Finite Group Databasebeta

← C107×#33347 #41059311

Subgroups — C107×#33347 #41059311

Order 27392.

1236 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3449C211yesmaximal, characteristic
2C2×#413×C107C211yesmaximal, characteristic, complemented
3C2×#410×C107C211yesmaximal, characteristic, complemented
4C107×#2123C212yesmaximal, complemented
5C107×#2122C212yesmaximal, complemented
6C107×#2121C214yesmaximal, complemented
7C107×#2120C214yesmaximal, complemented
8C22×#41×C107C411yescharacteristic, complemented
9C22×#41×C107C2211yescharacteristic
10C22×M16×C107—21no—
11#537×C107—21no—
12#537×C107—21no—
13#536×C107—21no—
14#536×C107C411yescharacteristic, complemented
15#536×C107C2211yescharacteristic
16#535×C107—21no—
17#535×C107C411yescharacteristic, complemented
18#535×C107C2211yescharacteristic
19#534×C107C412yescomplemented
20#534×C107C2212yes—
21#532×C107—21no—
22#532×C107—21no—
23#525×C107—21no—
24#525×C107—21no—
25#525×C107C412yescomplemented
26#525×C107C2212yes—
27C2×#117×C107—21no—
28C2×#117×C107C411yescharacteristic, complemented
29#413×C107—21no—
30#413×C107—21no—
31#413×C107C2212yes—
32#413×C107C2212yes—
33C2×#101×C107—21no—
34C2×#100×C107C2212yes—
35#410×C107—21no—
36#410×C107—21no—
37#410×C107C2212yes—
38#410×C107C2212yes—
39C2×#99×C107—21no—
40C2×#99×C107C2212yes—
41#352×C107C2218yescomplemented
42AΣL(1,𝔽16)×C107C2218yescomplemented
43C2×#41×C107—21no—
44C2×#41×C107—21no—
45C2×#41×C107—21no—
46C2×#41×C107—21no—
47C2×#41×C107—41no—
48C2×#41×C107—41no—
49C2×#41×C107—41no—
50C2×#41×C107—41no—
51C2×#41×C107—41no—
52C2×#41×C107—41no—
53C2×#41×C107—41no—
54C2×#41×C107—41no—
55C2×#41×C107C2×C411yescharacteristic
56C2×#41×C107C2×C411yescharacteristic
57C2×#41×C107D411yescharacteristic
58C2×#41×C107D411yescharacteristic
59C2×#41×C107D411yescharacteristic
60C2×#41×C107D411yescharacteristic
61C2×#41×C107C2311yescharacteristic
62C2×#41×C107C2311yescharacteristic
63C22×Q8×C107C2×C411yescharacteristic, complemented
64C22×Q8×C107D411yescharacteristic
65C22×D4×C107C2×C411yescharacteristic
66C22×D4×C107C2×C412yes—
67C22×D4×C107C2×C411yescharacteristic, complemented
68C22×D4×C107D411yescharacteristic
69C22×D4×C107C2311yescharacteristic
70C23×C4×C107C2×C411yescharacteristic
71C23×C4×C107C2×C412yescomplemented
72C23×C4×C107D411yescharacteristic
73C23×C4×C107D411yescharacteristic
74C2×M16×C107—22no—
75C2×M16×C107—22no—
76C2×M16×C107—22no—
77C2×M16×C107—41no—
78C2×M16×C107—41no—
79C2×M16×C107—41no—
80C22×C8×C107—41no—
81C4⋊Q8×C107—21no—
82C4⋊Q8×C107—21no—
83#127×C107—21no—
84#127×C107—21no—
85#124×C107—21no—
86#124×C107—21no—
87#124×C107—21no—
88#124×C107—21no—
89#123×C107—22no—
90#123×C107—22no—
91#123×C107C2×C412yes—
92#123×C107C2×C412yescomplemented
93#123×C107C2×C412yescomplemented
94#123×C107C2312yes—
95C22⋊Q8×C107—22no—
96C22⋊Q8×C107—22no—
