Finite Group Databasebeta

← C2×#11740118 #13523919

Subgroups — C2×#11740118 #13523919

Order 1792.

3266 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#121C211yesmaximal, characteristic
2C22×#6442C211yesmaximal, characteristic, complemented
3C2×#89994C211yesmaximal, characteristic, complemented
4C2×#89994C211yesmaximal, characteristic, complemented
5C2×#89994C211yesmaximal, characteristic, complemented
6C2×#89993C211yesmaximal, characteristic, complemented
7C2×#89992C211yesmaximal, characteristic, complemented
8C2×#89992C211yesmaximal, characteristic, complemented
9C2×#89982C211yesmaximal, characteristic, complemented
10C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
11#11740118C2116yesmaximal, direct product factor
12C2×#89758C211yesmaximal, characteristic, complemented
13C2×#89744C211yesmaximal, characteristic, complemented
14C2×#89717C211yesmaximal, characteristic, complemented
15C2×#89716C211yesmaximal, characteristic, complemented
16C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C23×C7×D4C2211yescharacteristic
19C23×C7×D4C2211yescharacteristic
20C24×C4×C7C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C2×C7×#121—28no—
23C2×C7×#121C2218yes—
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C22×C22⋊Dic7C2211yescharacteristic
35C22×C22⋊Dic7C2211yescharacteristic
36C22×C22⋊Dic7C2211yescharacteristic
37C22×C22⋊Dic7C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C2×#6442—28no—
47C2×#6442C2218yescomplemented
48#89994C2218yescomplemented
49#89994C2218yescomplemented
50#89994C2218yescomplemented
51#89993C2218yescomplemented
52#89992C2218yescomplemented
53#89992C2218yescomplemented
54#89982C2218yescomplemented
55C4×C22⋊Dic7C2218yescomplemented
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61C2×C7⋊#95C2211yescharacteristic
62C2×C7⋊#95C2211yescharacteristic
63C2×C7⋊#95C2211yescharacteristic
64#89758C2218yescomplemented
65#89744C2218yescomplemented
66#89717C2218yescomplemented
67#89716C2218yescomplemented
68C22⋊C4×Dic7C2218yescomplemented
69C2×#2559—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C25×C7C2311yescharacteristic
72C25×C7C2311yescharacteristic
73C22×C7×D4—24no—
74C22×C7×D4—24no—
75C22×C7×D4—24no—
76C22×C7×D4—24no—
77C22×C7×D4—24no—
78C22×C7×D4—24no—
79C22×C7×D4—42no—
80C22×C7×D4—42no—
81C22×C7×D4—42no—
82C22×C7×D4C2314yes—
83C22×C7×D4C2314yes—
84C22×C7×D4C2314yes—
85C23×C4×C7—24no—
86C23×C4×C7—24no—
87C23×C4×C7—42no—
88C23×C4×C7C2311yescharacteristic
89C23×C4×C7C2314yes—
90C23×C4×C7C2311yescharacteristic
91C23×C4×C7C2311yescharacteristic
92C23×C4×C7C2311yescharacteristic
93C23×Dic7—24no—
94C23×Dic7—42no—
95C23×Dic7—42no—
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2314yes—
105C7×#121—232no—
106C2×C7×C4⋊C4—24no—
107C2×C7×C4⋊C4C2314yes—
108C2×C7×C22⋊C4—24no—
109C2×C7×C22⋊C4D418yes—
110C2×C7×C22⋊C4C2314yes—
111C2×C7×C22⋊C4C2314yes—
112C2×C22⋊Dic7—24no—
113C2×C22⋊Dic7—24no—
114C2×C22⋊Dic7—24no—
115C2×C22⋊Dic7—24no—
116C2×C22⋊Dic7—24no—
117C2×C22⋊Dic7—24no—
118C2×C22⋊Dic7—24no—
119C2×C22⋊Dic7—24no—
120C2×C22⋊Dic7—42no—
121C2×C22⋊Dic7—42no—
122C2×C22⋊Dic7—42no—
123C2×C22⋊Dic7C2314yes—
124C2×C22⋊Dic7C2314yes—
