Finite Group Databasebeta

← C137×#22477 #46871863

Subgroups — C137×#22477 #46871863

Order 35072.

1294 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#551×C137C211yesmaximal, characteristic
2#2342×C137C212yesmaximal, complemented
3#1996×C137C212yesmaximal, complemented
4#1899×C137C212yesmaximal, complemented
5#1898×C137C212yesmaximal
6#1820×C137C211yesmaximal, characteristic, complemented
7#1819×C137C211yesmaximal, characteristic, complemented
8#1799×C137C211yesmaximal, characteristic, complemented
9C4×#99×C137C211yesmaximal, characteristic, complemented
10#1740×C137C211yesmaximal, characteristic, complemented
11C2×#342×C137C211yesmaximal, characteristic, complemented
12#551×C137—22no—
13#551×C137—22no—
14#551×C137—22no—
15#551×C137—22no—
16C2×#126×C137C411yescharacteristic, complemented
17C2×#126×C137C411yescharacteristic, complemented
18C2×#124×C137C411yescharacteristic, complemented
19C2×#123×C137C411yescharacteristic, complemented
20C2×#123×C137C411yescharacteristic, complemented
21C2×#123×C137C2211yescharacteristic
22C2×C22⋊Q8×C137C411yescharacteristic, complemented
23C2×C22⋊Q8×C137C2211yescharacteristic
24C2×#120×C137C2211yescharacteristic
25C2×C4×D4×C137C411yescharacteristic, complemented
26C2×C4×D4×C137C2211yescharacteristic
27C2×#117×C137C411yescharacteristic, complemented
28C2×#117×C137C2212yes—
29C2×#117×C137C2211yescharacteristic
30C22×C22⋊C4×C137C2211yescharacteristic
31C22×C22⋊C4×C137C2212yes—
32C22×C22⋊C4×C137C2211yescharacteristic
33C2×#99×C137C2212yes—
34C2×#99×C137C2212yes—
35#388×C137—22no—
36#388×C137—22no—
37#385×C137—22no—
38#381×C137C2212yes—
39#380×C137C2212yes—
40#379×C137C2212yes—
41C4×C22⋊C4×C137—22no—
42C4×C22⋊C4×C137C2212yes—
43#342×C137C2211yescharacteristic
44#342×C137C2211yescharacteristic
45#342×C137C2211yescharacteristic
46#342×C137C2212yes—
47#342×C137C2212yes—
48#342×C137C2212yes—
49#342×C137C2212yes—
50#342×C137C2211yescharacteristic
51C25×C137C2311yescharacteristic
52C22×Q8×C137C2×C411yescharacteristic, complemented
53C22×D4×C137C2×C411yescharacteristic
54C22×D4×C137C2×C411yescharacteristic
55C22×D4×C137C2311yescharacteristic
56C23×C4×C137—22no—
57C23×C4×C137C2×C411yescharacteristic
58C23×C4×C137C2×C411yescharacteristic
59C23×C4×C137C2×C411yescharacteristic, complemented
60C23×C4×C137C2311yescharacteristic
61C23×C4×C137C2311yescharacteristic
62#126×C137—22no—
63#126×C137—22no—
64#126×C137—22no—
65#126×C137—22no—
66#124×C137—22no—
67#124×C137—22no—
68#123×C137—22no—
69#123×C137—22no—
70#123×C137—22no—
71#123×C137—22no—
72#123×C137—22no—
73#123×C137—22no—
74C22⋊Q8×C137—22no—
75C22⋊Q8×C137—22no—
76C22⋊Q8×C137—22no—
77C22⋊Q8×C137—22no—
78#120×C137—22no—
79#120×C137—22no—
80C4×D4×C137—22no—
81C4×D4×C137—22no—
82C4×D4×C137—21no—
83C4×D4×C137—21no—
84C4×D4×C137—21no—
85C4×D4×C137—21no—
86#117×C137—22no—
87#117×C137—22no—
88#117×C137—21no—
89#117×C137—21no—
90#117×C137—21no—
91#117×C137—21no—
92#117×C137—24no—
93#117×C137—42no—
94C2×C4⋊C4×C137—22no—
95C2×C4⋊C4×C137—22no—
96C2×C4⋊C4×C137C2×C411yescharacteristic, complemented