97C22⋊Q8×C107—21no—
98C22⋊Q8×C107—21no—
99C22⋊Q8×C107—21no—
100C22⋊Q8×C107—21no—
101#121×C107—22no—
102#121×C107—22no—
103#121×C107—22no—
104#121×C107—22no—
105#121×C107—22no—
106#121×C107—22no—
107#121×C107—21no—
108#121×C107—21no—
109#121×C107—21no—
110#121×C107—21no—
111#120×C107—22no—
112#120×C107—22no—
113#120×C107C2×C412yes—
114#120×C107C2×C412yescomplemented
115#120×C107C2×C412yescomplemented
116#120×C107C2312yes—
117C4×D4×C107—22no—
118C4×D4×C107—22no—
119C4×D4×C107—22no—
120C4×D4×C107—22no—
121#117×C107—21no—
122#117×C107—21no—
123#117×C107—22no—
124#117×C107—22no—
125#117×C107—41no—
126#117×C107—41no—
127#117×C107C2×C412yescomplemented
128#117×C107C2×C411yescharacteristic, complemented
129#117×C107C2×C411yescharacteristic, complemented
130C2×C4⋊C4×C107—21no—
131C2×C4⋊C4×C107—41no—
132C2×C22⋊C4×C107—22no—
133C2×C22⋊C4×C107C2×C412yes—
134C2×C42×C107—21no—
135C2×C42×C107—41no—
136#101×C107—22no—
137#101×C107—22no—
138#100×C107—22no—
139#100×C107C2314yes—
140#99×C107—22no—
141#99×C107—22no—
142#99×C107—22no—
143#99×C107C2314yes—
144C24×C107C22⋊C411yescharacteristic
145C24×C107C22×C411yescharacteristic
146C24×C107C22×C412yes—
147C24×C107C2×D411yescharacteristic
148#41×C107—41no—
149#41×C107—41no—
150#41×C107—41no—
151#41×C107—41no—
152#41×C107—41no—
153#41×C107—41no—
154#41×C107—41no—
155#41×C107—41no—
156#41×C107—41no—
157#41×C107—41no—
158#41×C107—41no—
159#41×C107—41no—
160#41×C107—41no—
161#41×C107—41no—
162#41×C107—41no—
163#41×C107—41no—
164#41×C107—42no—
165#41×C107—42no—
166#41×C107—42no—
167#41×C107—42no—
168#41×C107—42no—
169#41×C107—42no—
170#41×C107—41no—
171#41×C107—41no—
172#41×C107—41no—
173#41×C107—41no—
174C2×Q8×C107—21no—
175C2×Q8×C107—21no—
176C2×Q8×C107—41no—
177C2×Q8×C107—41no—
178C2×Q8×C107—41no—
179C2×Q8×C107—41no—
180C2×Q8×C107C22⋊C411yescharacteristic
181C2×Q8×C107C22⋊C411yescharacteristic
182C2×Q8×C107C2×D411yescharacteristic
183C2×Q8×C107C2×D411yescharacteristic
184C2×D4×C107—22no—
185C2×D4×C107—22no—
186C2×D4×C107—22no—
187C2×D4×C107—22no—
188C2×D4×C107—22no—
189C2×D4×C107—22no—
190C2×D4×C107—21no—
191C2×D4×C107—21no—
192C2×D4×C107—41no—
193C2×D4×C107—41no—
194C2×D4×C107—41no—
195C2×D4×C107—41no—
196C2×D4×C107—41no—
197C2×D4×C107—41no—
198C2×D4×C107—41no—
199C2×D4×C107—41no—
200C2×D4×C107—42no—
201C2×D4×C107—42no—
202C2×D4×C107C22⋊C411yescharacteristic
203C2×D4×C107C22⋊C411yescharacteristic
204C2×D4×C107C22⋊C411yescharacteristic
205C2×D4×C107C22⋊C411yescharacteristic
206C2×D4×C107C22×C411yescharacteristic
207C2×D4×C107C22×C411yescharacteristic
208C2×D4×C107C22×C411yescharacteristic
209C2×D4×C107C2×D411yescharacteristic
210C2×D4×C107C2×D411yescharacteristic
211C2×D4×C107C2×D411yescharacteristic
212C2×D4×C107C2×D411yescharacteristic
213C2×D4×C107C2411yescharacteristic
214C22×C4×C107—21no—
