Finite Group Databasebeta

← C2×C107×#2121 #41059308

Subgroups — C2×C107×#2121 #41059308

Order 27392.

1494 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#534×C107C211yesmaximal, characteristic
2C22×#100×C107C211yesmaximal, characteristic, complemented
3C22×#99×C107C211yesmaximal, characteristic, complemented
4C107×#2121C218yesmaximal, direct product factor
5C2×#352×C107C212yesmaximal, complemented
6C2×AΣL(1,𝔽16)×C107C212yesmaximal, complemented
7C23×D4×C107C411yescharacteristic, complemented
8C23×D4×C107C2211yescharacteristic
9C22×M16×C107—21no—
10#534×C107—22no—
11#534×C107—22no—
12#534×C107C414yescomplemented
13#534×C107C2214yes—
14C2×#123×C107—21no—
15C2×#123×C107C411yescharacteristic, complemented
16C2×#123×C107C2211yescharacteristic
17C2×#121×C107—21no—
18C2×#121×C107—21no—
19C2×#120×C107—21no—
20C2×#120×C107C411yescharacteristic, complemented
21C2×#120×C107C2211yescharacteristic
22C22×C22⋊C4×C107—21no—
23C22×C22⋊C4×C107C411yescharacteristic, complemented
24C2×#100×C107—22no—
25C2×#100×C107—21no—
26C2×#100×C107C2212yes—
27C2×#100×C107C2214yescomplemented
28C2×#99×C107—22no—
29C2×#99×C107—21no—
30C2×#99×C107C2212yes—
31C2×#99×C107C2214yescomplemented
32#352×C107C2218yescomplemented
33AΣL(1,𝔽16)×C107C2218yescomplemented
34C25×C107C2×C411yescharacteristic
35C25×C107C2×C411yescharacteristic, complemented
36C25×C107D411yescharacteristic
37C22×D4×C107—21no—
38C22×D4×C107—22no—
39C22×D4×C107—21no—
40C22×D4×C107—21no—
41C22×D4×C107—21no—
42C22×D4×C107—41no—
43C22×D4×C107—41no—
44C22×D4×C107—42no—
45C22×D4×C107—42no—
46C22×D4×C107—41no—
47C22×D4×C107—41no—
48C22×D4×C107C2×C411yescharacteristic
49C22×D4×C107C2×C412yes—
50C22×D4×C107C2×C414yescomplemented
51C22×D4×C107D411yescharacteristic
52C22×D4×C107D412yes—
53C22×D4×C107D411yescharacteristic
54C22×D4×C107D412yes—
55C22×D4×C107C2311yescharacteristic
56C22×D4×C107C2312yes—
57C23×C4×C107—21no—
58C23×C4×C107—41no—
59C23×C4×C107C2×C411yescharacteristic, complemented
60C23×C4×C107D411yescharacteristic
61C2×M16×C107—22no—
62C2×M16×C107—24no—
63C2×M16×C107—42no—
64C2×M16×C107—41no—
65C22×C8×C107—41no—
66#123×C107—22no—
67#123×C107—21no—
68#123×C107—21no—
69#123×C107—24no—
70#123×C107—24no—
71#123×C107C2×C414yescomplemented
72#123×C107C2×C412yescomplemented
73#123×C107C2312yes—
74#121×C107—24no—
75#121×C107—24no—
76#121×C107—24no—
77#121×C107—24no—
78#120×C107—24no—
79#120×C107—24no—
80#120×C107—22no—
81#120×C107—21no—
82#120×C107—21no—
83#120×C107C2×C414yescomplemented
84#120×C107C2×C412yescomplemented
85#120×C107C2312yes—
86C2×C4⋊C4×C107—21no—
87C2×C4⋊C4×C107—21no—
88C2×C22⋊C4×C107—22no—
89C2×C22⋊C4×C107—21no—
90C2×C22⋊C4×C107—21no—
91C2×C22⋊C4×C107—21no—
92C2×C22⋊C4×C107—21no—
93C2×C22⋊C4×C107—21no—
94C2×C22⋊C4×C107—22no—
95C2×C22⋊C4×C107—24no—
96C2×C22⋊C4×C107—42no—
97C2×C22⋊C4×C107—41no—
98C2×C22⋊C4×C107C2×C411yescharacteristic, complemented
99C2×C22⋊C4×C107C2×C411yescharacteristic, complemented