97C2×C4⋊C4×C137C2×C411yescharacteristic, complemented
98C2×C4⋊C4×C137C2×C411yescharacteristic, complemented
99C2×C4⋊C4×C137C2×C411yescharacteristic, complemented
100C2×C4⋊C4×C137C2×C411yescharacteristic, complemented
101C2×C4⋊C4×C137C2×C411yescharacteristic, complemented
102C2×C4⋊C4×C137C2×C411yescharacteristic, complemented
103C2×C4⋊C4×C137C2×C411yescharacteristic, complemented
104C2×C22⋊C4×C137—22no—
105C2×C22⋊C4×C137—22no—
106C2×C22⋊C4×C137—24no—
107C2×C22⋊C4×C137—22no—
108C2×C22⋊C4×C137—22no—
109C2×C22⋊C4×C137—22no—
110C2×C22⋊C4×C137—42no—
111C2×C22⋊C4×C137C2×C411yescharacteristic
112C2×C22⋊C4×C137C2×C411yescharacteristic
113C2×C22⋊C4×C137C2×C411yescharacteristic
114C2×C22⋊C4×C137C2×C411yescharacteristic
115C2×C22⋊C4×C137C2×C411yescharacteristic
116C2×C22⋊C4×C137C2×C411yescharacteristic
117C2×C22⋊C4×C137C2×C411yescharacteristic
118C2×C22⋊C4×C137C2×C411yescharacteristic
119C2×C22⋊C4×C137C2×C411yescharacteristic, complemented
120C2×C22⋊C4×C137C2×C411yescharacteristic, complemented
121C2×C22⋊C4×C137C2×C411yescharacteristic, complemented
122C2×C22⋊C4×C137D412yes—
123C2×C22⋊C4×C137D412yes—
124C2×C22⋊C4×C137D412yes—
125C2×C22⋊C4×C137D412yes—
126C2×C22⋊C4×C137C2312yes—
127C2×C22⋊C4×C137C2312yes—
128C2×C22⋊C4×C137C2312yes—
129C2×C22⋊C4×C137C2311yescharacteristic
130C2×C22⋊C4×C137C2311yescharacteristic
131C2×C22⋊C4×C137C2311yescharacteristic
132C2×C22⋊C4×C137C2312yes—
133C2×C42×C137—22no—
134C2×C42×C137—22no—
135C2×C42×C137C2×C411yescharacteristic, complemented
136C2×C42×C137C2×C411yescharacteristic, complemented
137C2×C42×C137C2×C411yescharacteristic, complemented
138#99×C137—24no—
139#99×C137—42no—
140#95×C137—22no—
141#95×C137—22no—
142#95×C137—22no—
143#95×C137—22no—
144C24×C137—22no—
145C24×C137—21no—
146C24×C137—21no—
147C24×C137—42no—
148C24×C137—81no—
149C24×C137C22×C411yescharacteristic
150C24×C137C22×C411yescharacteristic
151C24×C137C22×C411yescharacteristic
152C24×C137C2×D412yes—
153C24×C137C2×D412yes—
154C24×C137C2411yescharacteristic
155C2×Q8×C137—22no—
156C2×Q8×C137—81no—
157C2×D4×C137—21no—
158C2×D4×C137—21no—
159C2×D4×C137—22no—
160C2×D4×C137—22no—
161C2×D4×C137—21no—
162C2×D4×C137—21no—
163C2×D4×C137—22no—
164C2×D4×C137—42no—
165C2×D4×C137—81no—
166C22×C4×C137—22no—
167C22×C4×C137—21no—
168C22×C4×C137—21no—
169C22×C4×C137—21no—
170C22×C4×C137—21no—
171C22×C4×C137—22no—
172C22×C4×C137—21no—
173C22×C4×C137—21no—
174C22×C4×C137—21no—
175C22×C4×C137—21no—
176C22×C4×C137—22no—
177C22×C4×C137—22no—
178C22×C4×C137—22no—
179C22×C4×C137—44no—
180C22×C4×C137—42no—
181C22×C4×C137—44no—
182C22×C4×C137—81no—
183C22×C4×C137—82no—
184C22×C4×C137—81no—
185C22×C4×C137—81no—
186C22×C4×C137C22×C411yescharacteristic
187C22×C4×C137C22×C411yescharacteristic
188C22×C4×C137C22×C411yescharacteristic
189C22×C4×C137C22×C411yescharacteristic
190C22×C4×C137C22×C411yescharacteristic
191C22×C4×C137C22×C411yescharacteristic
192C22×C4×C137C22×C411yescharacteristic
193C22×C4×C137C22×C411yescharacteristic
194C22×C4×C137C22×C411yescharacteristic