125C2×C22⋊Dic7C2314yes—
126C2×C22⋊Dic7C2314yes—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130C2×C22⋊Dic7C2314yes—
131C2×C22⋊Dic7C2314yes—
132C2×C22⋊Dic7C2314yes—
133C2×C22⋊Dic7C2314yes—
134C2×C4⋊Dic7—24no—
135C2×C4⋊Dic7C2314yes—
136C2×Dic7⋊C4—24no—
137C2×Dic7⋊C4—24no—
138C2×Dic7⋊C4—24no—
139C2×Dic7⋊C4—42no—
140C2×Dic7⋊C4C2314yes—
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C2×Dic7⋊C4C2314yes—
144C2×C4×Dic7—24no—
145C2×C4×Dic7—42no—
146C2×C4×Dic7—42no—
147C2×C4×Dic7C2314yes—
148C2×C4×Dic7C2314yes—
149C2×C4×Dic7C2314yes—
150#6442—232no—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#126—71no—
160C22×#121D711yescharacteristic
161#2559—716no—
162C2×#400—71no—
163C2×#394—71no—
164C2×#394—71no—
165C2×#394—71no—
166C2×#390—71no—
167C2×#389—71no—
168C2×#388—71no—
169C2×#388—71no—
170C2×#386—71no—
171C2×#386—71no—
172C2×#385—71no—
173C2×C4×C22⋊C4—71no—
174C2×C4×C22⋊C4—71no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7—22no—
182C24×C7—22no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7—22no—
188C24×C7—22no—
189C24×C7—22no—
190C24×C7—22no—
191C24×C7—22no—
192C24×C7—22no—
193C24×C7—22no—
194C24×C7C2×D414yes—
195C24×C7#4114yes—
196C24×C7C2412yes—
197C24×C7C2412yes—
198C24×C7C2412yes—
199C24×C7C2411yescharacteristic
200C2×C7×D4—28no—
201C2×C7×D4—28no—
202C2×C7×D4—28no—
203C2×C7×D4—28no—
204C2×C7×D4—28no—
205C2×C7×D4—28no—
206C2×C7×D4—44no—
207C2×C7×D4—44no—
208C2×C7×D4—44no—
209C2×C7×D4—416no—
210C2×C7×D4—416no—
211C2×C7×D4—416no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—28no—
222C22×C4×C7—28no—
223C22×C4×C7—44no—
224C22×C4×C7—416no—
225C22×C4×C7C2×D414yes—
226C22×C4×C7C2×D414yes—
227C22×C4×C7#4114yes—
228C22×C4×C7C2412yes—
229C22×C4×C7C2412yes—
230C22×C4×C7C2412yes—
231C22×C4×C7C2412yes—
232C22×Dic7—22no—
233C22×Dic7—22no—
234C22×Dic7—22no—
235C22×Dic7—22no—
236C22×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7—22no—
239C22×Dic7—22no—
240C22×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—28no—
255C22×Dic7—44no—
256C22×Dic7—44no—
257C22×Dic7—416no—
258C22×Dic7#4114yes—
259C22×Dic7#4114yes—
260C22×Dic7C2412yes—
261C22×Dic7C2412yes—
262C22×Dic7C2412yes—
263C22×Dic7C2412yes—
264C22×Dic7C2412yes—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C7×C4⋊C4—28no—
269C7×C22⋊C4—28no—
270C7×C22⋊C4C2×D4116yes—
271C22⋊Dic7—28no—
272C22⋊Dic7—28no—
273C22⋊Dic7—28no—
274C22⋊Dic7—28no—
275C22⋊Dic7—28no—
276C22⋊Dic7—28no—
277C22⋊Dic7—28no—
278C22⋊Dic7—28no—
279C22⋊Dic7—44no—
280C22⋊Dic7—44no—
281C22⋊Dic7—44no—
282C4⋊Dic7—28no—
283Dic7⋊C4—28no—
284Dic7⋊C4—28no—
285Dic7⋊C4—28no—
286Dic7⋊C4—44no—
287C4×Dic7—28no—
288C4×Dic7—44no—
289C4×Dic7—44no—
290C23×D4C2×D711yescharacteristic
291C23×D4C2×D711yescharacteristic
292C23×D4C2×D711yescharacteristic
293C24×C4—71no—
294C24×C4C2×D711yescharacteristic
295C2×#126—78no—
296C2×#126—148no—
297C2×#121—28no—
298C2×#121C2×D718yes—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C4⋊C4C2×D711yescharacteristic
305C22×C22⋊C4—71no—
306C22×C22⋊C4—71no—
307C22×C22⋊C4—71no—
308C22×C22⋊C4—71no—
309C22×C22⋊C4—71no—
310C22×C22⋊C4—71no—
311C22×C22⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C42—71no—