100C2×C22⋊C4×C107C2×C414yescomplemented
101#100×C107—22no—
102#100×C107—24no—
103#100×C107C2314yes—
104#99×C107—22no—
105#99×C107—24no—
106#99×C107C2314yes—
107C24×C107—21no—
108C24×C107—22no—
109C24×C107—21no—
110C24×C107—22no—
111C24×C107—21no—
112C24×C107—21no—
113C24×C107—21no—
114C24×C107—21no—
115C24×C107—41no—
116C24×C107—41no—
117C24×C107—82no—
118C24×C107—82no—
119C24×C107—82no—
120C24×C107C22⋊C411yescharacteristic
121C24×C107C22⋊C411yescharacteristic
122C24×C107C22⋊C412yes—
123C24×C107C22⋊C412yes—
124C24×C107C22⋊C411yescharacteristic
125C24×C107C22×C411yescharacteristic
126C24×C107C22×C412yes—
127C24×C107C22×C412yescomplemented
128C24×C107C2×D411yescharacteristic
129C24×C107C2×D412yes—
130C2×D4×C107—24no—
131C2×D4×C107—24no—
132C2×D4×C107—22no—
133C2×D4×C107—24no—
134C2×D4×C107—22no—
135C2×D4×C107—41no—
136C2×D4×C107—42no—
137C2×D4×C107—42no—
138C2×D4×C107—41no—
139C2×D4×C107—42no—
140C2×D4×C107—41no—
141C2×D4×C107—42no—
142C2×D4×C107—42no—
143C2×D4×C107—41no—
144C2×D4×C107—42no—
145C2×D4×C107—41no—
146C2×D4×C107—41no—
147C2×D4×C107—42no—
148C2×D4×C107—42no—
149C2×D4×C107—41no—
150C2×D4×C107—41no—
151C2×D4×C107—44no—
152C2×D4×C107—44no—
153C2×D4×C107—42no—
154C2×D4×C107—42no—
155C2×D4×C107—42no—
156C2×D4×C107—41no—
157C2×D4×C107—41no—
158C2×D4×C107—44no—
159C2×D4×C107—44no—
160C2×D4×C107—82no—
161C2×D4×C107—82no—
162C2×D4×C107C22⋊C412yes—
163C2×D4×C107C22⋊C412yes—
164C2×D4×C107C22⋊C412yes—
165C2×D4×C107C22×C412yes—
166C2×D4×C107C22×C411yescharacteristic
167C2×D4×C107C2×D411yescharacteristic
168C2×D4×C107C2×D412yes—
169C2×D4×C107C2×D411yescharacteristic
170C2×D4×C107C2×D412yes—
171C2×D4×C107C2411yescharacteristic
172C22×C4×C107—21no—
173C22×C4×C107—22no—
174C22×C4×C107—21no—
175C22×C4×C107—21no—
176C22×C4×C107—21no—
177C22×C4×C107—21no—
178C22×C4×C107—21no—
179C22×C4×C107—24no—
180C22×C4×C107—41no—
181C22×C4×C107—41no—
182C22×C4×C107—44no—
183C22×C4×C107—42no—
184C22×C4×C107—82no—
185C22×C4×C107—84no—
186C22×C4×C107C22⋊C411yescharacteristic
187C22×C4×C107C22⋊C412yes—
188C22×C4×C107C22×C412yescomplemented
189C22×C4×C107C2×D411yescharacteristic
190C22×C4×C107C2×D412yes—
191M16×C107—24no—
192M16×C107—42no—
193M16×C107—44no—
194C2×C8×C107—44no—
195C2×C8×C107—42no—
196C4⋊C4×C107—24no—
197C4⋊C4×C107—22no—
198C4⋊C4×C107—22no—
199C22⋊C4×C107—21no—
200C22⋊C4×C107—21no—
201C22⋊C4×C107—24no—
202C22⋊C4×C107—24no—
203C22⋊C4×C107—22no—
204C22⋊C4×C107—22no—
205C22⋊C4×C107—24no—
206C22⋊C4×C107—22no—
207C22⋊C4×C107—22no—
208C22⋊C4×C107—24no—
209C22⋊C4×C107—42no—
210C22⋊C4×C107—44no—
211C22⋊C4×C107C22×C412yescomplemented
212C22⋊C4×C107C22×C412yescomplemented
213C23×C107—22no—
214C23×C107—21no—
215C23×C107—21no—
216C23×C107—22no—
217C23×C107—21no—
218C23×C107—21no—
219C23×C107—21no—
220C23×C107—21no—
221C23×C107—21no—
222C23×C107—22no—
223C23×C107—22no—
224C23×C107—22no—
225C23×C107—22no—
226C23×C107—22no—
227C23×C107—21no—
228C23×C107—22no—
229C23×C107—22no—
230C23×C107—42no—
231C23×C107—42no—