195C22×C4×C137C22×C411yescharacteristic
196C22×C4×C137C22×C411yescharacteristic
197C22×C4×C137C2×D412yes—
198C22×C4×C137C2×D412yes—
199C22×C4×C137C2×D412yes—
200C22×C4×C137C2×D412yes—
201C4⋊C4×C137—22no—
202C4⋊C4×C137—21no—
203C4⋊C4×C137—21no—
204C4⋊C4×C137—22no—
205C4⋊C4×C137—21no—
206C4⋊C4×C137—21no—
207C4⋊C4×C137—22no—
208C4⋊C4×C137—21no—
209C4⋊C4×C137—21no—
210C4⋊C4×C137—22no—
211C4⋊C4×C137—22no—
212C4⋊C4×C137—44no—
213C4⋊C4×C137—82no—
214C22⋊C4×C137—22no—
215C22⋊C4×C137—22no—
216C22⋊C4×C137—21no—
217C22⋊C4×C137—21no—
218C22⋊C4×C137—22no—
219C22⋊C4×C137—22no—
220C22⋊C4×C137—22no—
221C22⋊C4×C137—22no—
222C22⋊C4×C137—22no—
223C22⋊C4×C137—22no—
224C22⋊C4×C137—21no—
225C22⋊C4×C137—21no—
226C22⋊C4×C137—22no—
227C22⋊C4×C137—22no—
228C22⋊C4×C137—22no—
229C22⋊C4×C137—22no—
230C22⋊C4×C137—22no—
231C22⋊C4×C137—22no—
232C22⋊C4×C137—22no—
233C22⋊C4×C137—44no—
234C22⋊C4×C137—44no—
235C22⋊C4×C137—82no—
236C22⋊C4×C137C22⋊C411yescharacteristic
237C22⋊C4×C137C22⋊C411yescharacteristic
238C22⋊C4×C137C22⋊C411yescharacteristic
239C22⋊C4×C137C22⋊C411yescharacteristic
240C22⋊C4×C137C22⋊C412yes—
241C22⋊C4×C137C22⋊C412yes—
242C22⋊C4×C137C22⋊C412yes—
243C22⋊C4×C137C22⋊C412yes—
244C22⋊C4×C137C22⋊C412yes—
245C22⋊C4×C137C22⋊C412yes—
246C22⋊C4×C137#4114yes—
247C42×C137—21no—
248C42×C137—21no—
249C42×C137—21no—
250C42×C137—21no—
251C42×C137—21no—
252C42×C137—21no—
253C42×C137—44no—
254C42×C137—82no—
255C23×C137—21no—
256C23×C137—21no—
257C23×C137—22no—
258C23×C137—22no—
259C23×C137—24no—
260C23×C137—22no—
261C23×C137—21no—
262C23×C137—21no—
263C23×C137—22no—
264C23×C137—22no—
265C23×C137—21no—
266C23×C137—21no—
267C23×C137—21no—
268C23×C137—41no—
269C23×C137—42no—
270C23×C137—41no—
271C23×C137—41no—
272C23×C137—42no—
273C23×C137—41no—
274C23×C137—41no—
275C23×C137—42no—
276C23×C137—41no—
277C23×C137—41no—
278C23×C137—84no—
279C23×C137—82no—
280C23×C137—82no—
281C23×C137C2×C22⋊C412yes—
282C23×C137C2×C22⋊C411yescharacteristic
283C23×C137C2×C22⋊C411yescharacteristic
284C23×C137C23×C411yescharacteristic
285C23×C137C22×D412yes—
286C23×C137C2×#4112yes—
287C23×C137H(5,𝔽2)11yescharacteristic
288C23×C1372−1+411yescharacteristic
289Q8×C137—82no—
290D4×C137—42no—
291D4×C137—42no—
292D4×C137—42no—
293D4×C137—42no—
294D4×C137—82no—
295C2×C4×C137—21no—
296C2×C4×C137—21no—
297C2×C4×C137—21no—
298C2×C4×C137—21no—
299C2×C4×C137—22no—
300C2×C4×C137—22no—
301C2×C4×C137—22no—
302C2×C4×C137—22no—
303C2×C4×C137—21no—
304C2×C4×C137—21no—
305C2×C4×C137—21no—
306C2×C4×C137—21no—
307C2×C4×C137—21no—
308C2×C4×C137—21no—
309C2×C4×C137—21no—
310C2×C4×C137—21no—
311C2×C4×C137—21no—
312C2×C4×C137—24no—
313C2×C4×C137—42no—
314C2×C4×C137—42no—
315C2×C4×C137—41no—
316C2×C4×C137—41no—
317C2×C4×C137—42no—
318C2×C4×C137—42no—
319C2×C4×C137—42no—
320C2×C4×C137—42no—
321C2×C4×C137—41no—
322C2×C4×C137—41no—
323C2×C4×C137—41no—
324C2×C4×C137—41no—
325C2×C4×C137—41no—
326C2×C4×C137—41no—
327C2×C4×C137—42no—
328C2×C4×C137—42no—
329C2×C4×C137—42no—
330C2×C4×C137—42no—
331C2×C4×C137—42no—
332C2×C4×C137—42no—
333C2×C4×C137—42no—
