Finite Group Databasebeta

← C109×#24403 #42142397

Subgroups — C109×#24403 #42142397

Order 27904.

1332 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C109C211yesmaximal, characteristic
2C2×#473×C109C211yesmaximal, characteristic, complemented
3C2×#471×C109C211yesmaximal, characteristic, complemented
4C109×#3007C211yesmaximal, characteristic, complemented
5C2×#452×C109C211yesmaximal, characteristic, complemented
6C109×#2880C211yesmaximal, characteristic, complemented
7C109×#2052C211yesmaximal, characteristic, complemented
8C109×#2051C211yesmaximal, characteristic, complemented
9C109×#2020C211yesmaximal, characteristic, complemented
10C109×#2019C211yesmaximal, characteristic, complemented
11C109×#1908C211yesmaximal, characteristic, complemented
12C109×#1907C211yesmaximal, characteristic, complemented
13C109×#1901C211yesmaximal, characteristic, complemented
14C109×#1855C211yesmaximal, characteristic, complemented
15C109×#1785C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C22×#41×C109C2211yescharacteristic
18#575×C109—24no—
19#575×C109—24no—
20C2×#137×C109—21no—
21C2×#137×C109C2211yescharacteristic
22C2×#137×C109C2211yescharacteristic
23C2×#137×C109C2211yescharacteristic
24C2×#137×C109C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C109—21no—
26C2×AGL(1,ℤ/8)×C109C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C109C2211yescharacteristic
28C2×#135×C109—21no—
29C2×#135×C109—21no—
30C22×Q16×C109C2211yescharacteristic, complemented
31C22×SD16×C109C2211yescharacteristic, complemented
32C2×#131×C109C2211yescharacteristic
33C2×#131×C109C2211yescharacteristic
34C22×M16×C109C2211yescharacteristic
35C2×C22⋊Q8×C109C2211yescharacteristic
36#473×C109—24no—
37#471×C109—24no—
38#452×C109—21no—
39#452×C109—21no—
40#452×C109—21no—
41#452×C109—21no—
42#452×C109—21no—
43#452×C109—21no—
44#451×C109—21no—
45#450×C109—21no—
46C2×#108×C109C2211yescharacteristic, complemented
47C2×#108×C109C2211yescharacteristic, complemented
48#417×C109C2211yescharacteristic
49#417×C109C2211yescharacteristic
50C2×#103×C109C2211yescharacteristic, complemented
51C2×#102×C109C2211yescharacteristic, complemented
52C2×#101×C109C2211yescharacteristic, complemented
53C2×#101×C109C2211yescharacteristic, complemented
54C2×#101×C109C2211yescharacteristic, complemented
55C2×#101×C109C2211yescharacteristic, complemented
56C2×#100×C109C2211yescharacteristic, complemented
57C2×#100×C109C2211yescharacteristic, complemented
58#408×C109—21no—
59#408×C109—21no—
60#408×C109C2211yescharacteristic
61#408×C109C2211yescharacteristic
62#407×C109—21no—
63#407×C109C2211yescharacteristic
64#407×C109C2211yescharacteristic
65C2×C22⋊C8×C109—21no—
66C2×C22⋊C8×C109C2211yescharacteristic
67#343×C109C2211yescharacteristic, complemented
68#343×C109C2211yescharacteristic, complemented
69#341×C109C2211yescharacteristic, complemented
