Finite Group Databasebeta

← C109×#25179 #42143173

Subgroups — C109×#25179 #42143173

Order 27904.

1206 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#460×C109C211yesmaximal, characteristic, complemented
2C2×#449×C109C211yesmaximal, characteristic, complemented
3C2×#449×C109C211yesmaximal, characteristic, complemented
4C2×#440×C109C211yesmaximal, characteristic, complemented
5C109×#2428C211yesmaximal, characteristic, complemented
6C109×#2341C211yesmaximal, characteristic, complemented
7C109×#2067C211yesmaximal, characteristic, complemented
8C109×#2034C211yesmaximal, characteristic, complemented
9C109×#2033C211yesmaximal, characteristic, complemented
10C109×#2011C211yesmaximal, characteristic, complemented
11C109×#1972C211yesmaximal, characteristic, complemented
12C109×#1924C211yesmaximal, characteristic, complemented
13C109×#1880C211yesmaximal, characteristic, complemented
14C109×#1879C211yesmaximal, characteristic, complemented
15C109×#1865C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C22×SD16×C109C2211yescharacteristic
18C22×SD16×C109C2211yescharacteristic
19C22×D8×C109C2211yescharacteristic
20C22×D8×C109C2211yescharacteristic
21C2×#127×C109C2211yescharacteristic
22C2×#121×C109—21no—
23C2×#121×C109C2211yescharacteristic
24C2×#121×C109C2211yescharacteristic
25C2×C4×Q8×C109C2211yescharacteristic
26C2×C4×Q8×C109C2211yescharacteristic
27C2×C4×D4×C109C2211yescharacteristic
28#460×C109—24no—
29#449×C109—24no—
30#449×C109—24no—
31#440×C109—24no—
32C2×#107×C109C2211yescharacteristic
33C2×#106×C109C2211yescharacteristic
34C2×C4⋊C8×C109C2211yescharacteristic
35C2×#103×C109C2211yescharacteristic
36C2×#103×C109C2211yescharacteristic
37C2×#102×C109C2211yescharacteristic
38C2×#102×C109C2211yescharacteristic
39C2×#102×C109C2211yescharacteristic
40C2×#102×C109C2211yescharacteristic
41C2×#102×C109C2211yescharacteristic
42C2×#102×C109C2211yescharacteristic
43C2×C22⋊C8×C109C2211yescharacteristic
44C2×C22⋊C8×C109C2211yescharacteristic
45C2×#97×C109C2211yescharacteristic
46#394×C109—21no—
47#392×C109—21no—
48#390×C109—21no—
49#390×C109—21no—
50#390×C109C2211yescharacteristic
51#390×C109C2211yescharacteristic
52#390×C109C2211yescharacteristic
53#389×C109C2211yescharacteristic
54#386×C109—21no—
55#380×C109—21no—
56#380×C109C2211yescharacteristic
57C4×C22⋊C4×C109—21no—
58C4×C22⋊C4×C109C2211yescharacteristic
59#340×C109C2211yescharacteristic
60#340×C109C2211yescharacteristic
61#336×C109C2211yescharacteristic
62#336×C109C2211yescharacteristic
63C2×#41×C109—22no—
64C2×#41×C109—22no—
65C2×#41×C109—22no—
66C2×#41×C109—22no—
67C2×#41×C109—41no—
68C2×#41×C109—41no—
69C22×Q8×C109C2311yescharacteristic
70C22×D4×C109—21no—
71C22×D4×C109—21no—
72C22×D4×C109—21no—
73C22×D4×C109—21no—
74C22×D4×C109—21no—
75C22×D4×C109C2311yescharacteristic
76C22×D4×C109C2311yescharacteristic
77C22×D4×C109C2311yescharacteristic
78C23×C4×C109—21no—
79C23×C4×C109—21no—
80C23×C4×C109C2311yescharacteristic
81C2×SD16×C109—22no—
82C2×SD16×C109—22no—
83C2×SD16×C109—22no—
84C2×SD16×C109—22no—
85C2×SD16×C109—22no—
86C2×SD16×C109D414yescomplemented
87C2×D8×C109—22no—
