Finite Group Databasebeta

← #13276032

Subgroups — #13276032

Order 1792.

2430 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D7C211yesmaximal, characteristic
2C2×C7×#380C211yesmaximal, characteristic, complemented
3C2×#89984C211yesmaximal, characteristic, complemented
4C2×#89759C211yesmaximal, characteristic, complemented
5C2×#89759C211yesmaximal, characteristic, complemented
6C2×#89749C211yesmaximal, characteristic, complemented
7C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
8#11729304C212yesmaximal
9#11729299C212yesmaximal, complemented
10#11727175C212yesmaximal, complemented
11#11727162C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C23×C22⋊D7C2211yescharacteristic
14C23×C4×D7C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2212yes—
18C22×C22⋊Dic7C2212yes—
19C22×C22⋊Dic7C2211yescharacteristic
20C2×C4×C22⋊D7—24no—
21C2×C4×C22⋊D7—24no—
22C2×C4×C22⋊D7C418yescomplemented
23C22×(C2×D7)⋊C4C2212yes—
24C22×(C2×D7)⋊C4C2212yes—
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×C4×Dic7C2212yes—
30C22×C4×Dic7C2211yescharacteristic
31C7×#380—24no—
32C2×C7×#95C2212yes—
33#89984—24no—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40#89759—24no—
41#89759—24no—
42#89749—24no—
43C4⋊C4×Dic7—24no—
44#13905—71nomaximal, Sylow
45C25×C7C2311yescharacteristic
46C24×D7C2311yescharacteristic
47C23×C4×C7—22no—
48C23×C4×C7—22no—
49C23×C4×C7—22no—
50C23×C4×C7—22no—
51C23×C4×C7—22no—
52C23×C4×C7—22no—
53C23×C4×C7C2×C414yes—
54C23×C4×C7C2312yes—
55C23×C4×C7C2311yescharacteristic
56C23×C4×C7C2312yes—
57C23×C4×C7C2311yescharacteristic
58C22×C22⋊D7—22no—
59C22×C22⋊D7—22no—
60C22×C22⋊D7—22no—
61C22×C22⋊D7—22no—
62C22×C22⋊D7—22no—
63C22×C22⋊D7—22no—
64C22×C22⋊D7C2×C414yes—
65C23×Dic7C2312yes—
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2312yes—
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C22×C4×D7—22no—
71C22×C4×D7—22no—
72C22×C4×D7—22no—
73C22×C4×D7—22no—
74C22×C4×D7—22no—
75C22×C4×D7—22no—
76C22×C4×D7C2×C414yes—
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4D414yescomplemented
83C2×C7×C22⋊C4—24no—
84C2×C7×C22⋊C4—24no—
85C2×C7×C22⋊C4—42no—
86C2×C22⋊Dic7—22no—
87C2×C22⋊Dic7—22no—
88C2×C22⋊Dic7—24no—
89C2×C22⋊Dic7—24no—
90C2×C22⋊Dic7—42no—
91C2×C22⋊Dic7C2×C414yes—
92C4×C22⋊D7—232no—
93C2×(C2×D7)⋊C4—22no—
94C2×(C2×D7)⋊C4—22no—
95C2×(C2×D7)⋊C4—24no—
96C2×(C2×D7)⋊C4—24no—
97C2×(C2×D7)⋊C4—24no—
98C2×(C2×D7)⋊C4—24no—
99C2×(C2×D7)⋊C4—42no—
100C2×(C2×D7)⋊C4—42no—
101C2×(C2×D7)⋊C4C2×C414yes—
102C2×C4⋊Dic7—22no—
103C2×C4⋊Dic7—22no—
104C2×C4⋊Dic7—22no—
105C2×C4⋊Dic7—22no—
106C2×C4⋊Dic7—22no—
107C2×C4⋊Dic7D414yescomplemented
108C2×Dic7⋊C4—22no—
109C2×Dic7⋊C4—22no—
110C2×Dic7⋊C4C2×C414yes—
111C2×C4×Dic7—24no—
