Finite Group Databasebeta

← C3×#78133 #11808942

Subgroups — C3×#78133 #11808942

Order 1152.

867 conjugacy classes of subgroups.

The subgroup lattice has 705 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#400C211yesmaximal, characteristic
2C3×#4983C211yesmaximal, characteristic
3C3×#4982C211yesmaximal, characteristic
4C3×Dic3×C4⋊C4C211yesmaximal, characteristic
5C3×Dic3×C4⋊C4C211yesmaximal, characteristic
6C3×#4660C211yesmaximal, characteristic
7C3×#4658C211yesmaximal, characteristic
8C3×#4658C211yesmaximal, characteristic
9C3×#4657C211yesmaximal, characteristic
10C3×#4657C211yesmaximal, characteristic
11C3×#4649C211yesmaximal, characteristic
12C3×#4649C211yesmaximal, characteristic
13C3×#4649C211yesmaximal, characteristic
14C3×#4649C211yesmaximal, characteristic
15C3×#4648C211yesmaximal, characteristic
16C3×#2402—31nomaximal
17#78133C311yesmaximal, characteristic, direct product factor
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×Dic3⋊C4C2211yescharacteristic
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C32×#95C2211yescharacteristic
38C32×#95C2211yescharacteristic
39C32×#95C2211yescharacteristic
40C32×#95C2211yescharacteristic
41C32×#95C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×#400—21no—
54C3×#400—31no—
55C3×#400—31no—
56C3×#400—31no—
57C3×#400D311yescharacteristic
58C3×#400C2×C311yescharacteristic
59C3×#398—31no—
60C3×#398—31no—
61C3×#398—31no—
62C3×#398—31no—
63C3×C4×C4⋊C4—31no—
64C3×C4×C4⋊C4—31no—
65C3×C4×C4⋊C4—31no—
66C3×C4×C4⋊C4—31no—
67C3×C4×C4⋊C4—31no—
68C3×C4×C4⋊C4—31no—
69C3×#376—31no—
70#4983C2×C311yescharacteristic
71#4982C2×C311yescharacteristic
72Dic3×C4⋊C4C2×C311yescharacteristic
73Dic3×C4⋊C4C2×C311yescharacteristic
74#4660C2×C311yescharacteristic
75#4658C2×C311yescharacteristic
76#4658C2×C311yescharacteristic
77#4657C2×C311yescharacteristic
78#4657C2×C311yescharacteristic
79#4649C2×C311yescharacteristic
80#4649C2×C311yescharacteristic
81#4649C2×C311yescharacteristic
82#4649C2×C311yescharacteristic
83#4648C2×C311yescharacteristic
84C22×C32×C4C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C32×C4⋊C4—22no—
100C32×C4⋊C4—22no—
101C3×C4⋊Dic3—22no—
102C3×C4⋊Dic3—22no—
103C3×Dic3⋊C4—22no—
104C3×Dic3⋊C4—22no—
105C3×Dic3⋊C4—22no—
106C3×Dic3⋊C4—22no—
107C3×Dic3⋊C4—22no—
108C3×Dic3⋊C4—22no—
109C3×Dic3⋊C4—22no—
110C3×Dic3⋊C4—22no—
111C3×C4×Dic3—22no—
112C3×C4×Dic3—22no—
113C3×C4×Dic3—22no—
114C3×C4×Dic3—22no—
115C3×C4×Dic3—22no—
116C3×C4×Dic3—22no—
117C3×C4×Dic3Q814yes—
118#2402—31noSylow
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—31no—
122C2×C3×C4⋊C4—31no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C4⋊C4—31no—
127C2×C3×C4⋊C4—31no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4C2×D311yescharacteristic
132C2×C3×C4⋊C4C2×D311yescharacteristic
133C2×C3×C4⋊C4C22×C311yescharacteristic
134C2×C3×C4⋊C4C22×C311yescharacteristic
135C2×C3×C42—31no—
136C2×C3×C42—31no—
137C2×C3×C42—31no—
138C2×C3×C42—31no—
139C2×C3×C42—31no—
140C2×C3×C42—31no—
141C2×C3×C42—31no—
142C2×C4⋊Dic3C22×C311yescharacteristic
143C2×C4⋊Dic3C22×C311yescharacteristic
144C2×Dic3⋊C4C22×C311yescharacteristic
145C2×Dic3⋊C4C22×C311yescharacteristic
146C2×Dic3⋊C4C22×C311yescharacteristic
147C2×Dic3⋊C4C22×C311yescharacteristic
148C2×Dic3⋊C4C22×C311yescharacteristic
149C2×Dic3⋊C4C22×C311yescharacteristic