232C23×C107—42no—
233C23×C107—44no—
234C23×C107—42no—
235C23×C107—42no—
236C23×C107—42no—
237C23×C107—42no—
238C23×C107—42no—
239C23×C107—42no—
240C23×C107—41no—
241C23×C107—41no—
242C23×C107—82no—
243C23×C107—82no—
244C23×C107—82no—
245C23×C107—82no—
246C23×C107—82no—
247C23×C107—82no—
248C23×C107—82no—
249C23×C107—82no—
250C23×C107—84no—
251C23×C107—84no—
252C23×C107—82no—
253C23×C107—84no—
254C23×C107—84no—
255C23×C107#9911yescharacteristic
256C23×C107#9911yescharacteristic
257C23×C107#9912yes—
258C23×C107C2×C22⋊C411yescharacteristic
259C23×C107C2×C22⋊C411yescharacteristic
260C23×C107C2×C22⋊C412yes—
261C23×C107C2×C22⋊C411yescharacteristic
262C23×C107C2×C22⋊C412yes—
263C23×C107C2×C22⋊C412yes—
264C23×C107C23×C411yescharacteristic
265C23×C107C22×D411yescharacteristic
266D4×C107—42no—
267D4×C107—42no—
268D4×C107—42no—
269D4×C107—42no—
270D4×C107—41no—
271D4×C107—41no—
272D4×C107—42no—
273D4×C107—41no—
274D4×C107—42no—
275D4×C107—41no—
276D4×C107—48no—
277D4×C107—44no—
278D4×C107—44no—
279D4×C107—84no—
280D4×C107—82no—
281D4×C107—82no—
282C2×C4×C107—22no—
283C2×C4×C107—21no—
284C2×C4×C107—22no—
285C2×C4×C107—21no—
286C2×C4×C107—22no—
287C2×C4×C107—22no—
288C2×C4×C107—21no—
289C2×C4×C107—21no—
290C2×C4×C107—22no—
291C2×C4×C107—22no—
292C2×C4×C107—22no—
293C2×C4×C107—42no—
294C2×C4×C107—42no—
295C2×C4×C107—42no—
296C2×C4×C107—41no—
297C2×C4×C107—41no—
298C2×C4×C107—42no—
299C2×C4×C107—44no—
300C2×C4×C107—84no—
301C2×C4×C107—88no—
302C2×C4×C107—84no—
303C2×C4×C107C2×C22⋊C412yes—
304C2×C4×C107C2×C22⋊C411yescharacteristic
305C2×C4×C107C22×D411yescharacteristic
306C8×C107—44no—
307C22×C107—22no—
308C22×C107—22no—
309C22×C107—22no—
310C22×C107—21no—
311C22×C107—21no—
312C22×C107—21no—
313C22×C107—22no—
314C22×C107—22no—
315C22×C107—21no—
316C22×C107—42no—
317C22×C107—42no—
318C22×C107—42no—
319C22×C107—42no—
320C22×C107—41no—
321C22×C107—41no—
322C22×C107—41no—
323C22×C107—41no—
324C22×C107—44no—
325C22×C107—42no—
326C22×C107—44no—
327C22×C107—42no—
328C22×C107—42no—
329C22×C107—42no—
330C22×C107—42no—
331C22×C107—42no—
332C22×C107—42no—
333C22×C107—42no—
334C22×C107—42no—
335C22×C107—81no—
336C22×C107—81no—
337C22×C107—82no—
338C22×C107—82no—
339C22×C107—82no—
340C22×C107—82no—
341C22×C107—82no—
342C22×C107—82no—
343C22×C107—82no—
344C22×C107—84no—
345C22×C107—84no—
346C22×C107—82no—
347C22×C107C2×#9911yescharacteristic
348C22×C107C2×#9912yes—
349C22×C107C2×#9912yes—
350C22×C107C2×#9911yescharacteristic
351C22×C107C22×C22⋊C411yescharacteristic
352C4×C107—21no—
353C4×C107—22no—
354C4×C107—21no—
355C4×C107—42no—
356C4×C107—42no—
357C4×C107—42no—
358C4×C107—84no—
359C2×#2121C10711yesmaximal, characteristic, direct product factor, Sylow
360C2×C107—21no—
361C2×C107—21no—
362C2×C107—22no—
363C2×C107—22no—
364C2×C107—41no—
365C2×C107—42no—
366C2×C107—41no—
367C2×C107—42no—
368C2×C107—41no—
369C2×C107—41no—
370C2×C107—82no—
371C2×C107#212112yesdirect product factor
372C2×C107C22×#9911yescharacteristic