112C2×C4×Dic7—42no—
113C2×C4×Dic7—42no—
114C2×C4×Dic7C2×C414yes—
115C2×C4×Dic7D414yes—
116C2×C4×Dic7D414yes—
117C7×#95—24no—
118C7⋊#95—24no—
119C7⋊#95—24no—
120C7⋊#95—24no—
121C7⋊#95—24no—
122C7⋊#95—24no—
123C7⋊#95—24no—
124C22×C4×D4—71no—
125C2×#382—71no—
126C2×#380—71no—
127C2×#380—71no—
128C2×#380—71no—
129C2×#380D711yescharacteristic, complemented
130C2×C4×C4⋊C4—71no—
131#1445—72no—
132#1438—72no—
133#1437—72no—
134#1437—72no—
135C24×C7—21no—
136C24×C7—21no—
137C24×C7—21no—
138C24×C7—21no—
139C24×C7—21no—
140C24×C7—21no—
141C24×C7—21no—
142C24×C7—21no—
143C24×C7—21no—
144C24×C7—21no—
145C24×C7—21no—
146C24×C7—21no—
147C24×C7C22×C412yes—
148C24×C7#4112yes—
149C24×C7#4112yes—
150C24×C7C2411yescharacteristic
151C23×D7—21no—
152C23×D7—21no—
153C23×D7—21no—
154C23×D7—21no—
155C23×D7—21no—
156C23×D7—21no—
157C23×D7—21no—
158C23×D7—21no—
159C23×D7—21no—
160C23×D7—21no—
161C23×D7—21no—
162C23×D7—21no—
163C23×D7C22×C412yes—
164C23×D7#4112yes—
165C23×D7#4112yes—
166C22×C4×C7—21no—
167C22×C4×C7—22no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—28no—
179C22×C4×C7—28no—
180C22×C4×C7—28no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—44no—
189C22×C4×C7—44no—
190C22×C4×C7—44no—
191C22×C4×C7—44no—
192C22×C4×C7C22×C412yes—
193C22×C4×C7C22×C412yes—
194C22×C4×C7C2×D414yes—
195C22×C4×C7C2×D412yes—
196C22×C4×C7C2×D412yes—
197C22×C4×C7C2×D412yes—
198C22×C4×C7C2×D412yes—
199C22×C4×C7#4112yes—
200C22×C4×C7#4112yes—
201C2×C22⋊D7—28no—
202C2×C22⋊D7—28no—
203C2×C22⋊D7—28no—
204C2×C22⋊D7—28no—
205C2×C22⋊D7—28no—
206C2×C22⋊D7—28no—
207C2×C22⋊D7—28no—
208C22×Dic7—21no—
209C22×Dic7—21no—
210C22×Dic7—21no—
211C22×Dic7—21no—
212C22×Dic7—21no—
213C22×Dic7—21no—
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—22no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—22no—
222C22×Dic7—22no—
223C22×Dic7—22no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—22no—
227C22×Dic7—22no—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7—22no—
231C22×Dic7—22no—
232C22×Dic7—22no—
233C22×Dic7—22no—
234C22×Dic7—22no—
235C22×Dic7C22×C412yes—
236C22×Dic7C22×C412yes—
237C22×Dic7C22×C412yes—
238C22×Dic7C2×D414yes—
239C22×Dic7C2×D412yes—
240C22×Dic7C2×D412yes—
241C22×Dic7C2×D412yes—
242C22×Dic7C2×D412yes—
243C2×C4×D7—28no—
244C2×C4×D7—28no—
245C2×C4×D7—28no—
246C2×C4×D7—44no—
247C2×C4×D7—44no—
248C2×C4×D7—44no—
249C2×C4×D7—44no—
250C7×C4⋊C4—28no—
251C7×C4⋊C4—44no—
252C7×C22⋊C4—48no—
253C22⋊Dic7—28no—
254C22⋊Dic7—48no—
255(C2×D7)⋊C4—28no—
256(C2×D7)⋊C4—48no—
257(C2×D7)⋊C4—48no—
258C4⋊Dic7—28no—
259C4⋊Dic7—44no—
260Dic7⋊C4—28no—
261C4×Dic7—48no—
262C4×Dic7C22⋊C4116yescomplemented
263C23×D4—71no—
264C24×C4—71no—
265C24×C4C2×D711yescharacteristic