319C22×C42—71no—
320C22×C42—71no—
321#400—78no—
322#394—78no—
323#394—78no—
324#394—78no—
325#390—78no—
326#389—78no—
327#388—78no—
328#388—78no—
329#386—78no—
330#386—78no—
331#385—78no—
332C4×C22⋊C4—78no—
333C4×C22⋊C4—78no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95—71no—
342C23×C7—28no—
343C23×C7—28no—
344C23×C7—28no—
345C23×C7—28no—
346C23×C7—28no—
347C23×C7—28no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—44no—
368C23×C7—44no—
369C23×C7—44no—
370C23×C7—44no—
371C23×C7—44no—
372C23×C7—44no—
373C23×C7—44no—
374C23×C7—44no—
375C23×C7—44no—
376C23×C7—44no—
377C23×C7—44no—
378C23×C7—44no—
379C23×C7—44no—
380C23×C7—44no—
381C23×C7—44no—
382C23×C7C22×D414yes—
383C23×C7C22×D412yes—
384C23×C7C2×#4114yes—
385C23×C7C2×#4112yes—
386C23×C7C2×#4112yes—
387C23×C7C2×#4112yes—
388C23×C7C2×#4112yes—
389C23×C7H(5,𝔽2)12yes—
390C23×C7H(5,𝔽2)12yes—
391C23×C7C2511yescharacteristic
392C7×D4—416no—
393C7×D4—416no—
394C7×D4—416no—
395C2×C4×C7—28no—
396C2×C4×C7—28no—
397C2×C4×C7—28no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—416no—
408C2×C4×C7—44no—
409C2×C4×C7C22×D414yes—
410C2×C4×C7C22×D414yes—
411C2×C4×C7C2×#4114yes—
412C2×Dic7—28no—
413C2×Dic7—28no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—22no—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—22no—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—416no—
437C2×Dic7—44no—
438C2×Dic7—44no—
439C2×Dic7—44no—
440C2×Dic7—44no—
441C2×Dic7—44no—
442C2×Dic7—44no—
443C2×Dic7C2×#4114yes—
444C2×Dic7C2×#4114yes—
445C25C22×D711yescharacteristic
446C25C22×D711yescharacteristic
447C25C22×D711yescharacteristic
448C22×D4—24no—
449C22×D4—24no—
450C22×D4—24no—
451C22×D4—24no—
452C22×D4—24no—
453C22×D4—24no—
454C22×D4—42no—
455C22×D4—42no—
456C22×D4—42no—
457C22×D4C22×D714yes—
458C22×D4C22×D714yes—
459C22×D4C22×D714yes—
460C23×C4—24no—
461C23×C4—24no—
462C23×C4—42no—
463C23×C4—71no—
464C23×C4—71no—
465C23×C4—71no—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—71no—
470C23×C4—71no—
471C23×C4—74no—
472C23×C4—144no—
473C23×C4—282no—
474C23×C4—282no—
475C23×C4C22×D711yescharacteristic
476C23×C4C22×D714yes—
477C23×C4C22×D711yescharacteristic
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D711yescharacteristic
480#126—1432no—
481#121—232no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—74no—
484C2×C4⋊C4—74no—
485C2×C4⋊C4—74no—
486C2×C4⋊C4—74no—
487C2×C4⋊C4—74no—
488C2×C4⋊C4—144no—
489C2×C4⋊C4—144no—
490C2×C4⋊C4—144no—
491C2×C4⋊C4—144no—
492C2×C4⋊C4—282no—
493C2×C4⋊C4C22×D714yes—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—74no—
496C2×C22⋊C4—74no—
497C2×C22⋊C4—74no—
498C2×C22⋊C4—74no—
499C2×C22⋊C4—74no—
500C2×C22⋊C4—74no—
501C2×C22⋊C4—74no—
502C2×C22⋊C4—74no—
503C2×C22⋊C4—74no—
504C2×C22⋊C4—74no—
505C2×C22⋊C4—74no—
506C2×C22⋊C4—144no—
507C2×C22⋊C4—144no—
508C2×C22⋊C4—144no—
509C2×C22⋊C4—144no—
510C2×C22⋊C4—144no—
511C2×C22⋊C4—144no—
512C2×C22⋊C4—144no—
513C2×C22⋊C4—144no—
514C2×C22⋊C4—282no—
515C2×C22⋊C4—282no—
516C2×C22⋊C4—282no—
517C2×C22⋊C4C22⋊D718yes—
518C2×C22⋊C4C22×D714yes—
519C2×C22⋊C4C22×D714yes—
520C2×C42—74no—
521C2×C42—74no—
522C2×C42—74no—
523C2×C42—144no—
524C2×C42—282no—