88C2×D8×C109—22no—
89C2×D8×C109—22no—
90C2×D8×C109—22no—
91C2×D8×C109—41no—
92C2×D8×C109—41no—
93C22×C8×C109C2311yescharacteristic
94C22×C8×C109C2311yescharacteristic
95C22×C8×C109C2311yescharacteristic
96C22×C8×C109C2311yescharacteristic
97#127×C109—22no—
98#127×C109—41no—
99#121×C109—22no—
100#121×C109—22no—
101#121×C109—44no—
102#121×C109—41no—
103#121×C109—41no—
104C4×Q8×C109—22no—
105C4×Q8×C109—22no—
106C4×Q8×C109—41no—
107C4×Q8×C109—41no—
108C4×D4×C109—22no—
109C4×D4×C109—41no—
110C2×C4⋊C4×C109—21no—
111C2×C4⋊C4×C109—21no—
112C2×C4⋊C4×C109—21no—
113C2×C4⋊C4×C109C2311yescharacteristic
114C2×C4⋊C4×C109C2311yescharacteristic
115C2×C4⋊C4×C109C2311yescharacteristic
116C2×C4⋊C4×C109C2311yescharacteristic
117C2×C22⋊C4×C109—21no—
118C2×C22⋊C4×C109—21no—
119C2×C22⋊C4×C109—21no—
120C2×C22⋊C4×C109—21no—
121C2×C22⋊C4×C109—21no—
122C2×C22⋊C4×C109—21no—
123C2×C22⋊C4×C109—21no—
124C2×C22⋊C4×C109—21no—
125C2×C22⋊C4×C109—21no—
126C2×C22⋊C4×C109—21no—
127C2×C22⋊C4×C109D411yescharacteristic
128C2×C22⋊C4×C109D411yescharacteristic
129C2×C42×C109—21no—
130C2×C42×C109—21no—
131C2×C42×C109C2311yescharacteristic
132C2×C42×C109C2311yescharacteristic
133#107×C109—22no—
134#106×C109—41no—
135C4⋊C8×C109—22no—
136#103×C109—22no—
137#103×C109D414yescomplemented
138#102×C109—22no—
139#102×C109—22no—
140#102×C109—22no—
141#102×C109—22no—
142#102×C109—22no—
143#102×C109—41no—
144C22⋊C8×C109—22no—
145C22⋊C8×C109—22no—
146#97×C109—22no—
147#95×C109—21no—
148#95×C109—21no—
149#95×C109D411yescharacteristic
150#95×C109D411yescharacteristic
151C24×C109—21no—
152C24×C109—21no—
153C24×C109—21no—
154C24×C109C2×D411yescharacteristic
155#41×C109—44no—
156#41×C109—44no—
157#41×C109—44no—
158#41×C109—44no—
159C2×Q8×C109—21no—
160C2×Q8×C109—21no—
161C2×Q8×C109—21no—
162C2×Q8×C109C2×D412yes—
163C2×Q8×C109C2×D412yes—
164C2×Q8×C109#4112yes—
165C2×D4×C109—24no—
166C2×D4×C109—21no—
167C2×D4×C109—21no—
168C2×D4×C109—21no—
169C2×D4×C109—21no—
170C2×D4×C109—21no—
171C2×D4×C109—21no—
172C2×D4×C109—21no—
173C2×D4×C109—21no—
174C2×D4×C109—21no—
175C2×D4×C109—21no—
176C2×D4×C109—21no—
177C2×D4×C109—21no—
178C2×D4×C109—21no—
179C2×D4×C109—21no—
180C2×D4×C109—21no—
181C2×D4×C109—21no—
182C2×D4×C109—42no—
183C2×D4×C109—42no—
184C2×D4×C109—42no—
185C2×D4×C109—42no—
186C2×D4×C109—42no—
187C2×D4×C109—42no—
188C2×D4×C109—42no—
189C2×D4×C109—42no—
190C2×D4×C109—42no—
191C2×D4×C109—42no—
192C2×D4×C109—81no—
193C2×D4×C109—81no—
194C2×D4×C109—81no—
195C2×D4×C109—81no—
196C2×D4×C109C2×D412yes—
197C2×D4×C109#4112yes—
198C22×C4×C109—21no—
199C22×C4×C109—24no—
200C22×C4×C109—21no—
201C22×C4×C109—21no—
202C22×C4×C109—21no—
203C22×C4×C109—21no—
204C22×C4×C109—21no—
205C22×C4×C109—21no—
206C22×C4×C109—21no—
207C22×C4×C109—21no—
208C22×C4×C109—21no—
209C22×C4×C109—21no—
210C22×C4×C109—42no—
211C22×C4×C109—42no—
212C22×C4×C109—42no—
213C22×C4×C109—42no—
214C22×C4×C109—81no—
215C22×C4×C109C2×D411yescharacteristic
216C22×C4×C109C2×D411yescharacteristic
217C22×C4×C109C2×D411yescharacteristic
218C22×C4×C109C2×D411yescharacteristic
219C22×C4×C109C2×D411yescharacteristic
220C22×C4×C109C2411yescharacteristic
