Finite Group Databasebeta

← C109×#22422 #42140416

Subgroups — C109×#22422 #42140416

Order 27904.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C109C211yesmaximal, characteristic
2C2×#435×C109C211yesmaximal, characteristic, complemented
3C2×#417×C109C211yesmaximal, characteristic, complemented
4C2×#416×C109C211yesmaximal, characteristic, complemented
5C109×#2352C211yesmaximal, characteristic, complemented
6C109×#1982C211yesmaximal, characteristic, complemented
7C109×#1961C211yesmaximal, characteristic, complemented
8C109×#1895C211yesmaximal, characteristic, complemented
9C109×#1893C211yesmaximal, characteristic, complemented
10C109×#1875C211yesmaximal, characteristic, complemented
11C109×#1874C211yesmaximal, characteristic, complemented
12C109×#1805C211yesmaximal, characteristic, complemented
13C109×#1788C211yesmaximal, characteristic, complemented
14C109×#1788C211yesmaximal, characteristic, complemented
15C109×#1763C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C22×#41×C109C2211yescharacteristic
18C22×M16×C109C2211yescharacteristic
19C23×C8×C109C2211yescharacteristic
20#550×C109—24no—
21#550×C109C418yescomplemented
22C2×#127×C109—21no—
23C2×#127×C109C2211yescharacteristic
24C2×#121×C109—21no—
25C2×#121×C109—21no—
26C2×#121×C109C2211yescharacteristic
27C2×#121×C109C2211yescharacteristic
28C2×C4×Q8×C109C2211yescharacteristic
29C2×C4×D4×C109—21no—
30C2×C4×D4×C109C2211yescharacteristic
31C2×#117×C109C2211yescharacteristic
32C22×C4⋊C4×C109C2211yescharacteristic
33#435×C109—24no—
34C2×C4⋊C8×C109C2211yescharacteristic
35#417×C109—24no—
36#416×C109—24no—
37C2×#103×C109C2211yescharacteristic
38C2×#103×C109C2211yescharacteristic
39C2×#103×C109C2211yescharacteristic
40C2×#103×C109C2211yescharacteristic
41C2×#102×C109C2211yescharacteristic
42C2×#102×C109C2211yescharacteristic
43C2×#102×C109C2211yescharacteristic
44C2×#102×C109C2211yescharacteristic
45C2×#102×C109C2211yescharacteristic
46C2×#102×C109C2211yescharacteristic
47C2×#102×C109C2211yescharacteristic
48C2×#102×C109C2211yescharacteristic
49C2×C22⋊C8×C109C2211yescharacteristic
50C2×C22⋊C8×C109C2211yescharacteristic
51C2×#97×C109C2211yescharacteristic
52#388×C109—21no—
53#387×C109—21no—
54#386×C109—21no—
55#382×C109C2211yescharacteristic
56#380×C109C2211yescharacteristic
57#380×C109C2211yescharacteristic
58C4×C4⋊C4×C109C2211yescharacteristic
59C4×C22⋊C4×C109—21no—
60#340×C109C2211yescharacteristic
61#340×C109C2211yescharacteristic
62#340×C109C2211yescharacteristic
63#340×C109C2211yescharacteristic
64C2×#41×C109—22no—
65C2×#41×C109—22no—
66C2×#41×C109—22no—
67C2×#41×C109—22no—
68C2×#41×C109—22no—
69C2×#41×C109—22no—
70C2×#41×C109—41no—
71C2×#41×C109—41no—
72C2×#41×C109—41no—
73C2×#41×C109—41no—
74C2×#41×C109C2×C414yes—
75C2×#41×C109C2×C414yescomplemented
76C22×Q8×C109C2311yescharacteristic
77C22×D4×C109—21no—
78C22×D4×C109—21no—