525C2×C42—282no—
526#95—74no—
527#95—74no—
528#95—74no—
529#95—74no—
530#95—74no—
531#95—74no—
532#95—74no—
533#95—74no—
534C22×C7—24no—
535C22×C7—24no—
536C22×C7—24no—
537C22×C7—24no—
538C22×C7—24no—
539C22×C7—24no—
540C22×C7—42no—
541C22×C7—42no—
542C22×C7—42no—
543C22×C7—42no—
544C22×C7—42no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—416no—
549C22×C7—416no—
550C22×C7—42no—
551C22×C7—42no—
552C22×C7—42no—
553C22×C7—42no—
554C22×C7—42no—
555C22×C7—42no—
556C22×C7—42no—
557C22×C7—88no—
558C22×C7#52914yes—
559C22×C7#53214yes—
560C22×C7#53814yes—
561C22×C7#54614yes—
562C22×C7#54614yes—
563C22×C7#55314yes—
564C22×C7#55314yes—
565C22×C7C23×D411yescharacteristic
566C22×C7C22×#4111yescharacteristic
567C22×C7C22×#4111yescharacteristic
568C22×C7C22×#4111yescharacteristic
569C22×C7C22×#4111yescharacteristic
570C22×C7C2×H(5,𝔽2)11yescharacteristic
571C22×C7C2×H(5,𝔽2)11yescharacteristic
572C4×C7—24no—
573C4×C7—24no—
574C4×C7—24no—
575C4×C7—42no—
576Dic7—24no—
577Dic7—24no—
578Dic7—42no—
579Dic7—42no—
580Dic7—42no—
581Dic7—42no—
582Dic7—42no—
583Dic7—42no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24#115914yes—
604C24C2×C22⋊D714yes—
605C24C23×D712yes—
606C24C23×D712yes—
607C24C23×D712yes—
608C24C23×D711yescharacteristic
609C2×D4—28no—
610C2×D4—28no—
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—28no—
614C2×D4—28no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—416no—
619C2×D4—416no—
620C2×D4—416no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—28no—
631C22×C4—28no—
632C22×C4—44no—
633C22×C4—416no—
634C22×C4—74no—
635C22×C4—74no—
636C22×C4—72no—
637C22×C4—72no—
638C22×C4—72no—
639C22×C4—72no—
640C22×C4—72no—
641C22×C4—72no—
642C22×C4—72no—
643C22×C4—72no—
644C22×C4—148no—
645C22×C4—142no—
646C22×C4—142no—
647C22×C4—142no—
648C22×C4—142no—
649C22×C4—142no—
650C22×C4—142no—
651C22×C4—142no—
652C22×C4—142no—
653C22×C4—142no—
654C22×C4—142no—
655C22×C4—142no—
656C22×C4—142no—
657C22×C4—142no—
658C22×C4—142no—
659C22×C4—142no—
660C22×C4—142no—
661C22×C4—142no—
662C22×C4—142no—
663C22×C4—142no—
664C22×C4—142no—
665C22×C4—142no—
666C22×C4—142no—
667C22×C4—284no—
668C22×C4—284no—
669C22×C4—2816no—
670C22×C4#115914yes—
671C22×C4C2×C22⋊D714yes—
672C22×C4C2×C22⋊D714yes—
673C22×C4C23×D712yes—
674C22×C4C23×D712yes—
675C22×C4C23×D712yes—
676C22×C4C23×D712yes—
677C4⋊C4—28no—
678C4⋊C4—148no—
679C4⋊C4—148no—
680C4⋊C4—148no—
681C4⋊C4—148no—
682C4⋊C4—284no—
683C22⋊C4—28no—
684C22⋊C4—148no—
685C22⋊C4—148no—
686C22⋊C4—148no—
687C22⋊C4—148no—
688C22⋊C4—148no—
689C22⋊C4—148no—
690C22⋊C4—148no—
691C22⋊C4—148no—
692C22⋊C4—284no—
693C22⋊C4—284no—
694C22⋊C4—284no—
695C22⋊C4C2×C22⋊D7116yes—
696C42—148no—
697C42—284no—
698C42—284no—
699C2×C7—44no—
700C2×C7—44no—
701C2×C7—82no—
702C2×C7#255918yescomplemented
703C2×C7C2×#52911yescharacteristic
704C2×C7C2×#53211yescharacteristic
705C2×C7C2×#53811yescharacteristic
706C2×C7C2×#54611yescharacteristic
707C2×C7C2×#54611yescharacteristic
708C2×C7C2×#55311yescharacteristic
709C2×C7C2×#55311yescharacteristic
710C23—28no—
711C23—28no—
712C23—28no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23C2×#115914yes—
751C23C2×#115912yes—