215C22×C4×C107—21no—
216C22×C4×C107—21no—
217C22×C4×C107—21no—
218C22×C4×C107—21no—
219C22×C4×C107—21no—
220C22×C4×C107—21no—
221C22×C4×C107—21no—
222C22×C4×C107—21no—
223C22×C4×C107—21no—
224C22×C4×C107—21no—
225C22×C4×C107—21no—
226C22×C4×C107—22no—
227C22×C4×C107—22no—
228C22×C4×C107—22no—
229C22×C4×C107—42no—
230C22×C4×C107—42no—
231C22×C4×C107—42no—
232C22×C4×C107C22⋊C411yescharacteristic
233C22×C4×C107C22⋊C411yescharacteristic
234C22×C4×C107C22⋊C411yescharacteristic
235C22×C4×C107C22⋊C411yescharacteristic
236C22×C4×C107C22⋊C411yescharacteristic
237C22×C4×C107C22⋊C411yescharacteristic
238C22×C4×C107C22⋊C411yescharacteristic
239C22×C4×C107C22⋊C411yescharacteristic
240C22×C4×C107C22⋊C411yescharacteristic
241C22×C4×C107C22×C411yescharacteristic
242C22×C4×C107C22×C411yescharacteristic
243C22×C4×C107C22×C412yes—
244C22×C4×C107C2×D411yescharacteristic
245C22×C4×C107C2×D411yescharacteristic
246C22×C4×C107C2×D411yescharacteristic
247C22×C4×C107C2×D411yescharacteristic
248C22×C4×C107C2×D411yescharacteristic
249M16×C107—24no—
250M16×C107—42no—
251M16×C107—42no—
252M16×C107—42no—
253C2×C8×C107—42no—
254C2×C8×C107—42no—
255C2×C8×C107—42no—
256C4⋊C4×C107—22no—
257C4⋊C4×C107—21no—
258C4⋊C4×C107—21no—
259C4⋊C4×C107—22no—
260C4⋊C4×C107—22no—
261C4⋊C4×C107—22no—
262C4⋊C4×C107—22no—
263C4⋊C4×C107—42no—
264C4⋊C4×C107—42no—
265C22⋊C4×C107—22no—
266C22⋊C4×C107—22no—
267C22⋊C4×C107—22no—
268C22⋊C4×C107—22no—
269C22⋊C4×C107—22no—
270C22⋊C4×C107—22no—
271C22⋊C4×C107—22no—
272C22⋊C4×C107—22no—
273C22⋊C4×C107—22no—
274C22⋊C4×C107—24no—
275C22⋊C4×C107—42no—
276C22⋊C4×C107C22×C412yes—
277C22⋊C4×C107C22×C412yes—
278C42×C107—22no—
279C42×C107—21no—
280C42×C107—21no—
281C42×C107—42no—
282C42×C107—42no—
283C23×C107—21no—
284C23×C107—21no—
285C23×C107—21no—
286C23×C107—21no—
287C23×C107—21no—
288C23×C107—21no—
289C23×C107—22no—
290C23×C107—42no—
291C23×C107—81no—
292C23×C107—81no—
293C23×C107—81no—
294C23×C107—82no—
295C23×C107C2×C22⋊C411yescharacteristic
296C23×C107C2×C22⋊C411yescharacteristic
297C23×C107C2×C22⋊C411yescharacteristic
298C23×C107C2×C22⋊C411yescharacteristic
299C23×C107C2×C22⋊C411yescharacteristic
300C23×C107C23×C411yescharacteristic
301C23×C107C22×D411yescharacteristic
302Q8×C107—41no—
303Q8×C107—41no—
304Q8×C107—41no—
305Q8×C107—41no—
306Q8×C107—42no—
307Q8×C107—41no—
308Q8×C107—41no—
309D4×C107—41no—
310D4×C107—41no—
311D4×C107—41no—
312D4×C107—41no—
313D4×C107—41no—
314D4×C107—41no—
315D4×C107—41no—
316D4×C107—41no—
317D4×C107—41no—
318D4×C107—41no—
319D4×C107—41no—
320D4×C107—41no—
321D4×C107—42no—
322D4×C107—44no—
323D4×C107—42no—
324D4×C107—42no—
325D4×C107—41no—
326D4×C107—41no—
327D4×C107—82no—
328D4×C107—82no—
329D4×C107—82no—
330D4×C107—82no—
331C2×C4×C107—21no—
332C2×C4×C107—21no—
333C2×C4×C107—21no—
334C2×C4×C107—21no—
335C2×C4×C107—21no—
