Finite Group Databasebeta

← C2×#11734186 #13559938

Subgroups — C2×#11734186 #13559938

Order 1792.

3322 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6498C211yesmaximal, characteristic, complemented
2C22×#6502C211yesmaximal, characteristic, complemented
3C2×C7×#392C211yesmaximal, characteristic, complemented
4C2×#89995C211yesmaximal, characteristic, complemented
5C2×#89995C211yesmaximal, characteristic, complemented
6C2×#89994C211yesmaximal, characteristic, complemented
7C2×#89994C211yesmaximal, characteristic, complemented
8C2×#89731C211yesmaximal, characteristic, complemented
9C2×#89731C211yesmaximal, characteristic, complemented
10C2×#89721C211yesmaximal, characteristic, complemented
11C2×#89720C211yesmaximal, characteristic, complemented
12C2×#89733C211yesmaximal, characteristic, complemented
13C2×#89714C211yesmaximal, characteristic, complemented
14#11734186C2116yesmaximal, direct product factor
15C2×#89448C211yesmaximal, characteristic, complemented
16C2×#89430C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C23×C7×D4C2211yescharacteristic
19C23×C7×D4C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C23×C22⋊D7C2211yescharacteristic
22C23×C22⋊D7C2211yescharacteristic
23C24×Dic7C2211yescharacteristic
24C22×C7×C22⋊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
35C2×#6502—28no—
36C2×#6502C2218yescomplemented
37C2×#6498—28no—
38C2×#6498C2218yescomplemented
39C22×(C2×D7)⋊C4C2211yescharacteristic
40C22×(C2×D7)⋊C4C2211yescharacteristic
41C22×(C2×D7)⋊C4C2211yescharacteristic
42C22×(C2×D7)⋊C4C2211yescharacteristic
43C22×C4⋊Dic7C2211yescharacteristic
44C22×Dic7⋊C4C2211yescharacteristic
45C22×Dic7⋊C4C2211yescharacteristic
46C22×Dic7⋊C4C2211yescharacteristic
47C22×Dic7⋊C4C2211yescharacteristic
48C22×Dic7⋊C4C2211yescharacteristic
49C22×Dic7⋊C4C2211yescharacteristic
50C7×#392C2218yescomplemented
51C2×C7×#95C2211yescharacteristic
52#89995C2218yescomplemented
53#89995C2218yescomplemented
54#89994C2218yescomplemented
55#89994C2218yescomplemented
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61#89733C2218yescomplemented
62#89731C2218yescomplemented
63#89731C2218yescomplemented
64#89721C2218yescomplemented
65#89720C2218yescomplemented
66#89714C2218yescomplemented
67#89448C2218yescomplemented
68#89430C2218yescomplemented
69C2×#2813—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C25×C7C2311yescharacteristic
72C25×C7C2311yescharacteristic
73C24×D7C2311yescharacteristic
74C22×C7×D4—24no—
75C22×C7×D4—24no—
76C22×C7×D4—42no—
77C22×C7×D4—42no—
78C22×C7×D4—42no—
79C22×C7×D4—42no—
80C22×C7×D4—42no—
81C22×C7×D4—42no—
82C22×C7×D4—42no—