334C2×C4×C137—42no—
335C2×C4×C137—42no—
336C2×C4×C137—81no—
337C2×C4×C137—81no—
338C2×C4×C137—81no—
339C2×C4×C137—81no—
340C2×C4×C137—88no—
341C2×C4×C137C2×C22⋊C411yescharacteristic
342C2×C4×C137C2×C22⋊C411yescharacteristic
343C2×C4×C137C2×C22⋊C411yescharacteristic
344C2×C4×C137C2×C22⋊C411yescharacteristic
345C2×C4×C137C2×C22⋊C412yes—
346C2×C4×C137C2×C22⋊C412yes—
347C22×C137—21no—
348C22×C137—22no—
349C22×C137—21no—
350C22×C137—22no—
351C22×C137—21no—
352C22×C137—21no—
353C22×C137—21no—
354C22×C137—22no—
355C22×C137—21no—
356C22×C137—22no—
357C22×C137—21no—
358C22×C137—22no—
359C22×C137—42no—
360C22×C137—41no—
361C22×C137—41no—
362C22×C137—44no—
363C22×C137—44no—
364C22×C137—42no—
365C22×C137—42no—
366C22×C137—41no—
367C22×C137—41no—
368C22×C137—41no—
369C22×C137—82no—
370C22×C137—82no—
371C22×C137—81no—
372C22×C137—81no—
373C22×C137—81no—
374C22×C137—81no—
375C22×C137#41012yes—
376C22×C137C22×C22⋊C411yescharacteristic
377C22×C137C4×#4111yescharacteristic
378C22×C137#52011yescharacteristic
379C22×C137#54612yes—
380C22×C137#54712yes—
381C4×C137—21no—
382C4×C137—22no—
383C4×C137—21no—
384C4×C137—21no—
385C4×C137—21no—
386C4×C137—22no—
387C4×C137—44no—
388C4×C137—41no—
389C4×C137—41no—
390C4×C137—41no—
391C4×C137—41no—
392C4×C137—41no—
393C4×C137—41no—
394C4×C137—41no—
395C4×C137—82no—
396C4×C137—82no—
397C4×C137—82no—
398C2×C137—22no—
399C2×C137—22no—
400C2×C137—22no—
401C2×C137—21no—
402C2×C137—21no—
403C2×C137—41no—
404C2×C137—42no—
405C2×C137—81no—
406C2×C137#233911yescharacteristic
407C2×C137C2×#41011yescharacteristic
408C2×C137#288311yescharacteristic
409#22477C13711yesmaximal, characteristic, direct product factor, Sylow
410C137#2247711yescharacteristic, direct product factor, Sylow
411C2×#551C2×C13711yescharacteristic
412#2342C2×C13712yescomplemented
413#1996C2×C13712yescomplemented
414#1899C2×C13712yescomplemented
415#1898C2×C13712yes—
416#1820C2×C13711yescharacteristic, complemented
417#1819C2×C13711yescharacteristic, complemented
418#1799C2×C13711yescharacteristic, complemented
419C4×#99C2×C13711yescharacteristic, complemented
420#1740C2×C13711yescharacteristic, complemented
421C2×#342C2×C13711yescharacteristic, complemented
422#551—22no—
423#551—22no—
424#551—22no—
425#551—22no—
426C2×#126C4×C13711yescharacteristic, complemented
427C2×#126C4×C13711yescharacteristic, complemented
428C2×#124C4×C13711yescharacteristic, complemented
429C2×#123C4×C13711yescharacteristic, complemented
430C2×#123C4×C13711yescharacteristic, complemented
431C2×#123C22×C13711yescharacteristic
432C2×C22⋊Q8C4×C13711yescharacteristic, complemented
433C2×C22⋊Q8C22×C13711yescharacteristic
434C2×#120C22×C13711yescharacteristic
435C2×C4×D4C4×C13711yescharacteristic, complemented
436C2×C4×D4C22×C13711yescharacteristic
437C2×#117C4×C13711yescharacteristic, complemented
438C2×#117C22×C13712yes—
439C2×#117C22×C13711yescharacteristic
440C22×C22⋊C4C22×C13711yescharacteristic
441C22×C22⋊C4C22×C13712yes—
442C22×C22⋊C4C22×C13711yescharacteristic
443C2×#99C22×C13712yes—