336C2×C4×C107—21no—
337C2×C4×C107—21no—
338C2×C4×C107—21no—
339C2×C4×C107—21no—
340C2×C4×C107—21no—
341C2×C4×C107—21no—
342C2×C4×C107—21no—
343C2×C4×C107—21no—
344C2×C4×C107—21no—
345C2×C4×C107—21no—
346C2×C4×C107—21no—
347C2×C4×C107—21no—
348C2×C4×C107—21no—
349C2×C4×C107—21no—
350C2×C4×C107—21no—
351C2×C4×C107—21no—
352C2×C4×C107—21no—
353C2×C4×C107—21no—
354C2×C4×C107—21no—
355C2×C4×C107—21no—
356C2×C4×C107—21no—
357C2×C4×C107—21no—
358C2×C4×C107—21no—
359C2×C4×C107—21no—
360C2×C4×C107—21no—
361C2×C4×C107—22no—
362C2×C4×C107—22no—
363C2×C4×C107—22no—
364C2×C4×C107—44no—
365C2×C4×C107—42no—
366C2×C4×C107—42no—
367C2×C4×C107—42no—
368C2×C4×C107—44no—
369C2×C4×C107—82no—
370C2×C4×C107—84no—
371C2×C4×C107#9911yescharacteristic
372C2×C4×C107#9911yescharacteristic
373C2×C4×C107#9911yescharacteristic
374C2×C4×C107#9911yescharacteristic
375C2×C4×C107C2×C22⋊C411yescharacteristic
376C2×C4×C107C2×C22⋊C411yescharacteristic
377C2×C4×C107C2×C22⋊C411yescharacteristic
378C2×C4×C107C2×C22⋊C411yescharacteristic
379C2×C4×C107C2×C22⋊C411yescharacteristic
380C2×C4×C107C2×C22⋊C411yescharacteristic
381C2×C4×C107C2×C22⋊C411yescharacteristic
382C2×C4×C107C22×D411yescharacteristic
383C8×C107—44no—
384C22×C107—21no—
385C22×C107—21no—
386C22×C107—21no—
387C22×C107—21no—
388C22×C107—21no—
389C22×C107—21no—
390C22×C107—41no—
391C22×C107—41no—
392C22×C107—41no—
393C22×C107—41no—
394C22×C107—41no—
395C22×C107—41no—
396C22×C107—41no—
397C22×C107—42no—
398C22×C107—42no—
399C22×C107—42no—
400C22×C107—42no—
401C22×C107—42no—
402C22×C107—81no—
403C22×C107—81no—
404C22×C107—81no—
405C22×C107—81no—
406C22×C107—84no—
407C22×C107C2×#9911yescharacteristic
408C22×C107C2×#9911yescharacteristic
409C22×C107C22×C22⋊C411yescharacteristic
410C4×C107—21no—
411C4×C107—21no—
412C4×C107—21no—
413C4×C107—21no—
414C4×C107—21no—
415C4×C107—21no—
416C4×C107—42no—
417C4×C107—42no—
418C4×C107—42no—
419C4×C107—84no—
420C4×C107C2×#9911yescharacteristic
421C4×C107C2×#9911yescharacteristic
422C4×C107C2×#9911yescharacteristic
423C4×C107C2×#9911yescharacteristic
424#33347C10711yesmaximal, characteristic, direct product factor, Sylow
425C2×C107—21no—
426C2×C107—21no—
427C2×C107—21no—
428C2×C107—41no—
429C2×C107—41no—
430C2×C107—41no—
431C2×C107—41no—
432C2×C107—41no—
433C2×C107—41no—
434C2×C107—82no—
435C2×C107C22×#9911yescharacteristic
436#3449C2×C10711yescharacteristic
437C2×#413C2×C10711yescharacteristic, complemented
438C2×#410C2×C10711yescharacteristic, complemented
439#2123C2×C10712yescomplemented
440#2122C2×C10712yescomplemented
441#2121C2×C10714yescomplemented
442#2120C2×C10714yescomplemented
443C107#3334711yescharacteristic, direct product factor, Sylow
444C22×#41C4×C10711yescharacteristic, complemented
445C22×#41C22×C10711yescharacteristic
446C22×M16—21no—
447#537—21no—
448#537—21no—