221SD16×C109—28no—
222SD16×C109—44no—
223D8×C109—44no—
224D8×C109—44no—
225C2×C8×C109—21no—
226C2×C8×C109—21no—
227C2×C8×C109—21no—
228C2×C8×C109—21no—
229C2×C8×C109—21no—
230C2×C8×C109—21no—
231C2×C8×C109—21no—
232C2×C8×C109—21no—
233C2×C8×C109—21no—
234C2×C8×C109—21no—
235C2×C8×C109C2×D412yes—
236C2×C8×C109C2×D412yes—
237C4⋊C4×C109—21no—
238C4⋊C4×C109—21no—
239C4⋊C4×C109—21no—
240C4⋊C4×C109—21no—
241C4⋊C4×C109—21no—
242C4⋊C4×C109—21no—
243C4⋊C4×C109—21no—
244C4⋊C4×C109—42no—
245C4⋊C4×C109—42no—
246C4⋊C4×C109—42no—
247C4⋊C4×C109C2×D412yes—
248C22⋊C4×C109—22no—
249C22⋊C4×C109—41no—
250C22⋊C4×C109—42no—
251C22⋊C4×C109—42no—
252C22⋊C4×C109—42no—
253C22⋊C4×C109—42no—
254C22⋊C4×C109—42no—
255C22⋊C4×C109—42no—
256C22⋊C4×C109—81no—
257C22⋊C4×C109—81no—
258C22⋊C4×C109—81no—
259C22⋊C4×C109—81no—
260C42×C109—21no—
261C42×C109—21no—
262C42×C109—21no—
263C42×C109—21no—
264C42×C109—42no—
265C42×C109—42no—
266C23×C109—21no—
267C23×C109—22no—
268C23×C109—22no—
269C23×C109—21no—
270C23×C109—21no—
271C23×C109—21no—
272C23×C109—21no—
273C23×C109—21no—
274C23×C109—21no—
275C23×C109—41no—
276C23×C109—41no—
277C23×C109—41no—
278C23×C109—41no—
279C23×C109—41no—
280C23×C109—41no—
281C23×C109—41no—
282C23×C109—41no—
283C23×C109—41no—
284C23×C109—41no—
285C23×C109—41no—
286C23×C109—41no—
287C23×C109—41no—
288C23×C109—41no—
289C23×C109—41no—
290C23×C109—41no—
291C23×C109—41no—
292C23×C109—41no—
293C23×C109—41no—
294C23×C109C22×D411yescharacteristic
295Q8×C109—22no—
296Q8×C109—22no—
297Q8×C109—22no—
298Q8×C109#12114yescomplemented
299D4×C109—22no—
300D4×C109—22no—
301D4×C109—22no—
302D4×C109—22no—
303D4×C109—48no—
304D4×C109—41no—
305D4×C109—41no—
306D4×C109—41no—
307D4×C109—41no—
308D4×C109—41no—
309D4×C109—41no—
310D4×C109—41no—
311D4×C109—41no—
312D4×C109—84no—
313D4×C109—84no—
314D4×C109—84no—
315D4×C109—84no—
316C2×C4×C109—22no—
317C2×C4×C109—21no—
318C2×C4×C109—22no—
319C2×C4×C109—22no—
320C2×C4×C109—21no—
321C2×C4×C109—21no—
322C2×C4×C109—21no—
323C2×C4×C109—21no—
324C2×C4×C109—21no—
325C2×C4×C109—22no—
326C2×C4×C109—21no—
327C2×C4×C109—21no—
328C2×C4×C109—21no—
329C2×C4×C109—21no—
330C2×C4×C109—21no—
331C2×C4×C109—21no—
332C2×C4×C109—21no—
333C2×C4×C109—21no—
334C2×C4×C109—48no—
335C2×C4×C109—41no—
336C2×C4×C109—41no—
337C2×C4×C109—41no—
338C2×C4×C109—41no—
339C2×C4×C109—41no—
340C2×C4×C109—41no—
341C2×C4×C109—41no—
342C2×C4×C109—41no—
343C2×C4×C109—41no—
344C2×C4×C109—41no—
345C2×C4×C109—41no—
346C2×C4×C109—41no—
347C2×C4×C109—41no—
348C2×C4×C109—41no—
349C2×C4×C109—41no—
350C2×C4×C109—84no—
351C2×C4×C109AGL(1,ℤ/8)12yes—
352C2×C4×C109C22×D411yescharacteristic
353C2×C4×C109C22×D411yescharacteristic
354C2×C4×C109C2×#4111yescharacteristic
355C2×C4×C109C2×#4111yescharacteristic
356C2×C4×C109H(5,𝔽2)11yescharacteristic
357C2×C4×C109H(5,𝔽2)11yescharacteristic
358C8×C109—22no—
359C8×C109—22no—
360C8×C109—41no—
361C8×C109—41no—
362C22×C109—41no—
363C22×C109—42no—
364C22×C109—41no—
365C22×C109—42no—
366C22×C109—42no—
367C22×C109—41no—
368C22×C109—42no—
369C22×C109—41no—
370C22×C109—42no—
371C22×C109—42no—
372C22×C109—41no—
373C22×C109—41no—
374C22×C109—41no—