70#341×C109C2211yescharacteristic, complemented
71C2×#41×C109—21no—
72C2×#41×C109—21no—
73C2×#41×C109—22no—
74C2×#41×C109—22no—
75C2×#41×C109—22no—
76C2×#41×C109—22no—
77C2×#41×C109—21no—
78C2×#41×C109—21no—
79C2×#41×C109—21no—
80C2×#41×C109—21no—
81C2×#41×C109—41no—
82C2×#41×C109—41no—
83C2×#41×C109—41no—
84C2×#41×C109—41no—
85C2×#41×C109D411yescharacteristic
86C2×#41×C109D411yescharacteristic
87C2×#41×C109C2311yescharacteristic
88C2×#41×C109C2311yescharacteristic
89C22×Q8×C109D411yescharacteristic
90C22×Q8×C109C2311yescharacteristic
91C22×Q8×C109C2311yescharacteristic
92C22×D4×C109—21no—
93C22×D4×C109—21no—
94C22×D4×C109D411yescharacteristic
95C22×D4×C109C2311yescharacteristic
96C23×C4×C109—21no—
97C23×C4×C109—21no—
98C23×C4×C109C2311yescharacteristic
99#137×C109—28no—
100#137×C109—22no—
101#137×C109—22no—
102#137×C109—22no—
103#137×C109—22no—
104#137×C109—22no—
105#137×C109—41no—
106#137×C109—41no—
107#137×C109D414yes—
108AGL(1,ℤ/8)×C109—28no—
109AGL(1,ℤ/8)×C109—22no—
110AGL(1,ℤ/8)×C109—22no—
111AGL(1,ℤ/8)×C109—22no—
112AGL(1,ℤ/8)×C109D414yes—
113#135×C109—28no—
114#135×C109—28no—
115C2×Q16×C109—21no—
116C2×Q16×C109—21no—
117C2×Q16×C109—22no—
118C2×Q16×C109—21no—
119C2×Q16×C109—21no—
120C2×Q16×C109—21no—
121C2×Q16×C109—21no—
122C2×Q16×C109—41no—
123C2×SD16×C109—21no—
124C2×SD16×C109—21no—
125C2×SD16×C109—21no—
126C2×SD16×C109—21no—
127C2×SD16×C109—22no—
128C2×SD16×C109—21no—
129C2×SD16×C109—21no—
130C2×SD16×C109—21no—
131C2×SD16×C109—21no—
132C2×SD16×C109—41no—
133C2×D8×C109—21no—
134C2×D8×C109—21no—
135#131×C109—22no—
136#131×C109—22no—
137#131×C109—41no—
138#131×C109—41no—
139C2×M16×C109—21no—
140C2×M16×C109—22no—
141C2×M16×C109—22no—
142C2×M16×C109—21no—
143C2×M16×C109—21no—
144C2×M16×C109C2311yescharacteristic
145C2×M16×C109C2311yescharacteristic
146C2×M16×C109C2311yescharacteristic
147C2×M16×C109C2311yescharacteristic
148C2×M16×C109C2311yescharacteristic
149C2×M16×C109C2311yescharacteristic
150C22×C8×C109—21no—
151C22×C8×C109—21no—
152C22×C8×C109—21no—
153C22×C8×C109C2311yescharacteristic
154C22×C8×C109C2311yescharacteristic
155C22⋊Q8×C109—21no—
156C22⋊Q8×C109—21no—
157C22⋊Q8×C109—21no—
158C22⋊Q8×C109—21no—
159C2×C4⋊C4×C109—21no—
160C2×C4⋊C4×C109C2311yescharacteristic
161C2×C22⋊C4×C109—21no—
162#108×C109—22no—
163#108×C109—22no—
164#103×C109—21no—
165#103×C109—21no—
166#103×C109—21no—
167#103×C109—21no—
168#102×C109—21no—
169#102×C109—21no—
170#102×C109—21no—
171#102×C109—21no—
172#101×C109—22no—
173#101×C109—22no—
174#101×C109—22no—
175#101×C109—41no—
176#100×C109—22no—
177#100×C109—41no—
178C22⋊C8×C109—21no—
179C22⋊C8×C109—21no—
180C22⋊C8×C109—21no—
181C22⋊C8×C109—21no—
182C22⋊C8×C109—21no—
183C22⋊C8×C109—21no—
184C22⋊C8×C109—21no—
185C22⋊C8×C109—21no—
186C22⋊C8×C109D411yescharacteristic
187C22⋊C8×C109D411yescharacteristic
188C22⋊C8×C109D411yescharacteristic
189C22⋊C8×C109D411yescharacteristic