449#536—21no—
450#536C4×C10711yescharacteristic, complemented
451#536C22×C10711yescharacteristic
452#535—21no—
453#535C4×C10711yescharacteristic, complemented
454#535C22×C10711yescharacteristic
455#534C4×C10712yescomplemented
456#534C22×C10712yes—
457#532—21no—
458#532—21no—
459#525—21no—
460#525—21no—
461#525C4×C10712yescomplemented
462#525C22×C10712yes—
463C2×#117—21no—
464C2×#117C4×C10711yescharacteristic, complemented
465#413—21no—
466#413—21no—
467#413C22×C10712yes—
468#413C22×C10712yes—
469C2×#101—21no—
470C2×#100C22×C10712yes—
471#410—21no—
472#410—21no—
473#410C22×C10712yes—
474#410C22×C10712yes—
475C2×#99—21no—
476C2×#99C22×C10712yes—
477#352C22×C10718yescomplemented
478AΣL(1,𝔽16)C22×C10718yescomplemented
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41—41no—
491C2×#41C2×C4×C10711yescharacteristic
492C2×#41C2×C4×C10711yescharacteristic
493C2×#41D4×C10711yescharacteristic
494C2×#41D4×C10711yescharacteristic
495C2×#41D4×C10711yescharacteristic
496C2×#41D4×C10711yescharacteristic
497C2×#41C23×C10711yescharacteristic
498C2×#41C23×C10711yescharacteristic
499C22×Q8C2×C4×C10711yescharacteristic, complemented
500C22×Q8D4×C10711yescharacteristic
501C22×D4C2×C4×C10711yescharacteristic
502C22×D4C2×C4×C10712yes—
503C22×D4C2×C4×C10711yescharacteristic, complemented
504C22×D4D4×C10711yescharacteristic
505C22×D4C23×C10711yescharacteristic
506C23×C4C2×C4×C10711yescharacteristic
507C23×C4C2×C4×C10712yescomplemented
508C23×C4D4×C10711yescharacteristic
509C23×C4D4×C10711yescharacteristic
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C2×M16—41no—
516C22×C8—41no—
517C4⋊Q8—21no—
518C4⋊Q8—21no—
519#127—21no—
520#127—21no—
521#124—21no—
522#124—21no—
523#124—21no—
524#124—21no—
525#123—22no—
526#123—22no—
527#123C2×C4×C10712yes—
528#123C2×C4×C10712yescomplemented
529#123C2×C4×C10712yescomplemented
530#123C23×C10712yes—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—22no—
542#121—22no—
543#121—21no—
544#121—21no—
545#121—21no—
546#121—21no—
547#120—22no—
548#120—22no—
549#120C2×C4×C10712yes—
550#120C2×C4×C10712yescomplemented
551#120C2×C4×C10712yescomplemented
552#120C23×C10712yes—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557#117—21no—
558#117—21no—
559#117—22no—
560#117—22no—
561#117—41no—
562#117—41no—
563#117C2×C4×C10712yescomplemented
564#117C2×C4×C10711yescharacteristic, complemented
565#117C2×C4×C10711yescharacteristic, complemented
566C2×C4⋊C4—21no—
567C2×C4⋊C4—41no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4C2×C4×C10712yes—
570C2×C42—21no—
571C2×C42—41no—
572#101—22no—
573#101—22no—
574#100—22no—
575#100C23×C10714yes—
576#99—22no—
577#99—22no—
578#99—22no—
579#99C23×C10714yes—
580C24C22⋊C4×C10711yescharacteristic
581C24C22×C4×C10711yescharacteristic
582C24C22×C4×C10712yes—
583C24C2×D4×C10711yescharacteristic