375C22×C109—81no—
376C22×C109—81no—
377C22×C109—81no—
378C22×C109—81no—
379C22×C109—81no—
380C22×C109—81no—
381C22×C109—81no—
382C22×C109—81no—
383C22×C109—81no—
384C22×C109—81no—
385C22×C109—81no—
386C22×C109—81no—
387C22×C109—81no—
388C22×C109—81no—
389C22×C109—81no—
390C22×C109#52511yescharacteristic
391C22×C109D4211yescharacteristic
392C22×C109D4211yescharacteristic
393C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
394C22×C109#57511yescharacteristic
395C22×C109#57611yescharacteristic
396C22×C109#57711yescharacteristic
397C4×C109—24no—
398C4×C109—22no—
399C4×C109—41no—
400C4×C109—41no—
401C4×C109—41no—
402C4×C109—41no—
403C4×C109—42no—
404C4×C109—81no—
405C4×C109—81no—
406C4×C109—81no—
407C4×C109C2×#12111yescharacteristic
408C4×C109#53811yescharacteristic
409C4×C109#54611yescharacteristic
410C4×C109#54611yescharacteristic
411#25179C10911yesmaximal, characteristic, direct product factor, Sylow
412C2×C109—81no—
413C2×C109—82no—
414C2×C109—82no—
415C2×C109—161no—
416C2×C109#242411yescharacteristic
417C2×C109#311511yescharacteristic
418C2×C109#311911yescharacteristic
419C2×C109#326511yescharacteristic
420C2×C109#326811yescharacteristic
421C2×C109#327111yescharacteristic
422C2×C109#327411yescharacteristic
423C2×#460C2×C10911yescharacteristic, complemented
424C2×#449C2×C10911yescharacteristic, complemented
425C2×#449C2×C10911yescharacteristic, complemented
426C2×#440C2×C10911yescharacteristic, complemented
427#2428C2×C10911yescharacteristic, complemented
428#2341C2×C10911yescharacteristic, complemented
429#2067C2×C10911yescharacteristic, complemented
430#2034C2×C10911yescharacteristic, complemented
431#2033C2×C10911yescharacteristic, complemented
432#2011C2×C10911yescharacteristic, complemented
433#1972C2×C10911yescharacteristic, complemented
434#1924C2×C10911yescharacteristic, complemented
435#1880C2×C10911yescharacteristic, complemented
436#1879C2×C10911yescharacteristic, complemented
437#1865C2×C10911yescharacteristic, complemented
438C109#2517911yescharacteristic, direct product factor, Sylow
439C22×#41C22×C10911yescharacteristic
440C22×SD16C22×C10911yescharacteristic
441C22×SD16C22×C10911yescharacteristic
442C22×D8C22×C10911yescharacteristic
443C22×D8C22×C10911yescharacteristic
444C2×#127C22×C10911yescharacteristic
445C2×#121—21no—
446C2×#121C22×C10911yescharacteristic
447C2×#121C22×C10911yescharacteristic
448C2×C4×Q8C22×C10911yescharacteristic
449C2×C4×Q8C22×C10911yescharacteristic
450C2×C4×D4C22×C10911yescharacteristic
451#460—24no—
452#449—24no—
453#449—24no—
454#440—24no—
455C2×#107C22×C10911yescharacteristic
456C2×#106C22×C10911yescharacteristic
457C2×C4⋊C8C22×C10911yescharacteristic
458C2×#103C22×C10911yescharacteristic
459C2×#103C22×C10911yescharacteristic
460C2×#102C22×C10911yescharacteristic
461C2×#102C22×C10911yescharacteristic
462C2×#102C22×C10911yescharacteristic
463C2×#102C22×C10911yescharacteristic
464C2×#102C22×C10911yescharacteristic
465C2×#102C22×C10911yescharacteristic
466C2×C22⋊C8C22×C10911yescharacteristic
467C2×C22⋊C8C22×C10911yescharacteristic
468C2×#97C22×C10911yescharacteristic