190C24×C109—21no—
191C24×C109—21no—
192C24×C109#4111yescharacteristic
193#41×C109—21no—
194#41×C109—21no—
195#41×C109—24no—
196#41×C109—24no—
197#41×C109—22no—
198#41×C109—22no—
199#41×C109—21no—
200#41×C109—21no—
201#41×C109—21no—
202#41×C109—21no—
203#41×C109—42no—
204#41×C109—42no—
205#41×C109—41no—
206#41×C109—41no—
207#41×C109—42no—
208#41×C109—42no—
209#41×C109—42no—
210#41×C109—42no—
211#41×C109—42no—
212#41×C109—42no—
213#41×C109—42no—
214#41×C109—42no—
215#41×C109C2×D412yes—
216#41×C109C2×D412yes—
217C2×Q8×C109—21no—
218C2×Q8×C109—21no—
219C2×Q8×C109—22no—
220C2×Q8×C109—21no—
221C2×Q8×C109—21no—
222C2×Q8×C109—21no—
223C2×Q8×C109—21no—
224C2×Q8×C109—21no—
225C2×Q8×C109—21no—
226C2×Q8×C109—21no—
227C2×Q8×C109—21no—
228C2×Q8×C109—21no—
229C2×Q8×C109—21no—
230C2×Q8×C109—41no—
231C2×Q8×C109C2×D412yes—
232C2×Q8×C109C2×D411yescharacteristic
233C2×Q8×C109C2×D411yescharacteristic
234C2×D4×C109—21no—
235C2×D4×C109—22no—
236C2×D4×C109—21no—
237C2×D4×C109—21no—
238C2×D4×C109—21no—
239C2×D4×C109—21no—
240C2×D4×C109—21no—
241C2×D4×C109—21no—
242C2×D4×C109—21no—
243C2×D4×C109—21no—
244C2×D4×C109—21no—
245C2×D4×C109—41no—
246C2×D4×C109—42no—
247C2×D4×C109—42no—
248C2×D4×C109—42no—
249C2×D4×C109—42no—
250C2×D4×C109—41no—
251C2×D4×C109—41no—
252C2×D4×C109C2×D412yes—
253C2×D4×C109C2×D411yescharacteristic
254C2×D4×C109C2×D411yescharacteristic
255C22×C4×C109—21no—
256C22×C4×C109—21no—
257C22×C4×C109—21no—
258C22×C4×C109—21no—
259C22×C4×C109—21no—
260C22×C4×C109—21no—
261C22×C4×C109—21no—
262C22×C4×C109—21no—
263C22×C4×C109—21no—
264C22×C4×C109—21no—
265C22×C4×C109—21no—
266C22×C4×C109—21no—
267C22×C4×C109—42no—
268C22×C4×C109—42no—
269C22×C4×C109—42no—
270C22×C4×C109—42no—
271C22×C4×C109—41no—
272C22×C4×C109—41no—
273C22×C4×C109C2×D411yescharacteristic
274C22×C4×C109C2×D411yescharacteristic
275C22×C4×C109C2×D411yescharacteristic
276C22×C4×C109C2×D411yescharacteristic
277C22×C4×C109#4111yescharacteristic
278C22×C4×C109C2411yescharacteristic
279Q16×C109—24no—
280Q16×C109—24no—
281Q16×C109—42no—
282Q16×C109—42no—
283Q16×C109—42no—
284Q16×C109—42no—
285SD16×C109—24no—
286SD16×C109—24no—
287SD16×C109—24no—
288SD16×C109—24no—
289SD16×C109—42no—
290SD16×C109—42no—
291SD16×C109—42no—
292SD16×C109—42no—
293D8×C109—24no—
294D8×C109—24no—
295M16×C109—24no—
296M16×C109—21no—
297M16×C109—21no—
298M16×C109—21no—
299M16×C109—21no—
300M16×C109—21no—
301M16×C109—21no—
302M16×C109—21no—
303M16×C109—21no—
304M16×C109—21no—
305M16×C109—21no—
306M16×C109—42no—
307M16×C109—42no—
308M16×C109C2×D412yes—
309M16×C109C2×D412yes—
310C2×C8×C109—24no—
311C2×C8×C109—21no—
312C2×C8×C109—21no—
313C2×C8×C109—21no—
314C2×C8×C109—21no—
315C2×C8×C109—21no—
316C2×C8×C109—21no—
317C2×C8×C109—21no—
318C2×C8×C109—21no—
319C2×C8×C109—21no—
320C2×C8×C109—21no—
321C2×C8×C109—42no—
322C2×C8×C109—42no—
323C2×C8×C109C2×D411yescharacteristic