83C22×C7×D4C2314yes—
84C22×C7×D4C2314yes—
85C22×C7×D4C2314yes—
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C23×C4×C7C2311yescharacteristic
89C23×C4×C7C2311yescharacteristic
90C22×C22⋊D7—24no—
91C22×C22⋊D7—24no—
92C22×C22⋊D7—42no—
93C22×C22⋊D7—42no—
94C22×C22⋊D7—42no—
95C22×C22⋊D7—42no—
96C22×C22⋊D7—42no—
97C22×C22⋊D7—42no—
98C22×C22⋊D7—42no—
99C22×C22⋊D7C2314yes—
100C22×C22⋊D7C2314yes—
101C22×C22⋊D7C2314yes—
102C23×Dic7—42no—
103C23×Dic7—42no—
104C23×Dic7D418yescomplemented
105C23×Dic7C2311yescharacteristic
106C23×Dic7C2311yescharacteristic
107C23×Dic7C2311yescharacteristic
108C23×Dic7C2311yescharacteristic
109C23×Dic7C2311yescharacteristic
110C23×Dic7C2311yescharacteristic
111C23×Dic7C2311yescharacteristic
112C23×Dic7C2314yes—
113C2×C7×C22⋊C4—42no—
114C2×C7×C22⋊C4—42no—
115C2×C7×C22⋊C4—42no—
116C2×C7×C22⋊C4C2314yes—
117C2×C7×C22⋊C4C2314yes—
118C2×C7×C22⋊C4C2314yes—
119C2×C22⋊Dic7—24no—
120C2×C22⋊Dic7—24no—
121C2×C22⋊Dic7—24no—
122C2×C22⋊Dic7—24no—
123C2×C22⋊Dic7—42no—
124C2×C22⋊Dic7—42no—
125C2×C22⋊Dic7—42no—
126C2×C22⋊Dic7—42no—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130C2×C22⋊Dic7C2314yes—
131C2×C22⋊Dic7C2314yes—
132C2×C22⋊Dic7C2314yes—
133C2×C22⋊Dic7C2314yes—
134C2×C22⋊Dic7C2314yes—
135#6502—232no—
136#6498—232no—
137C2×(C2×D7)⋊C4—24no—
138C2×(C2×D7)⋊C4—42no—
139C2×(C2×D7)⋊C4—42no—
140C2×(C2×D7)⋊C4—42no—
141C2×(C2×D7)⋊C4C2314yes—
142C2×(C2×D7)⋊C4C2314yes—
143C2×(C2×D7)⋊C4C2314yes—
144C2×(C2×D7)⋊C4C2314yes—
145C2×C4⋊Dic7—42no—
146C2×C4⋊Dic7C2314yes—
147C2×Dic7⋊C4—24no—
148C2×Dic7⋊C4—24no—
149C2×Dic7⋊C4—24no—
150C2×Dic7⋊C4—42no—
151C2×Dic7⋊C4—42no—
152C2×Dic7⋊C4—42no—
153C2×Dic7⋊C4C2314yes—
154C2×Dic7⋊C4C2314yes—
155C2×Dic7⋊C4C2314yes—
156C2×Dic7⋊C4C2314yes—
157C2×Dic7⋊C4C2314yes—
158C2×Dic7⋊C4C2314yes—
159C7×#95C2314yes—
160C7⋊#95C2314yes—
161C7⋊#95C2314yes—
162C7⋊#95C2314yes—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C22×#123—71no—
166C22×#121—71no—
167#2813—716no—
168C2×#400—71no—
169C2×#399—71no—
170C2×#396—71no—
171C2×#396—71no—
172C2×#394—71no—
173C2×#394—71no—
174C2×#394—71no—
175C2×#394—71no—
176C2×#394—71no—
177C2×#392—71no—
178C2×#392—71no—
179C2×#392D711yescharacteristic, complemented
180C2×#380—71no—
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×C7—22no—
195C24×C7—22no—
196C24×C7—22no—
197C24×C7—22no—
198C24×C7—22no—
199C24×C7—22no—
200C24×C7—22no—
201C24×C7C2×D414yes—
202C24×C7C2412yes—
203C24×C7C2412yes—
204C24×C7C2412yes—
205C24×C7C2411yescharacteristic
206C23×D7—22no—
207C23×D7—22no—
208C23×D7—22no—
209C23×D7—22no—
210C23×D7—22no—
211C23×D7—22no—
212C23×D7—22no—
213C23×D7C2412yes—