79C22×D4×C109—21no—
80C22×D4×C109—21no—
81C22×D4×C109—21no—
82C22×D4×C109—21no—
83C22×D4×C109D411yescharacteristic
84C22×D4×C109C2311yescharacteristic
85C22×D4×C109C2311yescharacteristic
86C23×C4×C109—21no—
87C23×C4×C109—21no—
88C23×C4×C109—21no—
89C23×C4×C109C2311yescharacteristic
90C23×C4×C109C2311yescharacteristic
91C2×M16×C109—22no—
92C2×M16×C109—22no—
93C2×M16×C109—41no—
94C22×C8×C109—22no—
95C22×C8×C109—22no—
96C22×C8×C109—41no—
97C22×C8×C109C2311yescharacteristic
98C22×C8×C109C2311yescharacteristic
99C22×C8×C109C2311yescharacteristic
100C22×C8×C109C2311yescharacteristic
101#127×C109—28no—
102#127×C109—22no—
103#127×C109C2×C414yescomplemented
104#121×C109—22no—
105#121×C109—22no—
106#121×C109—28no—
107#121×C109—28no—
108#121×C109C2×C414yes—
109#121×C109C2×C414yescomplemented
110C4×Q8×C109—22no—
111C4×Q8×C109C2×C414yescomplemented
112C4×D4×C109—28no—
113C4×D4×C109C2×C414yes—
114C4×D4×C109D414yes—
115#117×C109—22no—
116#117×C109—41no—
117C2×C4⋊C4×C109—21no—
118C2×C4⋊C4×C109—22no—
119C2×C4⋊C4×C109—21no—
120C2×C4⋊C4×C109—41no—
121C2×C4⋊C4×C109D411yescharacteristic
122C2×C4⋊C4×C109C2311yescharacteristic
123C2×C4⋊C4×C109C2311yescharacteristic
124C2×C4⋊C4×C109C2311yescharacteristic
125C2×C4⋊C4×C109C2311yescharacteristic
126C2×C4⋊C4×C109C2311yescharacteristic
127C2×C22⋊C4×C109—21no—
128C2×C22⋊C4×C109—21no—
129C2×C22⋊C4×C109—21no—
130C2×C22⋊C4×C109—21no—
131C2×C22⋊C4×C109—21no—
132C2×C22⋊C4×C109D411yescharacteristic
133C2×C22⋊C4×C109D411yescharacteristic
134C2×C42×C109—21no—
135C2×C42×C109—21no—
136C2×C42×C109—21no—
137C2×C42×C109C2311yescharacteristic
138C4⋊C8×C109—22no—
139#103×C109—22no—
140#103×C109—22no—
141#103×C109—22no—
142#103×C109D414yescomplemented
143#102×C109—22no—
144#102×C109—22no—
145#102×C109—22no—
146#102×C109—22no—
147#102×C109—41no—
148#102×C109—41no—
149#102×C109—41no—
150#102×C109—41no—
151C22⋊C8×C109—22no—
152C22⋊C8×C109—22no—
153#97×C109—22no—
154#95×C109—21no—
155#95×C109—21no—
156#95×C109—21no—
157#95×C109—21no—
158#95×C109—21no—
159C24×C109—21no—
160C24×C109—21no—
161C24×C109C2×D411yescharacteristic
162C24×C109C2×D411yescharacteristic
163#41×C109—28no—
164#41×C109—28no—
165#41×C109—44no—
166#41×C109—44no—
167#41×C109—44no—
168#41×C109—44no—
169#41×C109—44no—
170#41×C109—44no—
171C2×Q8×C109—21no—
172C2×Q8×C109—21no—
173C2×Q8×C109—21no—
174C2×Q8×C109C22×C412yes—
175C2×Q8×C109C2×D412yes—
176C2×Q8×C109#4112yes—
177C2×D4×C109—24no—
178C2×D4×C109—24no—
179C2×D4×C109—24no—
180C2×D4×C109—24no—
181C2×D4×C109—24no—
182C2×D4×C109—24no—
183C2×D4×C109—21no—
184C2×D4×C109—21no—
185C2×D4×C109—21no—
186C2×D4×C109—21no—
187C2×D4×C109—21no—
188C2×D4×C109—21no—
189C2×D4×C109—21no—
190C2×D4×C109—21no—
191C2×D4×C109—21no—
192C2×D4×C109—21no—
193C2×D4×C109—41no—
194C2×D4×C109—41no—
195C2×D4×C109—42no—
196C2×D4×C109—42no—
197C2×D4×C109—42no—
198C2×D4×C109—42no—
199C2×D4×C109—42no—