266C2×C4×D4—78no—
267C2×C4×D4—144no—
268C2×C4×D4—144no—
269C22×C4⋊C4—71no—
270C22×C4⋊C4—71no—
271C22×C4⋊C4—71no—
272C22×C4⋊C4C2×D711yescharacteristic
273C22×C4⋊C4C2×D711yescharacteristic
274C22×C22⋊C4—71no—
275C22×C22⋊C4—71no—
276C22×C22⋊C4—72no—
277C22×C22⋊C4—72no—
278C22×C22⋊C4—72no—
279C22×C22⋊C4C2×D712yes—
280C22×C42—71no—
281C22×C42—72no—
282#382—144no—
283#380—24no—
284#380—144no—
285#380—144no—
286#380—144no—
287C4×C4⋊C4—144no—
288C2×#95—72no—
289C2×#95—72no—
290C2×#95—72no—
291C2×#95—72no—
292C2×#95—72no—
293C2×#95—72no—
294C2×#95C2×D712yes—
295C23×C7—22no—
296C23×C7—22no—
297C23×C7—22no—
298C23×C7—22no—
299C23×C7—22no—
300C23×C7—22no—
301C23×C7—22no—
302C23×C7—22no—
303C23×C7—22no—
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—22no—
307C23×C7—22no—
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—41no—
314C23×C7—41no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7—41no—
318C23×C7—41no—
319C23×C7—41no—
320C23×C7—41no—
321C23×C7—41no—
322C23×C7—41no—
323C23×C7—41no—
324C23×C7—41no—
325C23×C7—41no—
326C23×C7—41no—
327C23×C7—41no—
328C23×C7—41no—
329C23×C7#11714yes—
330C23×C7C23×C411yescharacteristic
331C23×C7C22×D411yescharacteristic
332C23×C7C22×D411yescharacteristic
333C23×C7C22×D411yescharacteristic
334C23×C7C22×D411yescharacteristic
335C23×C7C2×#4111yescharacteristic
336C23×C7C2×#4111yescharacteristic
337C23×C7C2×#4111yescharacteristic
338C23×C7C2×#4111yescharacteristic
339C23×C7C2×#4111yescharacteristic
340C23×C7C2×#4111yescharacteristic
341C23×C7H(5,𝔽2)11yescharacteristic
342C23×C7H(5,𝔽2)11yescharacteristic
343C23×C72−1+411yescharacteristic
344C23×C72−1+411yescharacteristic
345C22×D7—22no—
346C22×D7—22no—
347C22×D7—22no—
348C22×D7—22no—
349C22×D7—22no—
350C22×D7—22no—
351C22×D7—22no—
352C22×D7—22no—
353C22×D7—22no—
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—41no—
364C22×D7—41no—
365C22×D7—41no—
366C22×D7—41no—
367C22×D7—41no—
368C22×D7—41no—
369C22×D7—41no—
370C22×D7—41no—
371C22×D7—41no—
372C22×D7—41no—
373C22×D7—41no—
374C22×D7—41no—
375C22×D7—41no—
376C22×D7—41no—
377C22×D7—41no—
378C22×D7—41no—
379C22×D7#11714yes—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—24no—
384C2×C4×C7—24no—
385C2×C4×C7—24no—
386C2×C4×C7—41no—
387C2×C4×C7—41no—
388C2×C4×C7—42no—
389C2×C4×C7—41no—
390C2×C4×C7—41no—
391C2×C4×C7—42no—
392C2×C4×C7—42no—
393C2×C4×C7—42no—
394C2×C4×C7—416no—
395C2×C4×C7—42no—
396C2×C4×C7—42no—
397C2×C4×C7—42no—
398C2×C4×C7—42no—
399C2×C4×C7—42no—
400C2×C4×C7—42no—
401C2×C4×C7—42no—
402C2×C4×C7C2×C22⋊C414yes—
403C2×C4×C7C4×D414yes—
404C2×C4×C7C4×D414yes—
405C2×C4×C7#12114yes—
406C2×C4×C7#12114yes—
407C2×C4×C7#12414yes—
408C2×C4×C7#12714yes—