214C2×C7×D4—28no—
215C2×C7×D4—28no—
216C2×C7×D4—44no—
217C2×C7×D4—44no—
218C2×C7×D4—44no—
219C2×C7×D4—44no—
220C2×C7×D4—44no—
221C2×C7×D4—44no—
222C2×C7×D4—44no—
223C2×C7×D4—416no—
224C2×C7×D4—416no—
225C2×C7×D4—416no—
226C22×C4×C7—22no—
227C22×C4×C7—22no—
228C22×C4×C7—22no—
229C22×C4×C7—22no—
230C22×C4×C7—22no—
231C22×C4×C7—22no—
232C22×C4×C7—22no—
233C22×C4×C7—22no—
234C22×C4×C7—22no—
235C22×C4×C7—22no—
236C22×C4×C7—22no—
237C22×C4×C7—22no—
238C22×C4×C7C2412yes—
239C22×C4×C7C2412yes—
240C22×C4×C7C2412yes—
241C22×C4×C7C2412yes—
242C2×C22⋊D7—28no—
243C2×C22⋊D7—28no—
244C2×C22⋊D7—44no—
245C2×C22⋊D7—44no—
246C2×C22⋊D7—44no—
247C2×C22⋊D7—44no—
248C2×C22⋊D7—44no—
249C2×C22⋊D7—44no—
250C2×C22⋊D7—44no—
251C2×C22⋊D7—416no—
252C2×C22⋊D7—416no—
253C2×C22⋊D7—416no—
254C22×Dic7—22no—
255C22×Dic7—22no—
256C22×Dic7—22no—
257C22×Dic7—22no—
258C22×Dic7—22no—
259C22×Dic7—22no—
260C22×Dic7—22no—
261C22×Dic7—22no—
262C22×Dic7—22no—
263C22×Dic7—22no—
264C22×Dic7—22no—
265C22×Dic7—22no—
266C22×Dic7—22no—
267C22×Dic7—22no—
268C22×Dic7—22no—
269C22×Dic7—22no—
270C22×Dic7—22no—
271C22×Dic7—22no—
272C22×Dic7—22no—
273C22×Dic7—416no—
274C22×Dic7—44no—
275C22×Dic7—44no—
276C22×Dic7C2×D414yes—
277C22×Dic7C2×D414yes—
278C22×Dic7C2×D4116yescomplemented
279C22×Dic7C2412yes—
280C22×Dic7C2412yes—
281C22×Dic7C2412yes—
282C22×Dic7C2412yes—
283C22×Dic7C2412yes—
284C22×Dic7C2412yes—
285C22×Dic7C2412yes—
286C7×C22⋊C4—44no—
287C7×C22⋊C4—44no—
288C7×C22⋊C4—44no—
289C22⋊Dic7—28no—
290C22⋊Dic7—28no—
291C22⋊Dic7—28no—
292C22⋊Dic7—28no—
293C22⋊Dic7—44no—
294C22⋊Dic7—44no—
295C22⋊Dic7—44no—
296C22⋊Dic7—44no—
297(C2×D7)⋊C4—28no—
298(C2×D7)⋊C4—44no—
299(C2×D7)⋊C4—44no—
300(C2×D7)⋊C4—44no—
301C4⋊Dic7—44no—
302Dic7⋊C4—28no—
303Dic7⋊C4—28no—
304Dic7⋊C4—28no—
305Dic7⋊C4—44no—
306Dic7⋊C4—44no—
307Dic7⋊C4—44no—
308C23×D4—71no—
309C23×D4—71no—
310C23×D4—71no—
311C23×D4C2×D711yescharacteristic
312C23×D4C2×D711yescharacteristic
313C23×D4C2×D711yescharacteristic
314C24×C4—71no—
315C2×#123—78no—
316C2×#123—148no—
317C2×#121—78no—
318C2×#121—148no—
319C22×C4⋊C4—71no—
320C22×C4⋊C4—71no—
321C22×C4⋊C4—71no—
322C22×C4⋊C4—71no—
323C22×C4⋊C4—71no—
324C22×C4⋊C4—71no—
325C22×C4⋊C4—71no—
326C22×C22⋊C4—71no—
327C22×C22⋊C4—71no—
328C22×C22⋊C4—71no—
329C22×C22⋊C4—71no—
330C22×C22⋊C4—71no—
331C22×C22⋊C4—71no—
332C22×C22⋊C4—71no—
333C22×C22⋊C4—71no—
334C22×C22⋊C4—71no—
335C22×C22⋊C4—71no—
336C22×C22⋊C4—71no—
337C22×C22⋊C4—71no—
338C22×C22⋊C4C2×D711yescharacteristic
339C22×C22⋊C4C2×D711yescharacteristic
340C22×C22⋊C4C2×D711yescharacteristic
341#400—78no—
342#399—78no—
343#396—78no—
344#396—78no—
345#394—78no—
346#394—78no—
