Finite Group Databasebeta

← #13156822

Subgroups — #13156822

Order 1728.

1290 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88804C211yesmaximal, characteristic
2C2×#88804C211yesmaximal, characteristic
3C2×#88804C211yesmaximal, characteristic
4C2×C3×#3724C211yesmaximal, characteristic, complemented
5C2×C3×Dic32C211yesmaximal, characteristic, complemented
6#11722082C211yesmaximal, characteristic, complemented
7C3×#63579C211yesmaximal, characteristic, complemented
8#10591289—31nomaximal
9#10591258—31nomaximal
10#10591202—31nomaximal
11C23×C3⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×C3⋊Dic3C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18#88804—22no—
19#88804—22no—
20#88804C414yescomplemented
21C3×#3724—22no—
22C3×Dic32—22no—
23C2×#3752—31no—
24C2×#3752—31no—
25C2×#3752—31no—
26C2×C3×Dic3⋊C4—31no—
27C2×C3×Dic3⋊C4—31no—
28C2×C3×C4×Dic3—31no—
29C2×C3×C4×Dic3—31no—
30C2×#3724D311yescharacteristic, complemented
31C2×#3722—31no—
32C2×#3722—31no—
33C2×#3722—31no—
34C2×#3722—31no—
35C2×#3722—31no—
36C2×#3722—31no—
37C2×#3722—61no—
38C2×#3722—61no—
39C2×#3722—61no—
40C2×Dic32D311yescharacteristic, complemented
41C3×C3⋊#95—31no—
42C3×C3⋊#95—31no—
43#63579—31no—
44#63579—31no—
45#63579—31no—
46#63579D311yescharacteristic, complemented
47C23×C33C2311yescharacteristic
48C22×C3⋊(C3⋊D3)—21no—
49C22×C3⋊(C3⋊D3)—21no—
50C22×C3⋊(C3⋊D3)—21no—
51C22×C3⋊(C3⋊D3)—21no—
52C22×C3⋊(C3⋊D3)—21no—
53C22×C3⋊(C3⋊D3)—21no—
54C22×C3⋊(C3⋊D3)C2×C412yes—
55C2×C3×C3⋊Dic3—21no—
56C2×C3×C3⋊Dic3—21no—
57C2×C3×C3⋊Dic3—21no—
58C2×C3×C3⋊Dic3—21no—
59C2×C3×C3⋊Dic3—21no—
60C2×C3×C3⋊Dic3—21no—
61C2×C3×C3⋊Dic3—21no—
62C2×C3×C3⋊Dic3C2×C412yes—
63C2×C3×C3⋊Dic3D412yes—
64C2×C32×Dic3—21no—
65C2×C32×Dic3—21no—
66C2×C32×Dic3—21no—
67C2×C32×Dic3—21no—
68C2×C32×Dic3—21no—
69C2×C32×Dic3—21no—
70C2×C32×Dic3—21no—
71C2×C32×Dic3C2×C412yes—
72C2×C32×Dic3D412yes—
73#4990—91no—
74#4940—91no—
75#4669—91no—
76C23×C3⋊D3—31no—
77C23×C3⋊D3—31no—
78C23×C3⋊D3—31no—
79C23×C3⋊D3—61no—
80C23×C3⋊D3—61no—
81C23×C3⋊D3—61no—
82C23×C3⋊D3—121no—
83C22×C32×C4—31no—
84C22×C32×C4—31no—
85C22×C32×C4—31no—
86C22×C3⋊Dic3C2×D311yescharacteristic
87C22×C3⋊Dic3C2×D311yescharacteristic
88C22×C3⋊Dic3C2×D311yescharacteristic
89C22×C3×Dic3—21no—
90C22×C3×Dic3—21no—
91C22×C3×Dic3—21no—
92C22×C3×Dic3—31no—
93C22×C3×Dic3—31no—
94C22×C3×Dic3—31no—
95C22×C3×Dic3—31no—
96C22×C3×Dic3—31no—
97C22×C3×Dic3—31no—
98C22×C3×Dic3—61no—
99C22×C3×Dic3—61no—
100C22×C3×Dic3—61no—
101C22×C3×Dic3C2×D311yescharacteristic
102C22×C3×Dic3C2×D311yescharacteristic
103C22×C3×Dic3C2×D311yescharacteristic
104C22×C3×Dic3C2×D311yescharacteristic