150C2×Dic3⋊C4C22×C311yescharacteristic
151C2×Dic3⋊C4C22×C311yescharacteristic
152C2×C4×Dic3C22×C311yescharacteristic
153C2×C4×Dic3C22×C311yescharacteristic
154C2×C4×Dic3C22×C311yescharacteristic
155C2×C4×Dic3C22×C311yescharacteristic
156C2×C4×Dic3C22×C311yescharacteristic
157C2×C4×Dic3C22×C311yescharacteristic
158C2×C4×Dic3C22×C311yescharacteristic
159C3×#95—21no—
160C3×#95—21no—
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164C3×#95—31no—
165C3×#95—31no—
166C3×#95—31no—
167C3×#95—31no—
168C3×#95—31no—
169C3×#95—31no—
170C3×#95—31no—
171C3×#95—31no—
172C3×#95—31no—
173C3×#95—31no—
174C3×#95—31no—
175C3×#95C2×D311yescharacteristic
176C3×#95C2×D311yescharacteristic
177C3×#95C2×D311yescharacteristic
178C3×#95C2×D311yescharacteristic
179C3×#95C2×D311yescharacteristic
180C3×#95C22×C311yescharacteristic
181C3×#95C22×C311yescharacteristic
182C3×#95C22×C311yescharacteristic
183C3×#95C22×C311yescharacteristic
184C3×#95C22×C311yescharacteristic
185C3⋊#95C22×C311yescharacteristic
186C3⋊#95C22×C311yescharacteristic
187C3⋊#95C22×C311yescharacteristic
188C3⋊#95C22×C311yescharacteristic
189C3⋊#95C22×C311yescharacteristic
190C3⋊#95C22×C311yescharacteristic
191C3⋊#95C22×C311yescharacteristic
192C3⋊#95C22×C311yescharacteristic
193C3⋊#95C22×C311yescharacteristic
194C3⋊#95C22×C311yescharacteristic
195C3⋊#95C22×C311yescharacteristic
196C23×C32C2411yescharacteristic
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4C2×Q812yes—
217C2×C32×C4#4112yes—
218C2×C3×Dic3—21no—
219C2×C3×Dic3—21no—
220C2×C3×Dic3—21no—
221C2×C3×Dic3—21no—
222C2×C3×Dic3—21no—
223C2×C3×Dic3—21no—
224C2×C3×Dic3—21no—
225C2×C3×Dic3—21no—
226C2×C3×Dic3—21no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3—21no—
231C2×C3×Dic3—21no—
232C2×C3×Dic3—21no—
233C2×C3×Dic3—21no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3C2×Q812yes—
236C2×C3×Dic3C2×Q812yes—
237C2×C3×Dic3#4112yes—
238C2×C3×Dic3#4112yes—
239C2×C3×Dic3#4112yes—
240C2×C3×Dic3#4112yes—
241C2×C3×Dic3#4112yes—
242#400—31no—
243#400—31no—
244#400—31no—
245#400C3×D311yescharacteristic
246#398—31no—
247#398—31no—
248#398—31no—
249#398—31no—
250C4×C4⋊C4—31no—
251C4×C4⋊C4—31no—
252C4×C4⋊C4—31no—
253C4×C4⋊C4—31no—
254C4×C4⋊C4—31no—
255C4×C4⋊C4—31no—
256#376—31no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—31no—
265C22×C3×C4—31no—
266C22×C3×C4—31no—
267C22×C3×C4—31no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4C22×D311yescharacteristic
273C22×C3×C4C22×D311yescharacteristic
274C22×C3×C4C22×D311yescharacteristic
275C22×C3×C4C22×D311yescharacteristic
276C22×C3×C4C22×D311yescharacteristic
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C23×C311yescharacteristic
280C22×C3×C4C23×C311yescharacteristic
281C22×C3×C4C23×C311yescharacteristic
282C22×C3×C4C23×C311yescharacteristic
283C22×C3×C4C23×C311yescharacteristic
284C22×C3×C4C23×C311yescharacteristic
285C22×C3×C4C23×C311yescharacteristic
286C22×Dic3C23×C311yescharacteristic
287C22×Dic3C23×C311yescharacteristic
288C22×Dic3C23×C311yescharacteristic
289C22×Dic3C23×C311yescharacteristic
290C22×Dic3C23×C311yescharacteristic
291C22×Dic3C23×C311yescharacteristic
292C22×Dic3C23×C311yescharacteristic
293C22×Dic3C23×C311yescharacteristic
294C3×C4⋊C4—22no—
295C3×C4⋊C4—22no—
296C3×C4⋊C4—22no—
297C3×C4⋊C4—22no—
298C3×C4⋊C4—42no—
299C3×C4⋊C4—42no—