347#394—78no—
348#394—78no—
349#394—78no—
350#392—78no—
351#392—78no—
352#392C2×D718yescomplemented
353#380—78no—
354C2×#95—71no—
355C2×#95—71no—
356C2×#95—71no—
357C2×#95—71no—
358C2×#95—71no—
359C2×#95C2×D711yescharacteristic
360C23×C7—28no—
361C23×C7—28no—
362C23×C7—28no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7—22no—
378C23×C7—22no—
379C23×C7—22no—
380C23×C7—22no—
381C23×C7—22no—
382C23×C7—22no—
383C23×C7—44no—
384C23×C7—44no—
385C23×C7—44no—
386C23×C7—44no—
387C23×C7—44no—
388C23×C7—44no—
389C23×C7—44no—
390C23×C7—44no—
391C23×C7—44no—
392C23×C7—44no—
393C23×C7—44no—
394C23×C7—44no—
395C23×C7—44no—
396C23×C7—44no—
397C23×C7—44no—
398C23×C7—44no—
399C23×C7—44no—
400C23×C7—44no—
401C23×C7C22×D414yes—
402C23×C7C22×D412yes—
403C23×C7H(5,𝔽2)12yes—
404C23×C7H(5,𝔽2)12yes—
405C23×C7H(5,𝔽2)12yes—
406C23×C7H(5,𝔽2)12yes—
407C23×C7H(5,𝔽2)12yes—
408C23×C72−1+412yes—
409C23×C7C2511yescharacteristic
410C22×D7—22no—
411C22×D7—22no—
412C22×D7—22no—
413C22×D7—22no—
414C22×D7—22no—
415C22×D7—22no—
416C22×D7—22no—
417C22×D7—44no—
418C22×D7—44no—
419C22×D7—44no—
420C22×D7—44no—
421C22×D7—44no—
422C22×D7—44no—
423C22×D7—44no—
424C7×D4—416no—
425C7×D4—416no—
426C7×D4—416no—
427C2×C4×C7—22no—
428C2×C4×C7—22no—
429C2×C4×C7—22no—
430C2×C4×C7—22no—
431C2×C4×C7—22no—
432C2×C4×C7—22no—
433C2×C4×C7—22no—
434C2×C4×C7—22no—
435C2×C4×C7—22no—
436C2×C4×C7—22no—
437C2×C4×C7—22no—
438C2×C4×C7—22no—
439C2×C4×C7—44no—
440C2×C4×C7—44no—
441C2×C4×C7—44no—
442C2×C4×C7—44no—
443C22⋊D7—416no—
444C22⋊D7—416no—
445C22⋊D7—416no—
446C2×Dic7—28no—
447C2×Dic7—28no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—22no—
453C2×Dic7—22no—
454C2×Dic7—22no—
455C2×Dic7—22no—
456C2×Dic7—22no—
457C2×Dic7—22no—
458C2×Dic7—22no—
459C2×Dic7—22no—
460C2×Dic7—22no—
461C2×Dic7—22no—
462C2×Dic7—22no—
463C2×Dic7—22no—
464C2×Dic7—22no—
465C2×Dic7—22no—
466C2×Dic7—22no—
467C2×Dic7—416no—
468C2×Dic7—44no—
469C2×Dic7—44no—
470C2×Dic7—44no—
471C2×Dic7—44no—
472C2×Dic7—44no—
473C2×Dic7C22×D414yes—
474C2×Dic7C22×D414yes—
475C25—71no—
476C25C22×D711yescharacteristic
477C25C22×D711yescharacteristic
478C25C22×D711yescharacteristic
479C22×D4—24no—
480C22×D4—24no—
481C22×D4—42no—
482C22×D4—42no—
483C22×D4—42no—
484C22×D4—42no—
485C22×D4—42no—
486C22×D4—42no—
487C22×D4—42no—
488C22×D4—74no—
489C22×D4—74no—
490C22×D4—74no—
491C22×D4—144no—
492C22×D4—144no—
493C22×D4—282no—
494C22×D4—282no—
495C22×D4—282no—
496C22×D4—282no—
497C22×D4—282no—
498C22×D4—282no—
499C22×D4—282no—
500C22×D4C22×D714yes—
501C22×D4C22×D714yes—
502C22×D4C22×D714yes—
503C23×C4—71no—
504C23×C4—71no—
505C23×C4—78no—
506C23×C4—74no—
507C23×C4—71no—
