C3⋊D3—271no—
214C2×C3×C3⋊D3—271no—
215C2×C3×C3⋊D3—272no—
216C2×C32×D3—271no—
217C2×C3⋊D9—31no—
218C2×C3⋊D9—31no—
219C2×C3⋊D9—31no—
220C2×C3⋊D9—91no—
221C2×C3⋊D9—91no—
222C2×C3⋊D9—91no—
223C2×AGL(1,ℤ/9)—91no—
224C2×AGL(1,ℤ/9)—91no—
225C2×AGL(1,ℤ/9)—91no—
226C2×AGL(1,ℤ/9)—91no—
227C2×AGL(1,ℤ/9)—91no—
228C2×AGL(1,ℤ/9)—91no—
229C2×AGL(1,ℤ/9)—91no—
230C2×AGL(1,ℤ/9)—91no—
231C2×AGL(1,ℤ/9)—91no—
232C2×AGL(1,ℤ/9)—271no—
233C2×AGL(1,ℤ/9)—271no—
234C2×(C3⋊D3)⋊C3—91no—
235C2×(C3⋊D3)⋊C3—91no—
236C2×(C3⋊D3)⋊C3—91no—
237C2×C3×D9—91no—
238C2×C3×D9—91no—
239C2×C3×D9—91no—
240C34C2×C3×D311yescharacteristic
241#737—21no—
242#737—21no—
243#737—21no—
244#737—21no—
245#737—21no—
246#737—21no—
247#737—21no—
248#737—21no—
249#737—21no—
250#737—21no—
251#737—21no—
252#737—21no—
253#737—61no—
254#737—61no—
255#737—61no—
256#737—61no—
257#737—61no—
258#737—61no—
259#737—61no—
260#737—61no—
261#737—61no—
262#737C2×C3×D311yescharacteristic, complemented
263#737C2×C3×D311yescharacteristic, complemented
264#737C2×C3×D311yescharacteristic, complemented
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—31no—
272C3×3−1+2—31no—
273C3×3−1+2—31no—
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+2—61no—
281C3×3−1+2—61no—
282C3×3−1+2—61no—
283C3×3−1+2C2×C3×D311yescharacteristic
284C3×3−1+2C2×C3×D311yescharacteristic
285C3×3−1+2C2×C3×D311yescharacteristic
286C3×H(3,𝔽3)—21no—
287C3×H(3,𝔽3)C2×C3⋊D311yescharacteristic
288C32×C9—21no—
289C32×C9C22×C3211yescharacteristic, complemented
290#733—21no—
291#733—21no—
292#733—21no—
293#733—21no—
294#733—21no—
295#733—21no—
296#733—21no—
297#733—21no—
298#733—21no—
299#732—21no—
300#732—21no—
301#732—21no—
302#732C2×C3×D311yescharacteristic, complemented
303#732C2×C3×D311yescharacteristic, complemented
304#732C2×C3×D311yescharacteristic, complemented
305#731—21no—
306#731—21no—
307#731—21no—
308#731—21no—
309#731—21no—
310#731—21no—
311#731—21no—
312#731—21no—
313#731—21no—
314#731—21no—
315#731—21no—
316#731—21no—
317#731C2×C3×D311yescharacteristic, complemented
318#731C2×C3×D311yescharacteristic, complemented
319#731C2×C3×D311yescharacteristic, complemented
320AΣL(1,𝔽27)—21no—
321AΣL(1,𝔽27)—21no—
322AΣL(1,𝔽27)—21no—
323AΣL(1,𝔽27)—21no—
324AΣL(1,𝔽27)—21no—
325AΣL(1,𝔽27)—21no—
326AΣL(1,𝔽27)—21no—
327AΣL(1,𝔽27)—21no—
328AΣL(1,𝔽27)—21no—
329AΣL(1,𝔽27)—21no—
330AΣL(1,𝔽27)—21no—
331AΣL(1,𝔽27)—21no—
332AΣL(1,𝔽27)C2×C3×D311yescharacteristic
333AΣL(1,𝔽27)C2×C3×D311yescharacteristic
334AΣL(1,𝔽27)C2×C3×D311yescharacteristic
335C2×C33—21no—
336C2×C33—31no—
337C2×C33—61no—
338C2×C33—61no—
339C2×C33—61no—
340C2×C33—181no—
341C2×C33—182no—
342C2×C33C32×D311yescharacteristic