584#41—41no—
585#41—41no—
586#41—41no—
587#41—41no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—41no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—41no—
613C2×Q8—41no—
614C2×Q8—41no—
615C2×Q8—41no—
616C2×Q8C22⋊C4×C10711yescharacteristic
617C2×Q8C22⋊C4×C10711yescharacteristic
618C2×Q8C2×D4×C10711yescharacteristic
619C2×Q8C2×D4×C10711yescharacteristic
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—41no—
633C2×D4—41no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4C22⋊C4×C10711yescharacteristic
639C2×D4C22⋊C4×C10711yescharacteristic
640C2×D4C22⋊C4×C10711yescharacteristic
641C2×D4C22⋊C4×C10711yescharacteristic
642C2×D4C22×C4×C10711yescharacteristic
643C2×D4C22×C4×C10711yescharacteristic
644C2×D4C22×C4×C10711yescharacteristic
645C2×D4C2×D4×C10711yescharacteristic
646C2×D4C2×D4×C10711yescharacteristic
647C2×D4C2×D4×C10711yescharacteristic
648C2×D4C2×D4×C10711yescharacteristic
649C2×D4C24×C10711yescharacteristic
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4C22⋊C4×C10711yescharacteristic
669C22×C4C22⋊C4×C10711yescharacteristic
670C22×C4C22⋊C4×C10711yescharacteristic
671C22×C4C22⋊C4×C10711yescharacteristic
672C22×C4C22⋊C4×C10711yescharacteristic
673C22×C4C22⋊C4×C10711yescharacteristic
674C22×C4C22⋊C4×C10711yescharacteristic
675C22×C4C22⋊C4×C10711yescharacteristic
676C22×C4C22⋊C4×C10711yescharacteristic
677C22×C4C22×C4×C10711yescharacteristic
678C22×C4C22×C4×C10711yescharacteristic
679C22×C4C22×C4×C10712yes—
680C22×C4C2×D4×C10711yescharacteristic
681C22×C4C2×D4×C10711yescharacteristic
682C22×C4C2×D4×C10711yescharacteristic
683C22×C4C2×D4×C10711yescharacteristic
684C22×C4C2×D4×C10711yescharacteristic
685M16—24no—
686M16—42no—
687M16—42no—
688M16—42no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8—42no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—24no—
711C22⋊C4—42no—
712C22⋊C4C22×C4×C10712yes—
713C22⋊C4C22×C4×C10712yes—
714C42—22no—
715C42—21no—
716C42—21no—
717C42—42no—
718C42—42no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—22no—
726C23—42no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23—82no—
731C23C2×C22⋊C4×C10711yescharacteristic
732C23C2×C22⋊C4×C10711yescharacteristic
733C23C2×C22⋊C4×C10711yescharacteristic
734C23C2×C22⋊C4×C10711yescharacteristic
735C23C2×C22⋊C4×C10711yescharacteristic
736C23C23×C4×C10711yescharacteristic
737C23C22×D4×C10711yescharacteristic
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—42no—
743Q8—41no—
744Q8—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—42no—
758D4—44no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—82no—
764D4—82no—
765D4—82no—
766D4—82no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—82no—
806C2×C4—84no—
807C2×C4#99×C10711yescharacteristic
808C2×C4#99×C10711yescharacteristic