105C22×C3×Dic3C2×D311yescharacteristic
106C22×C3×Dic3C2×D311yescharacteristic
107#3752—34no—
108#3752—62no—
109#3752—62no—
110C3×Dic3⋊C4—62no—
111C3×Dic3⋊C4—62no—
112C3×C4×Dic3—62no—
113C3×C4×Dic3—62no—
114#3724—22no—
115#3722—34no—
116#3722—34no—
117#3722—62no—
118#3722—62no—
119#3722—64no—
120#3722—64no—
121#3722—64no—
122#3722—62no—
123#3722—62no—
124Dic32—22no—
125C22×C33C22×C411yescharacteristic
126C22×C33C2×D411yescharacteristic
127C22×C33C2×D411yescharacteristic
128C22×C33#4111yescharacteristic
129C22×C33#4111yescharacteristic
130C22×C33#4111yescharacteristic
131C22×C33#4111yescharacteristic
132C2×C3⋊(C3⋊D3)—22no—
133C2×C3⋊(C3⋊D3)—22no—
134C2×C3⋊(C3⋊D3)—22no—
135C2×C3⋊(C3⋊D3)—41no—
136C2×C3⋊(C3⋊D3)—41no—
137C2×C3⋊(C3⋊D3)—41no—
138C2×C3⋊(C3⋊D3)—41no—
139C3×C3⋊Dic3—22no—
140C3×C3⋊Dic3—22no—
141C3×C3⋊Dic3—41no—
142C32×Dic3—22no—
143C32×Dic3—22no—
144C32×Dic3—41no—
145C2×C3×C4⋊C4—91no—
146C2×C3×C42—91no—
147C2×(C2×D3)⋊C4—91no—
148C2×(C2×D3)⋊C4—91no—
149C2×(C2×D3)⋊C4—91no—
150C2×(C2×D3)⋊C4—91no—
151C2×(C2×D3)⋊C4—91no—
152C2×(C2×D3)⋊C4—91no—
153C2×(C2×D3)⋊C4—91no—
154C2×(C2×D3)⋊C4—91no—
155C2×(C2×D3)⋊C4—91no—
156C2×(C2×D3)⋊C4—181no—
157C2×(C2×D3)⋊C4—181no—
158C2×(C2×D3)⋊C4—181no—
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—31no—
161C2×C4×Dic3—31no—
162C2×C4×Dic3—31no—
163C3×#95—91no—
164C3⋊#95—31no—
165C3⋊#95—31no—
166C3⋊#95—91no—
167C3⋊#95—91no—
168C3⋊#95—91no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—21no—
172C23×C32—41no—
173C23×C32C22×D311yescharacteristic
174C23×C32C22×D311yescharacteristic
175C23×C32C22×D311yescharacteristic
176C22×C3⋊D3—32no—
177C22×C3⋊D3—32no—
178C22×C3⋊D3—32no—
179C22×C3⋊D3—62no—
180C22×C3⋊D3—62no—
181C22×C3⋊D3—62no—
182C22×C3⋊D3—61no—
183C22×C3⋊D3—61no—
184C22×C3⋊D3—61no—
185C22×C3⋊D3—61no—
186C22×C3⋊D3—61no—
187C22×C3⋊D3—61no—
188C22×C3⋊D3—62no—
189C22×C3⋊D3—62no—
190C22×C3⋊D3—62no—
191C22×C3⋊D3—62no—
192C22×C3⋊D3—62no—
193C22×C3⋊D3—62no—
194C22×C3⋊D3—61no—
195C22×C3⋊D3—61no—
196C22×C3⋊D3—61no—
197C22×C3⋊D3—61no—
198C22×C3⋊D3—61no—
199C22×C3⋊D3—61no—
200C22×C3⋊D3—61no—
201C22×C3⋊D3—61no—
202C22×C3⋊D3—61no—
203C22×C3⋊D3—61no—
204C22×C3⋊D3—61no—
205C22×C3⋊D3—61no—
206C22×C3⋊D3—122no—
207C22×C3⋊D3—121no—
208C22×C3⋊D3—121no—
209C22×C3⋊D3—121no—
210C22×C3⋊D3—121no—
211C22×C3⋊D3—121no—
212C22×C3⋊D3—121no—
213C22×C3⋊D3—121no—
214C22×C3⋊D3—121no—
215C22×C3⋊D3—121no—
216C22×C3⋊D3—121no—
217C22×C3⋊D3—121no—
218C22×C3⋊D3—121no—
219C22×C3⋊D3—122no—
220C22×C3⋊D3—122no—
221C22×C3⋊D3—122no—
222C22×C3⋊D3—122no—
223C22×C3⋊D3—122no—
224C22×C3⋊D3—122no—
225C2×C32×C4—32no—
226C2×C32×C4—32no—
227C2×C32×C4—61no—
228C2×C32×C4—61no—
229C2×C32×C4—61no—