343C2×C33C3×C3⋊D311yescharacteristic
344C3⋊(C3⋊D3)—32no—
345C3×C3⋊D3—92no—
346C3×C3⋊D3—272no—
347C3×C3⋊D3—272no—
348C3×C3⋊D3—274no—
349C32×D3—272no—
350C2×3−1+2—21no—
351C2×3−1+2—21no—
352C2×3−1+2—21no—
353C2×3−1+2—21no—
354C2×3−1+2—21no—
355C2×3−1+2—21no—
356C2×3−1+2—21no—
357C2×3−1+2—21no—
358C2×3−1+2—21no—
359C2×3−1+2—21no—
360C2×3−1+2—21no—
361C2×3−1+2—21no—
362C2×3−1+2—31no—
363C2×3−1+2—31no—
364C2×3−1+2—31no—
365C2×3−1+2—31no—
366C2×3−1+2—31no—
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—61no—
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—61no—
410C2×3−1+2—61no—
411C2×3−1+2(C3⋊D3)⋊C311yescharacteristic
412C2×3−1+2(C3⋊D3)⋊C311yescharacteristic
413C2×3−1+2(C3⋊D3)⋊C311yescharacteristic
414C2×H(3,𝔽3)—21no—
415C2×H(3,𝔽3)—21no—
416C2×H(3,𝔽3)—21no—
417C2×H(3,𝔽3)—61no—
418C2×H(3,𝔽3)—61no—
419C2×H(3,𝔽3)—61no—
420C2×H(3,𝔽3)C3×C3⋊D311yescharacteristic
421C2×H(3,𝔽3)C3×C3⋊D311yescharacteristic
422C2×H(3,𝔽3)C3×C3⋊D311yescharacteristic
423C2×C3×C9—21no—
424C2×C3×C9—21no—
425C2×C3×C9—21no—
426C2×C3×C9—31no—
427C2×C3×C9—31no—
428C2×C3×C9—31no—
429C2×C3×C9—61no—
430C2×C3×C9—61no—
431C2×C3×C9—61no—
432C2×C3×C9—61no—
433C2×C3×C9—61no—
434C2×C3×C9—61no—
435C2×C3×C9—61no—
436C2×C3×C9—61no—
437C2×C3×C9—61no—
438C2×C3×C9—61no—
439C2×C3×C9—61no—
440C2×C3×C9—61no—
441C2×C3×C9—61no—
442C2×C3×C9—61no—
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×C9C32×D311yescharacteristic
451C2×C3×C9C32×D311yescharacteristic
452C2×C3×C9C32×D311yescharacteristic
453C3⋊D9—32no—
454C3⋊D9—32no—
455C3⋊D9—32no—
456C3⋊D9—92no—
457C3⋊D9—92no—
458C3⋊D9—92no—
459AGL(1,ℤ/9)—92no—
460AGL(1,ℤ/9)—92no—
461AGL(1,ℤ/9)—92no—
462AGL(1,ℤ/9)—92no—
463AGL(1,ℤ/9)—92no—
464AGL(1,ℤ/9)—92no—
465AGL(1,ℤ/9)—92no—
466AGL(1,ℤ/9)—92no—
467AGL(1,ℤ/9)—92no—
468AGL(1,ℤ/9)—272no—
469AGL(1,ℤ/9)—272no—
470(C3⋊D3)⋊C3—92no—
471(C3⋊D3)⋊C3—92no—
472(C3⋊D3)⋊C3—92no—
473C3×D9—92no—
474C3×D9—92no—
475C3×D9—92no—
476C22×C32—811no—
477C2×C3⋊D3—91no—
478C2×C3⋊D3—271no—
479C2×C3⋊D3—271no—
480C2×C3⋊D3—272no—
481C2×C3×D3—271no—
482C2×C3×D3—271no—
483C2×C3×D3—271no—
484C2×C3×D3—271no—
485C2×C3×D3—812no—
486C2×C3×D3—811no—
487C2×C3×D3—811no—
488C2×D9—91no—
489C2×D9—91no—
490C2×D9—91no—
491C2×D9—271no—
492C2×D9—271no—
493C33—21no—
494C33—31no—
495C33—61no—
496C33—61no—
497C33—61no—
498C33—181no—
499C33—182no—
500C33C2×C32×D311yescharacteristic
501C33C2×C3×C3⋊D311yescharacteristic
5023−1+2—21no—
5033−1+2—21no—
5043−1+2—21no—
5053−1+2—21no—
5063−1+2—21no—
5073−1+2—21no—
5083−1+2—21no—
5093−1+2—21no—
5103−1+2—21no—
5113−1+2—21no—
5123−1+2—21no—
5133−1+2—21no—
5143−1+2—31no—
5153−1+2—31no—
5163−1+2—31no—
5173−1+2—31no—