508C23×C4—71no—
509C23×C4—71no—
510C23×C4—71no—
511C23×C4—71no—
512C23×C4—282no—
513C23×C4—282no—
514C23×C4C22×D711yescharacteristic
515C23×C4C22×D711yescharacteristic
516C23×C4C22×D711yescharacteristic
517C23×C4C22×D711yescharacteristic
518#123—1432no—
519#121—1432no—
520C2×C4⋊C4—74no—
521C2×C4⋊C4—74no—
522C2×C4⋊C4—74no—
523C2×C4⋊C4—74no—
524C2×C4⋊C4—74no—
525C2×C4⋊C4—74no—
526C2×C4⋊C4—74no—
527C2×C4⋊C4—144no—
528C2×C4⋊C4—144no—
529C2×C4⋊C4—144no—
530C2×C4⋊C4—282no—
531C2×C4⋊C4—282no—
532C2×C4⋊C4—282no—
533C2×C4⋊C4—282no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—74no—
538C2×C22⋊C4—74no—
539C2×C22⋊C4—74no—
540C2×C22⋊C4—74no—
541C2×C22⋊C4—74no—
542C2×C22⋊C4—74no—
543C2×C22⋊C4—74no—
544C2×C22⋊C4—74no—
545C2×C22⋊C4—74no—
546C2×C22⋊C4—74no—
547C2×C22⋊C4—74no—
548C2×C22⋊C4—74no—
549C2×C22⋊C4—144no—
550C2×C22⋊C4—144no—
551C2×C22⋊C4—144no—
552C2×C22⋊C4—144no—
553C2×C22⋊C4—144no—
554C2×C22⋊C4—282no—
555C2×C22⋊C4—282no—
556C2×C22⋊C4—282no—
557C2×C22⋊C4—282no—
558C2×C22⋊C4—282no—
559C2×C22⋊C4—282no—
560C2×C22⋊C4—282no—
561C2×C22⋊C4C22×D714yes—
562C2×C22⋊C4C22×D714yes—
563C2×C22⋊C4C22×D714yes—
564#95—74no—
565#95—74no—
566#95—74no—
567#95—74no—
568#95—74no—
569#95C22×D714yes—
570C22×C7—24no—
571C22×C7—24no—
572C22×C7—24no—
573C22×C7—42no—
574C22×C7—42no—
575C22×C7—42no—
576C22×C7—42no—
577C22×C7—416no—
578C22×C7—42no—
579C22×C7—42no—
580C22×C7—42no—
581C22×C7—42no—
582C22×C7—42no—
583C22×C7—42no—
584C22×C7—42no—
585C22×C7—42no—
586C22×C7—42no—
587C22×C7—42no—
588C22×C7—42no—
589C22×C7—42no—
590C22×C7—42no—
591C22×C7—42no—
592C22×C7—88no—
593C22×C7—88no—
594C22×C7#53414yes—
595C22×C7#53514yes—
596C22×C7#53714yes—
597C22×C7#56014yes—
598C22×C7#56014yes—
599C22×C7#56214yes—
600C22×C7#56214yes—
601C22×C7C23×D411yescharacteristic
602C22×C7C2×H(5,𝔽2)11yescharacteristic
603C22×C7C2×H(5,𝔽2)11yescharacteristic
604C22×C7C2×H(5,𝔽2)11yescharacteristic
605C22×C7C2×H(5,𝔽2)11yescharacteristic
606C22×C7C2×H(5,𝔽2)11yescharacteristic
607C22×C7C2×2−1+411yescharacteristic
608C2×D7—42no—
609C2×D7—42no—
610C2×D7—42no—
611C2×D7—42no—
612C2×D7—42no—
613C2×D7—42no—
614C2×D7—42no—
615C2×D7—88no—
616C4×C7—42no—
617C4×C7—42no—
618C4×C7—42no—
619C4×C7—42no—
620Dic7—24no—
621Dic7—24no—
622Dic7—42no—
623Dic7—42no—
624Dic7—42no—
625Dic7—42no—
626Dic7—42no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—72no—
648C24—142no—
649C24—142no—
650C24—142no—
651C24—142no—
652C24—142no—
653C24—142no—
654C24—142no—
655C24D4×D714yes—
656C24C23×D712yes—
657C24C23×D712yes—
658C24C23×D712yes—
659C24C23×D711yescharacteristic
660C2×D4—28no—
661C2×D4—28no—