230C2×C32×C4—61no—
231C2×C32×C4—61no—
232C2×C32×C4—61no—
233C2×C32×C4—61no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3C4×D312yes—
242C2×C3⋊Dic3#6712yes—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—22no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—22no—
259C2×C3×Dic3—22no—
260C2×C3×Dic3—32no—
261C2×C3×Dic3—32no—
262C2×C3×Dic3—32no—
263C2×C3×Dic3—32no—
264C2×C3×Dic3—41no—
265C2×C3×Dic3—41no—
266C2×C3×Dic3—41no—
267C2×C3×Dic3—41no—
268C2×C3×Dic3—41no—
269C2×C3×Dic3—41no—
270C2×C3×Dic3—62no—
271C2×C3×Dic3—62no—
272C2×C3×Dic3—61no—
273C2×C3×Dic3—61no—
274C2×C3×Dic3—61no—
275C2×C3×Dic3—61no—
276C2×C3×Dic3—61no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—62no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3—121no—
288C2×C3×Dic3—121no—
289C2×C3×Dic3—121no—
290C2×C3×Dic3—121no—
291C2×C3×Dic3—121no—
292C2×C3×Dic3—121no—
293C2×C3×Dic3C4×D312yes—
294C2×C3×Dic3C4×D312yes—
295C2×C3×Dic3D1212yes—
296C2×C3×Dic3#6712yes—
297#388—271noSylow
298C2×C33#11711yescharacteristic
299C2×C33C4×D411yescharacteristic
300C2×C33C4×D411yescharacteristic
301C2×C33#12111yescharacteristic
302C2×C33#12311yescharacteristic
303C2×C33#12411yescharacteristic
304C2×C33#12611yescharacteristic
305C3⋊(C3⋊D3)—42no—
306C23×D3—91no—
307C23×D3—91no—
308C23×D3—91no—
309C23×D3—181no—
310C23×D3—181no—
311C23×D3—181no—
312C23×D3—361no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C22×C3×C4—91no—
323C22×C3×C4—91no—
324C22×C3×C4—91no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—31no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334C22×Dic3D3211yescharacteristic
335C22×Dic3D3211yescharacteristic
336C22×Dic3D3211yescharacteristic
337C3×C4⋊C4—182no—
338C3×C42—182no—
339(C2×D3)⋊C4—94no—
340(C2×D3)⋊C4—94no—
341(C2×D3)⋊C4—94no—
342(C2×D3)⋊C4—184no—
343(C2×D3)⋊C4—182no—
344(C2×D3)⋊C4—182no—
345(C2×D3)⋊C4—182no—
346(C2×D3)⋊C4—182no—
347(C2×D3)⋊C4—182no—
348(C2×D3)⋊C4—184no—
349(C2×D3)⋊C4—184no—
350(C2×D3)⋊C4—182no—
351Dic3⋊C4—62no—
352Dic3⋊C4—62no—
353C4×Dic3—62no—
354C4×Dic3—62no—
355C22×C32—21no—
356C22×C32—21no—
357C22×C32—21no—
358C22×C32—21no—
359C22×C32—21no—
360C22×C32—21no—
361C22×C32—21no—
362C22×C32—21no—
363C22×C32—21no—
364C22×C32—21no—
365C22×C32—21no—
366C22×C32—21no—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32—21no—
370C22×C32—21no—
371C22×C32—21no—
372C22×C32—21no—
373C22×C32—21no—
374C22×C32—21no—
375C22×C32—21no—
376C22×C32—41no—
377C22×C32—41no—
378C22×C32—41no—
379C22×C32—41no—
380C22×C32—41no—
381C22×C32—41no—
382C22×C32—41no—
383C22×C32C2×C4×D311yescharacteristic
384C22×C32C2×C4×D311yescharacteristic
385C22×C32C2×C4×D311yescharacteristic