5183−1+2—31no—
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—61no—
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+2C2×(C3⋊D3)⋊C311yescharacteristic
5643−1+2C2×(C3⋊D3)⋊C311yescharacteristic
5653−1+2C2×(C3⋊D3)⋊C311yescharacteristic
566H(3,𝔽3)—21no—
567H(3,𝔽3)—21no—
568H(3,𝔽3)—21no—
569H(3,𝔽3)—61no—
570H(3,𝔽3)—61no—
571H(3,𝔽3)—61no—
572H(3,𝔽3)C2×C3×C3⋊D311yescharacteristic
573H(3,𝔽3)C2×C3×C3⋊D311yescharacteristic
574H(3,𝔽3)C2×C3×C3⋊D311yescharacteristic
575C3×C9—21no—
576C3×C9—21no—
577C3×C9—21no—
578C3×C9—31no—
579C3×C9—31no—
580C3×C9—31no—
581C3×C9—61no—
582C3×C9—61no—
583C3×C9—61no—
584C3×C9—61no—
585C3×C9—61no—
586C3×C9—61no—
587C3×C9—61no—
588C3×C9—61no—
589C3×C9—61no—
590C3×C9—61no—
591C3×C9—61no—
592C3×C9—61no—
593C3×C9—61no—
594C3×C9—61no—
595C3×C9—61no—
596C3×C9—61no—
597C3×C9—61no—
598C3×C9—61no—
599C3×C9—61no—
600C3×C9—61no—
601C3×C9—61no—
602C3×C9C2×C32×D311yescharacteristic
603C3×C9C2×C32×D311yescharacteristic
604C3×C9C2×C32×D311yescharacteristic
605C2×C32—21no—
606C2×C32—31no—
607C2×C32—31no—
608C2×C32—32no—
609C2×C32—31no—
610C2×C32—61no—
611C2×C32—61no—
612C2×C32—61no—
613C2×C32—61no—
614C2×C32—61no—
615C2×C32—61no—
616C2×C32—92no—
617C2×C32—181no—
618C2×C32—181no—
619C2×C32—182no—
620C2×C32—181no—
621C2×C32—181no—
622C2×C32—541no—
623C2×C32—541no—
624C2×C32—812no—
625C2×C32C3⋊((C3⋊D3)⋊C3)11yescharacteristic
626C2×C32C32×C3⋊D311yescharacteristic
627C3⋊D3—92no—
628C3⋊D3—272no—
629C3⋊D3—272no—
630C3⋊D3—274no—
631C3×D3—272no—
632C3×D3—272no—
633C3×D3—272no—
634C3×D3—272no—
635C3×D3—814no—
636C3×D3—812no—
637C3×D3—812no—
638C2×C9—21no—
639C2×C9—21no—
640C2×C9—21no—
641C2×C9—31no—
642C2×C9—31no—
643C2×C9—61no—
644C2×C9—61no—
645C2×C9—61no—
646C2×C9—61no—
647C2×C9—61no—
648C2×C9—61no—
649C2×C9—61no—
650C2×C9—61no—
651C2×C9—61no—
652C2×C9—61no—
653C2×C9—61no—
654C2×C9C3×(C3⋊D3)⋊C311yescharacteristic
655C2×C9C3×(C3⋊D3)⋊C311yescharacteristic
656C2×C9C3×(C3⋊D3)⋊C311yescharacteristic
657D9—92no—
658D9—92no—
659D9—92no—
660D9—272no—
661D9—272no—
662C22×C3—811no—
663C22×C3—811no—
664C22×C3—811no—
665C22×C3—811no—
666C2×D3—271no—
667C2×D3—811no—
668C2×D3—812no—
669C2×D3—811no—
670C32—21no—
671C32—31no—
672C32—32no—
673C32—31no—
674C32—31no—
675C32—61no—
676C32—61no—
677C32—61no—
678C32—61no—
679C32—61no—
680C32—61no—
681C32—92no—
682C32—181no—
683C32—181no—
684C32—182no—
685C32—181no—
686C32—181no—
687C32—541no—
688C32—541no—
689C32C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
690C32C2×C32×C3⋊D311yescharacteristic
691C9—21no—
692C9—21no—
693C9—21no—
694C9—31no—
695C9—31no—
696C9—61no—
697C9—61no—
698C9—61no—
699C9—61no—
700C9—61no—