200C2×D4×C109—42no—
201C2×D4×C109—81no—
202C2×D4×C109—81no—
203C2×D4×C109—81no—
204C2×D4×C109—81no—
205C2×D4×C109—81no—
206C2×D4×C109—81no—
207C2×D4×C109C22⋊C414yes—
208C2×D4×C109C22×C412yes—
209C2×D4×C109C22×C412yes—
210C22×C4×C109—21no—
211C22×C4×C109—21no—
212C22×C4×C109—21no—
213C22×C4×C109—21no—
214C22×C4×C109—21no—
215C22×C4×C109—21no—
216C22×C4×C109—21no—
217C22×C4×C109—21no—
218C22×C4×C109—21no—
219C22×C4×C109—21no—
220C22×C4×C109—21no—
221C22×C4×C109—24no—
222C22×C4×C109—24no—
223C22×C4×C109—21no—
224C22×C4×C109—21no—
225C22×C4×C109—21no—
226C22×C4×C109—42no—
227C22×C4×C109—42no—
228C22×C4×C109—42no—
229C22×C4×C109—42no—
230C22×C4×C109—42no—
231C22×C4×C109—42no—
232C22×C4×C109—81no—
233C22×C4×C109C22×C412yes—
234C22×C4×C109C22×C412yes—
235C22×C4×C109C2×D411yescharacteristic
236C22×C4×C109C2×D411yescharacteristic
237C22×C4×C109C2×D411yescharacteristic
238C22×C4×C109C2×D411yescharacteristic
239C22×C4×C109C2×D412yes—
240C22×C4×C109C2×D412yes—
241C22×C4×C109C2411yescharacteristic
242M16×C109—44no—
243C2×C8×C109—21no—
244C2×C8×C109—21no—
245C2×C8×C109—21no—
246C2×C8×C109—21no—
247C2×C8×C109—21no—
248C2×C8×C109—21no—
249C2×C8×C109—21no—
250C2×C8×C109—21no—
251C2×C8×C109—21no—
252C2×C8×C109—21no—
253C2×C8×C109—21no—
254C2×C8×C109—44no—
255C2×C8×C109C2×D412yes—
256C4⋊C4×C109—24no—
257C4⋊C4×C109—21no—
258C4⋊C4×C109—21no—
259C4⋊C4×C109—21no—
260C4⋊C4×C109—21no—
261C4⋊C4×C109—21no—
262C4⋊C4×C109—21no—
263C4⋊C4×C109—21no—
264C4⋊C4×C109—21no—
265C4⋊C4×C109—42no—
266C4⋊C4×C109C22⋊C414yes—
267C4⋊C4×C109C22×C412yes—
268C4⋊C4×C109C2×D412yes—
269C22⋊C4×C109—24no—
270C22⋊C4×C109—24no—
271C22⋊C4×C109—42no—
272C22⋊C4×C109—42no—
273C22⋊C4×C109—81no—
274C22⋊C4×C109C22⋊C414yes—
275C22⋊C4×C109C22⋊C414yes—
276C42×C109—24no—
277C42×C109—42no—
278C42×C109—81no—
279C42×C109C22×C412yes—
280C42×C109C2×D412yes—
281C23×C109—21no—
282C23×C109—21no—
283C23×C109—21no—
284C23×C109—21no—
285C23×C109—21no—
286C23×C109—21no—
287C23×C109—21no—
288C23×C109—21no—
289C23×C109—21no—
290C23×C109—21no—
291C23×C109—21no—
292C23×C109—21no—
293C23×C109—22no—
294C23×C109—22no—
295C23×C109—41no—
296C23×C109—41no—
297C23×C109—41no—
298C23×C109—41no—
299C23×C109—41no—
300C23×C109—41no—
301C23×C109—41no—
302C23×C109—41no—
303C23×C109—41no—
304C23×C109—41no—
305C23×C109—41no—
306C23×C109—41no—
307C23×C109C2×C22⋊C412yes—
308C23×C109C2×C22⋊C412yes—
309C23×C109C22×D411yescharacteristic
310Q8×C109—22no—
311Q8×C109—22no—
312Q8×C109—22no—
313Q8×C109C4×D414yes—
314D4×C109—22no—
315D4×C109—22no—
316D4×C109—22no—
317D4×C109—22no—
318D4×C109—44no—
319D4×C109—48no—
320D4×C109—48no—
321D4×C109—48no—
322D4×C109—41no—
323D4×C109—41no—
324D4×C109—41no—
325D4×C109—41no—
326D4×C109—84no—
327D4×C109—84no—
328D4×C109—84no—
329C2×C4×C109—22no—
330C2×C4×C109—21no—
331C2×C4×C109—21no—
332C2×C4×C109—22no—
333C2×C4×C109—21no—
334C2×C4×C109—21no—