469#394—21no—
470#392—21no—
471#390—21no—
472#390—21no—
473#390C22×C10911yescharacteristic
474#390C22×C10911yescharacteristic
475#390C22×C10911yescharacteristic
476#389C22×C10911yescharacteristic
477#386—21no—
478#380—21no—
479#380C22×C10911yescharacteristic
480C4×C22⋊C4—21no—
481C4×C22⋊C4C22×C10911yescharacteristic
482#340C22×C10911yescharacteristic
483#340C22×C10911yescharacteristic
484#336C22×C10911yescharacteristic
485#336C22×C10911yescharacteristic
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—41no—
491C2×#41—41no—
492C22×Q8C23×C10911yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4C23×C10911yescharacteristic
499C22×D4C23×C10911yescharacteristic
500C22×D4C23×C10911yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4C23×C10911yescharacteristic
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16D4×C10914yescomplemented
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—41no—
515C2×D8—41no—
516C22×C8C23×C10911yescharacteristic
517C22×C8C23×C10911yescharacteristic
518C22×C8C23×C10911yescharacteristic
519C22×C8C23×C10911yescharacteristic
520#127—22no—
521#127—41no—
522#121—22no—
523#121—22no—
524#121—44no—
525#121—41no—
526#121—41no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—41no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4C23×C10911yescharacteristic
537C2×C4⋊C4C23×C10911yescharacteristic
538C2×C4⋊C4C23×C10911yescharacteristic
539C2×C4⋊C4C23×C10911yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C10911yescharacteristic
551C2×C22⋊C4D4×C10911yescharacteristic
552C2×C42—21no—
553C2×C42—21no—
554C2×C42C23×C10911yescharacteristic
555C2×C42C23×C10911yescharacteristic
556#107—22no—
557#106—41no—
558C4⋊C8—22no—
559#103—22no—
560#103D4×C10914yescomplemented
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—41no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569#97—22no—
570#95—21no—
571#95—21no—
572#95D4×C10911yescharacteristic
573#95D4×C10911yescharacteristic
574C24—21no—
575C24—21no—
576C24—21no—
577C24C2×D4×C10911yescharacteristic
578#41—44no—
579#41—44no—
580#41—44no—
581#41—44no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8C2×D4×C10912yes—
586C2×Q8C2×D4×C10912yes—
587C2×Q8#41×C10912yes—
588C2×D4—24no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C10912yes—
620C2×D4#41×C10912yes—
621C22×C4—21no—
622C22×C4—24no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4C2×D4×C10911yescharacteristic
639C22×C4C2×D4×C10911yescharacteristic
640C22×C4C2×D4×C10911yescharacteristic
641C22×C4C2×D4×C10911yescharacteristic
642C22×C4C2×D4×C10911yescharacteristic
643C22×C4C24×C10911yescharacteristic
644SD16—28no—
645SD16—44no—
646D8—44no—
647D8—44no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8C2×D4×C10912yes—
659C2×C8C2×D4×C10912yes—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4C2×D4×C10912yes—
671C22⋊C4—22no—
672C22⋊C4—41no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C22⋊C4—81no—
682C22⋊C4—81no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—42no—
688C42—42no—
689C23—21no—
690C23—22no—