324C2×C8×C109C2×D411yescharacteristic
325C2×C8×C109C2×D411yescharacteristic
326C2×C8×C109C2×D411yescharacteristic
327C4⋊C4×C109—21no—
328C4⋊C4×C109—21no—
329C4⋊C4×C109—41no—
330C4⋊C4×C109—41no—
331C22⋊C4×C109—41no—
332C22⋊C4×C109—41no—
333C23×C109—21no—
334C23×C109—21no—
335C23×C109—21no—
336C23×C109—21no—
337C23×C109—22no—
338C23×C109—41no—
339C23×C109—41no—
340C23×C109—42no—
341C23×C109—42no—
342C23×C109—41no—
343C23×C109—41no—
344C23×C109—81no—
345C23×C109—81no—
346C23×C109—81no—
347C23×C109#12111yescharacteristic
348C23×C109#12111yescharacteristic
349C23×C109C2×#4111yescharacteristic
350Q8×C109—21no—
351Q8×C109—21no—
352Q8×C109—22no—
353Q8×C109—21no—
354Q8×C109—22no—
355Q8×C109—42no—
356Q8×C109—41no—
357Q8×C109—41no—
358Q8×C109—41no—
359Q8×C109—41no—
360Q8×C109—41no—
361Q8×C109—41no—
362Q8×C109#12012yes—
363D4×C109—22no—
364D4×C109—22no—
365D4×C109—21no—
366D4×C109—22no—
367D4×C109—21no—
368D4×C109—21no—
369D4×C109—22no—
370D4×C109—42no—
371D4×C109—42no—
372D4×C109—42no—
373D4×C109—44no—
374D4×C109—44no—
375D4×C109—41no—
376D4×C109—41no—
377D4×C109—41no—
378D4×C109—41no—
379D4×C109#12012yes—
380C2×C4×C109—21no—
381C2×C4×C109—21no—
382C2×C4×C109—21no—
383C2×C4×C109—21no—
384C2×C4×C109—21no—
385C2×C4×C109—21no—
386C2×C4×C109—21no—
387C2×C4×C109—22no—
388C2×C4×C109—22no—
389C2×C4×C109—21no—
390C2×C4×C109—21no—
391C2×C4×C109—21no—
392C2×C4×C109—21no—
393C2×C4×C109—21no—
394C2×C4×C109—22no—
395C2×C4×C109—42no—
396C2×C4×C109—42no—
397C2×C4×C109—42no—
398C2×C4×C109—44no—
399C2×C4×C109—44no—
400C2×C4×C109—41no—
401C2×C4×C109—41no—
402C2×C4×C109—41no—
403C2×C4×C109—41no—
404C2×C4×C109—41no—
405C2×C4×C109—41no—
406C2×C4×C109—41no—
407C2×C4×C109—41no—
408C2×C4×C109—81no—
409C2×C4×C109#12111yescharacteristic
410C2×C4×C109#12111yescharacteristic
411C2×C4×C109C22×D411yescharacteristic
412C2×C4×C109C22×D411yescharacteristic
413C2×C4×C109C22×D411yescharacteristic
414C2×C4×C109C22×D411yescharacteristic
415C2×C4×C109H(5,𝔽2)11yescharacteristic
416C2×C4×C109H(5,𝔽2)11yescharacteristic
417C8×C109—22no—
418C8×C109—22no—
419C8×C109—21no—
420C8×C109—21no—
421C8×C109—21no—
422C8×C109—21no—
423C8×C109—41no—
424C8×C109—41no—
425C8×C109—41no—
426C8×C109—41no—
427C22×C109—21no—
428C22×C109—21no—
429C22×C109—21no—
430C22×C109—21no—
431C22×C109—22no—
432C22×C109—21no—
433C22×C109—21no—
434C22×C109—21no—
435C22×C109—21no—
436C22×C109—41no—
437C22×C109—41no—
438C22×C109—41no—
439C22×C109—42no—
440C22×C109—41no—
441C22×C109—41no—
442C22×C109—81no—
443C22×C109—81no—
444C22×C109—82no—
445C22×C109—82no—
446C22×C109—84no—
447C22×C109—81no—
448C22×C109—81no—
449C22×C109C2×#12111yescharacteristic
450C22×C109#54611yescharacteristic
451C22×C109#54611yescharacteristic
452C4×C109—21no—
453C4×C109—21no—
454C4×C109—22no—
455C4×C109—41no—
456C4×C109—42no—
457C4×C109—81no—
458C4×C109—81no—
459C4×C109C2×#12011yescharacteristic
460C4×C109#53411yescharacteristic