409C22⋊D7—232no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—22no—
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—24no—
426C2×Dic7—24no—
427C2×Dic7—24no—
428C2×Dic7—41no—
429C2×Dic7—41no—
430C2×Dic7—42no—
431C2×Dic7—41no—
432C2×Dic7—41no—
433C2×Dic7—42no—
434C2×Dic7—42no—
435C2×Dic7—42no—
436C2×Dic7—42no—
437C2×Dic7—42no—
438C2×Dic7—42no—
439C2×Dic7—42no—
440C2×Dic7—42no—
441C2×Dic7—42no—
442C2×Dic7—42no—
443C2×Dic7C2×C22⋊C414yes—
444C2×Dic7C2×C22⋊C414yes—
445C4×D7—416no—
446C25—71no—
447C25C22×D711yescharacteristic
448C22×D4—74no—
449C22×D4—142no—
450C22×D4—142no—
451C22×D4—142no—
452C22×D4—142no—
453C22×D4—142no—
454C22×D4—142no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4—22no—
459C23×C4—22no—
460C23×C4—22no—
461C23×C4—71no—
462C23×C4—71no—
463C23×C4—72no—
464C23×C4—71no—
465C23×C4—74no—
466C23×C4—72no—
467C23×C4—142no—
468C23×C4—142no—
469C23×C4—142no—
470C23×C4—142no—
471C23×C4—142no—
472C23×C4—142no—
473C23×C4C4×D714yes—
474C23×C4C22×D712yes—
475C23×C4C22×D711yescharacteristic
476C23×C4C22×D712yes—
477C23×C4C22×D711yescharacteristic
478C4×D4—1432no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—74no—
485C2×C4⋊C4—74no—
486C2×C4⋊C4—142no—
487C2×C4⋊C4—142no—
488C2×C4⋊C4—142no—
489C2×C4⋊C4—142no—
490C2×C4⋊C4—142no—
491C2×C4⋊C4—142no—
492C2×C4⋊C4—142no—
493C2×C4⋊C4C22⋊D714yescomplemented
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—74no—
498C2×C22⋊C4—74no—
499C2×C22⋊C4—142no—
500C2×C22⋊C4—142no—
501C2×C22⋊C4—142no—
502C2×C22⋊C4—142no—
503C2×C22⋊C4—144no—
504C2×C22⋊C4—144no—
505C2×C22⋊C4—144no—
506C2×C22⋊C4—144no—
507C2×C22⋊C4—144no—
508C2×C22⋊C4—144no—
509C2×C22⋊C4—282no—
510C2×C22⋊C4—282no—
511C2×C22⋊C4—282no—
512C2×C42—74no—
513C2×C42—74no—
514C2×C42—74no—
515C2×C42—144no—
516C2×C42—282no—
517C2×C42—282no—
518#95—24no—
519#95—144no—
520#95—144no—
521#95—144no—
522#95—144no—
523#95—144no—
524#95—144no—
525C22×C7—24no—
526C22×C7—24no—
527C22×C7—24no—
528C22×C7—42no—
529C22×C7—42no—
530C22×C7—42no—
531C22×C7—42no—
532C22×C7—42no—
533C22×C7—42no—
534C22×C7—42no—
535C22×C7—42no—
536C22×C7—42no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—42no—
540C22×C7C22×C22⋊C411yescharacteristic
541C22×C7C2×#11711yescharacteristic
542C22×C7C2×#11711yescharacteristic
543C22×C7C2×C4×D411yescharacteristic
544C22×C7C2×C4×D411yescharacteristic
545C22×C7#52011yescharacteristic
546C22×C7#52011yescharacteristic
547C22×C7C2×#12111yescharacteristic
548C22×C7C2×#12111yescharacteristic
549C22×C7#52511yescharacteristic
550C22×C7#52511yescharacteristic
551C22×C7#52511yescharacteristic
552C22×C7#52511yescharacteristic
553C22×C7C2×#12411yescharacteristic
554C22×C7C2×#12711yescharacteristic
555C22×C7#53511yescharacteristic
556C22×C7#53611yescharacteristic