444C2×#99C22×C13712yes—
445#388—22no—
446#388—22no—
447#385—22no—
448#381C22×C13712yes—
449#380C22×C13712yes—
450#379C22×C13712yes—
451C4×C22⋊C4—22no—
452C4×C22⋊C4C22×C13712yes—
453#342C22×C13711yescharacteristic
454#342C22×C13711yescharacteristic
455#342C22×C13711yescharacteristic
456#342C22×C13712yes—
457#342C22×C13712yes—
458#342C22×C13712yes—
459#342C22×C13712yes—
460#342C22×C13711yescharacteristic
461C25C23×C13711yescharacteristic
462C22×Q8C2×C4×C13711yescharacteristic, complemented
463C22×D4C2×C4×C13711yescharacteristic
464C22×D4C2×C4×C13711yescharacteristic
465C22×D4C23×C13711yescharacteristic
466C23×C4—22no—
467C23×C4C2×C4×C13711yescharacteristic
468C23×C4C2×C4×C13711yescharacteristic
469C23×C4C2×C4×C13711yescharacteristic, complemented
470C23×C4C23×C13711yescharacteristic
471C23×C4C23×C13711yescharacteristic
472#126—22no—
473#126—22no—
474#126—22no—
475#126—22no—
476#124—22no—
477#124—22no—
478#123—22no—
479#123—22no—
480#123—22no—
481#123—22no—
482#123—22no—
483#123—22no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488#120—22no—
489#120—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496#117—22no—
497#117—22no—
498#117—21no—
499#117—21no—
500#117—21no—
501#117—21no—
502#117—24no—
503#117—42no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4C2×C4×C13711yescharacteristic, complemented
507C2×C4⋊C4C2×C4×C13711yescharacteristic, complemented
508C2×C4⋊C4C2×C4×C13711yescharacteristic, complemented
509C2×C4⋊C4C2×C4×C13711yescharacteristic, complemented
510C2×C4⋊C4C2×C4×C13711yescharacteristic, complemented
511C2×C4⋊C4C2×C4×C13711yescharacteristic, complemented
512C2×C4⋊C4C2×C4×C13711yescharacteristic, complemented
513C2×C4⋊C4C2×C4×C13711yescharacteristic, complemented
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4C2×C4×C13711yescharacteristic
522C2×C22⋊C4C2×C4×C13711yescharacteristic
523C2×C22⋊C4C2×C4×C13711yescharacteristic
524C2×C22⋊C4C2×C4×C13711yescharacteristic
525C2×C22⋊C4C2×C4×C13711yescharacteristic
526C2×C22⋊C4C2×C4×C13711yescharacteristic
527C2×C22⋊C4C2×C4×C13711yescharacteristic
528C2×C22⋊C4C2×C4×C13711yescharacteristic
529C2×C22⋊C4C2×C4×C13711yescharacteristic, complemented
530C2×C22⋊C4C2×C4×C13711yescharacteristic, complemented
531C2×C22⋊C4C2×C4×C13711yescharacteristic, complemented
532C2×C22⋊C4D4×C13712yes—
533C2×C22⋊C4D4×C13712yes—
534C2×C22⋊C4D4×C13712yes—
535C2×C22⋊C4D4×C13712yes—
536C2×C22⋊C4C23×C13712yes—
537C2×C22⋊C4C23×C13712yes—
538C2×C22⋊C4C23×C13712yes—
539C2×C22⋊C4C23×C13711yescharacteristic
540C2×C22⋊C4C23×C13711yescharacteristic
541C2×C22⋊C4C23×C13711yescharacteristic
542C2×C22⋊C4C23×C13712yes—
543C2×C42—22no—
544C2×C42—22no—
545C2×C42C2×C4×C13711yescharacteristic, complemented
546C2×C42C2×C4×C13711yescharacteristic, complemented
547C2×C42C2×C4×C13711yescharacteristic, complemented
548#99—24no—
549#99—42no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95—22no—
554C24—22no—
555C24—21no—
556C24—21no—
557C24—42no—
558C24—81no—
559C24C22×C4×C13711yescharacteristic
560C24C22×C4×C13711yescharacteristic