373C2×#534C2×C10711yescharacteristic
374C22×#100C2×C10711yescharacteristic, complemented
375C22×#99C2×C10711yescharacteristic, complemented
376#2121C2×C10718yesdirect product factor
377C2×#352C2×C10712yescomplemented
378C2×AΣL(1,𝔽16)C2×C10712yescomplemented
379C107C2×#212111yescharacteristic, direct product factor, Sylow
380C23×D4C4×C10711yescharacteristic, complemented
381C23×D4C22×C10711yescharacteristic
382C22×M16—21no—
383#534—22no—
384#534—22no—
385#534C4×C10714yescomplemented
386#534C22×C10714yes—
387C2×#123—21no—
388C2×#123C4×C10711yescharacteristic, complemented
389C2×#123C22×C10711yescharacteristic
390C2×#121—21no—
391C2×#121—21no—
392C2×#120—21no—
393C2×#120C4×C10711yescharacteristic, complemented
394C2×#120C22×C10711yescharacteristic
395C22×C22⋊C4—21no—
396C22×C22⋊C4C4×C10711yescharacteristic, complemented
397C2×#100—22no—
398C2×#100—21no—
399C2×#100C22×C10712yes—
400C2×#100C22×C10714yescomplemented
401C2×#99—22no—
402C2×#99—21no—
403C2×#99C22×C10712yes—
404C2×#99C22×C10714yescomplemented
405#352C22×C10718yescomplemented
406AΣL(1,𝔽16)C22×C10718yescomplemented
407C25C2×C4×C10711yescharacteristic
408C25C2×C4×C10711yescharacteristic, complemented
409C25D4×C10711yescharacteristic
410C22×D4—21no—
411C22×D4—21no—
412C22×D4—22no—
413C22×D4—21no—
414C22×D4—21no—
415C22×D4—41no—
416C22×D4—41no—
417C22×D4—42no—
418C22×D4—41no—
419C22×D4—41no—
420C22×D4—42no—
421C22×D4C2×C4×C10711yescharacteristic
422C22×D4C2×C4×C10712yes—
423C22×D4C2×C4×C10714yescomplemented
424C22×D4D4×C10711yescharacteristic
425C22×D4D4×C10712yes—
426C22×D4D4×C10711yescharacteristic
427C22×D4D4×C10712yes—
428C22×D4C23×C10711yescharacteristic
429C22×D4C23×C10712yes—
430C23×C4—21no—
431C23×C4—41no—
432C23×C4C2×C4×C10711yescharacteristic, complemented
433C23×C4D4×C10711yescharacteristic
434C2×M16—22no—
435C2×M16—24no—
436C2×M16—41no—
437C2×M16—42no—
438C22×C8—41no—
439#123—22no—
440#123—21no—
441#123—21no—
442#123—24no—
443#123—24no—
444#123C2×C4×C10714yescomplemented
445#123C2×C4×C10712yescomplemented
446#123C23×C10712yes—
447#121—24no—
448#121—24no—
449#121—24no—
450#121—24no—
451#120—24no—
452#120—24no—
453#120—22no—
454#120—21no—
455#120—21no—
456#120C2×C4×C10714yescomplemented
457#120C2×C4×C10712yescomplemented
458#120C23×C10712yes—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—41no—
471C2×C22⋊C4C2×C4×C10711yescharacteristic, complemented
472C2×C22⋊C4C2×C4×C10711yescharacteristic, complemented
473C2×C22⋊C4C2×C4×C10714yescomplemented
474#100—22no—
475#100—24no—
476#100C23×C10714yes—
477#99—22no—
478#99—24no—
479#99C23×C10714yes—
480C24—21no—
481C24—21no—
482C24—22no—
483C24—21no—
484C24—21no—
485C24—22no—
486C24—21no—
487C24—21no—
488C24—41no—
489C24—41no—
490C24—82no—
491C24—82no—
492C24—82no—
493C24C22⋊C4×C10711yescharacteristic
494C24C22⋊C4×C10711yescharacteristic
495C24C22⋊C4×C10712yes—
496C24C22⋊C4×C10712yes—
497C24C22⋊C4×C10711yescharacteristic
498C24C22×C4×C10711yescharacteristic