691C23—22no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23C22×D4×C10911yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8#121×C10914yescomplemented
722D4—22no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—48no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—84no—
736D4—84no—
737D4—84no—
738D4—84no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—48no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4AGL(1,ℤ/8)×C10912yes—
775C2×C4C22×D4×C10911yescharacteristic
776C2×C4C22×D4×C10911yescharacteristic
777C2×C4C2×#41×C10911yescharacteristic
778C2×C4C2×#41×C10911yescharacteristic
779C2×C4H(5,𝔽2)×C10911yescharacteristic
780C2×C4H(5,𝔽2)×C10911yescharacteristic
781C8—22no—
782C8—22no—
783C8—41no—
784C8—41no—
785C22—41no—
786C22—42no—
787C22—42no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—42no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—42no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22#525×C10911yescharacteristic
814C22D42×C10911yescharacteristic
815C22D42×C10911yescharacteristic
816C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
817C22#575×C10911yescharacteristic
818C22#576×C10911yescharacteristic
819C22#577×C10911yescharacteristic
820C4—22no—
821C4—24no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—42no—
826C4—41no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4C2×#121×C10911yescharacteristic
831C4#538×C10911yescharacteristic
832C4#546×C10911yescharacteristic
833C4#546×C10911yescharacteristic
834C2—81no—
835C2—82no—
836C2—82no—
837C2—161no—
838C2C109×#242411yescharacteristic
839C2C109×#311511yescharacteristic
840C2C109×#311911yescharacteristic
841C2C109×#326511yescharacteristic
842C2C109×#326811yescharacteristic
843C2C109×#327111yescharacteristic
844C2C109×#327411yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C4×C22⋊C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#460×C109C2semidirect
2. C2×#449×C109C2semidirect
3. C2×#449×C109C2semidirect
4. C2×#440×C109C2semidirect
5. C109×#2428C2semidirect
6. C109×#2341C2semidirect
7. C109×#2067C2semidirect
8. C109×#2034C2semidirect
9. C109×#2033C2semidirect
10. C109×#2011C2semidirect
11. C109×#1972C2semidirect
12. C109×#1924C2semidirect
13. C109×#1880C2semidirect
14. C109×#1879C2semidirect
15. C109×#1865C2semidirect
86. C2×SD16×C109D4semidirect
137. #103×C109D4semidirect
298. Q8×C109#121semidirect
411. #25179C109direct (N × H)
423. C2×#460C2×C109semidirect
424. C2×#449C2×C109semidirect
425. C2×#449C2×C109semidirect
426. C2×#440C2×C109semidirect
427. #2428C2×C109semidirect
428. #2341C2×C109semidirect
429. #2067C2×C109semidirect
430. #2034C2×C109semidirect
431. #2033C2×C109semidirect
432. #2011C2×C109semidirect
433. #1972C2×C109semidirect
434. #1924C2×C109semidirect
435. #1880C2×C109semidirect
436. #1879C2×C109semidirect
437. #1865C2×C109semidirect
438. C109#25179direct (N × H)
509. C2×SD16D4×C109semidirect
560. #103D4×C109semidirect
721. Q8#121×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#460×C1092
C2×#449×C1092
C2×#440×C1092
C109×#24282
C109×#23412
C109×#20672
C109×#20342
C109×#20332
C109×#20112
C109×#19722
C109×#19242
C109×#18802
C109×#18792
C109×#18652
#25179109