557C22×C7#53711yescharacteristic
558C22×C7#53711yescharacteristic
559C22×C7#54611yescharacteristic
560C22×C7#54611yescharacteristic
561C22×C7#54611yescharacteristic
562C22×C7#54611yescharacteristic
563C22×C7#54811yescharacteristic
564C22×C7#54811yescharacteristic
565C22×C7#54811yescharacteristic
566C22×C7#54811yescharacteristic
567C22×C7#55211yescharacteristic
568C22×C7#55211yescharacteristic
569C22×C7#55211yescharacteristic
570C22×C7#55211yescharacteristic
571C22×C7#55311yescharacteristic
572C22×C7#55311yescharacteristic
573C22×C7#55311yescharacteristic
574C22×C7#55311yescharacteristic
575C2×D7—24no—
576C2×D7—24no—
577C2×D7—24no—
578C2×D7—42no—
579C2×D7—42no—
580C2×D7—42no—
581C2×D7—42no—
582C2×D7—42no—
583C2×D7—42no—
584C2×D7—42no—
585C2×D7—42no—
586C2×D7—42no—
587C2×D7—42no—
588C2×D7—42no—
589C2×D7—42no—
590C4×C7—44no—
591C4×C7—42no—
592C4×C7—82no—
593C4×C7#39018yes—
594Dic7—24no—
595Dic7—24no—
596Dic7—44no—
597Dic7—42no—
598Dic7—82no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—72no—
612C24—72no—
613C24—72no—
614C24—141no—
615C24—141no—
616C24—141no—
617C24—141no—
618C24—141no—
619C24—141no—
620C24—141no—
621C24—141no—
622C24—141no—
623C24—141no—
624C24—141no—
625C24—141no—
626C24C2×C4×D712yes—
627C24#115912yes—
628C24#116112yes—
629C24C23×D711yescharacteristic
630C2×D4—148no—
631C2×D4—148no—
632C2×D4—148no—
633C2×D4—148no—
634C2×D4—148no—
635C2×D4—148no—
636C2×D4—148no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—21no—
649C22×C4—28no—
650C22×C4—28no—
651C22×C4—28no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—72no—
664C22×C4—72no—
665C22×C4—72no—
666C22×C4—72no—
667C22×C4—72no—
668C22×C4—72no—
669C22×C4—72no—
670C22×C4—74no—
671C22×C4—141no—
672C22×C4—141no—
673C22×C4—141no—
674C22×C4—141no—
675C22×C4—141no—
676C22×C4—141no—
677C22×C4—141no—
678C22×C4—141no—
679C22×C4—142no—
680C22×C4—141no—
681C22×C4—141no—
682C22×C4—142no—
683C22×C4—141no—
684C22×C4—141no—
685C22×C4—141no—
686C22×C4—142no—
687C22×C4—142no—
688C22×C4—142no—
689C22×C4—142no—
690C22×C4—141no—
691C22×C4—148no—
692C22×C4—148no—
693C22×C4—148no—
694C22×C4—142no—
695C22×C4—142no—
696C22×C4—142no—
697C22×C4—142no—
698C22×C4—142no—
699C22×C4—142no—
700C22×C4—142no—
701C22×C4—284no—
702C22×C4—284no—
703C22×C4—284no—
704C22×C4—284no—
705C22×C4C2×C4×D712yes—
706C22×C4C2×C4×D712yes—
707C22×C4#115712yes—
708C22×C4D4×D712yes—
709C22×C4D4×D712yes—
710C22×C4D4×D712yes—
711C22×C4#115912yes—
712C22×C4C2×C22⋊D714yes—
713C22×C4C2×C22⋊D712yes—
714C4⋊C4—28no—
715C4⋊C4—44no—
716C4⋊C4—148no—
717C4⋊C4—148no—
718C4⋊C4—284no—
719C22⋊C4—48no—
720C22⋊C4—148no—
721C22⋊C4—148no—
722C22⋊C4—288no—
723C22⋊C4—288no—
724C22⋊C4—288no—
725C42—716no—