386C22×C32C2×D1211yescharacteristic
387C22×C32#23511yescharacteristic
388C22×C32#23511yescharacteristic
389C22×C32#23511yescharacteristic
390C22×C32#23511yescharacteristic
391C22×C32#23511yescharacteristic
392C22×C32#23511yescharacteristic
393C22×C32#23511yescharacteristic
394C22×C32D3×D411yescharacteristic
395C22×C32D3×D411yescharacteristic
396C22×C32D3×D411yescharacteristic
397C22×C32#23711yescharacteristic
398C22×C32#23711yescharacteristic
399C22×C32#23911yescharacteristic
400C22×C32#23911yescharacteristic
401C22×C32#23911yescharacteristic
402C22×C32C2×#6711yescharacteristic
403C22×C32C2×#6711yescharacteristic
404C2×C3⋊D3—62no—
405C2×C3⋊D3—62no—
406C2×C3⋊D3—62no—
407C2×C3⋊D3—64no—
408C2×C3⋊D3—64no—
409C2×C3⋊D3—64no—
410C2×C3⋊D3—62no—
411C2×C3⋊D3—62no—
412C2×C3⋊D3—62no—
413C2×C3⋊D3—62no—
414C2×C3⋊D3—62no—
415C2×C3⋊D3—62no—
416C2×C3⋊D3—122no—
417C2×C3⋊D3—122no—
418C2×C3⋊D3—122no—
419C2×C3⋊D3—122no—
420C2×C3⋊D3—122no—
421C2×C3⋊D3—122no—
422C2×C3⋊D3—124no—
423C2×C3⋊D3—124no—
424C2×C3⋊D3—124no—
425C2×C3⋊D3—122no—
426C2×C3⋊D3—122no—
427C2×C3⋊D3—122no—
428C2×C3⋊D3—122no—
429C2×C3⋊D3—122no—
430C2×C3⋊D3—122no—
431C2×C3⋊D3—122no—
432C2×C3⋊D3—122no—
433C2×C3⋊D3—122no—
434C2×C3⋊D3—122no—
435C2×C3⋊D3—122no—
436C2×C3⋊D3—122no—
437C2×C3⋊D3—124no—
438C2×C3⋊D3—124no—
439C2×C3⋊D3—124no—
440C2×C3⋊D3—124no—
441C2×C3⋊D3—121no—
442C2×C3⋊D3—121no—
443C2×C3⋊D3—121no—
444C2×C3⋊D3—121no—
445C2×C3⋊D3—121no—
446C2×C3⋊D3—121no—
447C2×C3⋊D3—121no—
448C2×C3⋊D3—121no—
449C2×C3⋊D3—121no—
450C2×C3⋊D3—121no—
451C2×C3⋊D3—121no—
452C2×C3⋊D3—121no—
453C32×C4—62no—
454C32×C4—62no—
455C32×C4—121no—
456C3⋊Dic3—22no—
457C3⋊Dic3—22no—
458C3⋊Dic3—41no—
459C3×Dic3—22no—
460C3×Dic3—22no—
461C3×Dic3—22no—
462C3×Dic3—22no—
463C3×Dic3—42no—
464C3×Dic3—42no—
465C3×Dic3—42no—
466C3×Dic3—41no—
467C3×Dic3—41no—
468C3×Dic3—62no—
469C3×Dic3—62no—
470C3×Dic3—62no—
471C3×Dic3—62no—
472C3×Dic3—122no—
473C3×Dic3—122no—
474C3×Dic3—122no—
475C3×Dic3—121no—
476C3×Dic3—121no—
477C2×C4⋊C4—91no—
478C2×C22⋊C4—271no—
479C2×C22⋊C4—271no—
480C2×C22⋊C4—271no—
481C2×C42—91no—
482#95—91no—
483#95—271no—
484C33#38811yescharacteristic, complemented, Sylow
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—41no—
489C23×C3C2×D3211yescharacteristic
490C23×C3C2×D3211yescharacteristic
491C23×C3C2×D3211yescharacteristic
492C22×D3—92no—
493C22×D3—92no—
494C22×D3—92no—
495C22×D3—182no—
496C22×D3—182no—
497C22×D3—182no—
498C22×D3—182no—
499C22×D3—182no—
500C22×D3—182no—
501C22×D3—182no—
502C22×D3—182no—
503C22×D3—182no—
504C22×D3—181no—
505C22×D3—181no—
506C22×D3—181no—
507C22×D3—181no—
508C22×D3—181no—
509C22×D3—181no—
510C22×D3—181no—
511C22×D3—181no—