335C2×C4×C109—22no—
336C2×C4×C109—21no—
337C2×C4×C109—21no—
338C2×C4×C109—21no—
339C2×C4×C109—21no—
340C2×C4×C109—22no—
341C2×C4×C109—22no—
342C2×C4×C109—22no—
343C2×C4×C109—22no—
344C2×C4×C109—22no—
345C2×C4×C109—22no—
346C2×C4×C109—22no—
347C2×C4×C109—22no—
348C2×C4×C109—22no—
349C2×C4×C109—22no—
350C2×C4×C109—48no—
351C2×C4×C109—48no—
352C2×C4×C109—41no—
353C2×C4×C109—41no—
354C2×C4×C109—41no—
355C2×C4×C109—41no—
356C2×C4×C109—41no—
357C2×C4×C109—41no—
358C2×C4×C109—41no—
359C2×C4×C109—41no—
360C2×C4×C109—41no—
361C2×C4×C109—41no—
362C2×C4×C109—41no—
363C2×C4×C109—41no—
364C2×C4×C109—41no—
365C2×C4×C109—84no—
366C2×C4×C109C2×C22⋊C412yes—
367C2×C4×C109C2×C22⋊C412yes—
368C2×C4×C109C2×C22⋊C412yes—
369C2×C4×C109C2×C22⋊C412yes—
370C2×C4×C109C23×C411yescharacteristic
371C2×C4×C109C22×D411yescharacteristic
372C2×C4×C109C22×D411yescharacteristic
373C2×C4×C109C2×#4111yescharacteristic
374C2×C4×C109H(5,𝔽2)11yescharacteristic
375C2×C4×C109H(5,𝔽2)11yescharacteristic
376C8×C109—22no—
377C8×C109—41no—
378C8×C109—41no—
379C8×C109—41no—
380C22×C109—22no—
381C22×C109—22no—
382C22×C109—22no—
383C22×C109—22no—
384C22×C109—22no—
385C22×C109—22no—
386C22×C109—41no—
387C22×C109—41no—
388C22×C109—41no—
389C22×C109—41no—
390C22×C109—41no—
391C22×C109—41no—
392C22×C109—41no—
393C22×C109—41no—
394C22×C109—42no—
395C22×C109—42no—
396C22×C109—42no—
397C22×C109—42no—
398C22×C109—42no—
399C22×C109—42no—
400C22×C109—81no—
401C22×C109—81no—
402C22×C109—81no—
403C22×C109—81no—
404C22×C109—81no—
405C22×C109—81no—
406C22×C109—81no—
407C22×C109—81no—
408C22×C109C22×C22⋊C411yescharacteristic
409C22×C109D4211yescharacteristic
410C22×C109#54611yescharacteristic
411C22×C109#57511yescharacteristic
412C22×C109#57511yescharacteristic
413C22×C109#57611yescharacteristic
414C22×C109#57711yescharacteristic
415C4×C109—22no—
416C4×C109—22no—
417C4×C109—24no—
418C4×C109—22no—
419C4×C109—22no—
420C4×C109—42no—
421C4×C109—42no—
422C4×C109—81no—
423C4×C109—81no—
424C4×C109—81no—
425C4×C109C2×C4×D411yescharacteristic
426C4×C109#51811yescharacteristic
427C4×C109D4211yescharacteristic
428C4×C109#54611yescharacteristic
429#22422C10911yesmaximal, characteristic, direct product factor, Sylow
430C2×C109—42no—
431C2×C109—42no—
432C2×C109—82no—
433C2×C109—82no—
434C2×C109D4×C22⋊C411yescharacteristic
435C2×C109#289611yescharacteristic
436C2×C109#289711yescharacteristic
437C2×C109#326811yescharacteristic
438C2×C109#327111yescharacteristic
439C2×C109#330911yescharacteristic
440C2×C109#331711yescharacteristic
441C2×#550C2×C10911yescharacteristic
442C2×#435C2×C10911yescharacteristic, complemented
443C2×#417C2×C10911yescharacteristic, complemented
444C2×#416C2×C10911yescharacteristic, complemented
445#2352C2×C10911yescharacteristic, complemented
446#1982C2×C10911yescharacteristic, complemented
447#1961C2×C10911yescharacteristic, complemented