726C42—288no—
727C2×C7—44no—
728C2×C7#228011yescharacteristic
729C2×C7C2×#39011yescharacteristic
730C2×C7#231111yescharacteristic
731C2×C7#235211yescharacteristic
732C2×C7#235211yescharacteristic
733C2×C7#235211yescharacteristic
734C2×C7#235211yescharacteristic
735C2×C7#253511yescharacteristic
736C2×C7#253511yescharacteristic
737C2×C7#253611yescharacteristic
738C2×C7#253611yescharacteristic
739C2×C7#254011yescharacteristic
740C2×C7#254011yescharacteristic
741C2×C7#256211yescharacteristic
742C2×C7#256211yescharacteristic
743D7—44no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—74no—
779C23—142no—
780C23—142no—
781C23—142no—
782C23—142no—
783C23—142no—
784C23—142no—
785C23—142no—
786C23—142no—
787C23—142no—
788C23—142no—
789C23—142no—
790C23—142no—
791C23—142no—
792C23—142no—
793C23—142no—
794C23—142no—
795C23—142no—
796C23—142no—
797C23—281no—
798C23—281no—
799C23—281no—
800C23—281no—
801C23—281no—
802C23—281no—
803C23—281no—
804C23—281no—
805C23—281no—
806C23—281no—
807C23—281no—
808C23—281no—
809C23—281no—
810C23—281no—
811C23—281no—
812C23—281no—
813C23#645514yes—
814C23C22×C4×D711yescharacteristic
815C23C2×#115711yescharacteristic
816C23C2×D4×D711yescharacteristic
817C23C2×D4×D711yescharacteristic
818C23C2×D4×D711yescharacteristic
819C23C2×#115911yescharacteristic
820C23C2×#115911yescharacteristic
821C23#654811yescharacteristic
822C23C2×#116111yescharacteristic
823C23#655111yescharacteristic
824C23D7×#4111yescharacteristic
825C23D7×#4111yescharacteristic
826C23#655311yescharacteristic
827C23#655411yescharacteristic
828C23C22×C22⋊D711yescharacteristic
829D4—1432no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—416no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—74no—
853C2×C4—74no—
854C2×C4—142no—
855C2×C4—142no—
856C2×C4—142no—
857C2×C4—142no—
858C2×C4—142no—
859C2×C4—142no—
860C2×C4—142no—
861C2×C4—142no—
862C2×C4—142no—
863C2×C4—142no—
864C2×C4—142no—
865C2×C4—142no—
866C2×C4—142no—
867C2×C4—142no—
868C2×C4—144no—
869C2×C4—142no—
870C2×C4—144no—
871C2×C4—144no—
872C2×C4—281no—
873C2×C4—281no—
874C2×C4—282no—
875C2×C4—282no—
876C2×C4—281no—
877C2×C4—281no—
878C2×C4—282no—
879C2×C4—282no—
880C2×C4—2816no—
881C2×C4—282no—
882C2×C4—282no—
883C2×C4—282no—
884C2×C4—282no—
885C2×C4—282no—
886C2×C4—282no—
887C2×C4—282no—
888C2×C4D7×C22⋊C414yes—
889C2×C4(C22⋊D7)⋊C414yes—
890C2×C4#644714yes—
891C2×C4#644814yes—
892C2×C4C4×C22⋊D714yes—
893C2×C4#650214yes—
894C2×C4#650314yes—
895C7#1390511yescharacteristic, complemented, Sylow
896C22—24no—
897C22—24no—
898C22—24no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—144no—
912C22—144no—
913C22—144no—
914C22—282no—
915C22—282no—
916C22—282no—
917C22—282no—
918C22—282no—