561C24C22×C4×C13711yescharacteristic
562C24C2×D4×C13712yes—
563C24C2×D4×C13712yes—
564C24C24×C13711yescharacteristic
565C2×Q8—22no—
566C2×Q8—81no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—42no—
575C2×D4—81no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—44no—
590C22×C4—42no—
591C22×C4—44no—
592C22×C4—81no—
593C22×C4—82no—
594C22×C4—81no—
595C22×C4—81no—
596C22×C4C22×C4×C13711yescharacteristic
597C22×C4C22×C4×C13711yescharacteristic
598C22×C4C22×C4×C13711yescharacteristic
599C22×C4C22×C4×C13711yescharacteristic
600C22×C4C22×C4×C13711yescharacteristic
601C22×C4C22×C4×C13711yescharacteristic
602C22×C4C22×C4×C13711yescharacteristic
603C22×C4C22×C4×C13711yescharacteristic
604C22×C4C22×C4×C13711yescharacteristic
605C22×C4C22×C4×C13711yescharacteristic
606C22×C4C22×C4×C13711yescharacteristic
607C22×C4C2×D4×C13712yes—
608C22×C4C2×D4×C13712yes—
609C22×C4C2×D4×C13712yes—
610C22×C4C2×D4×C13712yes—
611C4⋊C4—22no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—22no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—22no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—44no—
623C4⋊C4—82no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—82no—
646C22⋊C4C22⋊C4×C13711yescharacteristic
647C22⋊C4C22⋊C4×C13711yescharacteristic
648C22⋊C4C22⋊C4×C13711yescharacteristic
649C22⋊C4C22⋊C4×C13711yescharacteristic
650C22⋊C4C22⋊C4×C13712yes—
651C22⋊C4C22⋊C4×C13712yes—
652C22⋊C4C22⋊C4×C13712yes—
653C22⋊C4C22⋊C4×C13712yes—
654C22⋊C4C22⋊C4×C13712yes—
655C22⋊C4C22⋊C4×C13712yes—
656C22⋊C4#41×C13714yes—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—44no—
664C42—82no—
665C23—24no—
666C23—22no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—22no—
674C23—22no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—41no—
679C23—42no—
680C23—41no—
681C23—41no—
682C23—42no—
683C23—41no—
684C23—41no—
685C23—42no—
686C23—41no—
687C23—41no—
688C23—84no—
689C23—82no—
690C23—82no—
691C23C2×C22⋊C4×C13712yes—
692C23C2×C22⋊C4×C13711yescharacteristic
693C23C2×C22⋊C4×C13711yescharacteristic
694C23C23×C4×C13711yescharacteristic
695C23C22×D4×C13712yes—
696C23C2×#41×C13712yes—
697C23H(5,𝔽2)×C13711yescharacteristic
698C232−1+4×C13711yescharacteristic
699Q8—82no—
700D4—42no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—82no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—24no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—88no—
751C2×C4C2×C22⋊C4×C13711yescharacteristic
752C2×C4C2×C22⋊C4×C13711yescharacteristic
753C2×C4C2×C22⋊C4×C13711yescharacteristic
754C2×C4C2×C22⋊C4×C13711yescharacteristic
755C2×C4C2×C22⋊C4×C13712yes—
756C2×C4C2×C22⋊C4×C13712yes—
757C22—21no—
758C22—22no—
759C22—21no—
760C22—22no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—22no—
765C22—21no—
766C22—22no—
767C22—21no—
768C22—22no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—44no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—82no—
780C22—82no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22#410×C13712yes—
786C22C22×C22⋊C4×C13711yescharacteristic