461C4×C109D4211yescharacteristic
462C4×C109D4211yescharacteristic
463#24403C10911yesmaximal, characteristic, direct product factor, Sylow
464C2×C109—21no—
465C2×C109—21no—
466C2×C109—41no—
467C2×C109—41no—
468C2×C109—42no—
469C2×C109—81no—
470C2×C109—82no—
471C2×C109#241011yescharacteristic
472C2×C109#306711yescharacteristic
473C2×C109#306911yescharacteristic
474C2×#575C2×C10911yescharacteristic
475C2×#473C2×C10911yescharacteristic, complemented
476C2×#471C2×C10911yescharacteristic, complemented
477#3007C2×C10911yescharacteristic, complemented
478C2×#452C2×C10911yescharacteristic, complemented
479#2880C2×C10911yescharacteristic, complemented
480#2052C2×C10911yescharacteristic, complemented
481#2051C2×C10911yescharacteristic, complemented
482#2020C2×C10911yescharacteristic, complemented
483#2019C2×C10911yescharacteristic, complemented
484#1908C2×C10911yescharacteristic, complemented
485#1907C2×C10911yescharacteristic, complemented
486#1901C2×C10911yescharacteristic, complemented
487#1855C2×C10911yescharacteristic, complemented
488#1785C2×C10911yescharacteristic, complemented
489C109#2440311yescharacteristic, direct product factor, Sylow
490C22×#41C22×C10911yescharacteristic
491C22×#41C22×C10911yescharacteristic
492#575—24no—
493#575—24no—
494C2×#137—21no—
495C2×#137C22×C10911yescharacteristic
496C2×#137C22×C10911yescharacteristic
497C2×#137C22×C10911yescharacteristic
498C2×#137C22×C10911yescharacteristic
499C2×AGL(1,ℤ/8)—21no—
500C2×AGL(1,ℤ/8)C22×C10911yescharacteristic
501C2×AGL(1,ℤ/8)C22×C10911yescharacteristic
502C2×#135—21no—
503C2×#135—21no—
504C22×Q16C22×C10911yescharacteristic, complemented
505C22×SD16C22×C10911yescharacteristic, complemented
506C2×#131C22×C10911yescharacteristic
507C2×#131C22×C10911yescharacteristic
508C22×M16C22×C10911yescharacteristic
509C2×C22⋊Q8C22×C10911yescharacteristic
510#473—24no—
511#471—24no—
512#452—21no—
513#452—21no—
514#452—21no—
515#452—21no—
516#452—21no—
517#452—21no—
518#451—21no—
519#450—21no—
520C2×#108C22×C10911yescharacteristic, complemented
521C2×#108C22×C10911yescharacteristic, complemented
522#417C22×C10911yescharacteristic
523#417C22×C10911yescharacteristic
524C2×#103C22×C10911yescharacteristic, complemented
525C2×#102C22×C10911yescharacteristic, complemented
526C2×#101C22×C10911yescharacteristic, complemented
527C2×#101C22×C10911yescharacteristic, complemented
528C2×#101C22×C10911yescharacteristic, complemented
529C2×#101C22×C10911yescharacteristic, complemented
530C2×#100C22×C10911yescharacteristic, complemented
531C2×#100C22×C10911yescharacteristic, complemented
532#408—21no—
533#408—21no—
534#408C22×C10911yescharacteristic
535#408C22×C10911yescharacteristic
536#407—21no—
537#407C22×C10911yescharacteristic
538#407C22×C10911yescharacteristic
539C2×C22⋊C8—21no—
540C2×C22⋊C8C22×C10911yescharacteristic
541#343C22×C10911yescharacteristic, complemented