300C3×C4⋊C4—62no—
301C3×C4⋊C4—62no—
302C3×C4⋊C4—62no—
303C3×C4⋊C4—62no—
304C3×C4⋊C4—62no—
305C3×C4⋊C4—62no—
306C3×C4⋊C4—62no—
307C3×C4⋊C4—62no—
308C3×C4⋊C4—62no—
309C3×C4⋊C4—62no—
310C3×C42—34no—
311C3×C42—62no—
312C3×C42—62no—
313C3×C42—62no—
314C3×C42—62no—
315C3×C42—62no—
316C3×C42—62no—
317C4⋊Dic3—22no—
318C4⋊Dic3—22no—
319Dic3⋊C4—22no—
320Dic3⋊C4—22no—
321Dic3⋊C4—22no—
322Dic3⋊C4—22no—
323Dic3⋊C4—22no—
324Dic3⋊C4—22no—
325Dic3⋊C4—22no—
326Dic3⋊C4—22no—
327C4×Dic3—22no—
328C4×Dic3—22no—
329C4×Dic3—22no—
330C4×Dic3—22no—
331C4×Dic3—22no—
332C4×Dic3—22no—
333C4×Dic3C3×Q814yes—
334C22×C32C22×Q811yescharacteristic
335C22×C32C2×#4111yescharacteristic
336C22×C32C2×#4111yescharacteristic
337C22×C32C2×#4111yescharacteristic
338C22×C32C2×#4111yescharacteristic
339C22×C32C2×#4111yescharacteristic
340C22×C32C2×#4111yescharacteristic
341C32×C4—22no—
342C32×C4—22no—
343C32×C4—41no—
344C32×C4—41no—
345C32×C4—41no—
346C32×C4—41no—
347C32×C4—41no—
348C3×Dic3—22no—
349C3×Dic3—22no—
350C3×Dic3—22no—
351C3×Dic3—22no—
352C3×Dic3—41no—
353C3×Dic3—41no—
354C3×Dic3—41no—
355C3×Dic3#12514yes—
356C2×C4⋊C4—31no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4C2×C3×D311yescharacteristic
367C2×C4⋊C4C2×C3×D311yescharacteristic
368C2×C42—31no—
369C2×C42—31no—
370C2×C42—31no—
371C2×C42—31no—
372C2×C42—31no—
373C2×C42—31no—
374C2×C42—31no—
375#95—31no—
376#95—31no—
377#95—31no—
378#95—31no—
379#95—31no—
380#95—31no—
381#95—31no—
382#95—31no—
383#95—31no—
384#95—31no—
385#95—31no—
386#95C2×C3×D311yescharacteristic
387#95C2×C3×D311yescharacteristic
388#95C2×C3×D311yescharacteristic
389#95C2×C3×D311yescharacteristic
390#95C2×C3×D311yescharacteristic
391C23×C3—21no—
392C23×C3C23×D311yescharacteristic
393C23×C3C24×C311yescharacteristic
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—32no—
435C2×C3×C4—32no—
436C2×C3×C4—32no—
437C2×C3×C4—32no—
438C2×C3×C4—32no—
439C2×C3×C4—32no—
440C2×C3×C4—32no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4#23712yes—
478C2×C3×C4D3×Q812yes—
479C2×C3×C4C2×C3×Q812yes—
480C2×C3×C4C3×#4112yes—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3C2×C3×Q812yes—
499C2×Dic3C2×C3×Q812yes—
500C2×Dic3C3×#4112yes—
501C2×Dic3C3×#4112yes—
502C2×Dic3C3×#4112yes—
503C2×Dic3C3×#4112yes—
504C2×Dic3C3×#4112yes—
505C2×C32C2×#12511yescharacteristic
506C2×C32#52911yescharacteristic
507C2×C32#52911yescharacteristic
508C2×C32#52911yescharacteristic
509C2×C32#52911yescharacteristic
510C2×C32#53311yescharacteristic
511C2×C32#53311yescharacteristic
512C22×C4—31no—
513C22×C4—31no—
514C22×C4—31no—
515C22×C4—31no—
516C22×C4—31no—
517C22×C4—31no—
518C22×C4—31no—
519C22×C4—31no—
520C22×C4C22×C3×D311yescharacteristic
521C22×C4C22×C3×D311yescharacteristic
522C22×C4C22×C3×D311yescharacteristic
523C22×C4C22×C3×D311yescharacteristic
524C22×C4C22×C3×D311yescharacteristic
525C22×C4C22×C3×D311yescharacteristic
526C22×C4C22×C3×D311yescharacteristic
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—62no—
530C4⋊C4—62no—
531C4⋊C4—62no—
532C4⋊C4—62no—
533C4⋊C4—62no—
534C4⋊C4—62no—
535C4⋊C4—62no—
536C4⋊C4—62no—
537C4⋊C4—62no—
538C4⋊C4—62no—
539C42—34no—
540C42—62no—
541C42—62no—
542C42—62no—
543C42—62no—
544C42—62no—
545C42—62no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3C2×#23711yescharacteristic
554C22×C3C2×D3×Q811yescharacteristic