701C9—61no—
702C9—61no—
703C9—61no—
704C9—61no—
705C9—61no—
706C9—61no—
707C9C2×C3×(C3⋊D3)⋊C311yescharacteristic
708C9C2×C3×(C3⋊D3)⋊C311yescharacteristic
709C9C2×C3×(C3⋊D3)⋊C311yescharacteristic
710C2×C3—32no—
711C2×C3—31no—
712C2×C3—31no—
713C2×C3—61no—
714C2×C3—61no—
715C2×C3—181no—
716C2×C3—181no—
717C2×C3—181no—
718C2×C3—181no—
719C2×C3—181no—
720C2×C3—181no—
721C2×C3—181no—
722C2×C3—812no—
723C2×C3—812no—
724C2×C3—812no—
725C2×C3—812no—
726C2×C3C3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
727D3—272no—
728D3—812no—
729D3—814no—
730D3—812no—
731C22—811noSylow
732C3—32no—
733C3—31no—
734C3—31no—
735C3—61no—
736C3—61no—
737C3—181no—
738C3—181no—
739C3—181no—
740C3—181no—
741C3—181no—
742C3—181no—
743C3—181no—
744C3C2×C3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
745C2—812no—
746C2#1309166011yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#13091660
commutator, cosocle, hypocenterC32×C9C22×C32
FrattiniC32C2×C32×C3⋊D3
FittingC2×#10624934C2
socleC2×C3C3×C3⋊((C3⋊D3)⋊C3)
LCSG ▷ C32×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #13091660C2direct (N × H)
2. C2×#10624934C2semidirect
3. C2×C3⋊(C3⋊AGL(1,ℤ/9))C3semidirect
5. C2×#92330C3semidirect
6. C2×#92330C3semidirect
7. C2×#92330C3semidirect
11. #10624934C22semidirect
13. C2×3−1+4D3semidirect
14. C2×C32×3−1+2C2×C3semidirect
15. C3⋊(C3⋊AGL(1,ℤ/9))C2×C3semidirect
27. C2×#6911D3semidirect
29. C2×#6910D3semidirect
33. C2×#6908C2×C3semidirect
34. C2×#6908C2×C3semidirect
35. C2×#6908C2×C3semidirect
38. #92330C2×C3semidirect
39. #92330C2×C3semidirect
40. #92330C2×C3semidirect
45. C2×C3⋊(C3⋊D9)C32semidirect
69. 3−1+4C2×D3semidirect
70. C32×3−1+2C22×C3semidirect
81. #6911C2×D3semidirect
83. #6910C2×D3semidirect
87. #6908C22×C3semidirect
88. #6908C22×C3semidirect
89. #6908C22×C3semidirect
115. C2×#737C3×D3semidirect
116. C2×#737C3×D3semidirect
117. C2×#737C3×D3semidirect
142. C2×C32×C9C2×C32semidirect
143. C3⋊(C3⋊D9)C2×C32semidirect
169. C2×#732C3×D3semidirect
170. C2×#732C3×D3semidirect
171. C2×#732C3×D3semidirect
184. C2×#731C3×D3semidirect
185. C2×#731C3×D3semidirect
186. C2×#731C3×D3semidirect
262. #737C2×C3×D3semidirect
263. #737C2×C3×D3semidirect
264. #737C2×C3×D3semidirect
289. C32×C9C22×C32semidirect
302. #732C2×C3×D3semidirect
303. #732C2×C3×D3semidirect
304. #732C2×C3×D3semidirect
317. #731C2×C3×D3semidirect
318. #731C2×C3×D3semidirect
319. #731C2×C3×D3semidirect
746. C2#13091660direct (N × H)

Maximal subgroups

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

subgroupindex
#130916602
C2×#106249342
C2×C3⋊(C3⋊AGL(1,ℤ/9))3
C2×#4207⋊C33
C2×#923303
C2×#4179⋊C33
C2×#4177⋊C33
C2×C3×#41753