542#343C22×C10911yescharacteristic, complemented
543#341C22×C10911yescharacteristic, complemented
544#341C22×C10911yescharacteristic, complemented
545C2×#41—21no—
546C2×#41—21no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41—41no—
556C2×#41—41no—
557C2×#41—41no—
558C2×#41—41no—
559C2×#41D4×C10911yescharacteristic
560C2×#41D4×C10911yescharacteristic
561C2×#41C23×C10911yescharacteristic
562C2×#41C23×C10911yescharacteristic
563C22×Q8D4×C10911yescharacteristic
564C22×Q8C23×C10911yescharacteristic
565C22×Q8C23×C10911yescharacteristic
566C22×D4—21no—
567C22×D4—21no—
568C22×D4D4×C10911yescharacteristic
569C22×D4C23×C10911yescharacteristic
570C23×C4—21no—
571C23×C4—21no—
572C23×C4C23×C10911yescharacteristic
573#137—28no—
574#137—22no—
575#137—22no—
576#137—22no—
577#137—22no—
578#137—22no—
579#137—41no—
580#137—41no—
581#137D4×C10914yes—
582AGL(1,ℤ/8)—28no—
583AGL(1,ℤ/8)—22no—
584AGL(1,ℤ/8)—22no—
585AGL(1,ℤ/8)—22no—
586AGL(1,ℤ/8)D4×C10914yes—
587#135—28no—
588#135—28no—
589C2×Q16—21no—
590C2×Q16—21no—
591C2×Q16—22no—
592C2×Q16—21no—
593C2×Q16—21no—
594C2×Q16—21no—
595C2×Q16—21no—
596C2×Q16—41no—
597C2×SD16—21no—
598C2×SD16—21no—
599C2×SD16—21no—
600C2×SD16—21no—
601C2×SD16—22no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—21no—
606C2×SD16—41no—
607C2×D8—21no—
608C2×D8—21no—
609#131—22no—
610#131—22no—
611#131—41no—
612#131—41no—
613C2×M16—21no—
614C2×M16—22no—
615C2×M16—22no—
616C2×M16—21no—
617C2×M16—21no—
618C2×M16C23×C10911yescharacteristic
619C2×M16C23×C10911yescharacteristic
620C2×M16C23×C10911yescharacteristic
621C2×M16C23×C10911yescharacteristic
622C2×M16C23×C10911yescharacteristic
623C2×M16C23×C10911yescharacteristic
624C22×C8—21no—
625C22×C8—21no—
626C22×C8—21no—
627C22×C8C23×C10911yescharacteristic
628C22×C8C23×C10911yescharacteristic
629C22⋊Q8—21no—
630C22⋊Q8—21no—
631C22⋊Q8—21no—
632C22⋊Q8—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4C23×C10911yescharacteristic
635C2×C22⋊C4—21no—
636#108—22no—
637#108—22no—
638#103—21no—
639#103—21no—
640#103—21no—
641#103—21no—
642#102—21no—
643#102—21no—
644#102—21no—
645#102—21no—
646#101—22no—
647#101—22no—
648#101—22no—
649#101—41no—
650#100—22no—
651#100—41no—
652C22⋊C8—21no—
653C22⋊C8—21no—
654C22⋊C8—21no—
655C22⋊C8—21no—
656C22⋊C8—21no—
657C22⋊C8—21no—
658C22⋊C8—21no—
659C22⋊C8—21no—
660C22⋊C8D4×C10911yescharacteristic
661C22⋊C8D4×C10911yescharacteristic
662C22⋊C8D4×C10911yescharacteristic
663C22⋊C8D4×C10911yescharacteristic
664C24—21no—
665C24—21no—
666C24#41×C10911yescharacteristic
667#41—21no—
668#41—21no—
669#41—24no—
670#41—24no—
671#41—22no—
672#41—22no—
673#41—21no—
674#41—21no—
675#41—21no—
676#41—21no—
677#41—42no—
678#41—42no—
679#41—41no—
680#41—41no—
681#41—42no—
682#41—42no—
683#41—42no—
684#41—42no—
685#41—42no—
686#41—42no—
687#41—42no—
688#41—42no—
689#41C2×D4×C10912yes—