919C22—282no—
920C22—282no—
921C22—282no—
922C22—282no—
923C22—282no—
924C22—282no—
925C22—282no—
926C22C2×D7×C22⋊C411yescharacteristic
927C22C2×(C22⋊D7)⋊C411yescharacteristic
928C22C2×#644711yescharacteristic
929C22C2×#644811yescharacteristic
930C22C2×#645511yescharacteristic
931C22#9019511yescharacteristic
932C22#9020411yescharacteristic
933C22#9020511yescharacteristic
934C22D7×#11711yescharacteristic
935C22#9021411yescharacteristic
936C22#9022011yescharacteristic
937C22#9022111yescharacteristic
938C22#9028911yescharacteristic
939C22#9029711yescharacteristic
940C22#9029711yescharacteristic
941C22#9029811yescharacteristic
942C22#9029911yescharacteristic
943C22#9030311yescharacteristic
944C22#9030511yescharacteristic
945C22#9030911yescharacteristic
946C22#9031811yescharacteristic
947C22#9031811yescharacteristic
948C22#9031911yescharacteristic
949C22#9032011yescharacteristic
950C22#9032111yescharacteristic
951C22#9032411yescharacteristic
952C22#9033011yescharacteristic
953C22#9033311yescharacteristic
954C22C2×C4×C22⋊D711yescharacteristic
955C22C2×#650211yescharacteristic
956C22C2×#650311yescharacteristic
957C22#9049711yescharacteristic
958C22#9050811yescharacteristic
959C22#9052011yescharacteristic
960C22#9052211yescharacteristic
961C4—42no—
962C4—44no—
963C4—82no—
964C4—144no—
965C4—144no—
966C4—282no—
967C4—284no—
968C4—562no—
969C4#8972918yes—
970C2—44no—
971C2—284no—
972C2#1173130711yescharacteristic
973C2#1173132811yescharacteristic
974C2#1173137811yescharacteristic
975C2#1173137911yescharacteristic
976C2#1173138511yescharacteristic
977C2#1173138611yescharacteristic
978C2#1173144811yescharacteristic
979C2#1173145711yescharacteristic
980C2C2×#8972911yescharacteristic
981C2#1173960611yescharacteristic
982C2#1173971711yescharacteristic
983C2#1174011111yescharacteristic
984C2#1174011311yescharacteristic
985C2#1174022211yescharacteristic
986C2#1174022411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#380C2
socle, cosocleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#380D7
hypocenterC7#13905
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×C7×#380C2semidirect
3. C2×#89984C2semidirect
4. C2×#89759C2semidirect
5. C2×#89759C2semidirect
6. C2×#89749C2semidirect
7. C2×C4⋊C4×Dic7C2semidirect
9. #11729299C2semidirect
10. #11727175C2semidirect
11. #11727162C2semidirect
22. C2×C4×C22⋊D7C4semidirect
82. C2×C7×C4⋊C4D4semidirect
107. C2×C4⋊Dic7D4semidirect
129. C2×#380D7semidirect
262. C4×Dic7C22⋊C4semidirect
493. C2×C4⋊C4C22⋊D7semidirect
895. C7#13905semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D72
C2×C7×#3802
C2×#899842
C2×#897592
C2×#897492
C2×C4⋊C4×Dic72
#117293042
#117292992
#117271752
#117271622
#139057