499C24C22×C4×C10712yes—
500C24C22×C4×C10712yescomplemented
501C24C2×D4×C10711yescharacteristic
502C24C2×D4×C10712yes—
503C2×D4—24no—
504C2×D4—24no—
505C2×D4—22no—
506C2×D4—24no—
507C2×D4—22no—
508C2×D4—41no—
509C2×D4—41no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—41no—
513C2×D4—42no—
514C2×D4—41no—
515C2×D4—42no—
516C2×D4—41no—
517C2×D4—42no—
518C2×D4—41no—
519C2×D4—42no—
520C2×D4—41no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—41no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—41no—
529C2×D4—41no—
530C2×D4—42no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—82no—
534C2×D4—82no—
535C2×D4C22⋊C4×C10712yes—
536C2×D4C22⋊C4×C10712yes—
537C2×D4C22⋊C4×C10712yes—
538C2×D4C22×C4×C10712yes—
539C2×D4C22×C4×C10711yescharacteristic
540C2×D4C2×D4×C10711yescharacteristic
541C2×D4C2×D4×C10712yes—
542C2×D4C2×D4×C10711yescharacteristic
543C2×D4C2×D4×C10712yes—
544C2×D4C24×C10711yescharacteristic
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—42no—
556C22×C4—44no—
557C22×C4—82no—
558C22×C4—84no—
559C22×C4C22⋊C4×C10711yescharacteristic
560C22×C4C22⋊C4×C10712yes—
561C22×C4C22×C4×C10712yescomplemented
562C22×C4C2×D4×C10711yescharacteristic
563C22×C4C2×D4×C10712yes—
564M16—24no—
565M16—42no—
566M16—44no—
567C2×C8—42no—
568C2×C8—44no—
569C4⋊C4—24no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—24no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—24no—
582C22⋊C4—42no—
583C22⋊C4—44no—
584C22⋊C4C22×C4×C10712yescomplemented
585C22⋊C4C22×C4×C10712yescomplemented
586C23—22no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—22no—
593C23—21no—
594C23—21no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—21no—
601C23—22no—
602C23—22no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—44no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—82no—
616C23—82no—
617C23—82no—
618C23—82no—
619C23—82no—
620C23—82no—
621C23—82no—
622C23—82no—
623C23—84no—
624C23—84no—
625C23—82no—
626C23—84no—
627C23—84no—
628C23#99×C10711yescharacteristic
629C23#99×C10711yescharacteristic
630C23#99×C10712yes—
631C23C2×C22⋊C4×C10711yescharacteristic
632C23C2×C22⋊C4×C10711yescharacteristic
633C23C2×C22⋊C4×C10712yes—
634C23C2×C22⋊C4×C10711yescharacteristic
635C23C2×C22⋊C4×C10712yes—
636C23C2×C22⋊C4×C10712yes—
637C23C23×C4×C10711yescharacteristic
638C23C22×D4×C10711yescharacteristic
639D4—42no—
640D4—42no—
641D4—42no—
642D4—42no—
643D4—41no—
644D4—41no—
645D4—42no—
646D4—41no—
647D4—42no—
648D4—41no—
649D4—48no—
650D4—44no—
651D4—44no—
652D4—84no—
653D4—82no—
654D4—82no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—44no—
673C2×C4—84no—
674C2×C4—88no—
675C2×C4—84no—
676C2×C4C2×C22⋊C4×C10712yes—
677C2×C4C2×C22⋊C4×C10711yescharacteristic
678C2×C4C22×D4×C10711yescharacteristic
679C8—44no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—22no—
687C22—22no—
688C22—21no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—44no—
698C22—42no—
699C22—42no—