662C2×D4—44no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—416no—
670C2×D4—416no—
671C2×D4—416no—
672C2×D4—148no—
673C2×D4—148no—
674C2×D4—284no—
675C2×D4—284no—
676C2×D4—284no—
677C2×D4—284no—
678C2×D4—284no—
679C2×D4—284no—
680C2×D4—284no—
681C2×D4—2816no—
682C2×D4—2816no—
683C2×D4—2816no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—74no—
697C22×C4—74no—
698C22×C4—72no—
699C22×C4—72no—
700C22×C4—716no—
701C22×C4—72no—
702C22×C4—72no—
703C22×C4—72no—
704C22×C4—72no—
705C22×C4—72no—
706C22×C4—142no—
707C22×C4—142no—
708C22×C4—142no—
709C22×C4—142no—
710C22×C4—142no—
711C22×C4—142no—
712C22×C4—142no—
713C22×C4—142no—
714C22×C4—142no—
715C22×C4—142no—
716C22×C4—142no—
717C22×C4—142no—
718C22×C4—142no—
719C22×C4—142no—
720C22×C4—142no—
721C22×C4—142no—
722C22×C4—142no—
723C22×C4—142no—
724C22×C4—142no—
725C22×C4—2816no—
726C22×C4—284no—
727C22×C4—284no—
728C22×C4C23×D712yes—
729C22×C4C23×D712yes—
730C22×C4C23×D712yes—
731C22×C4C23×D712yes—
732C4⋊C4—148no—
733C4⋊C4—148no—
734C4⋊C4—148no—
735C4⋊C4—284no—
736C4⋊C4—284no—
737C4⋊C4—284no—
738C4⋊C4—284no—
739C22⋊C4—44no—
740C22⋊C4—44no—
741C22⋊C4—44no—
742C22⋊C4—148no—
743C22⋊C4—148no—
744C22⋊C4—148no—
745C22⋊C4—148no—
746C22⋊C4—148no—
747C22⋊C4—284no—
748C22⋊C4—284no—
749C22⋊C4—284no—
750C22⋊C4—284no—
751C22⋊C4—284no—
752C22⋊C4—284no—
753C22⋊C4—284no—
754C2×C7—44no—
755C2×C7—82no—
756C2×C7—82no—
757C2×C7#281318yescomplemented
758C2×C7C2×#53411yescharacteristic
759C2×C7C2×#53511yescharacteristic
760C2×C7C2×#53711yescharacteristic
761C2×C7C2×#56011yescharacteristic
762C2×C7C2×#56011yescharacteristic
763C2×C7C2×#56211yescharacteristic
764C2×C7C2×#56211yescharacteristic
765D7—82no—
766C23—28no—
767C23—28no—
768C23—28no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—44no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—44no—
799C23—44no—
800C23—44no—
801C23—44no—
802C23—44no—
803C23—44no—
804C23—44no—
805C23—44no—
806C23—44no—
807C23—142no—
808C23—142no—
809C23—142no—
810C23—142no—
811C23—142no—
812C23—142no—
813C23—142no—
814C23—284no—
815C23—284no—
816C23—284no—
817C23—284no—
818C23—284no—
819C23—284no—
820C23—284no—
821C23C2×D4×D714yes—
822C23C2×D4×D712yes—
823C23#654812yes—
824C23#654812yes—
825C23#654812yes—
826C23#654812yes—
827C23#654812yes—
828C23#655412yes—
829C23C24×D711yescharacteristic
830D4—416no—
831D4—416no—
832D4—416no—
833D4—2816no—
834D4—2816no—
835D4—2816no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—74no—
853C2×C4—74no—
854C2×C4—148no—
855C2×C4—148no—
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—142no—
869C2×C4—142no—
870C2×C4—142no—
871C2×C4—142no—
872C2×C4—142no—
873C2×C4—142no—