512C22×D3—181no—
513C22×D3—181no—
514C22×D3—181no—
515C22×D3—181no—
516C22×D3—181no—
517C22×D3—181no—
518C22×D3—181no—
519C22×D3—181no—
520C22×D3—181no—
521C22×D3—181no—
522C22×D3—362no—
523C22×D3—361no—
524C22×D3—361no—
525C22×D3—361no—
526C22×D3—361no—
527C22×D3—361no—
528C22×D3—361no—
529C22×D3—361no—
530C22×D3—361no—
531C22×D3—361no—
532C22×D3—361no—
533C22×D3—361no—
534C22×D3—361no—
535C22×D3—362no—
536C22×D3—362no—
537C22×D3—362no—
538C22×D3—362no—
539C22×D3—362no—
540C22×D3—362no—
541C2×C3×C4—32no—
542C2×C3×C4—32no—
543C2×C3×C4—32no—
544C2×C3×C4—32no—
545C2×C3×C4—62no—
546C2×C3×C4—62no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—62no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—92no—
563C2×C3×C4—92no—
564C2×C3×C4—121no—
565C2×C3×C4—121no—
566C2×C3×C4—121no—
567C2×C3×C4—121no—
568C2×C3×C4—121no—
569C2×C3×C4—121no—
570C2×C3×C4—181no—
571C2×C3×C4—181no—
572C2×C3×C4—181no—
573C2×C3×C4—181no—
574C2×C3×C4—181no—
575C2×C3×C4—181no—
576C2×C3×C4—181no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—32no—
585C2×Dic3—32no—
586C2×Dic3—32no—
587C2×Dic3—32no—
588C2×Dic3—62no—
589C2×Dic3—62no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—62no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—121no—
606C2×Dic3—121no—
607C2×Dic3—121no—
608C2×Dic3—121no—
609C2×Dic3—121no—
610C2×Dic3—121no—
611C2×Dic3#62412yes—
612C2×Dic3#62612yes—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—21no—
616C2×C32—21no—
617C2×C32—21no—
618C2×C32—21no—
619C2×C32—21no—
620C2×C32—21no—
621C2×C32—21no—
622C2×C32—21no—
623C2×C32—21no—
624C2×C32—21no—
625C2×C32—21no—
626C2×C32—21no—
627C2×C32—21no—
628C2×C32—21no—
629C2×C32—21no—
630C2×C32—21no—
631C2×C32—21no—
632C2×C32—21no—
633C2×C32—21no—
634C2×C32—41no—
635C2×C32—41no—
636C2×C32—41no—
637C2×C32—41no—
638C2×C32—41no—
639C2×C32—41no—
640C2×C32—41no—
641C2×C32#87211yescharacteristic
642C2×C32#87211yescharacteristic
643C2×C32C4×D1211yescharacteristic
644C2×C32#87511yescharacteristic
645C2×C32#87611yescharacteristic
646C2×C32#67⋊C411yescharacteristic
647C2×C32#88411yescharacteristic
648C2×C32#88511yescharacteristic
649C2×C32#89211yescharacteristic
650C2×C32#89311yescharacteristic
651C2×C32#89311yescharacteristic
652C2×C32#89411yescharacteristic
653C2×C32#89411yescharacteristic
654C2×C32#89811yescharacteristic
655C2×C32#89811yescharacteristic
656C2×C32C4×#6711yescharacteristic
657C2×C32C4×#6711yescharacteristic
658C2×C32#92911yescharacteristic
659C2×C32#93011yescharacteristic
660C2×C32#93911yescharacteristic
661C2×C32#94711yescharacteristic
662C3⋊D3—124no—
663C3⋊D3—124no—
664C3⋊D3—124no—
665C3⋊D3—128no—
666C3⋊D3—122no—