690#41C2×D4×C10912yes—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—22no—
694C2×Q8—21no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—41no—
705C2×Q8C2×D4×C10912yes—
706C2×Q8C2×D4×C10911yescharacteristic
707C2×Q8C2×D4×C10911yescharacteristic
708C2×D4—21no—
709C2×D4—22no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—41no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—41no—
725C2×D4—41no—
726C2×D4C2×D4×C10912yes—
727C2×D4C2×D4×C10911yescharacteristic
728C2×D4C2×D4×C10911yescharacteristic
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—41no—
746C22×C4—41no—
747C22×C4C2×D4×C10911yescharacteristic
748C22×C4C2×D4×C10911yescharacteristic
749C22×C4C2×D4×C10911yescharacteristic
750C22×C4C2×D4×C10911yescharacteristic
751C22×C4#41×C10911yescharacteristic
752C22×C4C24×C10911yescharacteristic
753Q16—24no—
754Q16—24no—
755Q16—42no—
756Q16—42no—
757Q16—42no—
758Q16—42no—
759SD16—24no—
760SD16—24no—
761SD16—24no—
762SD16—24no—
763SD16—42no—
764SD16—42no—
765SD16—42no—
766SD16—42no—
767D8—24no—
768D8—24no—
769M16—24no—
770M16—21no—
771M16—21no—
772M16—21no—
773M16—21no—
774M16—21no—
775M16—21no—
776M16—21no—
777M16—21no—
778M16—21no—
779M16—21no—
780M16—42no—
781M16—42no—
782M16C2×D4×C10912yes—
783M16C2×D4×C10912yes—
784C2×C8—24no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—42no—
796C2×C8—42no—
797C2×C8C2×D4×C10911yescharacteristic
798C2×C8C2×D4×C10911yescharacteristic
799C2×C8C2×D4×C10911yescharacteristic
800C2×C8C2×D4×C10911yescharacteristic
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—41no—
804C4⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—41no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—41no—
813C23—41no—
814C23—42no—
815C23—42no—
816C23—41no—
817C23—41no—
818C23—81no—
819C23—81no—
820C23—81no—
821C23#121×C10911yescharacteristic
822C23#121×C10911yescharacteristic
823C23C2×#41×C10911yescharacteristic
824Q8—21no—
825Q8—21no—
826Q8—22no—
827Q8—21no—
828Q8—22no—
829Q8—42no—
830Q8—41no—
831Q8—41no—
832Q8—41no—
833Q8—41no—
834Q8—41no—
835Q8—41no—
836Q8#120×C10912yes—
837D4—22no—
838D4—22no—
839D4—21no—
840D4—22no—
841D4—21no—
842D4—21no—
843D4—22no—
844D4—42no—
845D4—42no—
846D4—42no—
847D4—44no—
848D4—44no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4#120×C10912yes—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—81no—
883C2×C4#121×C10911yescharacteristic
884C2×C4#121×C10911yescharacteristic
885C2×C4C22×D4×C10911yescharacteristic
886C2×C4C22×D4×C10911yescharacteristic
887C2×C4C22×D4×C10911yescharacteristic
888C2×C4C22×D4×C10911yescharacteristic
889C2×C4H(5,𝔽2)×C10911yescharacteristic
890C2×C4H(5,𝔽2)×C10911yescharacteristic
891C8—22no—
892C8—22no—
893C8—21no—
894C8—21no—
895C8—21no—
896C8—21no—
897C8—41no—
898C8—41no—
899C8—41no—
900C8—41no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—22no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—42no—