752C23C2×#115912yes—
753C23#654812yes—
754C23#654812yes—
755C23D7×#4112yes—
756C23D7×#4112yes—
757C23C22×C22⋊D714yes—
758C23C22×C22⋊D712yes—
759C23C24×D711yescharacteristic
760D4—416no—
761D4—416no—
762D4—416no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—416no—
776C2×C4—44no—
777C2×C4—74no—
778C2×C4—74no—
779C2×C4—148no—
780C2×C4—148no—
781C2×C4—142no—
782C2×C4—142no—
783C2×C4—142no—
784C2×C4—142no—
785C2×C4—142no—
786C2×C4—142no—
787C2×C4—142no—
788C2×C4—142no—
789C2×C4—142no—
790C2×C4—142no—
791C2×C4—142no—
792C2×C4—142no—
793C2×C4—142no—
794C2×C4—142no—
795C2×C4—142no—
796C2×C4—142no—
797C2×C4—142no—
798C2×C4—142no—
799C2×C4—142no—
800C2×C4—142no—
801C2×C4—142no—
802C2×C4—142no—
803C2×C4—2816no—
804C2×C4—284no—
805C2×C4—284no—
806C2×C4—284no—
807C2×C4—284no—
808C2×C4—284no—
809C2×C4—284no—
810C2×C4C2×#115914yes—
811C2×C4C22×C22⋊D714yes—
812C2×C4C22×C22⋊D714yes—
813C7C2×#255911yescharacteristic, complemented, Sylow
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—416no—
829C22—416no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—88no—
838C22#9029114yes—
839C22#9029214yes—
840C22#9030414yes—
841C22#9030514yes—
842C22#9049714yes—
843C22#9049714yes—
844C22#9052314yes—
845C22C22×#115911yescharacteristic
846C22C22×#115911yescharacteristic
847C22C2×#654811yescharacteristic
848C22C2×#654811yescharacteristic
849C22C2×D7×#4111yescharacteristic
850C22C2×D7×#4111yescharacteristic
851C22C23×C22⋊D711yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—42no—
856C4—144no—
857C4—144no—
858C4—282no—
859C4—282no—
860C4—282no—
861C4—282no—
862C4—282no—
863C4—282no—
864C2—44no—
865C2—44no—
866C2—82no—
867C2#1174011818yesdirect product factor
868C2C2×#9029111yescharacteristic
869C2C2×#9029211yescharacteristic
870C2C2×#9030411yescharacteristic
871C2C2×#9030511yescharacteristic
872C2C2×#9049711yescharacteristic
873C2C2×#9049711yescharacteristic
874C2C2×#9052311yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
Fitting, prime radicalC22×C7×#121C2
socleC24×C7C24
hypercenterC22×#121D7
hypocenterC7C2×#2559
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
2. C22×#6442C2semidirect
3. C2×#89994C2semidirect
4. C2×#89994C2semidirect
5. C2×#89994C2semidirect
6. C2×#89993C2semidirect
7. C2×#89992C2semidirect
8. C2×#89992C2semidirect
9. C2×#89982C2semidirect
10. C2×C4×C22⋊Dic7C2semidirect
11. #11740118C2direct (N × H)
12. C2×#89758C2semidirect
13. C2×#89744C2semidirect
14. C2×#89717C2semidirect
15. C2×#89716C2semidirect
16. C2×C22⋊C4×Dic7C2semidirect
47. C2×#6442C22semidirect
48. #89994C22semidirect
49. #89994C22semidirect
50. #89994C22semidirect
51. #89993C22semidirect
52. #89992C22semidirect
53. #89992C22semidirect
54. #89982C22semidirect
55. C4×C22⋊Dic7C22semidirect
64. #89758C22semidirect
65. #89744C22semidirect
66. #89717C22semidirect
67. #89716C22semidirect
68. C22⋊C4×Dic7C22semidirect
702. C2×C7#2559semidirect
813. C7C2×#2559semidirect
867. C2#11740118direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1212
C22×#64422
C2×#899942
C2×#899932
C2×#899922
C2×#899822
C2×C4×C22⋊Dic72
#117401182
C2×#897582
C2×#897442
C2×#897172
C2×#897162
C2×C22⋊C4×Dic72
C2×#25597