700C22—44no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—81no—
709C22—81no—
710C22—82no—
711C22—82no—
712C22—82no—
713C22—82no—
714C22—82no—
715C22—82no—
716C22—82no—
717C22—84no—
718C22—84no—
719C22—82no—
720C22C2×#99×C10711yescharacteristic
721C22C2×#99×C10712yes—
722C22C2×#99×C10712yes—
723C22C2×#99×C10711yescharacteristic
724C22C22×C22⋊C4×C10711yescharacteristic
725C4—21no—
726C4—22no—
727C4—21no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—84no—
732C2—21no—
733C2—21no—
734C2—22no—
735C2—22no—
736C2—41no—
737C2—42no—
738C2—41no—
739C2—41no—
740C2—41no—
741C2—42no—
742C2—82no—
743C2C107×#212112yesdirect product factor
744C2C22×#99×C10711yescharacteristic
subgroupG/H
center, socleC22×C107C2×#99
commutatorC23C23×C4×C107
Frattini, cosocleC2×D4C24×C107
prime radicalC2×#534×C107C2
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C24×C107 ◁ C23×D4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#100×C107C2semidirect
3. C22×#99×C107C2semidirect
4. C107×#2121C2direct (N × H)
5. C2×#352×C107C2semidirect
6. C2×AΣL(1,𝔽16)×C107C2semidirect
7. C23×D4×C107C4semidirect
12. #534×C107C4semidirect
15. C2×#123×C107C4semidirect
20. C2×#120×C107C4semidirect
23. C22×C22⋊C4×C107C4semidirect
27. C2×#100×C107C22semidirect
31. C2×#99×C107C22semidirect
32. #352×C107C22semidirect
33. AΣL(1,𝔽16)×C107C22semidirect
35. C25×C107C2×C4semidirect
50. C22×D4×C107C2×C4semidirect
59. C23×C4×C107C2×C4semidirect
71. #123×C107C2×C4semidirect
72. #123×C107C2×C4semidirect
83. #120×C107C2×C4semidirect
84. #120×C107C2×C4semidirect
98. C2×C22⋊C4×C107C2×C4semidirect
99. C2×C22⋊C4×C107C2×C4semidirect
100. C2×C22⋊C4×C107C2×C4semidirect
127. C24×C107C22×C4semidirect
188. C22×C4×C107C22×C4semidirect
211. C22⋊C4×C107C22×C4semidirect
212. C22⋊C4×C107C22×C4semidirect
359. C2×#2121C107direct (N × H)
371. C2×C107#2121direct (N × H)
374. C22×#100C2×C107semidirect
375. C22×#99C2×C107semidirect
376. #2121C2×C107direct (N × H)
377. C2×#352C2×C107semidirect
378. C2×AΣL(1,𝔽16)C2×C107semidirect
379. C107C2×#2121direct (N × H)
380. C23×D4C4×C107semidirect
385. #534C4×C107semidirect
388. C2×#123C4×C107semidirect
393. C2×#120C4×C107semidirect
396. C22×C22⋊C4C4×C107semidirect
400. C2×#100C22×C107semidirect
404. C2×#99C22×C107semidirect
405. #352C22×C107semidirect
406. AΣL(1,𝔽16)C22×C107semidirect
408. C25C2×C4×C107semidirect
423. C22×D4C2×C4×C107semidirect
432. C23×C4C2×C4×C107semidirect
444. #123C2×C4×C107semidirect
445. #123C2×C4×C107semidirect
456. #120C2×C4×C107semidirect
457. #120C2×C4×C107semidirect
471. C2×C22⋊C4C2×C4×C107semidirect
472. C2×C22⋊C4C2×C4×C107semidirect
473. C2×C22⋊C4C2×C4×C107semidirect
500. C24C22×C4×C107semidirect
561. C22×C4C22×C4×C107semidirect
584. C22⋊C4C22×C4×C107semidirect
585. C22⋊C4C22×C4×C107semidirect
743. C2C107×#2121direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#534×C1072
C22×#100×C1072
C22×#99×C1072
C107×#21212
C2×#352×C1072
C2×AΣL(1,𝔽16)×C1072
C2×#2121107