667C3⋊D3—122no—
668C3⋊D3—122no—
669C24—271no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—91no—
674C22×C4—91no—
675C22×C4—91no—
676C4⋊C4—182no—
677C22⋊C4—274no—
678C22⋊C4—542no—
679C22⋊C4—542no—
680C42—182no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3#379611yescharacteristic
710C22×C3#379811yescharacteristic
711C22×C3#379811yescharacteristic
712C22×C3#379811yescharacteristic
713C22×C3#379911yescharacteristic
714C22×C3#379911yescharacteristic
715C22×C3#379911yescharacteristic
716C22×C3#379911yescharacteristic
717C22×C3#379911yescharacteristic
718C22×C3C4×D3211yescharacteristic
719C22×C3C4×D3211yescharacteristic
720C22×C3D3×D1211yescharacteristic
721C22×C3#380411yescharacteristic
722C22×C3#380411yescharacteristic
723C22×C3#380411yescharacteristic
724C22×C3C2×#62411yescharacteristic
725C22×C3C2×#62611yescharacteristic
726C22×C3D3×#6711yescharacteristic
727C22×C3D3×#6711yescharacteristic
728C22×C3D3×#6711yescharacteristic
729C22×C3#381111yescharacteristic
730C2×D3—184no—
731C2×D3—184no—
732C2×D3—184no—
733C2×D3—182no—
734C2×D3—182no—
735C2×D3—182no—
736C2×D3—182no—
737C2×D3—182no—
738C2×D3—182no—
739C2×D3—182no—
740C2×D3—182no—
741C2×D3—182no—
742C2×D3—362no—
743C2×D3—362no—
744C2×D3—362no—
745C2×D3—362no—
746C2×D3—362no—
747C2×D3—362no—
748C2×D3—364no—
749C2×D3—364no—
750C2×D3—364no—
751C2×D3—362no—
752C2×D3—362no—
753C2×D3—362no—
754C2×D3—362no—
755C2×D3—362no—
756C2×D3—362no—
757C2×D3—362no—
758C2×D3—362no—
759C2×D3—362no—
760C2×D3—362no—
761C2×D3—362no—
762C2×D3—362no—
763C2×D3—364no—
764C2×D3—364no—
765C2×D3—364no—
766C2×D3—364no—
767C2×D3—361no—
768C2×D3—361no—
769C2×D3—361no—
770C2×D3—361no—
771C2×D3—361no—
772C2×D3—361no—
773C2×D3—361no—
774C2×D3—361no—
775C2×D3—361no—
776C2×D3—361no—
777C2×D3—361no—
778C2×D3—361no—
779C3×C4—62no—
780C3×C4—62no—
781C3×C4—62no—
782C3×C4—62no—
783C3×C4—122no—
784C3×C4—122no—
785C3×C4—122no—
786C3×C4—121no—
787C3×C4—121no—
788C3×C4—182no—
789C3×C4—182no—
790C3×C4—361no—
791Dic3—22no—
792Dic3—22no—
793Dic3—41no—
794Dic3—62no—
795Dic3—62no—
796Dic3—62no—
797Dic3—62no—
798Dic3—122no—
799Dic3—122no—
800Dic3—122no—
801Dic3—121no—
802Dic3—121no—
803C32—21no—
804C32—21no—
805C32—21no—
806C32—41no—
807C32#466911yescharacteristic, complemented
808C32#494011yescharacteristic, complemented
809C32#499011yescharacteristic, complemented
810C23—272no—
811C23—541no—
812C23—541no—
813C23—541no—
814C23—541no—
815C23—541no—
816C23—541no—
817C23D3311yescharacteristic
818C2×C4—32no—
819C2×C4—32no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—92no—
828C2×C4—92no—
829C2×C4—181no—
830C2×C4—181no—
831C2×C4—181no—
832C2×C4—181no—