448#1895C2×C10911yescharacteristic, complemented
449#1893C2×C10911yescharacteristic, complemented
450#1875C2×C10911yescharacteristic, complemented
451#1874C2×C10911yescharacteristic, complemented
452#1805C2×C10911yescharacteristic, complemented
453#1788C2×C10911yescharacteristic, complemented
454#1788C2×C10911yescharacteristic, complemented
455#1763C2×C10911yescharacteristic, complemented
456C109#2242211yescharacteristic, direct product factor, Sylow
457C22×#41C22×C10911yescharacteristic
458C22×#41C22×C10911yescharacteristic
459C22×M16C22×C10911yescharacteristic
460C23×C8C22×C10911yescharacteristic
461#550—24no—
462#550C4×C10918yescomplemented
463C2×#127—21no—
464C2×#127C22×C10911yescharacteristic
465C2×#121—21no—
466C2×#121—21no—
467C2×#121C22×C10911yescharacteristic
468C2×#121C22×C10911yescharacteristic
469C2×C4×Q8C22×C10911yescharacteristic
470C2×C4×D4—21no—
471C2×C4×D4C22×C10911yescharacteristic
472C2×#117C22×C10911yescharacteristic
473C22×C4⋊C4C22×C10911yescharacteristic
474#435—24no—
475C2×C4⋊C8C22×C10911yescharacteristic
476#417—24no—
477#416—24no—
478C2×#103C22×C10911yescharacteristic
479C2×#103C22×C10911yescharacteristic
480C2×#103C22×C10911yescharacteristic
481C2×#103C22×C10911yescharacteristic
482C2×#102C22×C10911yescharacteristic
483C2×#102C22×C10911yescharacteristic
484C2×#102C22×C10911yescharacteristic
485C2×#102C22×C10911yescharacteristic
486C2×#102C22×C10911yescharacteristic
487C2×#102C22×C10911yescharacteristic
488C2×#102C22×C10911yescharacteristic
489C2×#102C22×C10911yescharacteristic
490C2×C22⋊C8C22×C10911yescharacteristic
491C2×C22⋊C8C22×C10911yescharacteristic
492C2×#97C22×C10911yescharacteristic
493#388—21no—
494#387—21no—
495#386—21no—
496#382C22×C10911yescharacteristic
497#380C22×C10911yescharacteristic
498#380C22×C10911yescharacteristic
499C4×C4⋊C4C22×C10911yescharacteristic
500C4×C22⋊C4—21no—
501#340C22×C10911yescharacteristic
502#340C22×C10911yescharacteristic
503#340C22×C10911yescharacteristic
504#340C22×C10911yescharacteristic
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×C4×C10914yes—
516C2×#41C2×C4×C10914yescomplemented
517C22×Q8C23×C10911yescharacteristic
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4D4×C10911yescharacteristic
525C22×D4C23×C10911yescharacteristic
526C22×D4C23×C10911yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C23×C10911yescharacteristic
531C23×C4C23×C10911yescharacteristic
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—41no—
535C22×C8—22no—
536C22×C8—22no—
537C22×C8—41no—
538C22×C8C23×C10911yescharacteristic
539C22×C8C23×C10911yescharacteristic
540C22×C8C23×C10911yescharacteristic
541C22×C8C23×C10911yescharacteristic
542#127—28no—
543#127—22no—
544#127C2×C4×C10914yescomplemented
545#121—22no—
546#121—22no—
547#121—28no—
548#121—28no—
549#121C2×C4×C10914yes—
550#121C2×C4×C10914yescomplemented