787C22C4×#41×C13711yescharacteristic
788C22#520×C13711yescharacteristic
789C22#546×C13712yes—
790C22#547×C13712yes—
791C4—21no—
792C4—22no—
793C4—21no—
794C4—21no—
795C4—21no—
796C4—22no—
797C4—44no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—82no—
806C4—82no—
807C4—82no—
808C2—22no—
809C2—22no—
810C2—22no—
811C2—21no—
812C2—21no—
813C2—41no—
814C2—42no—
815C2—81no—
816C2#2339×C13711yescharacteristic
817C2C2×#410×C13711yescharacteristic
818C2#2883×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C22×C22⋊C4
commutatorC23C23×C4×C137
Frattini, cosocleC24C24×C137
prime radicalC2×#120×C137C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C22×C22⋊C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2342×C137C2semidirect
3. #1996×C137C2semidirect
4. #1899×C137C2semidirect
6. #1820×C137C2semidirect
7. #1819×C137C2semidirect
8. #1799×C137C2semidirect
9. C4×#99×C137C2semidirect
10. #1740×C137C2semidirect
11. C2×#342×C137C2semidirect
16. C2×#126×C137C4semidirect
17. C2×#126×C137C4semidirect
18. C2×#124×C137C4semidirect
19. C2×#123×C137C4semidirect
20. C2×#123×C137C4semidirect
22. C2×C22⋊Q8×C137C4semidirect
25. C2×C4×D4×C137C4semidirect
27. C2×#117×C137C4semidirect
52. C22×Q8×C137C2×C4semidirect
59. C23×C4×C137C2×C4semidirect
96. C2×C4⋊C4×C137C2×C4semidirect
97. C2×C4⋊C4×C137C2×C4semidirect
98. C2×C4⋊C4×C137C2×C4semidirect
99. C2×C4⋊C4×C137C2×C4semidirect
100. C2×C4⋊C4×C137C2×C4semidirect
101. C2×C4⋊C4×C137C2×C4semidirect
102. C2×C4⋊C4×C137C2×C4semidirect
103. C2×C4⋊C4×C137C2×C4semidirect
119. C2×C22⋊C4×C137C2×C4semidirect
120. C2×C22⋊C4×C137C2×C4semidirect
121. C2×C22⋊C4×C137C2×C4semidirect
135. C2×C42×C137C2×C4semidirect
136. C2×C42×C137C2×C4semidirect
137. C2×C42×C137C2×C4semidirect
409. #22477C137direct (N × H)
410. C137#22477direct (N × H)
412. #2342C2×C137semidirect
413. #1996C2×C137semidirect
414. #1899C2×C137semidirect
416. #1820C2×C137semidirect
417. #1819C2×C137semidirect
418. #1799C2×C137semidirect
419. C4×#99C2×C137semidirect
420. #1740C2×C137semidirect
421. C2×#342C2×C137semidirect
426. C2×#126C4×C137semidirect
427. C2×#126C4×C137semidirect
428. C2×#124C4×C137semidirect
429. C2×#123C4×C137semidirect
430. C2×#123C4×C137semidirect
432. C2×C22⋊Q8C4×C137semidirect
435. C2×C4×D4C4×C137semidirect
437. C2×#117C4×C137semidirect
462. C22×Q8C2×C4×C137semidirect
469. C23×C4C2×C4×C137semidirect
506. C2×C4⋊C4C2×C4×C137semidirect
507. C2×C4⋊C4C2×C4×C137semidirect
508. C2×C4⋊C4C2×C4×C137semidirect
509. C2×C4⋊C4C2×C4×C137semidirect
510. C2×C4⋊C4C2×C4×C137semidirect
511. C2×C4⋊C4C2×C4×C137semidirect
512. C2×C4⋊C4C2×C4×C137semidirect
513. C2×C4⋊C4C2×C4×C137semidirect
529. C2×C22⋊C4C2×C4×C137semidirect
530. C2×C22⋊C4C2×C4×C137semidirect
531. C2×C22⋊C4C2×C4×C137semidirect
545. C2×C42C2×C4×C137semidirect
546. C2×C42C2×C4×C137semidirect
547. C2×C42C2×C4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#551×C1372
#2342×C1372
#1996×C1372
#1899×C1372
#1898×C1372
#1820×C1372
#1819×C1372
#1799×C1372
C4×#99×C1372
#1740×C1372
C2×#342×C1372
#22477137