916C22—81no—
917C22—81no—
918C22—82no—
919C22—82no—
920C22—84no—
921C22—81no—
922C22—81no—
923C22C2×#121×C10911yescharacteristic
924C22#546×C10911yescharacteristic
925C22#546×C10911yescharacteristic
926C4—21no—
927C4—21no—
928C4—22no—
929C4—41no—
930C4—42no—
931C4—81no—
932C4—81no—
933C4C2×#120×C10911yescharacteristic
934C4#534×C10911yescharacteristic
935C4D42×C10911yescharacteristic
936C4D42×C10911yescharacteristic
937C2—21no—
938C2—21no—
939C2—41no—
940C2—41no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C109×#241011yescharacteristic
945C2C109×#306711yescharacteristic
946C2C109×#306911yescharacteristic
subgroupG/H
center, socleC22×C109C2×#121
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC2×#575×C109C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C109 ◁ C23×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#473×C109C2semidirect
3. C2×#471×C109C2semidirect
4. C109×#3007C2semidirect
5. C2×#452×C109C2semidirect
6. C109×#2880C2semidirect
7. C109×#2052C2semidirect
8. C109×#2051C2semidirect
9. C109×#2020C2semidirect
10. C109×#2019C2semidirect
11. C109×#1908C2semidirect
12. C109×#1907C2semidirect
13. C109×#1901C2semidirect
14. C109×#1855C2semidirect
15. C109×#1785C2semidirect
30. C22×Q16×C109C22semidirect
31. C22×SD16×C109C22semidirect
46. C2×#108×C109C22semidirect
47. C2×#108×C109C22semidirect
50. C2×#103×C109C22semidirect
51. C2×#102×C109C22semidirect
52. C2×#101×C109C22semidirect
53. C2×#101×C109C22semidirect
54. C2×#101×C109C22semidirect
55. C2×#101×C109C22semidirect
56. C2×#100×C109C22semidirect
57. C2×#100×C109C22semidirect
67. #343×C109C22semidirect
68. #343×C109C22semidirect
69. #341×C109C22semidirect
70. #341×C109C22semidirect
463. #24403C109direct (N × H)
475. C2×#473C2×C109semidirect
476. C2×#471C2×C109semidirect
477. #3007C2×C109semidirect
478. C2×#452C2×C109semidirect
479. #2880C2×C109semidirect
480. #2052C2×C109semidirect
481. #2051C2×C109semidirect
482. #2020C2×C109semidirect
483. #2019C2×C109semidirect
484. #1908C2×C109semidirect
485. #1907C2×C109semidirect
486. #1901C2×C109semidirect
487. #1855C2×C109semidirect
488. #1785C2×C109semidirect
489. C109#24403direct (N × H)
504. C22×Q16C22×C109semidirect
505. C22×SD16C22×C109semidirect
520. C2×#108C22×C109semidirect
521. C2×#108C22×C109semidirect
524. C2×#103C22×C109semidirect
525. C2×#102C22×C109semidirect
526. C2×#101C22×C109semidirect
527. C2×#101C22×C109semidirect
528. C2×#101C22×C109semidirect
529. C2×#101C22×C109semidirect
530. C2×#100C22×C109semidirect
531. C2×#100C22×C109semidirect
541. #343C22×C109semidirect
542. #343C22×C109semidirect
543. #341C22×C109semidirect
544. #341C22×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1092
C2×#473×C1092
C2×#471×C1092
C109×#30072
C2×#452×C1092
C109×#28802
C109×#20522
C109×#20512
C109×#20202
C109×#20192
C109×#19082
C109×#19072
C109×#19012
C109×#18552
C109×#17852
#24403109