833C2×C4—181no—
834C2×C4—181no—
835C2×C4—181no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—41no—
858C2×C3—41no—
859C2×C3—41no—
860C2×C3—41no—
861C2×C3—41no—
862C2×C3—41no—
863C2×C3—41no—
864C2×C3#6383611yescharacteristic
865C2×C3#6383611yescharacteristic
866C2×C3#6384811yescharacteristic
867C2×C3#6385011yescharacteristic
868C2×C3#6385011yescharacteristic
869C2×C3#6385211yescharacteristic
870C2×C3#6386411yescharacteristic
871C2×C3#6386811yescharacteristic
872C2×C3#6386811yescharacteristic
873C2×C3#6387411yescharacteristic
874C2×C3#6388111yescharacteristic
875C2×C3#6389411yescharacteristic
876C2×C3#6389711yescharacteristic
877C2×C3C4×#62611yescharacteristic
878C2×C3#6390411yescharacteristic
879C2×C3#6390411yescharacteristic
880C2×C3#6390611yescharacteristic
881C2×C3#6390711yescharacteristic
882C2×C3#6395211yescharacteristic
883C2×C3#6397111yescharacteristic
884C2×C3#6397811yescharacteristic
885D3—364no—
886D3—364no—
887D3—364no—
888D3—368no—
889D3—362no—
890D3—362no—
891D3—362no—
892C22—542no—
893C22—542no—
894C22—542no—
895C22—1081no—
896C22—1081no—
897C22—1081no—
898C22—1081no—
899C22D3×#62411yescharacteristic
900C22D3×#62611yescharacteristic
901C22#8895211yescharacteristic
902C22#8895911yescharacteristic
903C22#8896211yescharacteristic
904C22#8896511yescharacteristic
905C22#8896511yescharacteristic
906C4—62no—
907C4—62no—
908C4—121no—
909C4—182no—
910C4—182no—
911C4—361no—
912C3—21no—
913C3—21no—
914C3—21no—
915C3—41no—
916C3#1059120211yescharacteristic, complemented
917C3#1059125811yescharacteristic, complemented
918C3#1059128911yescharacteristic, complemented
919C2—1082no—
920C2#1172291811yescharacteristic
921C2#1172293311yescharacteristic
922C2#1172293511yescharacteristic
923C2#1172295811yescharacteristic
924C2#1172299311yescharacteristic
925C2#1172300311yescharacteristic
926C2#1172302111yescharacteristic
subgroupG/H
center, Frattini, hypercenterC23D33
commutatorC22×C33C22×C4
Fitting, socle, cosocleC23×C33C23
prime radicalC23×C3⋊(C3⋊D3)C22
hypocenterC33#388
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
4. C2×C3×#3724C2semidirect
5. C2×C3×Dic32C2semidirect
6. #11722082C2semidirect
7. C3×#63579C2semidirect
20. #88804C4semidirect
30. C2×#3724D3semidirect
40. C2×Dic32D3semidirect
46. #63579D3semidirect
484. C33#388semidirect
807. C32#4669semidirect
808. C32#4940semidirect
809. C32#4990semidirect
916. C3#10591202semidirect
917. C3#10591258semidirect
918. C3#10591289semidirect

Maximal subgroups

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

subgroupindex
C2×#888042
C2×C3×#37242
C2×C3×Dic322
#117220822
C3×#635792
#105912893
#105912583
#105912023