551C4×Q8—22no—
552C4×Q8C2×C4×C10914yescomplemented
553C4×D4—28no—
554C4×D4C2×C4×C10914yes—
555C4×D4D4×C10914yes—
556#117—22no—
557#117—41no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4D4×C10911yescharacteristic
563C2×C4⋊C4C23×C10911yescharacteristic
564C2×C4⋊C4C23×C10911yescharacteristic
565C2×C4⋊C4C23×C10911yescharacteristic
566C2×C4⋊C4C23×C10911yescharacteristic
567C2×C4⋊C4C23×C10911yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4D4×C10911yescharacteristic
574C2×C22⋊C4D4×C10911yescharacteristic
575C2×C42—21no—
576C2×C42—21no—
577C2×C42—21no—
578C2×C42C23×C10911yescharacteristic
579C4⋊C8—22no—
580#103—22no—
581#103—22no—
582#103—22no—
583#103D4×C10914yescomplemented
584#102—22no—
585#102—22no—
586#102—22no—
587#102—22no—
588#102—41no—
589#102—41no—
590#102—41no—
591#102—41no—
592C22⋊C8—22no—
593C22⋊C8—22no—
594#97—22no—
595#95—21no—
596#95—21no—
597#95—21no—
598#95—21no—
599#95—21no—
600C24—21no—
601C24—21no—
602C24C2×D4×C10911yescharacteristic
603C24C2×D4×C10911yescharacteristic
604#41—28no—
605#41—28no—
606#41—44no—
607#41—44no—
608#41—44no—
609#41—44no—
610#41—44no—
611#41—44no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8C22×C4×C10912yes—
616C2×Q8C2×D4×C10912yes—
617C2×Q8#41×C10912yes—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊C4×C10914yes—
649C2×D4C22×C4×C10912yes—
650C2×D4C22×C4×C10912yes—
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—24no—
663C22×C4—24no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—81no—
674C22×C4C22×C4×C10912yes—
675C22×C4C22×C4×C10912yes—
676C22×C4C2×D4×C10911yescharacteristic
677C22×C4C2×D4×C10911yescharacteristic
678C22×C4C2×D4×C10911yescharacteristic
679C22×C4C2×D4×C10911yescharacteristic
680C22×C4C2×D4×C10912yes—
681C22×C4C2×D4×C10912yes—
682C22×C4C24×C10911yescharacteristic
683M16—44no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—44no—
696C2×C8C2×D4×C10912yes—
697C4⋊C4—24no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—42no—
707C4⋊C4C22⋊C4×C10914yes—
708C4⋊C4C22×C4×C10912yes—
709C4⋊C4C2×D4×C10912yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—81no—
715C22⋊C4C22⋊C4×C10914yes—
716C22⋊C4C22⋊C4×C10914yes—
717C42—24no—
718C42—42no—
719C42—81no—
720C42C22×C4×C10912yes—
721C42C2×D4×C10912yes—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—22no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23C2×C22⋊C4×C10912yes—
749C23C2×C22⋊C4×C10912yes—
750C23C22×D4×C10911yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8C4×D4×C10914yes—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—44no—
760D4—48no—
761D4—48no—
762D4—48no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—84no—
768D4—84no—
769D4—84no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—48no—
792C2×C4—48no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—84no—
807C2×C4C2×C22⋊C4×C10912yes—
808C2×C4C2×C22⋊C4×C10912yes—