874C2×C4—142no—
875C2×C4—2816no—
876C2×C4—284no—
877C2×C4—284no—
878C2×C4—284no—
879C2×C4—284no—
880C2×C4—284no—
881C7C2×#281311yescharacteristic, complemented, Sylow
882C22—24no—
883C22—24no—
884C22—24no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—416no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—88no—
905C22—88no—
906C22—282no—
907C22—282no—
908C22—282no—
909C22—282no—
910C22—282no—
911C22—282no—
912C22—282no—
913C22—568no—
914C22#9028014yes—
915C22#9028314yes—
916C22#9028614yes—
917C22#9028814yes—
918C22#9031214yes—
919C22#9031214yes—
920C22#9041114yes—
921C22C22×D4×D711yescharacteristic
922C22C2×#654811yescharacteristic
923C22C2×#654811yescharacteristic
924C22C2×#654811yescharacteristic
925C22C2×#654811yescharacteristic
926C22C2×#654811yescharacteristic
927C22C2×#655411yescharacteristic
928C4—42no—
929C4—42no—
930C4—42no—
931C4—42no—
932C4—144no—
933C4—144no—
934C4—282no—
935C4—282no—
936C4—282no—
937C4—282no—
938C4—282no—
939C2—44no—
940C2—82no—
941C2—82no—
942C2—562no—
943C2#1173418618yesdirect product factor
944C2C2×#9028311yescharacteristic
945C2C2×#9028011yescharacteristic
946C2C2×#9028611yescharacteristic
947C2C2×#9028811yescharacteristic
948C2C2×#9031211yescharacteristic
949C2C2×#9031211yescharacteristic
950C2C2×#9041111yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#392C2
socleC24×C7C24
hypercenterC2×#392D7
hypocenterC7C2×#2813
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#6498C2semidirect
2. C22×#6502C2semidirect
3. C2×C7×#392C2semidirect
4. C2×#89995C2semidirect
5. C2×#89995C2semidirect
6. C2×#89994C2semidirect
7. C2×#89994C2semidirect
8. C2×#89731C2semidirect
9. C2×#89731C2semidirect
10. C2×#89721C2semidirect
11. C2×#89720C2semidirect
12. C2×#89733C2semidirect
13. C2×#89714C2semidirect
14. #11734186C2direct (N × H)
15. C2×#89448C2semidirect
16. C2×#89430C2semidirect
36. C2×#6502C22semidirect
38. C2×#6498C22semidirect
50. C7×#392C22semidirect
52. #89995C22semidirect
53. #89995C22semidirect
54. #89994C22semidirect
55. #89994C22semidirect
61. #89733C22semidirect
62. #89731C22semidirect
63. #89731C22semidirect
64. #89721C22semidirect
65. #89720C22semidirect
66. #89714C22semidirect
67. #89448C22semidirect
68. #89430C22semidirect
104. C23×Dic7D4semidirect
179. C2×#392D7semidirect
278. C22×Dic7C2×D4semidirect
352. #392C2×D7semidirect
757. C2×C7#2813semidirect
881. C7C2×#2813semidirect
943. C2#11734186direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64982
C22×#65022
C2×C7×#3922
C2×#899952
C2×#899942
C2×#897312
C2×#897212
C2×#897202
C2×#897332
C2×#897142
#117341862
C2×#894482
C2×#894302
C2×#28137