555C22×C3D3×#4111yescharacteristic
556C22×C3D3×#4111yescharacteristic
557C22×C3D3×#4111yescharacteristic
558C22×C3D3×#4111yescharacteristic
559C22×C3D3×#4111yescharacteristic
560C22×C3C22×C3×Q811yescharacteristic
561C22×C3C2×C3×#4111yescharacteristic
562C22×C3C2×C3×#4111yescharacteristic
563C22×C3C2×C3×#4111yescharacteristic
564C22×C3C2×C3×#4111yescharacteristic
565C22×C3C2×C3×#4111yescharacteristic
566C22×C3C2×C3×#4111yescharacteristic
567C3×C4—22no—
568C3×C4—22no—
569C3×C4—22no—
570C3×C4—22no—
571C3×C4—34no—
572C3×C4—42no—
573C3×C4—42no—
574C3×C4—41no—
575C3×C4—41no—
576C3×C4—41no—
577C3×C4—41no—
578C3×C4—41no—
579C3×C4—41no—
580C3×C4—41no—
581C3×C4—41no—
582C3×C4—41no—
583C3×C4—41no—
584C3×C4—62no—
585C3×C4—62no—
586C3×C4—62no—
587C3×C4—62no—
588C3×C4—81no—
589C3×C4—81no—
590C3×C4—81no—
591C3×C4—81no—
592C3×C4—81no—
593C3×C4—121no—
594C3×C4—121no—
595C3×C4—121no—
596Dic3—22no—
597Dic3—22no—
598Dic3—22no—
599Dic3—22no—
600Dic3—41no—
601Dic3—41no—
602Dic3—41no—
603Dic3C3×#12514yes—
604C32#240211yescharacteristic, complemented, Sylow
605C23C23×C3×D311yescharacteristic
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—32no—
626C2×C4—32no—
627C2×C4—32no—
628C2×C4—32no—
629C2×C4—32no—
630C2×C4—32no—
631C2×C4—32no—
632C2×C4—61no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—61no—
638C2×C4—61no—
639C2×C4—61no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4C3×#23712yes—
650C2×C4C3×D3×Q812yes—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3#562211yescharacteristic
659C2×C3#564911yescharacteristic
660C2×C3#568011yescharacteristic
661C2×C3D3×#12511yescharacteristic
662C2×C3#568811yescharacteristic
663C2×C3#570611yescharacteristic
664C2×C3#570611yescharacteristic
665C2×C3C2×C3×#12511yescharacteristic
666C2×C3C3×#52911yescharacteristic
667C2×C3C3×#52911yescharacteristic
668C2×C3C3×#52911yescharacteristic
669C2×C3C3×#52911yescharacteristic
670C2×C3C3×#53311yescharacteristic
671C2×C3C3×#53311yescharacteristic
672C22C2×C3×#23711yescharacteristic
673C22C2×C3×D3×Q811yescharacteristic
674C22C3×D3×#4111yescharacteristic
675C22C3×D3×#4111yescharacteristic
676C22C3×D3×#4111yescharacteristic
677C22C3×D3×#4111yescharacteristic
678C22C3×D3×#4111yescharacteristic
679C4—22no—
680C4—22no—
681C4—34no—
682C4—41no—
683C4—41no—
684C4—41no—
685C4—41no—
686C4—41no—
687C4—62no—
688C4—62no—
689C4—62no—
690C4—62no—
691C4—121no—
692C4—121no—
693C4—121no—
694C3—21no—
695C3#7813311yescharacteristic, direct product factor
696C3C3×#240211yescharacteristic, complemented
697C2C3×#562211yescharacteristic
698C2C3×#564911yescharacteristic
699C2C3×#568011yescharacteristic
700C2C3×D3×#12511yescharacteristic
701C2C3×#568811yescharacteristic
702C2C3×#570611yescharacteristic
703C2C3×#570611yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#400C2
socle, prime radicalC23×C32C24
hypercenterC3×#400D3
hypocenterC3C3×#2402
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#400

Complements

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

NH ≅ G/Ntype
17. #78133C3direct (N × H)
604. C32#2402semidirect
695. C3#78133direct (N × H)
696. C3C3×#2402semidirect

Maximal subgroups

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

subgroupindex
C32×#4002
C3×#49832
C3×#49822
C3×Dic3×C4⋊C42
C3×#46602
C3×#46582
C3×#46572
C3×#46492
C3×#46482
C3×#24023
#781333