809C2×C4#99×C10711yescharacteristic
810C2×C4#99×C10711yescharacteristic
811C2×C4C2×C22⋊C4×C10711yescharacteristic
812C2×C4C2×C22⋊C4×C10711yescharacteristic
813C2×C4C2×C22⋊C4×C10711yescharacteristic
814C2×C4C2×C22⋊C4×C10711yescharacteristic
815C2×C4C2×C22⋊C4×C10711yescharacteristic
816C2×C4C2×C22⋊C4×C10711yescharacteristic
817C2×C4C2×C22⋊C4×C10711yescharacteristic
818C2×C4C22×D4×C10711yescharacteristic
819C8—44no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—84no—
843C22C2×#99×C10711yescharacteristic
844C22C2×#99×C10711yescharacteristic
845C22C22×C22⋊C4×C10711yescharacteristic
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—84no—
856C4C2×#99×C10711yescharacteristic
857C4C2×#99×C10711yescharacteristic
858C4C2×#99×C10711yescharacteristic
859C4C2×#99×C10711yescharacteristic
860C2—21no—
861C2—21no—
862C2—21no—
863C2—41no—
864C2—41no—
865C2—41no—
866C2—41no—
867C2—41no—
868C2—41no—
869C2—82no—
870C2C22×#99×C10711yescharacteristic
subgroupG/H
centerC4×C107C2×#99
commutatorC23C23×C4×C107
Frattini, cosocleC2×D4C24×C107
socleC2×C107C22×#99
prime radicalC107×#3449C2
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C107 ◁ C22×C4×C107 ◁ C22×#41×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#413×C107C2semidirect
3. C2×#410×C107C2semidirect
4. C107×#2123C2semidirect
5. C107×#2122C2semidirect
6. C107×#2121C2semidirect
7. C107×#2120C2semidirect
8. C22×#41×C107C4semidirect
14. #536×C107C4semidirect
17. #535×C107C4semidirect
19. #534×C107C4semidirect
25. #525×C107C4semidirect
28. C2×#117×C107C4semidirect
41. #352×C107C22semidirect
42. AΣL(1,𝔽16)×C107C22semidirect
63. C22×Q8×C107C2×C4semidirect
67. C22×D4×C107C2×C4semidirect
71. C23×C4×C107C2×C4semidirect
92. #123×C107C2×C4semidirect
93. #123×C107C2×C4semidirect
114. #120×C107C2×C4semidirect
115. #120×C107C2×C4semidirect
127. #117×C107C2×C4semidirect
128. #117×C107C2×C4semidirect
129. #117×C107C2×C4semidirect
424. #33347C107direct (N × H)
437. C2×#413C2×C107semidirect
438. C2×#410C2×C107semidirect
439. #2123C2×C107semidirect
440. #2122C2×C107semidirect
441. #2121C2×C107semidirect
442. #2120C2×C107semidirect
443. C107#33347direct (N × H)
444. C22×#41C4×C107semidirect
450. #536C4×C107semidirect
453. #535C4×C107semidirect
455. #534C4×C107semidirect
461. #525C4×C107semidirect
464. C2×#117C4×C107semidirect
477. #352C22×C107semidirect
478. AΣL(1,𝔽16)C22×C107semidirect
499. C22×Q8C2×C4×C107semidirect
503. C22×D4C2×C4×C107semidirect
507. C23×C4C2×C4×C107semidirect
528. #123C2×C4×C107semidirect
529. #123C2×C4×C107semidirect
550. #120C2×C4×C107semidirect
551. #120C2×C4×C107semidirect
563. #117C2×C4×C107semidirect
564. #117C2×C4×C107semidirect
565. #117C2×C4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#34492
C2×#413×C1072
C2×#410×C1072
C107×#21232
C107×#21222
C107×#21212
C107×#21202
#33347107