809C2×C4C2×C22⋊C4×C10912yes—
810C2×C4C2×C22⋊C4×C10912yes—
811C2×C4C23×C4×C10911yescharacteristic
812C2×C4C22×D4×C10911yescharacteristic
813C2×C4C22×D4×C10911yescharacteristic
814C2×C4C2×#41×C10911yescharacteristic
815C2×C4H(5,𝔽2)×C10911yescharacteristic
816C2×C4H(5,𝔽2)×C10911yescharacteristic
817C8—22no—
818C8—41no—
819C8—41no—
820C8—41no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22C22×C22⋊C4×C10911yescharacteristic
850C22D42×C10911yescharacteristic
851C22#546×C10911yescharacteristic
852C22#575×C10911yescharacteristic
853C22#575×C10911yescharacteristic
854C22#576×C10911yescharacteristic
855C22#577×C10911yescharacteristic
856C4—22no—
857C4—22no—
858C4—24no—
859C4—22no—
860C4—22no—
861C4—42no—
862C4—42no—
863C4—81no—
864C4—81no—
865C4—81no—
866C4C2×C4×D4×C10911yescharacteristic
867C4#518×C10911yescharacteristic
868C4D42×C10911yescharacteristic
869C4#546×C10911yescharacteristic
870C2—42no—
871C2—42no—
872C2—82no—
873C2—82no—
874C2D4×C22⋊C4×C10911yescharacteristic
875C2C109×#289611yescharacteristic
876C2C109×#289711yescharacteristic
877C2C109×#326811yescharacteristic
878C2C109×#327111yescharacteristic
879C2C109×#330911yescharacteristic
880C2C109×#331711yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutatorC2×C4C23×C4×C109
Frattini, cosocleC22×C4C24×C109
prime radicalC2×#550×C109C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C2×C4×D4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#435×C109C2semidirect
3. C2×#417×C109C2semidirect
4. C2×#416×C109C2semidirect
5. C109×#2352C2semidirect
6. C109×#1982C2semidirect
7. C109×#1961C2semidirect
8. C109×#1895C2semidirect
9. C109×#1893C2semidirect
10. C109×#1875C2semidirect
11. C109×#1874C2semidirect
12. C109×#1805C2semidirect
13. C109×#1788C2semidirect
14. C109×#1788C2semidirect
15. C109×#1763C2semidirect
21. #550×C109C4semidirect
75. C2×#41×C109C2×C4semidirect
103. #127×C109C2×C4semidirect
109. #121×C109C2×C4semidirect
111. C4×Q8×C109C2×C4semidirect
142. #103×C109D4semidirect
429. #22422C109direct (N × H)
442. C2×#435C2×C109semidirect
443. C2×#417C2×C109semidirect
444. C2×#416C2×C109semidirect
445. #2352C2×C109semidirect
446. #1982C2×C109semidirect
447. #1961C2×C109semidirect
448. #1895C2×C109semidirect
449. #1893C2×C109semidirect
450. #1875C2×C109semidirect
451. #1874C2×C109semidirect
452. #1805C2×C109semidirect
453. #1788C2×C109semidirect
454. #1788C2×C109semidirect
455. #1763C2×C109semidirect
456. C109#22422direct (N × H)
462. #550C4×C109semidirect
516. C2×#41C2×C4×C109semidirect
544. #127C2×C4×C109semidirect
550. #121C2×C4×C109semidirect
552. C4×Q8C2×C4×C109semidirect
583. #103D4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1092
C2×#435×C1092
C2×#417×C1092
C2×#416×C1092
C109×#23522
C109×#19822
C109×#19612
C109×#18952
C109×#18932
C109×#18752
C109×#18742
C109×#18052
C109×#17882
C109×#17632
#22422109